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Microwave spectroscopic and mass spectrometric studies of glow discharges: Microwave pressure -broadening of the silicon monofluoride cation in neon and argon

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MICROWAVE SPECTROSCOPIC AND MASS SPECTROMETRIC STUDIES OF
GLOW DISCHARGES: MICROWAVE PRESSURE BROADENING OF THE
SILICON MONOFLUORIDE CATION IN NEON AND ARGON.
by
Charley Clifton Langley
A dissertation submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
(Chemistry)
at the
University of Wisconsin-Madison
2002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 3072822
Copyright 2002 by
Langley, Charley Clifton, III
All rights reserved.
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Copyright © Charley Clifton Langley 2002
All Rights Reserved
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C om m ittee’s Page. This page is not to be hand-written except for
A dissertation entitled
Microwave Spectroscopic and Mass Spectrometric Studies of
Glow Discharges: Microwave Pressure Broadening of the
Silicon Monofluoride Cation in Neon and Argon
submitted to the Graduate School of the
University of Wisconsin-Madison
in partial fulfillment of the requirements for the
degree of Doctor of Philosophy
by
Charley Clifton Langley
Date of Final Oral Examination:
August 22, 2002
Com m ittee’s Page. This page is not to be hand-written except for the signatures
Months Year Degree to be awarded/December
. May
August
*************** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Approval Signatures of Dissertation Committee
Signature, Dean of Graduate School
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MICROWAVE SPECTROSCOPIC AND MASS SPECTROMETRIC STUDIES OF GLOW
DISCHARGES: MICROWAVE PRESSURE BROADENING OF THE SILICON
MONOFLUROIDE CATION IN NEON AND ARGON
Charley C. Langley
Under the supervision of Professor R. Claude Woods
At the University of Wisconsin-Madison
Combined microwave spectroscopic and mass spectrometric experiments in DC glow
discharges were conducted at pressures of 10*100 mTorr. The microwave spectrometer cell is a
10 cm diameter by 3 m long discharge tube that can be LN2 cooled and subjected to an axial
magnetic field of up to 300 G.
The pressure broadening parameters r of the J = 6-7 transition of SiF* at 267,320.977
MHz for broadening by both argon and neon were measured in magnetically confined discharges
with small amounts of SiF4 in one of these carrier gases. The experimental spectra were fit to a
convolution of a low pressure reference spectrum and a Lorentzian line shape function,
according to a scheme developed by Pickett. An expanded form of ATC theory developed by
Buffa et al., which incorporates velocity distributions and straight line trajectories, was used to
calculate T values for these same two cases, as was the simple Langevin model. The
experimental, ATC, and Langevin values of T for neon broadening at 102 ± 8 K were 6.3 ± 0.S
MHz/Torr, 7.4 MHz/Torr, and 5.9 MHz/Torr, respectively. For argon at 93 ± 2 K the
corresponding values were 8.7 ± 0.4 MHz/Torr, 10.6 MHz/Torr, and 9.7 MHz/Torr,
respectively.'
A quadrupole mass spectrometer, which samples ions through a pinhole in the wall of the
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discharge tube, was used to optimize the conditions for the production of a desired ionic species.
A computer control scheme for acquisition and analysis of mass spectral data, was implemented
and employed for extensive characterization for several discharge chemistries, e.g., Ne + CHF3
or Ar + CHF3 for production of CHF2+ and Ne + SiF4+ 02for the production of SiP.
UVININ GRADUATE SCHOOL
AU6 20&B
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CONTENTS
A B S T R A C T .........................................................................................................................
LIST O F T A B L E S ............................................................................................................... v iii
LIST O F F IG U R E S .......................................................................................................... x v iii
A C K N O W L E D G M E N T S .................................................................................................xix
Chapter
1
In tr o d u c tio n ..................................................................................................................
1
2
In stru m en ta tio n ............................................................................................................
10
2.1
2.2
2.3
2.4
2.5
2.6
3
3.1
3.2
3.3
4
4.1
4.2
4.3
Introduction .............................................................................................................. 10
Instrum ent O verview .................................................................................................. 10
Microwave S p e c tro m e te r........................................................................................... 14
Mass Spectrometer S y stem ............................................................................................ 25
Hardware M odification.................................................................................................. 35
The Glow D is c h a r g e ......................................................................................................38
S e n sitiv ity an d D isp ersio n ........................................................................................
43
In tro d u ctio n ...................................................................................................................... 43
Spectrometer S e n sitiv ity ................................................................................................43
Dispersion E ffects.............................................................................................................59
M ass S p ectrom etry o f G low D isch a rg es............................................................... 67
In tro d u ctio n ...................................................................................................................... 67
General E x p e r im e n ta l................................................................................................... 6 8
SF 6 D is c h a rg e s ................................................................................................................ 8 6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.4
4.5
5
Argon and O 2 Discharges .............................................................................................96
Neon Discharge S t u d y ............................................................................................... 101
M ass Sp ectrom etric S tu d ies o f F luorocarbon and S iF 4 D isch a rg es
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6
I ll
In tro d u ctio n .....................................................................................................................I l l
Introduction to Fluorocarbon D ischarges..................................................................I l l
Carbon T etrafluoride..................................................................................................... 112
CHF 3 D isch arg es.......................................................................................................... 122
Ion Chemistry of CHF 3 .................................................................................................136
CH Fj Fractional Abundance .................................................................................... 142
SiF 4 D ischarges...............................................................................................................143
M icrow ave S ea rch es.....................................................................................................156
6.1
In tro d u ctio n ................................................................................................................. 156
6.2 Asymmetric T o p s ............................................................................................................157
6.3 0 3 S tu d ie s.........................................................................................................................164
6.4 The Unidentified Line at 268695 M H z.........................................................................196
6.5 CHFj ...........................................................................................................................210
6 .6
T he Asymmetric Top C hallen g e................................................................................. 227
7
7.1
7.2
7.3
7.4
7.5
7.6
8
8.1
8.2
8.3
8.4
8.5
8 .6
T h eo ry and A p p lication s o f L in eb road en in g .....................................................234
In tro d u ctio n ....................................................................................................................234
Theory of Line B roadening.......................................................................................... 236
Methods of Line W idth D e te rm in a tio n .................................................................... 245
Pickett’s Convolution M e th o d .................................................................................... 250
Carbonyl Sulfide Pressure B r o a d e n in g .................................................................... 272
Carbonyl Sulfide Pressure Dependent Frequency S h i f t s ........................................278
P ressu re In du ced L inebroadening and freq u en cy S h ifts o f S iF + ...............280
Pressure Broadening of SiF+ ........................................................................................280
Neon B ro ad en in g ...........................................................................................................284
Argon B r o a d e n in g ........................................................................................................296
D iscussion ....................................................................................................................... 309
Comparison with the Langevin M odel........................................................................315
Pressure Dependent Line Shifts of SiF+ .....................................................................319
Appendices
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iii
A.
B.
C.
Instrum entation................................................................................................................327
Mass Spectrometry D ata Acquisition and Analysis Programs ............................ 329
Linebroadening P ro g ra m ................................................................................................329
R E F E R E N C E S .....................................................................................................................330
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4.6
Summary of integrated relative intensities for m /z 46 to 51 for the Oo and SF 6
discharge.................................................................................................................... 9 3
4.7
Literature values of the enthaplies of formation for NS+ and H 2 CS+
4.8
Relative intensities, to m /z 44, of peaks in the m /z 44-51 range of
................95
16C>2
and
l8 C>2 seeded Ar d is c h a rg e s ..................................................................................... 1 0 0
4.9
Electron impact ionization for argon and neon assuming an electron tempera­
ture of 4 e V ...............................................................................................................107
5.1
Relative intensities to CF 3 and fractional abundance of selected peaks for the
CF 4 and Ar concentration study.
.........................................................................118
5.2
Electron impact ionization energies for CHF 3
5.3
Total reaction rate constants for the formation of CHF + 2 ..................................... 139
5.4
Summary of Integrate Area for m /z 51 and Fractional A b u n d a n ce .....................142
5.5
Summary of Petrmichl’s optimum SiF+ discharge c o n d itio n s .............................. 145
5.6
Geometries of the 1A” and 3 A” states of F 2 H+ determined from ab initio
........................................................ 137
methods........................................................................................................................146
6.1
Diatomic cations observed by microwave spectroscopy.
........................................ 158
6.2
Linear molecular ions observed by microwave sp ectro sco p y .................................. 158
6.3
Symmetric top molecular ions observed by microwave sp e c tro sc o p y .................. 159
6.4
Asymmetric top molecular ions reported in literature...............................................159
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6.5
Asymmetric selection rules
...................................................................................... 163
6 .6
Summary of the experimetnally and theoretically determined structure of O 3 . 165
6.7
Summary of the rotational constants derived from O 3 equilibrium geometries . 166
6 .8
Rotation Constants corrected for rotation/vibration interaction............................. 167
6.9
Values of the propagated uncertainty for the rotation constants calculated from
experimentally determined structures of O 3
......................................................167
6.10 Spectroscopic constants of O 3 as reported by Peterson et al................................ 169
6.11 Perpendicular Zeeman effect for a molecule in a E state with angular momentuml75
6.12 A summary of the experimental conditions used for the three primary searches
conducted for O j ........................................................................................................177
6.13 Summary of observed ground state O 3 l i n e s ............................................................ 183
6.14 Summary of the observed O 3 (100) tra n s itio n s.........................................................184
6.15 Summary of observed O 3 (001) tra n s itio n s ............................................................... 185
6.16 Observed O3 (010) transitions........................................................................................186
6.17 Observed O 3 (020) tra n s itio n s..................................................................................... 186
6.18 Observed O3 asym 180 tra n s itio n s............................................................................... 187
6.19 Observed O 3 sym 180 tr a n s itio n s ............................................................................... 187
6.20 Predicted transition frequencies for l6 0
170 16
O
..................................
191
6.21 Summary of unidentified and non reproduced transitions below a source fre­
quency of 89500 GHz.................................................................................................194
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vii
6.22 Summary of unidentified lines with source frequencies > 89500 GHz.................... 195
6.23 Values used to estimate the magnitude of the Doppler shift th at would occur
for O 3 a t a frequency fo 268,695 MHz, a pressure of 30 mTorr and a
tem perature of 85 K .................................................................................................. 199
6.24 Results of Statistical Analysis of Doppler Shift Experiment on Unknown Line 1205
6.25 Structure of the CHFj ion as determined from CCSD(T)/cc-pVDZ calculations212
6.26 Predicted CHFj" rotational c o n s ta n ts ........................................................................ 215
6.27 Summary of lines observed in a CHF 3 negative glow discharge in the source
range of 87.9 GHz to 89.8 GHz with third harmonics filtr a tio n ..................... 225
6.28 Values used in
7
calculations for CHFj" and SiF+ .................................................. 231
6.29 Comparison of 7 values for CHFj and SiF+ ........................................................... 232
7.1
Summary of experimental and theoretical values of the pressure broadening
coefficients of HCO+ by Ar and Ne........................................................................ 243
7.2
Summary of the predicted pressure broadening values for SiF+ with both argon
and neon collisional partners....................................................................................243
7.3
Initial and final parameters used in the fitting of the spectrum shown in Fig. 7.3
by the Pickett method.............................................................................................. 254
7.4
Pickett Param eters for Scaling T e s t ...........................................................................261
7.5
Optimized paramters for Pickett convolution com parionson..................................265
7.6
Selected pressure broadening coefficents of OCS in lite r a tu r e .............................. 273
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viii
7.7
Carbonyl Slufide self broadening coefficents
...........................................................275
8.1
Experimental Conditions for SiF+ Pressure Broadeing E x p e rim e n ts .................. 282
8.2
F it Param eters and the 95% confidence levels of the Neon
1
and 2 Experiements291
8.3
F it results for various subsets of the neon 3 e x p e rim e n t....................................... 294
8.4
Summary of pressure broadening of SiF+ by a rg o n .................................................303
8.5
Pressure Broadening S u m m a r y .................................................................................313
8 .6
Pressure broadening coefficients for the neon and argon broadening of SiF+
8.7
Pressure Broadening Summary
. 313
................................................................................. 318
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ix
LIST OF FIGURES
2.1 A diagram of the microwave spectrometer system....................................................
11
2.2 Diagram of the microwave source................................................................................
15
2.3 A lineshape model of the signal emitted from the source............................................21
2.4 Effects of the baseline suppression algorithm on a model line shape.........................22
2.5 Apparent linewidth related to actual linewidth............................................................. 24
2.6 A diagram of the mass spectrometer system.................................................................. 26
2.7
Plot of the model transmission function used to correct for mass descrimination
effects in mass spectra................................................................................................. 34
2.8
Diagram showing the various regions of a typical glow discharge............................. 39
3.1
Raw spectrum of the J =22-23 Ol3 C34S transition with a measured frequency
of 271879.4670 MHz.................................................................................................... 45
3.2
Spectrum of the 0
13C34S
J=22-23 transition near 271,879 MHz.............................. 49
3.3
The baseline suppressed spectrum of the J=22-23 transition of 0
3.4
Raw spectrum of the J=22-23 transition of 0
3.5
Raw spectrum of the J=37-38 transition line of 0 13CS near 460421 MHz. . . .
13 C 34 S.
...
50
13C34S...................................................51
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53
X
3.6
Baseline suppressed and fit spectrum of the J=37-38 transition of 0 13CS near
460421 MHz...................................................................................................................54
3.7 Raw spectrum of the J=37-38 line of 0 13CS near 460421 MHz................................. 55
3.8 Baseline suppressed and fit spectrum of the J=37-38 transition of O l 3 CS. . . .
3.9
56
The raw spectrum of the optimized and filtered spectrum of the J=37-38 tran­
sition of 0 13CS..............................................................................................................57
3.10 Baseline suppressed and fit spectrum of the J = 37-38 transition of O l3CS with
source optimization and harmonic filtration............................................................ 58
3.11 Plots of the absorbance and dispersion functions of a p a rticle ...................................61
3.12 Comparison of the absorbance function and the sum of the absorbance and
dispersion functions......................................................................................................63
3.13 Spectrum showing the sinusoidal baseline due to standing waves in the dis­
charge cell...................................................................................................................... 65
4.1
Mass Spectrum of Background Species in the Mass Spectrometer and Calibra­
tion Point Illustration.................................................................................................. 69
4.2
Comparison of a Ne -I- CHF 3 spectrum with and without quadrupole trans­
mission correction.........................................................................................................75
4.3
Voltage dependent splitting of peaks in a mass spectrum .......................................... 76
4.4
Diagram illustrating the potential distribution within the respective regions of
the discharge..................................................................................................................78
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xi
4.5
O utput of the FCCv02.vi program showing the fitted lineshapes and subtrac­
tion effects.................................................................................................................. 8 1
4.6
Digitized mass spectrum showing the peak definition used with the areaXY
function.......................................................................................................................82
4.7
High and low resolution chart strip recordings of mass spectra collected from
a SF6 + CO + Ar d is c h a rg e ................................................................................ 84
4.8
Centroid mass spectra of the SF6 4- CO -I-Ardischarge............................................. 89
4.9
Centroid mass spectra of an l602 + SF6-I-Ar discharge.............................................. 91
4.10 Digitized chart strip traces of mass spectra collected from a SF6 -I- Ar -I- H2
discharge......................................................................................................................... 9 7
4.11 Spectrum of a
l6 0 2
+ Ar discharge.................................................................................98
4.12 Spectru of the
180 2
+ Ar d isc h a rg e .............................................................................. 9 9
4.13 Neon discharge background spectrum used in the NeJ s tu d y ............................... 1 0 2
4.14 Mass spectrum of Ne discharge at high c u rre n t........................................................104
4.15 Mass spectra of the moderate current Ne discharge..................................................105
4.16 Mass spectra of the low current Ne discharge............................................................ 106
4.17 Electron energy dependent cross section function forAr and Ne............................. 108
4.18 Electron energy distribution assuming an electron tem perature of 4 eV.................110
5.1
Mass spectrum for positive ions sampled from a CF 4 + Ar discharge with a
CF4:Ar ratio of 0.10....................................................................................................113
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xii
5.2
Mass spectrum for positive ions sampled from a CF 4 4 - Ar discharge with a
CF4:Ar ratio of 0.14................................................................................................... 114
5.3
Mass spectrum for positive ions sampled from a CF 4 4 - Ar discharge with a
CF4:Ar ratio of 0.20................................................................................................... 115
5.4
Plot of the fractional abundance of selected peaks observed in CF 4 and Ar
discharges as a function of the CF4:Ar ratio......................................................... 119
5.5
Comparison of the changes of relative intensity between CO 2 and the uniden­
tified species from Fig. 5.4........................................................................................120
5.6
Mass spectrum of a low current and low pressure Ar 4- CHF 3 discharge
123
5.7
Mass spectrum of a moderate current, low pressure Ar 4 - C H F3 discharge.
5.8
Mass spectra of a moderate current and moderate pressure Ar -I- CHF 3 discharge. 126
5.9
Mass spectrum of the ions sampled from a moderate current, moderate pressure
. . 125
Ne 4- CHF 3 discharge................................................................................................ 128
5.10 This is a mass spectrum of a high current, moderate pressure Ne 4 - CHF 3
discharge...................................................................................................................... 129
5.11 Mass spectrum of the discharge that was shown to have the largest CHF 3
fractional abundance..................................................................................................131
5.12 Mass spectrum of a moderate current, high pressure Ne 4 - CHF 3 discharge. . . 133
5.13 The mass spectrum for a moderate current, moderate pressure Ne 4 - CHF 3
spectrum...................................................................................................................... 134
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xiii
5.14 The pure CHF 3 discharge obtained by shutting of the neon flow after discharge
initiation.......................................................................................................................135
5.15 The C F f signal at m /z 50 range in Fig. 5.11............................................................ 141
5.16 Mass spectrum of high current, low SiF 4 concentration, SiF 4 + Ne discharge. . 144
5.17 Mass spectrum of moderate current Ne + SiF 4 discharge.........................................148
5.18 Mass spectrum of a low current Ne ■+* SiF 4 discharge.............................................. 149
5.19 Mass spectrum of a Ne + SiF 4 + O 2 discharge......................................................... 150
5.20 Mass spectrum of a Ne +O 2 + SiF4 discharge with
moderate current............. 151
5.21 Mass spectrum of a Ne + O 2 -I- SiF4 discharge with
highcurrent...................... 152
5.22 Mass spectrum of a low to moderate current Ne-l- SiF4 +H 2 discharge...................154
5.23 Mass spectrum of a moderate current N e+ SiF 4 -t-H2 discharge............................... 155
6.1
The predicted Q branch spectrum for O f using spectroscopic constants deter­
mined from ab initio methods..................................................................................171
6.2
The spectra of the K _i=2 series for selected theoretical and experimental struc­
tures of O f .................................................................................................................. 172
6.3
An unfitted microwave spectrum showing transitions for O 3 , HO 2 , and an
unidentified s p e c ie s .................................................................................................. 180
6.4
Spectrum showing the fit of an unidentified peak near 268,617 MHz.....................181
6.5
A spectrum showing the
281 ,2 7
272,26
transition of HO2 ....................................... 182
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XIV
6 .6
Unfitted spectrum showing the O 3 (001) 13o,i3
1 2 i,i 2
transition (A) at
270,923.3550 MHz and the 16o,i6 *— 15i,is l6 0 l7 0 160 spin state transitions
near 361,250 MHz.....................................................................................................188
6.7
A spectrum of the spin hyperfine structure of the 16o,i6 <— 15i,i5 l6 Ol7 O l60
transition.
6 .8
...................................................................................................... 189
Unfitted spectrum showing transitions for O 3 (100), 0 3 (010) and 0 3 within a
single spectrum ............................................................................... .........................190
6.9
Spectrum of the unidentified line near 268,695 MHz observed in O 2 discharges. 192
6.10 A diagram showing the effect of an electric field between two electrodes on the
velocity of ions in a glow discharge................
197
6.11 Plot of the frequency residuals for multiple measurements of the unknown line
near 268,695 MHz vs the discharge voltage...........................................................200
6.12 Baseline function effects on the measurement of the frequency.............................202
6.13 A plot showing the lack of frequency dependence on the baseline position of
the measured transition.............................................................................................204
6.14 Dependence of O 2 discharge study unknown # 1 on N 2 partial pressure
6.15 Dependence of the intensity of the
. . . . 207
search unknown # 1 on the partial
pressure of CO............................................................................................................ 208
6.16 Effect of H2 addition to the discharge on the integrated intensities of the
unidentified line a t 268,695 M H z ............................................................................209
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XV
6.17 The Q branch of the predicted C H FJ spectrum using the spectroscopic con­
stants determined from theoretical structures.......................................................213
6.18 Tem perature dependence of the absorption coefficient for C H F J.....................214
6.19 The predicted Q branch spectrum of C H FJ in the search region 352-358GHz.
216
6.20 This is the J = 16—>17 transition of CHF 3 with K’ = 0 transition frequency of
351,638.54 ± 0.15 MHz............................................................................................. 218
6.21 Spectrum of the J= 12—>13 transition of CHF 3 near 268,971 M H z .............. 220
6 .2 2
The spectrum of the
62,5
to 5i ,4 transition of COF 2 ................................................. 222
6.23 The second of two initially promising lines th at spurred the search around
87,900 MHz for C H F J ............................................................................................223
6.24 The spectral pattern observed near 88623 MHz in a CHF 3 discharge.................... 224
6.25 Mass spectrum of the ions sampled from a SiF 4 discharge in the positive column
mode............................................................................................................................. 231
7.1
Comparision of the direct and Pickett fits on a spectrum of the J =
6
—> 7
transition of SiF+....................................................................................................... 247
7.2
Comparison of the HWHM values, At/ and the Pickett broadening parameters
obtained for the neon broadened J =
6
—> 7 transition of SiF+.........................249
7.3
Effects of erronous initial s values for use in Pickett’s method...............................255
7.4
The effect of the intial values of s on the final fitted value of c..............................257
7.5
The effects of the initial values of w and s on the fitted values of w and s.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
. . 258
xvi
7.6 Comparison of an unsealed data spectrum and a low pressure reference spectrum. 259
7.7 Spectrum with sensitivity and vertical scaling factors corrected for....................... 260
7.8
Pickett Fit to Baseline Suppressed S p e c tru m ....................................................... 263
7.9
Pickett Fit of Spectrum with Baseline Suppression and Subtraction................. 264
7.10 Baseline Supression compared with Baseline Suppression/Subtraction for Ne
experiment 2 ............................................................................................................... 266
7.11 Baseline Supression compared with Baseline Suppression/Subtraction for Ar
experiment 3............................................................................................................... 267
7.12 Comparison of the effect of internal and external reference files on the value
of T............................................................................................................................... 269
7.13 An Example of a Poor Direct Method F it................................................................. 270
7.14 An example of a good Direct method fit.................................................................... 271
7.15 Self broadening of OCS.................................................................................................. 274
7.16 Comparison of the effect uisng a Gaussian or Lorentzian line shape model on
the value of T..............................................................................................................277
7.17 Pressure dependent lineshifts of the 0 13CS J = 21 —+2 2 transition...................... 278
8.1
Pressure broadening of SiF+ by neon, using the direct method and the neon
experiment
8.2
1
data set................................................................................................ 286
Pressure broadening of SiF+ by neon as determined using Pickett’s method
and the neon experiment 1 d ata set........................................................................287
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xvii
8.3
Overlap of the FM sidebands by a pressure broadened main line......................... 288
8.4
Direct method analysis of the pressure broadening of SiF+ by neon experiment
2..................................................................................................................................... 289
8.5
Pickett analysis of the pressure broadening of SiF+ by neon experiment 2.
. . 290
8 .6
Direct method analysis of the neon experiment 3 study of SiF+ pressure broad­
ening by neon.............................................................................................................. 293
8.7
Pickett’s m ethod treatm ent of the neon experiment 3 study of the pressure
broadening of SiF+ by neon......................................................................................295
8 .8
Direct method analysis of SiF+ pressure broadening by argon: experiment 1. . 298
8.9
Pickett method analysis of SiF+ pressure broadening by argon: experiment 1 . 299
8.10 Direct m ethod analysis of the SiF+ pressure broadening by argon: experiment 2.301
8.11 Pickett method analysis of the spectra obtained in the argon 2 experiment.
. 302
8.12 Direct Method Analysis of the Pressure Broadening of SiF+ by Argon: exper­
iment 3..........................................................................................................................305
8.13 Plot of Argon 3 Pickett method w values vs A P ..................................................... 306
8.14 Direct m ethod analysis of combined argon data set...................................................308
8.15 Plot of the combined sets of the argon broadening of SiF+ ......................................310
8.16 Pickett m ethod analysis of the combined argon pressure broadening experiments311
8.17 Pressure dependent line shift determined from the neon experiment 1 .................. 320
8.18 Pressure dependent lineshift determined from neon experiment 2.......................... 321
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xviii
8.19 A plot of the s values
for the combined neon 3 d ata set................................ 323
8.20 Line shift parameters
s, from the edited argon combinded
d a ta set, plotted
against A P................................................................................................................... 324
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ACKNOWLEDGMENTS
I would like to express my thanks to Dr. Woods for his patience and efforts in assisting
me in this endeavor. Many thanks must also be given to the great support staff here at
Wisconsin, who helped me keep things running. In particular Jerry and Ed in the machine
shop, and Jerry in the electronic shop. I must also acknowledge the support from many
of the professors whose encouragement and enthusiasm have been greatly appreciated.
This degree would not have been possible without the great support given me by teaching
supervisors Dr. Ed Turner and Dr. M artha Vestling, their willingness to allow me the
flexibility and the time to pursue my research has made all of the difference. I must also
acknowledge Dr. Frank Turecek at the University of Washington, who graciously allowed
me to begin my Post Doctoral appoint prior to the completion of this work.
But the greatest thanks must be given to my family. To my parents who have always
encouraged me to "Think The Problem Through" , to my sons Dallin and Clifton who
have patiently waited for Daddy to finish his big project. The greatest thanks must be
given to my wife, Cheryl, whose patience, love and support have made this possible. To
all of these I am greatly indebted.
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1
CHAPTER 1
Introduction
The observation and characterization of molecular ions by microwave spectroscopy
has been an active field of study for nearly three decades.
W ith the information pro­
duced being of importance to fields as diverse as radio-astronomy and materials science,
microwave spectroscopy studies of molecular ions remains an im portant area of study.
Characterization of species thought to exist in the interstellar medium and the effects of
intermolecular forces on the width and shape of spectral lines are two of the reasons why
microwave spectroscopy remains an important method.
In addition, microwave spec­
troscopy is also used as a diagnostic tool used with industrial plasma discharges. On a
more fundamental level, a t this time in the field several challenges remain. Among these
are the use of microwave spectroscopy to characterize molecular anionic species and the
observation of asymmetric top ions where heavy atoms create the asymmetry.
Our study of molecular ions in DC glow discharges utilizes two complementary meth­
ods, microwave spectroscopy and mass spectrometry.
While limitations inherent with
the methods and with our instrument have prevented us from obtaining hilly complemen­
tary data from these methods, we have been able to obtain significant insights into the
chemistry of these discharges.
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2
A brief introduction to the instrument is presented in Chapter 2, where we give a
general description of the microwave and mass spectrometers, their operation, and the
limitations of each instrument. Several modifications made to each of the instruments are
described in more detail. Two of these modifications have had significant impact on the
operation of these instruments the d ata obtained from them.
of a probe to measure the plasma potential of the discharge.
The first is the addition
Previously, the plasma
potential was measured at the interface between the discharge cell and the quadrupole
mass spectrometer system. W ith the addition of the probe, this interface could be biased,
improving both the transmission of ions trough the instrument, and the quantity of the
ions sampled. Prior to the start of the C H F j search and the pressure broadening studies,
the harmonic mixer in circuit used to control the sweep of the source, the S-band circuit,
failed. The replacement harmonic mixer was not identical to the original and resulted in
the extension of the source sweep range by several gigahertz. Various limitations of the
instrument are also addressed, including the transmission of ions through the quadrupole
system and the systematic narrowing of the HWHM values of microwave spectra subjected
to a baseline suppression routine used in spectrum analysis.
In C hapter 3 we discuss the effects of resolution, systematic peak deformations, cal­
ibration and spectrom eter transmission. In addition, an operational overview and com­
parison of the d a ta analysis methods used to interpret the mass spectra is provided.
A m ajor improvement in the use of the system has been the implementation of com­
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3
puterized d a ta acquisition for the mass spectrometer. Using Labview, we created a suite
of programs th at allow the experimentalist to control the sweep of the mass spectrome­
ter, to observe the collection of the spectra in real time, to have limited control over the
precision of the measured intensity values, and to control the content of spectra created
by averaging multiple sweeps. Also written were a suite of d ata analysis programs that
enable calibration, baseline correction, determination of integrated intensity, correction
of mass discrimination errors, and simple deconvolution of overlapping peaks.
Mass spectrometric studies of various discharge chemistries are presented in Chapter
4. Prior to discussing the various experiments, we discuss several factors th a t affect the
quality of the acquired mass spectra and th at of the information that can be obtained
from them.
We present several mass spectrometric studies in Chapter 4.
These studies grew
in depth and complexity following the implementation of computerized d a ta acquisition.
The first study considered the chemistry of Ar -1- SF 6 discharges, with particular empha­
sis on the determination of the optimum discharge conditions for production of the SF+
ion. The effects of the addition of H2 , O 2 and CO on the discharge chemistry were also
investigated. The mass ranges used in this experiment, conducted prior to the imple­
m entation of the computerized d a ta acquisition, were limited due to the time intensive
analysis methods used. While this lim itation prevented a determination of the true ionic
fractional abundance of the SF+ signal, we observed th a t the production of SF+ follows
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4
the reactions reported by Sparrapan et a il for the reaction of SF 6 + Ar. We also con­
cluded th at SF+ production from SF 6 discharges will probably not produce sufficient SF+
signal to be detectable in our present microwave spectrometer.
The next study performed was an attem pt to identify a line at m /z 44 observed in
Ar + O 2 discharges, shortly following the completion of the SF 6 experiments.
It was
thought that the oxygen may be reacting with SF6 or other fluorinated compounds at
the surface of the reaction cell to form SiO+.
Previous attem pts to produce SiO+ in
0 2 + SifLi discharges, had merely resulted in the rapid and excessive deposition of S i0 2
on the surfaces of the discharge chamber and the electrode, leading to unstable or noisy
discharges. The possibility th at we were forming SiO+, even though remote, justified the
effort to unambiguously assign this line.
use of an lsO isotopic substitution study.
Identification of the species was made by the
The results of this experiment showed quite
clearly th a t the species a t m /z 44 was CO 2 and not SiO+.
The neon studies were made to determine if a large signal at m /z 40, observed in pure
neon discharges but not discharges containing neon and other gases, was due to
to trace argon contamination.
20 Ne2
or
Our studies show that the signal is indeed Ar+ arising
from trace contamination of the neon gas. We further provide a mechanism to account
for the large signal and discuss the relevance of this mechanism to discharge chemistry.
C hapter 5 describes the mass spectrometric studies of fluorocarbon and SiF 4 con­
taining discharges.
The study of the chemistry of CF 4 and CHF 3 discharges by mass
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5
spectrom etry was conducted with the hope th a t the CHF^ ion could be produced in suf­
ficient abundance to justify a microwave search. We found th at Ne + C H F 3 discharge at
moderate currents, ~ 300 mA, and moderate pressures, ~ 40 mTorr, produce the largest
C H F j concentrations. Determining th at total abundance of CHF 2 was only ~
6%
under
optimal conditions, we knew, based on calculated absorption coefficients, th at a search for
the ion in non magnetically confined discharges would not be successful. We were able to
restrict our studies to the magnetically confined discharges, where we expected a larger
fractional abundance of the ion. The mass spectrometric characterization of the discharge
showed the presence of many ions attributed to the products of chemical processes a t the
surface of the discharge cell wall. From this we expected th at the spectrum obtained
in the search for CHF 2 would have many interfering lines, as indeed it did.
The SiF 4
discharges were studied in an effort to expand on the previous work of Petrmichl , 2 by
determining the optimum current conditions for production of SiF 4 and the effects th at
H2 and O 2 addition would have on signal intensity.
The microwave studies relating to searches for O 3 and CHFj are presented and dis­
cussed in C hapter 6 . Also presented is a discussion on the calibration of the spectrometer,
effects of instrument tuning and the use of harmonic filters, and the effects of anomalous
dispersion.
Microwave spectroscopic studies of molecular ions have by and large been limited
to cationic diatomic, symmetric top, or nearly symmetric asymmetric top species.
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To
6
date no true asymmetric top molecule has been characterized by microwave spectroscopy,
and only the SH~ and SD- anionic species have been characterized using microwave
spectroscopy .3
Our search for O j, begun prior to the reporting of the SH~ and SD”
species, sought to take advantage of the large amount of O 3 formed in O 2 discharges,
the availability of spectroscopic constants based on high level ab initio computations and
the simplifications to the predicted spectra introduced by the equivalent atoms and a E
electronic electronic state. Our searches reveal a surprising number of transitions assigned
to excited vibrational states of ozone. While interesting, these lines badly cluttered the
spectra taken. After identifying as many of the lines as possible, we found, th at of several
dozen lines th at could not be assigned, two lines were very reproducible and, as far as we
could determine, transient in nature.
Of these only one was suitable for use in studies
to determine the chemical composition and ionic character of the carrier species. These
studies addressed the effects of varying the discharge gas mixture, the Doppler shift of
the frequency, and the Zeeman effect.
Doppler shifts in the observed frequencies of ionic species in glow discharges similar
to ours arise from the interaction of the ionic charge with the electric field vector and the
sign of the charge determines direction of the drift motion of the ion in the electric field.
The net effect is th a t ions of opposite charge to the polarity of the electrode nearest to the
detector will exhibit a blue shift in their transition frequencies, while those of the same
charge to the electrode experience a red shift. Our measurements of the line, w ith both
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7
positive and negative polarity, indicated th at there is a 0.163 MHz frequency shift between
the two polarity conditions. Statistical treatm ent shows th at there is a 95% probability,
th at this shift is real.
This shift magnitude is much smaller than is predicted, and the
scatter in the observed points is quite pronounced. Though it seems the shift is real, we
cannot be sure of its origin.
Based on the results of preliminary mass spectrometric investigations and a favorable
discharge chemistry, several searches were made in an attem pt to locate a transition of
CHFj •
The C H FJ ion is the principal ionization product of CHF 3 and one of the
principal ionization products of CF 4 . Since both of these species play im portant roles
in industrial applications and in the chemistry of the atmosphere, a characterization
of the C H F j molecule is of importance.
O ur mass spectrometric studies suggested
th at magnetically confined negative glow discharges offered the best conditions for the
production of this ion. Searches of these discharges found many COF 2 , CF 2 and CHF 3
transitions in the optimum search region for our instrument, 250 to 280 GHz. Searches
in higher frequency ranges results in less clutter, but also decreased the sensitivity of
the instrument.
None of our searches produced a clearly identifiable CHF 2 line.
Our
results w ith the CHF 2 study forced us to re-examine the suitability of the instrument for
studies of asymmetric top molecules. Using the fractional abundance of SiF+ determined
by mass spectrometric techniques and a microwave spectrum of the J= 6-7 transition of
SiF+ recorded a t the same time, it was possible to correlate the two techniques.
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The
8
results of this work suggest th at the observation of asymmetric top transitions w ith the
current design of the spectrometer will be very difficult. The major cause of this is the
inability to control the rotational tem perature of the molecules such th at the rotational
state distribution collapses sufficiently to allow for signal detection. Another im portant
cause is the relatively low power of the source. W ith higher source power we expect th at
previously unobserved lines will be found.
The pressure broadening of SiF+ by argon and neon is discussed in Chapter 8 . Pres­
sure broadening of neutrals has been well studied, but pressure broadening studies of
ions have been limited to a single ion, HCO+. This is surprising, since an experimental
observed dependence of the pressure broadening coefficient, T = Au/p, on the rotational
state of the ion, is not predicted well at high J states by the current pressure broaden­
ing models.
The failure of most of the pressure broadening models occurs when the
7
value reaches the value predicted by a Langevin capture model. This is due to the cap­
ture behavior incorporated into most pressure broadening models.
Those models that
use ATC theory do not go to the Langevin limit, but they do not accurately describe
the pressure broadening at high J either.
Our study compares the effects of different
collisional partners have on the pressure broadening of SiF+. The results of our study
show th at the monopole-monopole-induced dipole interaction of the Langevin model is
not correct and th a t the dipole-induced dipole interaction used in the ATC theory is more
accurate.
The failure of all pressure broadening models shows th at the true potential
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9
interaction has not been correctly determined.
The dependence of pressure broadening
on the rotational state had profound impact on our search methods. For some time we
have operated under the assumption th at the pressure broadening of an ion was always
greater than the neutral, and we had considered many of the observed lines to be neutrals
based on linewidth considerations. This assumption is no longer valid, and every line in
future searches should be more closely scrutinized.
The studies of pressure broadening were greatly aided by the use of fitting routine
developed by H. M. Pickett. This routine convolutes a low pressure reference spectrum
with a model Lorentzian function, that depends only on the pressure broadening and
pressure shifting, and fits this to a high pressure spectrum.
The optimized Lorentzian
parameters represent the pressure broadening contribution to the fine width and the pres­
sure dependent frequency shift. A computer program written to apply this convolution
and fitting routine on selected spectra is described, in C hapter 7 and the potential sources
of error arising from the use of Pickett’s method are considered.
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10
CHAPTER 2
Instrumentation
2.1
Introduction
Studies of the ions formed in glow discharges have been conducted using an instru­
ment th at combines microwave spectroscopic and mass spectrometric techniques.
In
this chapter the instrument will be described, modifications made to instrument will be
detailed, and a brief introduction to glow discharges will be provided. Design and opera­
tional details not provided here can be found in the dissertations of N. N. Haese,4 W. T.
Conner ,5 R. H. Petrmichl ,2 and other sources, as cited.
2.2
Instrum ent Overview
In this section an overview of the construction and basic operational considerations
is provided.
The instrument can be subdivided into six m ajor components: source,
buffer/reactant gas introduction manifold, discharge cell, detector, mass spectrometer,
and the computer d ata acquisition and control system. A diagram of the instrument is
shown in Fig. 2.1.
Gas mixtures of reactant and buffer gases axe prepared in, and adm itted to the dis­
charge cell from a glass manifold.
Two mass flow controllers are used to regulate the
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11
Figure 2 .1 : A diagram of the microwave spectrometer system. Gas is fed into the system
from a glass manifold (A), and then passed into the discharge cell (B), where it is ionized
by the application of a potential between the north electrode (C), and the south electrode
(D) or the tower electrode (E). The cell is wrapped with teflon tubing for coolant and
is coaxial with a solenoid magnet. Pressures are measured near the south electrode by
a capacitance manometer. Microwave signals are generated by the computer controlled
source (F), propagated through the discharge cell (B), and finally collected and passed to
the InSb detector (G). Signals from the detector are passed to the lock-in amplifier (H) and
then to a Vax computer (I) for data analysis. Mass spectrometric studies are conducted
using the mass spectrom eter system (J). Three Varian VHS-4 diffusion p u m p s(# l-# 3 )
are used to provide a differential pumping scheme for the mass spectrometer system.
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12
flow of the buffer gas into the glass manifold, while reactant gases are adm itted through
several ports using needle valves for flow control.
Pressure readings are taken using
a thermocouple pressure sensor and are referred to as the glass manifold pressure(s) or
GMPs. The gas mixture is continuously admitted to the discharge cell, and one must be
careful to avoid creation of a path to ground, as the discharge can extend back into the
manifold.
The discharge cell is L shaped with a 3 m long microwave path and 2 m side arm.
Composed of 10 cm diam eter Pyrex tubing, the two arms are joined by a Pyrex cross
to create the L shape.
the 3 m side.
A large solenoid magnet extends almost the entire length of
This magnet is concentric with the 3 m side and capable of producing
axial fields of 0-300 G. Crosses are also used to provide interface locations for the mass
spectrometer pumps, electrical and water connections for the electrodes, ports for the
insertion of probes, and the placement of quartz windows.
Pressure within the cell is
measured by the use of a capacitance manometer, sampling a t the joining cross, near the
feedthroughs for the south electrode and by a Varian ion gauge above the gate valve and
diffusion pump # 3 .
Three electrodes are present in the system which allow the discharge to be extended
down the arm for sampling by the mass spectrometer or to be kept within the solenoid
region for magnetic confinement.2 The north electrode, near the gas inlet and the source,
is biased with a positive or negative voltage, relative to the other electrode, which is
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13
held at ground. The south electrode is placed within the joining cross and is used when
magnetic confinement of the discharge is required. The third electrode is a large coil of
m etal tubing mounted vertically above diffusion pump # 3 . This “tower” electrode is used
to extend the discharge down the base of the cell, allowing for sampling of the discharge
by the mass spectrometer. The north and south electrodes are cylinders of stainless steel
with internal channels to allow cooling water to flow through. They are mounted along
the axis of the Pyrex tube to allow relatively free propagation of microwave radiation and
gas flow through them.
Cooling and electrical connections are made through stainless
steel tubing welded to the electrode and spatially arranged so as not to interfere with the
p ath of the microwave radiation. More details on the properties of these electrodes can
be found in R. Petrmichl’s Ph.D . thesis .2
The use of a differential pumping scheme ensures pressures of 10- 7 Torr in the electro­
static lens array (ESLA) chamber (Section 2.4.2) and pressures of a few times 10- 8 Torr
in the mass spectrometer. These pressures can be obtained even when gas pressures of
10- 2 — 10~l Torr are present in the discharge cell. Three Varian oil diffusion pumps are
used: unit # 1 pumps the mass spectrometer chamber, unit # 2 pumps the ESLA cham­
ber, and unit # 3 pumps the m ain discharge chamber. Pumping rates are controlled by
adjusting the position of gate valves used to isolate the diffusion pumps from the system.
Cooling of the cell is accomplished by flowing coolant through Teflon tubing wrapped
around the discharge cell. The tem perature is measured by three thermocouples placed
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14
in the middle and at either end of the main arm. The side arm can also be cooled using
a Pyrex coil inside the discharge tube.
Unfortunately, there is no way to measure the
tem perature, limiting the temperature dependent mass spectrometric studies of discharges
to wall tem peratures of ~77 K or ~300 K.
Microwave radiation is passed through Teflon lenses and down the main arm of the
cell to the InSb detector .2
O utput from the detector is passed to an SRS 850 lock-in
amplifier and on to the VAX computer for processing.
Control of the microwave spectrometer is handled by a VAX workstation running
Microwave.for, a FORTRAN program, written by C. Woods.6 The program provides the
user interface for control of the sweep of the spectrometer and for acquisition and analysis
of the data. Descriptions of the source and mass spectrometer are given in Sections 2.3.1
and 2.4.
2.3
Microwave Spectrometer
2.3.1
Source
Several years ago the microwave source underwent a major upgrade.
Klystrons
were replaced with a Gunn Diode source built by J. E. Carlstrom ,7 and the previously
constructed 2 phase lock loops (PLLs) were replaced by a PLL contained in the Gunn diode
phase lock module (Model 800A) built by XL Microwave. A diagram of the current source
is shown in Fig. 2.2 and a listing of the components is given in Appendix A..
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15
C19
C18
C 17
C 20
C 21
C2
C 22
!S25l
dE
S26
C15
_£23
S10
C3
C14
S 11
C6
C4
C24
C 29
C 28
Figure 2 .2 : Diagram of the microwave source. The S-band circuit, locared in the shaded
region, produces the IF signal that is used to control the sweep of the Gunn diode. A
tunable frequency from the Ailtech frequency synthesizer (C19), is combined with a 6 GHz
signal supplied a frequency source (S9) in a Miteq mixer (S8 ). The resultant signal is then
filtered by an Omniyig 4-8 GHz YIG band-pass filter (S9). The selected frequency is then
amplified using an OmniPac amplifier (S10) and passed into the Hughes harmonic mixer.
The appropriate signal from the S-band circuit is mixed with the attenuated (C12,13)
output signal from the Gunn diode (C15) to produce the IF signal used by the Gunn
Phase Lock Module (S16). As the Ailtech is swept, the IF signal drifts away from a
100 MHz reference frequency (C22) causing the PLL to adjust the potential applied to
the Gunn diode. This changes the output frequency of the Gunn to the value needed
to produce an IF frequency of 100 MHz. The signal to be passed through the sample
cell is first passed through a directional couple (C4), where the power is measured using
a therm istor (C 6 ) and a power meter (C29). The output signal is then multiplied in the
Millitech frequency tripler to produce third, fourth and fifth harmonics of the fundamental.
An enlarged diagram and complete component list are provided in Appendix A..
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16
Components with labels beginning with an S belong to the S band circuit, th at is
used to control the sweep of the Gunn oscillator.
Detailed descriptions of similar S
band circuits are available ,2,8 but a brief description is required to provide a context for
an im portant modification.
The S band receives a variable input frequency ~ 1 GHz
signal from an Ailtech frequency synthesizer.
6
This frequency is then combined with a
GHz signal, passed to a band pass filter, and the selected sum or difference frequency
is passed to a harmonic mixer.
An appropriate harmonic and the output of the Gunn
oscillator are then combined producing the IF frequency passed to the Gunn phase lock
module (GPLM). The IF signal is compared with a reference frequency (100 MHz). If
the reference frequency and the mixer output frequency differ, the potential applied to
the Gunn diode is adjusted within a range of values until the mixer output equals the
reference frequency.
Prior to the sta rt of the CHF£ search, the heating element on the YIG filter (S7)
shorted to ground, resulting in the destruction of a diode within the harmonic mixer
(S ll).
As no direct replacement or repair of the mixer was possible, the mixer was
replaced w ith a mixer optimized for a slightly higher frequency range.
Although the optimum operating range of the new mixer is 90-140 GHz, it is possible
to use the mixer at lower frequencies, but with lower power output.
To determine the
effective operating range of the entire circuit, several OCS lines were selected in the range
of 72,945 - 94,820 GHz, and attem pts were made to obtain phase lock, and maintain
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17
source stability while scanning the regions near these lines. This last point is important,
as it has been observed th at certain source frequency and source harmonic combinations,
are stable until frequency sweeping begins, but then the phase lock is lost. These effects
typically occur when the Gunn diode is tuned properly for a specific frequency, but the
output power is too low, while being swept, to maintain an IF input signal above the
required -70 dbm threshold.
The lines used for the tuning and results of the tests are
itemized in Table 2.1. The stable operating range of the modified S band circuit is from
~78 GHz - 95 GHz, but the closer to these limits the Gunn diode frequency is, the more
sensitive the system is to the tuning of the Gunn diode.
The m odulation is mixed into the signal at this point. To ensure th at the modulation
waveform is correct, the Gunn diode output signal is monitored using a spectrum analyzer.
The modulated radiation is then passed to a frequency tripler, where the third, fourth
and fifth harmonics of the source are generated and launched into the discharge cell.
2.3.2
Modulation and Detection
Microwave signals from the source are modulated using a tone burst modulation
scheme2 ,8 ’9 This scheme was first suggested by Pickett ,9 and implemented in our system
with modifications by Gudeman .8
The FM tone burst modulation uses a sine wave
envelope for the tone bursts. One of the m ajor advantages of the tone burst modulation
is th a t the carrier signal necessary for phase locking is always present, so source unlocks
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18
Table 2.1: Modified source range of operation. Transitions are OCS lines that correspond to
5th harmonics of the Gunn diode frequency, or GDF. The GDF range value corresponds to the
low frequency in the sweep range that encompasses the transition. The upper loop harmonic is
related to the frequency passed to the harmonic mixer from the YIG Filter.
Transition
Frequency
GDF Range“
(MHz)
(MHz)
29-30
364748.9600
72949
30-31
376897.4200
75379
31-32
389041.0000
77808
32-33
401191.3880
80231
33-34
413336.8447
82660
34-35
425484.2366
85089
35-36
437624.5628
87517
35-36
437624.5628
87517
449766.7085
36-37
89946
461907.7259
92374
37-38
38-39
474047.5600
94802
39-40
486184.2000
96260
a) Line center in GDF Frequency
b) no lock
c) lock but unstable
Upper Loop
(b)
(c)
12
12
12
12
12
13
12
13
13
(b)
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19
are minimized. This modulation scheme, however, prevents discrimination between types
of species and transitions ,8 in addition to some line distortion. An InSb crystal detector
built by Advanced Kinetics is used to measure the intensity of the incident radiation.
O utput from the detector is passed to the SRS 850 lock-in amplifier and then to the
computer for signal averaging and analysis.
2.3.3
D ata Analysis
The d a ta collected from the lock-in amplifier is processed using the d ata analysis
portions of the microwave.for program.
At the time of collection the user is required
to enter specific experimental information, e.g., modulation parameters, and to perform
the intial d a ta analysis.
This analysis is limited to selection of the scan pairs to be
averaged and saved in the final spectrum.
A scan pair is composed of two sweeps of
the scan range, or scan width, one sweeping from low to high frequencies and the other
from high to low frequencies.
The user can reject those scan pairs th at contain spikes,
which upon application of the baseline suppression routine can become an artifact peak
(see below).
Once the user has completed the spike suppression process, the averaged
spectrum is stored, and no further spike suppression is possible.
The principal function of the data analysis program following the acquistion is the
fitting of the line using a non-linear least squares method, with Lortenzian and Gaussian
line shape models.
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20
2.3.4
Baseline Suppression
Reflections of the microwave radiation off the lenses and interior surfaces of the dis­
charge cell create a standing wave pattern with an amplitude th at is usually much greater
than the molecular absorption .8 , 10 This standing wave pattern is very helpful in correct­
ing the effects of anomalous dispersion ,8 but the large amplitude leads to less sensitive
lock-in settings, limiting the intensity of the desired signal.
A digital filter is used to
remove the low frequency components from a spectrum. See Fig. 6.3 for an example of
the baseline.. The algorithm of the filter is
=
(2 . 1)
,
where fn is the sampled function at point n, gn is the output of the digital filter, and
s is the FM m odulation frequency as a point interval. 10
The filter works admirably,
but application of the filter also increases the apparent intensity of the line, reduces the
apparent linewidth, and introduces additional sidebands.
The baseline suppression process can be demonstrated using a model of the modulated
signal. Created by using three Lorentzian functions, Fig. 2.3, one of which represents the
m ain absorption line and the other two the modulation sidebands, the model represents
an idealized case, where no second modulation sidebands exist. In practice, the second
set of sidebands are often present, complicating the suppressed spectra and introducing
a potential source of error, as the direct fitting method (see below) does not account for
any second or third m odulation sidebands, but only the principal ones. The Lorentzian
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21
1.0
0.5
w
c
ID
JQ
w
<
0.0
55
c
Q)
-0.5
-
1.0
21
22
23
24
26
27
28
Frequency Units
Figure 2.3: A line shape model of the signal emitted from the source. This line shape was
created from the sum of three Lorentzian functions, Eq.( 2.2,0 with the HWHM of each
line being equal and the intensities of the side bands being one half th a t of the main line.
A line w idth of 0.200 frequency units is used with the side bands at ± 2 frequency units.
The line width of the resultant line shape is 0.1983 frequency units, while the individual
Lorentzian are generated using a 0.200 frequency unit HWHM.
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22
2
0.5 -
0.5
•
-
-
-2 -
■E
-
2-
-1.5
70
80
90
70
100
80
90
Frequency Units
Frequency Units
100
110
70
80
90
100
110
Frequency Units
Figure 2.4: Shown in this series of graphs are the lineshapes th at result from one, two and
three applications of the baseline suppression algorithm on the lineshape in Fig. 2.3, from
left to right, respectively. The emergence of suppression sidebands created during the
application of the suppression algorithm is clearly demonstrated. Also, observable is the
increase in the apparent intensity of the line, wtiich is also a by product of the application
of the suppression routine.
peaks were created using the following form of a Lorentzian function
2/o
(2.2)
( x - x 0)2 '
1+
Ax 2
In this form of the Lorentzian, Ax is the HWHM, x 0 is the line center, and y0 the
V=
maximum.
The effects of successive applications of the baseline suppression algorithm
on the spectra are shown in Fig. 2.4, where the algorithm has been applied once, twice,
and three times to the line shape in Fig. 2.3. Two noticeable effects are illustrated, first
the appearance of new sidebands and second, the amplification of the apparent intensity
of the lines. Each successive application of the suppression algorithm introduces a new set
of sidebands. The number and relative intensity of the sidebands for up to five algorithm
applications axe listed in Table 2.2.
Of concern is the effect th a t the distortion of the
peak will have on the value of the HWHM.
Piltch , 10 addressed this issue regarding
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23
Table 2.2: The relative intensities of the peaks created by the application of the baseline sup­
pression algorithm, Eq. 2.1, on a line shape similar to the line shape shown in Fig.2.3, but with
zero linewidth.
Number of
Applications
0
1
2
3
4
Center
1.0000
1.5000
2.5000
4.3750
7.8750
1st
-0.5000
-1.0000
-1.8750
-3.5000
-6.5625
Sideband Set
2nd
3rd
4th
0.2500
0.7500
1.7500
3.7500
-0.1250
-0.5000 0.0625
-1.4062 0.3125
5th
-0.03125
the effects of a single baseline suppression, but since most of the spectra have two or
three baseline suppressions, it was necessary to determine the effect of multiple baseline
suppressions on the apparent HWHM. Although the correction factors are automatically
applied when spectra are analyzed using the Microwave.for program, it is necessary to
have an understanding of the discrepancy between the apparent and actual line widths if
visual or other methods are used for d ata interpretation.
The distortion effect was quantized by creating similar lines to the one in Fig. 2.3,
varying the FM frequency for a given line width, and then subjecting the line to three
baseline suppressions.
This was performed over a range of line widths, the obtained
HWHM were used to find the ratio of the apparent line width to the actual line width,
A vapp/A v act.
2 .5
The resulting d a ta were plotted against the ratio of FM /HW H M (Fig.
), and from this the impact of the baseline suppression routine can quickly be gauged
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24
qso oo o
1.0
0.8
0.6
0.4
0.2
0.0
0
10
20
30
40
50
FM/HWHM
Figure 2.5: The ratio of the apparent linewidth, Avapt, following three baseline suppres­
sions, to the actual, Awact, as a function of the FM sideband frequency divided by the
HWHM. At large FM/HWHM (large FM, small HWHM) the separation between the
sidebands and the main line is sufficient so th at no distortion occurs, but this rapidly
begins to change as the HWHM gets larger.
and corrected for.
The effect of the baseline suppression routine on HWHM values is already corrected
for in the microwave, for program, and as will be shown, completely accounted for in the
Pickett method. A discussion on the effects of the baseline suppression distorting of the
peaks on the Pickett algorithm is presented in Section 7.4.
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25
2.4
Mass Spectrometer System
Characterization of the ionic content of glow discharges is accomplished by extracting
ions from the discharge, and focusing them into a quadrupole mass spectrometer, where
they are mass analyzed.
Extraction of the ions is performed using a biased extraction
element to remove the ions from the discharge and adm it them into an electrostatic lens
array.
The electrostatic lens array focuses the ions onto the entrance aperture of an
Extranuclear (now ABB Extrel) quadrupole mass spectrometer. A differential pumping
scheme is used between the discharge, electrostatic lens array, and the quadrupole regions,
to ensure operating pressures of 10- 7 to 10- 8 Torr for the quadrupole.
In addition to
ionic composition, the neutral composition of glow discharges can also be studied. This
is achieved by using the electron impact ionization source of the mass spectrometer to
ionize the gas flow from the discharge cell.
2.4.1
The Quadrupole Mass Spectrometer
The Extranuclear quadrupole, illustrated in Fig. 2.6, consists of an ionization source,
quadrupole filter, and detector. Electron impact ionization (El) is the selected method
of ion production when the instrument is being used to study neutral molecules from
the discharge or background gases within the spectrometer. The E l source is capable of
providing ionization energies of +3 to -1-103 eV with a value of ~100 eV being typical.
After ionization the ions are accelerated out of the ionization region and focused into the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2 .6 : A diagram of the mass spectrometer system. The ESLA used to extract ions
from the plasma and focus them at the entrance aperture of the quadrupole are: the
extraction element (El), small lens (E2), taper lens (E3), large or long lens (E4), the
up/window lenses (E5), the door (E 6 ), the partition (E7) and the down lens (E8 ). Quadru­
pole elements are: the ionizer (Q l), the quadrupole source optics (Q 2 ), the quadrupole
(Q3) and the electron multiplier (Q4). Potential of the discharge is measured w ith the
probe (SI). Isolation of the mass spectrometer chamber from the ESLA chamber is ac­
complished by the diagonal valve (S2).
quadrupole, where they are filtered.
Ions transm itted by the quadrupole are collected
into a 21 stage CuBe Venetian blind electron multiplier.
both positive and negatively charged ions.
The detector can measure
To minimize the measurement of ions of
opposite charge, but with sufficient energy to pass through the quadrupole and into the
detector, the multiplier is offset from the main axis of the quadrupole. This arrangement
also minimizes signal due to metastable species.
Signal from the multiplier is passed
as current to the electrometer where the output is converted to a voltage and amplified
before being routed to the A /D convertor of the control computer or to an oscilloscope.
Operationally the quadrupole has been used in three different modes:
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1)
sweep, 2)
27
manual, and 3) external command.
In the sweep mode a voltage ramp is applied from
an external source to sweep the instrument through a given mass range.
Electrometer
output is typically read off an oscilloscope or off a strip chart recorder.
W ith m anual
mass tuning the user selects the desired mass and a voltage corresponding to the signal
is provided to the quadrupole mass filter.
This mode offers the ability to “sit” on a
particular m /z value and tune the discharge to maximize this signal. External command
allows for computer control of the sweep to be implemented.
In this mode a current
between 0 and 1 mA is applied to the input to select the desired m /z value.
W ith a sweep range of 0-200 m /z and a resolution of ~1700 at 200 (Section 4.2.2), the
spectrometer is well suited for characterizing the composition of glow discharges.
The
limited mass range is not normally a problem, due to the type of molecules that are
studied using the instrument. Rarely are species with m /z ratios of over 100 observed.
Limitations on the resolution are acceptable, as the cost and complexity of adding an in­
strum ent with sufficient resolving power to distinguish between small molecules of similar
mass, e.g., N 2 and CO, is prohibitive.
2.4.2
Electrostatic Lens Array
Extraction and focusing of ions from the discharge is accomplished using a set of
electrostatic lenses and an extraction element, collectively referred to as the Electrostatic
Lens Array (ESLA). The extraction element is a stainless steel cylinder with a n approxi­
mately 2 cm outer diam eter and closed a t one end except for a 510 /xm pinhole ,2 through
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28
which the ions are adm itted to the system. Following extraction, a set of stainless steel
cylindrical lenses (Fig. 2.4.2) are used to focus the ion beam through a ~ 3 mm entrance
aperture into the quadrupole region. As detailed in Section 2.5, several modifications
were made to the electrostatic lens array to improve the control of the extraction process.
2.4.3
Plasma Voltage Follower
Plasma voltages of several hundred volts are typical in the regions of the discharge
sampled by the mass spectrometer.
Ions with kinetic energies of this magnitude will
pass through the quadrupole without being mass analyzed. A 50 V potential difference
between the plasma voltage and the quadrupole common, has been shown to be the limit
where our quadrupole loses all signal.2 A voltage follower circuit, built by C. Spraggins,
floats the common for the quadrupole (VCOimnon) and the ESLA (Vt ) to within a user
defined voltage differential of the plasma potential (Vaenae).
Measurements of Vaenae
were originally made on the extraction element, E l (Fig 2.6), and later using a probe, as
described below in Section 2.5.1.
2.4.4
Mass Spectral D ata Acquisition and Analysis
Initial efforts in using mass spectrometry to characterize the ionic composition of the
discharge utilized chart recorders as the d ata recording method. Although, readily used
for qualitative analysis, chart recorded mass spectra are difficult to use when quantitative
studies are needed. It was determined th at mass ranges of m /z 10 gave the best resolu­
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29
tion for the optim um combination of sweep rate, time constant, and chart speed available.
The use of this sweep range results in an extensive amount of d a ta work up before useful
quantitative information can be extracted.
As the scope and number of mass spectro­
scopic investigations increased, it became impossible to effectively analyze the obtained
data. Implementation of computerized data acquisition became essential. Superior to
chart strips in every way except for ease of deployment and portability, computer data
acquisition provides the user not only smaller acquisition and preparation times, but also
presents d ata in a format th at is easily analyzed.
The choice of the computer platform to use for the acquisition program was based on
the desire to allow for simultaneous microwave and mass spectrom etry data acquisition.
The ease of implementation and maximization of platform compatibility were also primary
considerations. It was determined that a PC using LabView software, would offer the
greatest flexibility and ease of implementation. Initially control and acquisition programs
were executed on a 333 MHz AMD K 6 based PC with Windows 98se operating system
using LabView 5.1.1. Later the computer was upgraded to a much more advanced 1
GHz Pentium H I based PC , Windows 98se operating system, and LabView 6.02. Both
machines used the ATDAQ 1612 AD/DA board sold by Cyber-Research, for acquiring the
output signal of the electrometer and providing the ram p voltage to control the sweep of
the mass spectrometer. The control, acquisition, and analysis programs used in the mass
spectrometric studies were programmed in Labview. Neither FORTRAN, C + + , nor any
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30
other common computer language can match LabView in ease of programming code for
instrument control and data acquisition.
Analysis of the acquired data is conducted using a suite of programs th at allow the
user to average multiple scans of the same experiment, to extract a subset of the overall
d a ta set, to calibrate the data for improved accuracy, to subtract a fitted baseline, to
create a centroid version of the mass spectrum, and to correct for the mass discrimination
error of the spectrometer. Detailed explanations of these programs are given in Appendix
B..
Interfacing the computer with the mass spectrometer system is a straightforward
process. The output voltage (0-10 V) from the chart recorder output of the electrometer
is passed to an interface box, where it is routed to the A /D connector of the board. At
each step in the voltage ramp, an user defined number of measurements of the output
voltage are made. T he average and standard deviation of these sample points are recorded
as the measured value and the uncertainty, respectively. Signals from the D /A channel
to the mass spectrom eter are also passed through this same box. As the computer and
the o u tp u t/in p u t circuits of the mass spectrometer were at the same ground potential,
single ended inputs were used. Control of the m /z value to be sampled by the quadrupole
is accomplished by converting the D /A output voltage into current, which is supplied to
the External Command (EXT CMD) input on the quadrupole control box. Conversion of
the voltage to current is accomplished using a circuit composed of a precision resistor in
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31
series with a variable resistor. The variable resistor is used to tune the series resistance to
yield a one milliampere current when the D /A output voltage is 10 V. A one milliampere
current applied to the EXT CMD input, will result in transmission of ions with mass
equal to the full scale value of the mass range, typically 200 m/z. Small errors in the
resistance th at may lead to a less than m /z
200
value at the maximum current, are not
important, as all of our measurements are at much smaller m /z values. For smaller sweep
ranges these small errors can be corrected for by simply expanding the sweep range and
then correcting the d ata set by calibration.
2.4.5
Ion Transmission through the Quadrupole System
It is well known th at the efficiency of transmission of ions through a quadrupole is a
non-linear function of mass. While it is possible to adjust the tuning of the quadrupole to
remove the mass discrimination, our instrument has no provision to adjust this parameter
while mass scanning is occurring. The errors caused by the mass discrimination, must,
therefore, be corrected for after the acquisition period.
Mass discrimination in the quadrupole system arises in several portions of the instru­
ment.
Mass discrimination of the ions arises in the extraction process of ions from the
source, transmission through the quadrupole, and non-uniform responses in the electron
multiplier and the ion current amplifier. 11 The magnitudes of these errors are highly de­
pendent on the timing of a n instrument, and each instrument has a different transmission
function.
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32
Transmission of an ion through a quadrupole mass spectrometer is very dependent
on the mass, the charge, and initial velocity of the ion.
Transmission also depends on
the relationship between the DC and RF potentials applied to the quadrupole rods . 12 In
the source the mass discrimination is due in large part to the mass dependent variation
in the kinetic energy of an ion. 11 A constant extraction potential applied to the electron
impact source region, will result in heavier particles being accelerated to lower velocities,
which in turn will affect the stability of the trajectory within the quadrupole field. The
change in the stability causes a change in the transfer efficiency of the ion . 12
For a simple model that assumes th at ions entering a quadrupole have trajectories
parallel with the axis of the quadrupole, the transmission through the quadrupole will be
100%
if the initial velocities obey the relationship , 12
(S)..(J).<0“~(/tT ■
M
Here r 0 is the radius of the quadrupole, u is the angular frequency of the applied RF field,
A M /M is the resolution of the quadrupole. We can see that if the AM , the FWHM of
the peak, remains constant then the range of velocities th at will be transm itted decreases
for increasing mass.
Although the number of ions with sufficient velocity should not
decrease appreciably, the velocity distribution center and HWHM are also decreasing, and
the slower velocities of the heavier ions keep them in the quadrupole field for more RF
cycles leading to increased dispersion and loss of transmission . 12 This effect is dependent
on the resolution, and the effect is more pronounced at the highest resolution. At high
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33
resolution the range of stable trajectories is very small, so ions with masses significantly
different from the mass the instrument was timed to will be transm itted less efficiently.
It is im portant to note th at the parameter A M can be tuned using the resolution and
A M controls on the spectrometer.
Ions sampled from the plasma have an additional source of mass discrimination, the
mass dependency of diffusion rates through the plasma sheath. The ambipolar diffusion of
ions through the plasma sheath can be described using the ambipolar diffusion coefficient
given by 13
D„ a f t (1 +
.
(2.4)
The electron and ion tem peratures are noted Te and 7*, respectively, while the ion diffusion
coefficient, D{ is given by
A =
kT
— 7
TTliVi
,
(2.5)
where m,- and u, are the mass and the velocity of the ion , respectively. As can be seen
a less massive molecule will diffuse through the sheath faster than a heavier ion. This
means th at there will be more low mass ions near the pinhole, this discrepancy will lead
to signals th at are not representative of the plasma in general.
To account for the non-linear transmission through the instrument, it would be nec­
essary to determine the transmission function of the entire ESLA and quadrupole system.
This has not yet been done, but we can use the transmission function determined by
Wojcik and Bederski11 as an approximate transmission function to allow for correction of
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34
0.8
0.7
0.6
CD
CO
c
0.5
s
0.4
0.3
0
20
40
60
80
too
120
140
m/z
Figure 2.7: This is the model transmission function of Wdjcik and Bederski11 used to
correct for mass descrimination effects in mass spectra. The orginal data, (O)i and the
fit to a double exponential function, solid line, are shown.
our data. A plot of the model transition function is shown in Fig. 2.7. We obtained the
fit function by fitting the d ata to a double exponential function. W ith the transmission
function we corrected the observed signal using the following function
(fm /z )r — — {Jm fs)0
>
( 2 .6 )
where Ir denotes the intensity of the real, or corrected signal, while IQdenotes the observed
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35
signal. The value of the transmission function at a given m /z is tc, and is calculated by
the MSTransmission.vi program from the mass spectrometry program suite (Appendix
B.).
The MSTransmission.vi program calculates the real spectrum from the inputted
observed spectrum. In Section 4.2.3 we discuss the use of the MSTransmission program
and the results obtained from it.
2.5
Hardware Modification
Concerns with low signal intensity and control of the kinetic energy of ions entering
the system led to the incorporation of the capability to bias the extraction element. This
capability allows for more control over the number of ions extracted and provides greater
control over the potential energy of the extracted ions.
2.5.1
Probe
Implementation of a bias-able extraction element required the addition of a planar
type probe for measurement of the plasma potential. Constructed of molybdenum, the
circular planar probe tip is spot welded to a tungsten rod, which in tu rn is attached
to copper wire.
This wire is then connected to the plasma voltage follower circuit.
Initially it was connected directly to the circuit and later through a buffer circuit. The
only surface of the probe tip exposed to the plasma is the face; the rear is enclosed with
ceramic material. The ceramic m aterial also forms a seal with a glass capillary tube that
contains the tungsten rod. This assembly is then inserted partially into a larger Pyrex
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36
tube, with the joint sealed by ceramic material. Originally built by P. Doolittle , 14 the
probe was adapted for use in the system described here by shortening it overall length. A
complete discussion of probe design, construction, and operation is given by Doolittle . 14
As mentioned previously the probe is inserted directly across from the extraction element
(Fig. 2.6). The tip of the probe should placed at the same radial position as the extraction
element.
2.5.2
Extraction Element
Once the probe was in place, the extractor element was wired to a potentiometer on
the ESLA control panel. This allows for variation of the potential applied to the element.
Originally, a new potentiometer was to be added, but this would have required a complete
rebuild of the entire ESLA front panel. To allow for rapid implementation it was decided
to tie two of the lenses, Taper and Large, together on the same potentiometer and to
connect the extraction element to the freed one.
It was believed th a t this would have
little or no impact on the functionality of the electrostatic lenses.
One unexpected consequence of the modification has been a time dependent degra­
dation of the resolution obtainable. Several tests were performed to try to determine the
origin of the resolution loss. We sought to determine if the effect was merely due to the
biasing of the extractor creating a tim e dependent charge buildup on the surface of the
extraction element. Such a charge buildup would affect the sheath and fringe fields near
the pinhole, affecting the trajectory and velocity distributions of the ions.
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This would
37
result in the loss of resolution . 12 If the problem was merely charge association, shutting off
the discharge and powering down the V l/V com m circuit and the ESLA should result in
surface charge being discharged and upon reinitiation of the discharge the splitting effect
should disappear. This, however, was not observed. Even if the plasma was re-initiated
within a couple of hours, the resolution problems persisted. Another possibility is the
deposition of m aterial on the surface of the extraction element, which can be ionized or
attract charged particles to the surface, resulting in a build up of the surface charge cre­
ating the observed effect. If the effect is due to deposited material, simply shutting down
the discharge and shorting the extraction element would not be sufficient to correct the
problem. Only cleaning off the deposited material could restore the desired resolution.
Petrmichl 2 discovered that O 2 based discharges have a great scouring effect on the
inner chamber walls.
electrode.
It was decided to ground the extraction element, making it an
It was hoped th at ionic bombardment of the surface would remove the built
up m aterial and allow for normal focusing. Scrubbing of the extractor surface proved to
be a remedy for the loss of resolution, strong evidence th at the effect is due to build up
of deposits near the pin hole of the extractor. A more detailed discussion of the effects
on the line shape is included in Section 4.2.4.
2.5.3
Buffer Circuit
Plasm a discharges typically have low impedances of 1 0 II to 200 kf I and consequently
can load down a circuit th at is electrically connected to them. To minimize loading of the
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38
probe by the plasma, a buffer circuit was designed and built by Mike Green to provide
a high voltage source to the
V sen se
input of the plasma voltage follower, without drawing
any current through the probe. A schematic of this circuit is given in Appendix A..
2.6
The Glow Discharge
The use of DC glow discharges as the sample medium for microwave spectroscopic
studies of molecular ions began in this laboratory in the early 1970’s.15 Since th at time a
significant amount of effort has been expended to study and characterize these discharges.
In this section a brief description of the most im portant properties of the glow discharges
is provided.
Creation of a glow discharge is achieved by supplying a voltage across two electrodes
sufficient to cause the electrical breakdown of a gaseous medium between them. Electrical
breakdown is characterized by the formation of ion/electron pairs from the components
of the gas. Once breakdown occurs and the discharge is initiated, a voltage is required
to m aintain the discharge . 16
This maintenance voltage does not equal the breakdown
voltage and is normally much less.2,16
Indeed, it is often necessary to create a gas mix
with a lower breakdown voltage than th a t of a desired gas mix to allow for initiation of the
discharge.
Following discharge initiation, the gas mix can be readjusted to the desired
composition. T he voltage drop across the discharge is referred to as the discharge voltage
and denoted by V q - Discharge current is measured across a ballast resistor in the power
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39
Aston Dark
Cathodo Dark
Andodo Qlow
Faraday Dark
Spaoa
Cathodo Layor
Nagativa
Glow
'//.
Postiva Column
^
Anodo
Spaco
Figure 2.8: Diagram showing the various regions of a typical glow discharge.
supply and denoted by the symbol I d .
A glow discharge contains several regions, as illustrated in Fig.2.8. The Aston dark
space is a region immediately above the cathode surface, where electrons created by ion
bombardment of the cathode surface (cathode electrons) create a space of net negative
charge.
These cathode electrons, prior to acceleration by the cathode potential, can
collide elastically with species from the discharge resulting in emissions that create the
cathode layer.
The cathode dark space (CDS) is characterized by a large drop in the
plasma potential referred to as the cathode fall.
Those cathode electrons th at diffuse
beyond the cathode layer are accelerated by the cathode fall, resulting in kinetic energies
sufficient to cause impact ionization. The cathode fall represents the m ajor potential drop
in the discharge, and electrons generated in the plasma are unable to enter the cathode fall
region. The region near the cathode fall is marked by increase in the number cool plasma
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40
electrons and by collisions of the beam electrons with molecules.
The collisions of the
beam electrons and molecules leads to observable emissions. This region is referred to as
the negative glow. A region of nearly equal ion and electron densities, thenegative glow
has a veiy weak field. W ithin the negative glow, the principal ionization mechanisms are
impact ionization by the high energy cathode electrons.
As the cathode electrons pass
through the negative glow, there is a continued loss of kinetic energy through collisions.
When the electrons lack sufficient energy to promote excitation, the discharge becomes
dark. This region is known as the Faraday dark space (FDS). After the FDS there is an
increase in the electric field. This field accelerates the electrons towards the anode, and
ionization processes are sustained by these locally accelerated plasma electrons, instead
of the beam electrons. The point where the locally accelerated plasma electrons initiate
ionization is the beginning of the positive column. In this region ionization is less than
that of the negative glow by one to two orders of magnitude .2
A thin layer of a strong electric field, called the sheath, is present at all the walls of the
cell. The sheath field strength drops quickly in space, as the shielding between the charged
particles in the discharge weakens the field. Positively charged ions are accelerated to the
wall when diffusive movement brings them into the sheath region, while anionic species
and low tem perature electrons are repelled by the field.
The classification of discharges created using cylindrical electrodes instead of planar
electrodes, differs somewhat from the more conventional case. Conventional classifications
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41
of discharges are based on the current to voltage relationship.
Normal glow discharges
occur when an increase in the discharge current does not lead to an increase in the current
density at the cathode surface, and the discharge voltage remains constant.
Abnormal
glow discharges show an increase in current density a t the cathode surface and discharge
voltage, as the discharge current is increased.2 ,16 W ith the use of cylindrical electrodes
two general types of discharges are produced.
The “positive column” mode is similar
to the normal glow in the current to voltage relationship and is characterized by high
discharge currents. Discharges with the current to voltage properties of an abnormal glow
mode, that exhibit low electron energies and low currents are classified as “negative glow”
discharges.
The transitions between the positive column and negative glow modes are
rarely stable processes. Frequently, experimental conditions are such th at the discharge
transitions between modes in an uncontrollable fashion. This most often occurs with
gas mixtures th at have a large breakdown voltage, such as neon. Glow discharge mode
transitions are determined by many factors. Among these are: the gas mix, cell wall
temperature, presence of an axial magnetic field, the applied voltage, and the presence of
deposited m aterial on the cell wall.
While not required by definition, negative glow discharges in our system are never
observed in the absence of an axial magnetic field. This field confines the cathode elec­
trons, th at pass over the cathode fall, into a beam th a t passes down the center of the
discharge. If the magnetic field was not present, these beam electrons would diffuse away
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42
from the center and to the walls, in a distance much less than the length of the cell. W ith
magnetic confinement, first proposed by De Lucia et a / . , 17 the focused electron beam can
pass the entire length of the cell. This extends the collisional path, increasing the total
ionization. In addition to increasing the total ionization, the decrease of electron diffusion
to the cell wall weakens the ambipoloar field. This reduction of the ambipolar field slows
ion diffusion to wall.
There does appear to be a limit to the benefits of the magnetic field. Petrmichl 2 found
th at for a range of magnetic field strengths transition intensities increased with field, but
once over a threshold value, a further increase of the magnetic field actually leads to a
diminution of the signal.
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43
CHAPTER 3
Sensitivity and Dispersion
3.1
Introduction
Several experimental factors limit the performance of the instrument, among these are
the sensitivity of the instrument and the dispersion signal that arises from reflections of
the microwave radiation off the interior surfaces of the cells. The effects of the instrument
sensitivity have im portant consequences on the potential for observation of a molecular
ion, while the dispersion signal can limit the accuracy of measured frequencies.
3.2
Spectrometer Sensitivity
The sensitivity of the spectrometer is the central factor in determining if a microwave
search is feasible. Determination of the limit of the values of 7 below which transitions
cannot be observed is necessary if predicted
for a successful microwave search.
7
values are to be used to assess the potential
Because the power output of the harmonic mixer
decreases as the harmonic increases, lines corresponding to third and fifth harmonics were
chosen to determine the extremes of the instrument sensitivity.
Determination of the sensitivity requires measurement of the transitions of a well
characterized molecule.
Carbonyl sulfide is the natural choice, because it is one of the
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45
5
-
0 -
-5
-
90.6200
90.6225
90.6250
90.6275
90.6300
GDF (GHz)
Figure 3.1: Raw spectrum of the J =22-23 0 13C34S transition with a measured frequency
of 271,879.4670 MHz. The spectrum is the average of 188 sweeps a t 20 fiV sensitivity
and a 3 ms time constant. The pressure of OCS was 3.9 mTorr at a tem perature of ~300
K. Vertical axis is intensity with a -10 V to 10 V range corresponding to the selected
lock-in sensitivity. The x axis in this spectrum is the Gunn diode frequency(GDF), or
the source frequency, prior to harmonic multiplication.
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46
Table 3.1: Summary of the spectroscopic constants from literature, for OCS and some of its
isotopomers.
Species
B (MHz)a
lc0 12C32S 6081.493
“ O ^ C ^ S 5932.838
160 13 C32S 6061.925
180 12C32S 5704.861
160 13C34S 5911.733
l7 0 12C32S 5883.675
a) from Lovas19
b) from Burenin et al.20
D (exp) kHz
1.301777“
1.2691“
1.2993“
1.1353“
1.237 867(84)6
singly substituted isotopic lines. By use of the baseline suppression routine (Sec. 2.3.4)
it was determined th at the line was a third harmonic. Assignment of this line began by
calculating the transition frequency of several isotopic species, using the expression for
the transition frequency of a linear rotor 18
v = 2B (J + 1 ) —AD{J + 1 ) [(J + l ) 2 —Z2]
,
(3.1)
and the spectroscopic constants listed in Table 3.1. This expression accounts for I type
doubling, which occurs when a linear molecule vibrates in such away as to break the
rotational degeneracy of the two perpendicular rotational axes. Using Eq. (3.1) and the
values in Table 3.1, spectra for several species in the ground vibrational states (I = 0)
were calculated. A line in the spectrum of
160 13 C34S
was found to m atch the unknown,
this being the J=22-23 transition with a predicted frequency of 271,879.47 MHz.
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47
Calculation of the absorption coefficient followed the method outlined in Section 6 .6 . 1 ,
using
vj
_
7
3cK TAv
'
'
where /3 is the fraction of the sample corresponding to the species of interest, N the
number density of the species, T the tem perature of the sample, and
|^ - |2
is the square
of the dipole moment m atrix element. The center frequency of the transition and the
HWHM, are noted by the symbols u0 and A u, respectively. The fraction of molecules in
the ground state of the transition, / r , is calculated using the high J form of Eq. (6.26).
The value of /3 is given by the abundance of the isotopomer.
Using the methods in
Section 6.6.1 and the values listed in Table 3.2 absorption coefficients for low pressure
and high pressure conditions were calculated.
Using the 0
13 C34S
J= 2 2 —>23 line, the third harmonic sensitivity can be established.
Two spectra were used, the first a t low pressures (3.9 mTorr) the second at moderate
pressures (32 mTorr), of OCS. The 7 values for the two cases are quite different. At first
glance this is surprising, since Eq. (3.2) should be independent of the pressure. This is
because both the N and Au values are proportional to pressure. The Au value for the
low pressure is most likely in error due to the dominance of the Doppler and modulation
broadening contributions to the total linewidth (Chapter 7).
The low pressure raw
spectrum (Fig. 3.2) and the baseline suppressed spectrum (Fig. 3.3) show th a t lines with
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48
Table 3.2: Values used in calculating
7
for
at two pressures
Low Pressure
3.9
1.26
271879.4670
0.2263
High Pressure
32
10.3
271879.4678
0.3861
14
Pressure (mTorr)
N (xl0 14cm-3)
Transition Frequency (MHz)
Linewidth (MHz)
2 .8
7 (xlO - 6 cm-1)
24
S/N Ratio
86
0.35
0.47
7 m (x l 0 ~ 6 cm-1)
=
1.26
xlO14,
T=300 K, 0 = 4.620 xlO"4, N
/x = 0.7125 D
B“ = 5911.733 MHz, f R =0.0435
a) F. Lovas19
7
« 10" 6 cm ' 1 can easily be observed.
Considering the strength of the observed lines,
we would like to estimate a limit of detectability.
noise (S/N) ratio, dividing this into the
7
This is made by using the signal to
value, and then multiplying this value by three
to arrive a t the threshold. Using the S/N values in Table 3.2, we estimate the threshold
value,
7
m, to be ~
10-7
cm - 1 for this instrument.
Maximization of the S/N ratio is an extremely important part of any measurement.
In our experiments the optimization of the source is our most im portant method for
improvement of the S /N ratio. Optimization of the source requires the user to adjust the
frequency tripler to maxim ize the power of the signal, determine the S-band and Gunn
diode frequency combination which will produce the most stable IF signal, and to adjust
the G unn diode to produce an output th at is of the desired frequency and with maximum
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49
2
0
-1
-2
90.6200
90.6225
90.6250
90.6275
90.6300
GDF (GHz)
Figure 3.2: Spectrum of the Ol 3 C34S J =22-23 transition with a measured frequency of
271,879.4670 MHz. The spectrum is the average of 188 scans. Scaling on the y axis is
such th at a -10 V to 10 V range corresponds to the full sensitivity at which the spectrum
was acquired. The y axis therefore represents ~ 1/4 of the 20 /iV scale or approximately
what the spectrum would have looked like if a 5 fiV sensitivity had been used. The
spectrum is presented in this fashion to aid visual comparisons. The pressure of OCS
was 3.9 mTorr, and the tem perature ~300 K.
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50
10
5
0
-5
-10
271.865
271.870
271.875
271.880
271.885
Frequency GHz
Figure 3.3: The baseline suppressed spectrum of the J=22-23 transition of O ^ C ^ S . This
spectrum was obtained by performing two third harmonic baseline suppressions, followed
by an expansion of 15 on the spectrum in Fig. (3.2). The y axis scale is 1/15 of th a t in
Fig. (3.1). The cacluated 7 is 2.8 xlO- 6 cm-1. Based on the signal to noise ratio of this
line, it is expected th at lines with 7 ~ 1 0 - 7 cm - 1 could be observed.
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51
10
5
0
-5
•71879.4678 MHz
-10
90.620
90.625
90.630
90.635
GDF (GHz)
Figure 3.4: Raw spectrum of the J=22-23 transition of Ol 3 C 34 S. This spectrum is the
average of 100 scans a t 10 /zV sensitivity, a pressure of 32 mTorr OCS and a temperature
of ~300 K. The vertical axis corresponds to the full 10 /zV range, and the horizontal axis
is the Gunn diode frequency.
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52
Table 3.3: Values used in calculating 7 for l6 Ol3CS with and without optimization and also with
filtering out of the third and fourth harmonics.______________________________________
No Optimize
Pressure (mTorr)
34.7
N x l 0 15(cm-3)
1.117
Transition Frequency (MHz)
460421.22
Linewidth (MHz)
0.75
470
7 x l 0 - 6 (cm_1)
3.2
S/N Ratio
440
7 mx l 0 " 6 (cm -1)
T=300 K, 0 = 1.43xl0-2 , = 0.7125 D
B“ = 6061.92510(59) MHz, f R =0.25577
a) F. Lovas19
Optimize Only
34.1
1.097
460421.27
0.72
480
1 2 .6
Optimize and Filter
31.7
0.9975
460421.28
0.63
540
19.0
110
86
power.
The effects of source optimization are clearly demonstrated by comparing three spec­
tra of the J=37-38 transition of O l3 CS. This line was measured without optimization,
with optimization and with optimization and filtering out the 3rd and 4th harmonics.
Absorption coefficients were calculated for each case and the results are listed in Table
3.3. Plots of the spectra used and relevant experimental information are shown in Figs.
(3.5-3.10). A comparison of the spectra show the dram atic effect th a t source optimiza­
tion can have on the intensity of a line. The filter increases the amount of the power
em itted by the source, at the fifth harmonic, which leads to a dram atic increase in the
signal to noise.
It is clear, given the relatively weak signal of this line and the large calculated 7 value,
th a t the power output at the fifth harmonic is very low. A rough estim ate of the
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7
value
53
10
5
0
•5
10
92.076
92.080
92.084
92.088
GDF (GHZ)
Figure 3.5: Raw spectrum of the J=37-38 transition line of Ol3CS near 460421 MHz. The
lock-in amplifier had a sensitivity setting of 10 fiV and a time constant of 3 ms. The
OCS pressure was 34.7 mTorr. The spectrum is an average of 100 scans. Modulation
used FM sidebands of 2.0 MHz and an AM frequency of 21.0 kHz.
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54
JQ
■I
L. I . L I
276.230
I
I
I
I
I
I
I
I
276.240
I
I
I
I
I
I
I
I
I
I
276.250
I
I
1
I
1
I
I
I
I
I
I
I
I
I
I
276.260
GDF (GHz)
Figure 3.6: Baseline suppressed and fit spectrum of the J=37-38 transition of 0 13CS at
460,421.22 MHz. Original d a ta points are denoted by o, while the fit is a line. The
raw spectrum (Fig. 3.5) was subjected to three fifth harmonic baseline suppressions and
vertical expansion by a factor of ten. Expansion scales the y axis to 1/10 of th at in (Fig.
3.5). Besides the transition frequency, the least squares fit determined the linewidth to
be 0.75 MHz. The value for 7 is 470 xlO - 4 cm-1, with a signal to noise ratio of 3.2. It is
obvious th at the spectrometer sensitivity is very poor for fifth harmonic lines.
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55
5
-
&
aa>
'w
92.076
92.080
92.084
92.088
GDF (GHz)
Figure 3.7: Raw spectrum of the J=37-38 line of 0 13CS near 460421 MHz. This spectrum
was acquired following the tuning of the source to optimize the signal of this line. The
lock-in amplifier had a sensitivity of 10 /xV and a r = 3 ms. The spectrum is an average
of 84 scans taken at a pressure of 34.1 mTorr OCS and a tem perature of ~ 300 K. The
m odulation use 2 MHz FM sidebands and an AM frequency of 21 kHz with a n amplitude
of - 1 1 dbm.
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56
10
5
&
't/»
c
QJ
-5
-10
460.38
460.40
460.42
460.44
GDF (GHz)
Figure 3.8: Baseline suppressed and fit spectrum of the J=37-38 transition of Ol 3 CS. Orig­
inal d ata points are denoted by o, while the fit is a line. The spectrum in Fig. 3.7 was
subjected to two fifth harmonic baselines followed by a vertical scale expansion of six,
the y axis values are 1/6 those of Fig. 3.7. A least squares fit using a Lorentzian model
function determined the frequency to be 460,421.27 MHz and the linewidth to be 0.72
MHz. The absorption coefficent is determined to be 7 = 4 8 0 xlO - 6 cm-1. W ith a signal
to noise ratio of 13:1, the effects of optimizing the source is dramatic.
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57
5
-
-5
-
92.075
92.080
92.085
92.090
GDF (GHz)
Figure 3.9: The raw spectrum of the optimized and filtered spectrum of the J=37-38 tran­
sition of 0 13CS. In this spectrum a cutoff filter was used to filter out the third and fourth
harmonics. The spectrum is an avearge of 100 scans taken at a pressure of 31.7 mTorr
OCS and a tem perature of ~ 300 K. The lock-in amplifier had a sensitivity of 10 fiV and
a r = 3 ms. Modulation parameters are the same as in the previous 0 13CS spectra.
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58
10
5
0
-5
-10
460.400
460.420
460.440
GDF (GHz)
Figure 3.10: Baseline suppressed and fit spectrum. Original d a ta points are denoted by
o, while the fit is a line.
Three fifth order baseline suppressions and a vertical scale
expansion of 1.5 were performed on the raw spectrum (Fig. 3.9) to produce this spectrum.
A least squares fit using a Lorentzian line shape was used to determine the transition
frequency and linewidth of 460,421.28 MHz and 0.59 MHz, respectively. Signal to noise
has again increased dramatically from 13:1 to 19:1. Again assuming linear absorption it
should be possible to observe fifth harmonic lines with 7 = 80xl0-4 cm-1.
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59
for a C H F j Q branch transition near 450 GHz and J as 45 yields
7
=
1 .7
x
10“ 6
cm-1.
This is very far from the 7 m » 85 xlO- 6 cm - 1 obtained for the optimized and filtered 5th
order line studied.
Based on this comparison it is very unlikely th at any 5 th harmonic
lines of a molecule similar to CHF^ will be seen. To observe the higher harmonic lines,
frequency multipliers optimized for these regions will be required.
It should be noted th at the values determined for 7 represent a liberal estimate, as the
assumption / v= l is not strictly true, and no accounting for OCS degradation has been
done. The instrum ent is almost certainly more sensitive than reported here.
3.3
Dispersion Effects
In the case where the sample cell of a spectrometer is enclosed by two partially reflect­
ing windows, a standing wave pattern is created within the cell, which leads to the mixing
of absorption and dispersion profiles.
In low light conditions, the two profiles combine
linearly to create the observed spectrum .9 This can have an effect on the accuracy of the
center frequency determination, and the effects of this mixing must be accounted for in
Doppler shift measurements.
The refractive index of a substance near a transition point is given by
+
•
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<M>
60
and the absorption function 7 , is defined
TmaxA*'2-----7
( i ' — i/ 0 ) 2 —
Au 2
’
as given by Townes and Schawlow. 18 In these equations, A(i/0 —v) is the index of refraction
dependent wavelength of the incident radiation, Au is the HWHM of the line, uQis the
resonance frequency, and v is the frequency of the incident radiation.
constant of a gas near a transition frequency is given by Eq. (3.3).
The dielectric
The change in the
dielectric constant from an initial value K0, as a function of frequency is shown in Fig.
3.11. Also shown is the plot of the absorption function given in Eq. (3.4).
Dispersion is classified into two types, normal and anomalous.
Normal dispersion
occurs when the slope of the K — K q function is positive and the value of n(v) <C 1 .
Anomalous dispersion occurs when the slope of the dispersion function, d(K — K0)/duj,
is negative. W hen this occurs the absorption function
7
, is strong.
Dispersion signals
are typically much less intense than are absorption signals,but the dispersion signal is still
observed at the detector. The magnitude of dispersion is dependent on the spectrometer
and the nature of samples being studied, and is of great importance, because of the effect
dispersion has on the observed line shape.
A sum of the dispersion and absorption profiles, the line shape is still principally a
Lorentzian, but it is now somewhat distorted with the apparent maxim um shifted away
from the true absorption maximum.
A comparison of the pure absorption and mixed
absorption line shapes is shown in Fig. 3.12, here the magnitude of th e dispersion function
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61
K-K
0.0
1.0
2.0
V (arb. units)
3.0
4.0
Figure 3.11: Plots of the functions K — K 0 and 7 as given by Eqs. (3.3) and (3.4). The
dispersion line shape, K — K q, in this example is exaggerated for clarity.
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62
is greatly magnified, so the effect is more readily seen.
Because it is the anomalous
portion of the dispersion th at creates the frequency shift, we will refer to the effect as the
anomalous dispersion shift. The frequency of the distorted line is given by
^
l^o “1” fi^disp ,
(3.5)
where u is the observed frequency, uq is the frequency of the line without dispersion, and
Svdisp is the frequency shift.
Gudeman8 showed th at the anomalous dispersion shift can be expressed to the first
order by
$Vdisp = A&vre~accuL s i n ( ^ ^ )
,
(3.6)
where Au is the HWHM of the line, r is the reflection coefficient, a ceu is the attenuation
per unit length of the sample cell, and L the distance between the microwave horns.
In the region near a transition, the refractive index is not constant, Eq. (3.3), and the
wavelength of the incident radiation changes accordingly. This variance in the wavelength
is accounted for by the factor Ag,
A , =
2
^
.
( 3 .7 )
The value of the fit factor, A, in Eq. (3.6) is determined by the m ethod used to determine
the center frequency.
Use of a least squares method to fit the observed line shape to
a model line shape, will result in a minimization of the residuals in the regions of the
half maximum.
The result of this is th a t the center frequency is effectively found by
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63
Y+ K-K
0.0
1.0
2.0
V (arb. units)
3.0
4.0
Figure 3.12: A plot of the absorption function, 7 , from Eq. (3.4) and the sum of the
absorption, and the dispersion functions, (K — K q) 4 - 7 . The dielectric K function is
defined in Eq. (3.3). As can be seen the maximum of the sum function is shifted away
from th at of the true absorbance function. We will refer to this shift as the anomalous
dispersion shift.
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64
interpolation between the least squares half maximum points, and in this case A will
equal two.
For the case where the center frequency is determined using a m ethod th at
locates the peak absorption, A will have the value of one.
Reflections of the microwave signal from the horns, lenses, and other surfaces of a
spectrom eter create a standing wave pattern with the resonance condition given by
This standing wave pattern creates a sinusoidal baseline present in every spectrum, e.g.,
in Fig. 3.13, and is accounted for in the expression for Su [Eq. (3.6)] as the sine term.
By adjusting the horn to horn separation, L, to bring the transition to an extrem a of the
baseline, the sine term is forced to zero, and so is the dispersion shift. While conceptually
simple, the application of this method is more complicated.
In this treatm ent we have considered the effects of monochromatic radiation, but,
the actual baseline arises from the reflections of the three different harmonics produced
by the frequency tripler (Section 2.3). Another complication in reducing the anomalous
dispersion shift is due to time dependent variations in the baseline.
Even without the
complication of three frequencies, changes in either the cell length L, the refractive index
n(v), the spacing between the cell windows, or other factors, may result in a shifting of
the baseline maximum.
For example, the cooling of the discharge cell will result in a
small change in the length of the cell, and a t 300 GHz a change of only 0.005 cm will shift
the frequency of the baseline extrema by 5 MHz.
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65
10
5
&
c=
<d
0
'co
-5
10
89560.00
89565.00
89570.00
Source Frequency (GHz)
Figure 3.13: The unidentified transition # 1 prior to baseline suppression and fitting.
Shown is the sinusoidal baseline arising from the standing wave p attern within the cell.
Detector sensitivity is 10 /zV. The discharge current was 63 mA, with potential of 1100
V, and a pressure of 30.1±1.0 mTorr. The tem perature of the cell wall was 87.0±0.3 K.
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66
The deviation from the optimized baseline position is generally slow, and if significant
signal averaging is not required, the method works quite well. If, however, the discharge is
being operated under conditions which are optimal for peak intensity, but not for baseline
stability, it can be very difficult or impossible, to acquire an averaged spectrum where the
peak is a t the maximum. This most seriously affects measurements of weak lines.
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67
CHAPTER 4
Mass Spectrometry of Glow Discharges
4.1
Introduction
Mass spectrometric characterizations of positive column discharges can provide the
experimentalist with information necessary to evaluate the potential for detecting an ion
of interest. In the first part of this chapter we discuss general experimental methods and
concepts necessary to properly analyze and interpret the mass spectral d a ta presented in
the second part.
O ur studies of various discharge chemistries were motivated by the need to identify
optim al discharge conditions for the production of ions of interest. Discharge chemistries
studied include: SFg + Ar, CF 4 -t- Ar, CHF 3 + Ar and CHF 3 + Ne. W ith the SF 6 study
the ion of interest was SF+ , and with the fluorocarbon chemistries, CHFj
spectrometric studies of the fluorocarbon are described in Chapter 5.
The mass
We also studied
pure Ne discharges to identify a line at m /z 40. This line is identified as Ar+ th at arises
from trace contamination.
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68
4.2
General Experimental
In this section several topics are discussed which will provide a context within which
to interpret the spectra presented in subsequent sections.
Relevant topics include: cal­
ibration, resolution, peak shape, and an introduction to the methods used in finding
integrated intensities.
4.2.1
Calibration
Correct interpretation of mass spectra requires careful calibration of the mass numbers
of the peaks.
At the time of the experiment the instrument is calibrated such th at the
sharp falling edge of a peak should correspond to the nominal m /z value, as shown in
Fig. 4.1.
It has been observed that the instrument calibration is not linear over sweep
intervals of greater than m /z 10-20. Spectra with scan widths greater than 20 m /z units
need post acquisition calibration.
Calibration of mass spectra was performed using a
routine provided in the package of programs written for mass spectra acquisition and
analysis.
The collection of mass spectrometry programs are described in Appendix B..
W hen using the calibration program, two or more calibration points are selected. When
the spectrum is well resolved, the middle of the falling edge is selected, as in Fig. 4.1, but
often resolution is so poor th at the peak maximum is selected.
Where the calibration
point is on the peak is not important, as long as the same point is used for every peak
in the calibration d a ta set.
Once the calibration points are selected, the user can fit
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69
16.0
17.0
18.0
19.0
m/z Ratio
10
12
14
16
18
20
22
24
26
28
30
m/z Ratio
Figure 4.1: A clearly resolved mass spectrum of the background gasses in the quadrupole
chamber taken by computer d ata acquisition. The peak a t m /z 18 is H2 0 +; also visible
are HO+, 0 +, N+ and C+ . The inset shows the point (A) which would be used for the
calibration of the instrum ent. Post acquisition calibration would also use this point as
the falling edges are well resolved. The mass spectrometer had a resolution setting of
8.4, a AM of 0, a time constant, r of 30 ms, and a detector bias of 3.5 kV. O n the E l
source the electron energy was set to 98.9 eV, the emission to 6 V, the extractor element
to -3.6 V and the focusing lens elements lens 1 , lens 2 and lens 3 were set to -323.2 V,
-40.9 V and -0.70 V, respectively.
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70
a polynomial function to the points and obtain a calibration curve.
Even with the
calibration program the true m /z value of each peak does not always correspond to the
calibration point of the peak, but due to the single mass unit resolution of our studies
this is not a problem.
4.2.2
Quadrupole Resolution
A quadrupole mass spectrometer is used to filter ions by setting the relationship
between the DC potential and RF fields on the quadrupole rods such th at only ions of a
given mass to charge ratio have stable trajectories through the length of the quadrupole.
The resolution of the quadrupole mass spectrometer is dependent on the amount of time,
or equivalently the number of RF cycles, the ion spends within the quadrupole field. 12
The functional dependence of the resolution on the number of RF cycles an ion spends
within the RF field is not known exactly, but it has been experimentally shown to be of
the following form : 12
M = — Nn
K
’
AM
(4
{
i)
}
where AT is the number of cycles during which the ion is exposed to the RF field, n is
an empirically determined value approximately equal to 2, A M is the full w idth at half
maximum, and M is the mass of the ion . 12
Related to the definition of AM, K is an
empirically determined constant , 12 with values typically being ~ 2 0 .
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71
The relationship between the injection energy, V2, which is the energy the ion possesses
when injected into the quadrupole, and the resolution is expressed by recasting Eq. (4.1)
in terms of the injection energy:
where L is the length of the quadrupole, / the frequency of the RF supply frequency, e is
the electron charge in coulombs, m is atomic mass in kg, and A m is the half width half
maximum in units of kg . 12
The kinetic energy of an ion entering the quadrupole is dependent on the relationship
between the local potential and the potential of the sheath covering the pinhole on the
extraction element.
The thickness of the sheath, Section 2.6, depends on the plasma density and is not
easily predicted.
It is known th at for low pressure/high density plasmas the collisional
cross section is small within the sheath, and an ion is able to pass through the sheath
with little change in its kinetic energy. Most of the discharges used in the experiments
described in this work, are classified as high pressure/low density discharges.
A low
pressure discharge will have a pressure ~ 2 mTorr, while a high pressure discharge will be
~ 30 mTorr. In a high pressure/low density discharge, the mean free path through the
sheath is smaller than the sheath thickness. The increased collisional frequency causes a
distribution of the kinetic energies between zero and the sheath potential.
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72
From Eq. (4.2) it is obvious that a distribution of energies will result in a loss of
resolution and a broadening of the peak. It is believed th at this is one of the causes of
the poor peak shape observed in some discharges. See Section 4.2.4 for more on peak
deformation.
As the ions pass through the electrostatic lens array, ESLA, the ion beam is focused,
such th at the beam passes through the diagonal valve, or conductance limit, th at separates
the ESLA chamber from the quadrupole and onto the entrance aperture of the quadrupole.
A schematic of the instrument is shown in Fig. 2.6.
Ions entering the quadrupole pass
through the ionizer first, and are further focused by the lenses in this section, onto the
entrance aperture of the quadrupole rods.
Due to the conservation of total energy of
electrostatic fields in a vacuum, the energy an ion will possesses at any given moment is
the difference between the plasma potential at the point in the sheath where the ion was
formed and the reference potential of the quadrupole rods. If the ions are formed by the
ionizer, as required for the study of neutral species, the ion injection energy is equal to
the Ion Energy setting. There is a minimum energy required for injection, and Dawson12
gives this threshold as 2 eV.
A change in the plasma potential, relative to the reference voltage of the quadrupole
rod assembly, will cause a change in the injection energy, and consequently a change
in the resolution.
Petrmichl2 reports for the system described here, th a t a maximum
potential difference of 50 V between the plasma potential and reference voltages of the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
quadrupole/ESLA system, can be tolerated before significant loss of resolved signal occurs.
The initial kinetic energy of a typical ion, in a glow discharge ,2 is on the order of 0.03 eV,
a value that is negligible when compared with the 102 - 103 eV a particle in our system
could have if it were extracted with a system potential at ground. While the ESLA can
often be used to time the resolution back into acceptable limits, see Section 2.4.2, the very
nature of glow discharges leads to variations of the discharge potential at sufficiently high
frequencies th at the manually tuned ESLA cannot adequately compensate for them. To
keep the potential difference less than the 50 V limit, a voltage regulator circuit, is used to
force the circuit common of the ESLA, Vi, and th at of the quadrupole, Vcommon, to track
within a user defined offset of the plasma potential. This circuit and modifications made
to it are described in Sections 2.4 and 2.5.
The time constant of the voltage regulator
circuit is such th a t spikes in the discharge potential are not followed.
The operational
range of the voltage regulator is limited by the power supply(s) settings th at are used to
power the circuit.
4.2.3
Mass Spectrometer Transmission
The effects of the mass dependent non linear ion transmission through a quadrupole
spectrometer needs to be determined, and if appropriate, corrected for. Using the spec­
trum in from the Ne + CHF 3 study, Fig. 5.9, and the MS Transmission.vi program,
Section 2.4.5, the effects of mass discrimination are removed from the spectrum. At this
time we use as a model for the transmission function of our instrument.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This model
74
transmission function is for a similar quadrupole instrument and was determined by Wojcik and Bederski. 11 The corrected spectrum is shown superimposed on the original in Fig.
We then used the FCCv02.vi program to determine the area of the m /z 51 peak,
4.2.
-0.00568 intensity units, and the total integrated area of the spectrum, -0.5428 intensity
units.
Using these values the fractional abundance of the m /z 51 peak is calculated to
be 0.011.
Comparing these value with the value of the fractional abundance, 0.010, of
m /z 51 determined for the uncorrected spectrum, shows that there is no significant error
introduced using the observed spectrum. This is true because the majority of our signal
lies within a range of ~ 30 m /z units, so there is a near uniform correction applied, and
the correction factor is effectively averaged out when the fractional abundance is deter­
mined. The effects of ambipolar diffusion, Section 2.4.5, are not, of course, modeled by
Wdjcik and Bederski, although their model does include discrimination effects th at arise
from the extraction of ions from the source into the quadrupole.
4.2.4 Peak Deformation
Following the incorporation of the probe ( 2.5) an apparent plasma dependent peak
splitting was observed. The magnitude of the splitting seemed to be linearly dependent
on the magnitude of the plasma potential. Mass spectra of neutral background species
w ith no discharge present did not exhibit peak splitting. Comparison of experimental
conditions between the background analysis and the plasma sampling suggested four pos­
sible sources for the splitting effect:
1)
a build up of contaminants a t the pin hole,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2)
75
-0.16
-0.14
0.12
•
-
(A
C
=3
-e
0.10
•0.08
ea
-0.06
a>
c=
-0.04
-
0.02
0.00
20
40
60
80
m/z
Figure 4.2: Comparison of a Ne -1- CHF 3 spectrum with and without quadrupole transmis­
sion correction. This is the same spectrum th at is shown in Fig. 5.9. The differences
between the orginal spectrum, (—), and the corrected spectrum, (.....), are very evident.
As it should, the descrepancy between the two spectra increases a t higher mass. But in
this case the m ajority of the signal is within a 30 m /z range, so the effect on the fractional
abundance measurements is small.
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76
20
30
40
50
60
20
Chart Position
20
30
40
Chart Position
(c)
30
40
60
Chart Position
50
60
20
30
40
50
60
Chart Position
(d)
Figure 4.3: Voltage dependence of the peak splitting effect. The clear dependence of the
splitting effect on the Vaerwe voltage used to determine the tracking voltage for the quadrupole and ESLA commons is shown in the four spectra. Applied voltages are: (a) 100V,
(b) 300 V, (c) 500 V, (d) 500 V. Although due to space considerations the 0 V case is not
shown the peak shape is indistinguishable from the 100 V peak. The spectra in (c) and
(d) illustrate the reproducibility of the effect. Species shown are the background gases of
the spectrometer. The units are in chart position and are not calibrated to mass. The
m ain peak a t m /z 18 corresponds to H2 0 + .
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77
problems with the electrostatic lenses , 3) a problem in the Vi./ 'Vcommon tracking circuit,
or 4) a problem in the quadrupole th at was not manifest when operated near laboratory
ground.
To determine if the problem was in the V i/ Vcommon circuit a simple experiment was
conducted. A DC power supply was used to provide a virtual plasma potential which
could then be varied and the effects of the potential on background neutral lines could
be evaluated. If the peak splitting was observed, then the problem was with either the
Vl/Vc ommon. board or with the quadrupole. Results of the test are summarized in Fig 4.3.
Each trace corresponds to a mass range of approximately 15-19 amu with mass values
increasing from right to left. Three different voltages are shown here: 100 V, 300 V and
500 V. It is quite apparent that the splitting is due to a problem associated with the
voltage applied to the V3ense input. The observed splitting pattern is very similar to
a pattern arising from defects in either in the ion source or in the quadrupole held, as
described by Dawson12 .
As illustrated in Fig. 4.4, the plasma potential is relatively high throughout the
discharge, until the cathode fall. Because the cathode fall occurs over a small space, the
probe almost certainly measures the high plasma potential when the tower electrode, see
Fig. 2.1, is used as the cathode.
Since the tower electrode is always a t the laboratory
ground, Section 2.2, the potential measured by the probe will be the plasma potential.
Potential values of several hundred volts are not uncommon, and as can be seen in Fig.
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79
4.3, these values would produce spectra that would be unreadable. To correct for this
problem, it was decided to reverse the polarity of the power supply, resulting in the tower
electrode becoming the anode. This is accomplished by applying a negative voltage to the
north electrode, making it the cathode. And the potential difference between the plasma
and the laboratory ground is now very small.
This work around did not completely
remove the peak splitting, but it did reduce it to an acceptable level.
The problem arose from an error in the rewiring of the Vaense interface at the time
of the probe addition. The effect was to tie two sources for Vsense, one coming from
the probe/buffer circuit system the other from the extraction element, together. When
this was discovered, disconnecting the extraction circuit wiring from V3Cnse corrected the
splitting problem, and no additional peak splitting problems have been observed. Indeed
discharges with greater potentials than those used in the above study have been used
without any observed splitting.
A time dependent broadening, or de-focusing of the mass spectral lines has been
observed in these studies.
As explained in Section 4.2.4, this broadening is due to
contamination on the surface of the extraction element. Removal of the contamination
by ionic bombardment, restores the resolution. Mass spectral lines of systems using Ar
as the carrier gas tend to be broader and less well resolved than those using Ne as the
carrier gas.
4.2.5
Methods for Determining Peak Area
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80
Determination of integrated intensity is accomplished using one of two methods, the
Fit Curve Calculation v02.vi, or FCCv02.vi, and the areaXY function of Igor Pro. Each
method has its advantages and disadvantages, the Fit Curve program is most effective
when there is considerable of overlap between peaks, while the areaXY function method
is much faster.
The FCCv02.vi program allows the user to enter various peak parameters required to
calculate the line profile using one of a selected group of line shape models (Appendix B.).
The calculated line is displayed on a plot of the experimentally obtained spectrum. If the
user wishes, the calculated curve can be subtracted from the d ata set to allow for the
fitting of overlapped peaks. Up to six peaks can be fit and utilized simultaneously. To aid
in fitting the peaks, a curve representing the sum of selected peaks can be displayed on the
plot to allow the user to fit the summation curve to the d a ta set to better account for peak
overlap. Figure 4.5 is a screen shot of the displays produced during a fitting procedure.
As previously alluded to, the strength of this method is the capability to deconvolute the
peaks and more accurately determine the integrated intensity. An impediment to the use
of the FCCv02.vi program, is the lack of a line fitting algorithm th at would allow for the
autom atic peak fitting. As the manual fitting process can be a time consuming process,
the method is generally used only when overlap is a concern.
Igor Pro, the graphing program sold by Wavemetries,21 offers many advanced functions
to the user. Among these is the ability to determine the area under the curve defined by a
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81
Figure 4.5: The plot on the left illustrates the superposition of fitted line shapes on the
original data spectrum, while the plot on the right shows the d a ta set with the two fitted
lines removed
set of XY d ata by using the “areaXY” function. The exact method is not documented, but
values obtained for a test peak using the areaXY function and values from the FCCv02.vi
method match well enough to preclude the introduction of any serious systematic error.
While much faster th an the line fitting routine, the areaXY method cannot correct
for the overlap of the peaks or for area due to baseline offsets.
Correction of the area
arising from baseline offsets can be accomplished by integrating regions of the baseline
of the same size as the region for the peak of interest, averaging the resultant areas, and
subtracting the average out. A n example of a peak region is shown in Fig. 4.6.
An example of the application of the two methods can be made using selected spectra
from a SF6+ CO
Ar discharge [Figs. 4.7(a) and (b)] and determining the area using
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
250
-
200
used with Igor Pro
150
CO
§
“
100
50
-
-
2900
2910
2920
2930
2940
2950
2960
2970
Chart Position
Figure 4.6: A digitized form of the chart strip recording where the mass spectrum, in the
range of m /z 45-55, of an A r -f SF6 discharge was recorded. The x-axis scaling corresponds
to the scale imposed upon the entire chart strip a t the time it was digitized, see Section
4.2.6. The m /z increases right to left. The region integrated to determine the intensity
of one peak is dem arcated by the arrows. As the digitization process often results in
non uniform step sizes, each spectrum is resampled digitally using an interpolation tool
of Igor Pro to provide the uniform step sizes necessary for the areaXY function. The
experimental conditions are listed in Table 4.3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
both the areaXY and FCCv02.vi methods. The spectrum in Fig. 4.7(a) test the ability
of the functions to determine the area of a well resolved peak, while the spectrum in
Fig. 4.7(b) is used to test the poor resolution case. The absolute and relative intensities
determined are listed in Tables 4.1 and 4.2.
Comparison of the values show that the
areaXY m ethod is at least as accurate as the more sophisticated FCCv02.vi routine,
except when significant overlap of the peaks occurs.
Further comparison of the values listed in Table 4.1 and of the spectra in Fig. 4.7
show th at the most im portant factor in determining the accuracy of the integrated area
is the peak resolution. For the spectrum in Fig. 4.7(a) the peaks are sufficiently resolved
th at for all on scale peaks the difference in determined area between the two methods is
< 6%. In contrast, for the spectrum in Fig. 4.7(b) the differences are < 21% for absolute
integrated intensities.
4.2.6
Conversion of C hart Strip to Digital Format
C hart strips are converted into digital format by a series of steps outlined here. First
markers, noting the number of squares from a reference point, are w ritten on the chart strip
over its entire length. Once the scale is present the chart strip is scanned into a computer
one segment at a time.
Segments are overlapped to ensure no d ata is lost.
Once the
entire chart strip is scanned the image files are imported into TechDig,22 a program th at
allows the user to superimpose an arbitrary xy coordinate system on the image and obtain
values of marker measurements relative to this coordinate system. After completing the
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84
250 - \
250
200
-
200
150
-
1
*
150
^
100
.-e*
ez
03
C/3
S
-
50
-
0 -4
2900
2925
2950
m/z Ratio
(a)
2500
2520
2540
2560
m/z Ratio
(b)
Figure 4.7: Digitized chart strips of two sweeps of a SF6 and CO experiment where the
high resolution spectrum (a) and the poor resolution spectrum (b) were used to determine
the integrated area using both the areaXY and FCCv02.vi methods. Poor resolution can
create differences between the two methods of up to 21%. The experimental conditions
are given in Table 4.3, with spectrum (a) corresponding to segment 1 and spectrum (b)
to segment 2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
T able 4.1: T h e absolute integrated intensities, determ ined using th e areaX Y a n d FCCv02.vi
m ethods, of th e spectrum shown in Fig. 4.7. T h e ratios of th e areas o b tain ed from th e two
m ethods are also given. T h e experim ental conditions are given in T able 4.3, w ith sp ectru m (a)
corresponding to segm ent 1 an d sp ectru m (b) to segm ent 2 .
Mass
Number
46
47
48
49
50
51
Areas
B) Areas
C) Areas
D) Areas
,. x
(A)
457.894
371.14
3785.6
364.697
112.671
178.794
for spectrum
for spectrum
for spectrum
for spectrum
tryx
Ratio
(C)
(D>
A:B
475.376
392.728
0.99
219.995
261.607
1.03
..........
1299.26
1099.71
375.714
504.046
485.211
0.97
113.086
67.507
62.9985
1.00
70.5258
65.2474
168.336
1.06
in Fig. 4.7(a) determined using areaXY.
in Fig. 4.7(a) determined using FCCv02.vi
in Fig. 4.7(b) determined using areaXY
in Fig. 4.7(b) determined using FCCv02.vi
(B)
462.467
361.771
Ratio
C:D
1.21
0.84
1.18
1.04
1.07
1.08
T able 4.2: R elative intensities for ions in a SF 6 an d CO discharge o b tain ed from th e areaX Y and
th e FC C v02.vi m ethods. R atios o f th e values obtained from th e tw o m eth o d s are also listed.
T h e experim ental conditions are given in Table 4.3, w ith spectrum (a) corresponding to segment
1 an d sp ectru m (b) to segm ent 2 .
i i
U
A)
B)
C)
D)
(A)
(B)
(C)
(D)
Ratio
A:B
1
1.04
1
1
1
1
46
0.463
0.666
0.810
0.782
47
....
...
2.733
2.800
8.267
48
1.060
0.796
0.812
1.235
0.98
49
0.1420
0.1604
0.246
0.245
1.00
50
0.1484
0.390
0.364
0.1661
1.07
51
For spectrum in Fig. 4.7(a) determined using areaXY.
For spectrum in Fig. 4.7(a) determined using FCCv02.vi
For spectrum in Fig. 4.7(b) determined using areaXY
For spectrum in Fig. 4.7(b) determined using FCCv02.vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ratio
C:D
1
0.70
0.98
0.86
0.89
0.89
86
digitizing, the user can combine the respective segments to obtain a digitized form of the
chart strip.
As long as the mass to chart strip relationship is known the user can use
the digitized form of the chart with the programs in the MS Program Shell.vi to produce
calibrated, baseline corrected and/or centroid versions of the data. W ith a common mass
scale, segments th at are successive in mass can be combined to produce a single spectrum.
Of course doing this requires scaling adjustments and other corrections, such as those for
baseline offsets. The whole process is quite time consuming and has been superseded by
the computerized data acquisition.
4.3
SF6 Discharges
Our studies of SF6 discharge chemistry were motivated by the desire to produce SF+
in sufficient quantity to make a microwave characterization of SF+ feasible.
It was the
goal of these studies to determine the discharge conditions which would optimize the
production of SF+ .
In seeking to optimize the conditions th at would produce the greatest SF+ signal we
considered not only the SF6 + Ar chemistry, b u t also investigated the influence of added
species, i.e., CO, H 2 , and O 2 , on the production of SF+. As these studies focused on the
optimization of the m /z 51 signal, mass spectra taken cover a range between m /z 45 and
m /z 55.
Each experiment was recorded on one or more chart strips.
To aid in the analysis
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87
Table 4.3: Sum m ary of th e experim ental conditions for th e mass sp ectra obtained from sam pling
th e SF 6 + C O 4- A r discharge. T he discharge voltage, V d , was not m easured for every spectral
segem ent, nor was th e discharge current, Id for sp ectru m (g). T he A t q u an tity is th e to tal tim e
from th e sta r t o f th e recording period.___________________________________________
Entry
1
2
3
4
5
6
7
8
9
10
Figure
**
*
4.8(a)
4.8(b)
4.8(c)
4.8(d)
Id
(mA)
500
500
575
575
725
575
>575
500
500
600
VD
(Volts)
1000
Pressure (mTorr)
At
Total Ar SF6 CO (min)
~40 ~40 2.3
0
~40 ~40 2.3
1
~40 ~40 2.3
2
~40 ~40 2.3 trace
3
43.5 ~40 2.3
0.7
4
~40 2.3 trace
43
7
45
~40 2.3 trace
11
45
~40 2.3 >0.7
12
45
2.3
~40
>0.7
12
43
~40 2.3 trace
19
-
-
-
1250
1000
of the spectra, each chart strip was sub-divided into what will be referred to as "reaction
segments".
A reaction segment corresponds to a time interval where on or more of
the experimental parameters, e.g., the composition of the gas mixture, has been varied
systematically and the spectrum in a given mass range is being observed.
A reaction
segment will almost always contain multiple sweeps over the mass range, which in the case
of these experiments is m /z 45 to 50.
W hen analyzing the data, selected spectra were
converted from chart strip to digital format, following the procedure outlined in Section
4.2.6 and analyzed using methods outlined in Section 4.2.5. The experimental conditions
are tabulated in Table 4.3.
Determination of the integrated area followed the procedures contained in Section
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88
4.2.5.
The axeaXY method was typically used, but the poor peak shape observed in
some spectra required the use of the FCCv02.vi program. As described in Section 4.2.5,
the expected difference between the values of the integrated areas obtained from the two
methods are < 6% for well resolved peaks and < 20% for poorly resolved peaks.
The gain of the electrometer amplifier was set so as to optimize the apparent intensities
for a m ajority of the peaks. This frequently resulted in the m /z 48 peak over-ranging.
Areas of these peaks were not calculated and are denoted in the table entries as os and
in the figures by a vertical line with a * at the top.
The mass spectra for the CO addition experiment are presented in Fig. 4.8 with inten­
sities relative to the m /z 46 peak. Use of the m /z 46 peak as the reference is a departure
from the standard convention of calculating the relative intensities in relation to the most
intense line. W ith the most intense line, at m /z 48, frequently over-ranged, we selected
the m /z 46 line for use as the reference line. This was desirable because the m /z 46 line
was the most intense, well resolved, and reproducible peak th at did not over-range in any
of the spectra. Spectra from the SF6 + O 2 experiment followed the standard convention.
The effects of CO addition on the relative intensities of peaks in the m /z 45-55 range
are shown in Table 4.4.
The variations in the m /z 51 relative intensities appear to be
independent of the carbon monoxide concentration.
Relative percentages of the signal
observed in the region of 46-55 are listed in Table 4.4.
Because of the restricted m /z
ranges used in the SF6 studies, the fractional abundance values of the m /z 51 signal
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89
m/z Ratio
(a)
m/z Ratio
(c)
m/z Ratio
(b)
m/z Ratio
Figure 4.8: Centroid spectra of the selected reaction segments of a CO, ~ 30 mTorr, seeded
Ar -+- SF6 discharge, ~ 40 mTorr and ~ 2.3 mTorr, respectively. Spectra (a) and (b) are
baseline segments th a t correspond to entries 3 and 4 of Table 4.4. Comparison of these
spectra, show the reproducibility of the intensities using either the areaXY or FCCv02.vi
methods. In spectrum (c), CO has been added to the gas mixture, and we see an increase
in the intensity of the m /z 47 line, but no change in the intensity of the m /z 51 signal.
Approximately 2 minutes after shutting off the CO flow, the relative intensities are back
to th e original levels, spectrum (d)
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90
Table 4.4: S um m ary of th e integrated intensities, relative to th e m /z 46 peak, from th e A r +
SF6 + CO discharge studies. Entries labeled, os, were offscale peaks for which accurate areas
could not be determ ined.. T h e entries correspond to those in Table 4.3. T he last colum notes
which integration m ethod was used, either th e FCCv02.vi, LV, o r th e areaXY, EP.
Entry
1
2
3
4
5
6
7
8
9
10
Figure
4.8(a)
4.8(b)
4.8(c)
4.8(d)
46
1
1
1
1
1
1
1
1
1
1
Relative
47
48
0.81 8.27
0.78 os
0.46 2.73
0.67 2.8
1.12 os
0.94 os
OS
0.91
0.94 3.95
1.02 4.81
1.19 O S
Intensity
49
50
0.80 0.25
0.81 0.24
1.06 0.14
1.24 0.16
1.33 0.16
1.35 0.11
1.19 0.11
0.96 0.22
1.23 0.21
1.60 0.26
51 % 51
0.39
3.4
0.36
0.15
2.7
0.17
0.32
0.19
0.22
0.32
4.3
0.18
2.1
0.05
50:48
0.030
49:48
0.1
0.055
0.057
0.38
0.44
0.056
0.044
0.24
0.26
F.M.
LV
IP
LV
IP
IP
IP
IP
IP
IP
IP
determined m ust represent will be an upper limit on any values of the fractional abundance
determined from a much larger scan region. For those cases where the m /z 48 intensity
is available, an estim ate of the upper bound of SF+ abundance was determined, and these
values are tabulated in Table 4.4. The upper limits of the SF+ fractional abundance are
all considerably less than the 0.16 SiF+ fractional abundance reported in the absorption
coefficient calibration study, described in Section 6.6. W ith the actual abundance of SF+
expected to be much less than the abundance values determined, it is expected th at the
absorption coefficients will be to small to allow for a reasonable chance of observation,
and a microwave search for SF+ in a SF6 -f Ar or SF6 + CO -I- Ar discharges will most
likely be unsuccessful.
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91
1.0 - I
1.0 - i
0.8
-
0.8
-
0 .6
-
0.2
-
5T
•C
1 °-4
.
“
Sg?
0.2 ~
0.0 - I
m/z Ratio
(b)
m/z Ratio
(a)
1.0 -T
0.8
0.8
-
1 . 0i -
5
~
0.0
0.4 -
M
f °'2 “
-
0.2
-
0.0 - I
-
m/z Ratio
(c)
m/z Ratio
«fl
Figure 4.9: The centroid mass spectra for the 0 2 + SF6+ A r discharge. Unlike CO results,
the peaks here are relative to m /z 48. Spectrum (a) shows the base line conditions, no
0 2 added. Spectra (a) and (c), both have added 0 2, spectrum (b) has » 1.0 mTorr,
while spectrum (c) has ~ l mTorr. Spectrum (d) corresponds to the system after the
0 2 flow has been shut off and when only trace amounts of 0 2 are expected to be present.
The case when 0 2 »
1.0 mTorr, corresponds to the tim e immediately following the
admission of 0 2. In this case we see a dram atic increase in the intensity of the m /z 46
line, once the flow has been regulated, the observed intensity distribution returns to the
original state, (a). None of these conditions enhances the m /z 51 signal.
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92
The effects of adding O 2 to the SFe + Ar mixture were also investigated. The mass
spectra obtained were analyzed in the similar fashion to the SF6 + CO experiment The
conditions and results of the O 2 addition experiment are given in Tables 4.5 and 4.6,
respectively.
Unlike the SF6 + CO experiment, the m /z 48 line did not go off scale in
the SF6 -t- O 2 experiment, and so the intensities were determined relative to the m /z 48
peak.Comparison of the percent
SF+ from the SF6 + Ar baseline segments with
-f Ar baseline segments from the CO experiment show good agreement.
the SF6
The decrease
of the fractional abundance of the m /z 51 line in the m /z 46-55 range when O 2 is added
is real, but not surprising.
A mass spectrometric and G2(MP2) ab initio study of the
gas phase chemistry of SF£ molecules, with CO, O 2 and other molecules by Sparrapan
et a il showed th a t collisions of SF+ with CO and Oo produce F-SO+ and SCO4" as the
principal products. Theoretically, the reactions are
SF+ + O 2
—♦ FSO+ -I- O
-23.9 kcal/mol
(4.3a)
SF+ -h CO
-» SCO+ 4- F ‘
28.3 kcal/mol.
(4.3b)
The slight reduction in the SF+ signed observed in the O 2 experiment and the observed
insensitivity of the SF+ signal to CO addition are consistent with the energetics of the
reactions in Eqs. (4.3a) and (4.3a), respectively.
Identification of the corresponding species to the peaks in the spectra is not com­
plicated.
As stated previously, m /z 51 is almost certainly SF+, and with reasonable
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93
Table 4.5: Summary of the experimental conditions for the mass spectra obtained from sampling
the SF6 4- O2 + Ar discharge. Pressures are given in mTorr, current in mA, and voltage in V.
Spectrum
4.9(a)
4.9(b)
4.9(c)
4.9(d)
Id
mA
600
600
625
625
VD Pressure
V
mTorr
~43
1100
~44
1200
~44
~43
Ar
mTorr
~34
~34
~34
~34
sf6
mTorr
2.9
2.9
2.9
2.9
o2
mTorr
-
>1.0
~1.0
trace
Table 4.6: Summary of integrated relative intensities for m/z 46 to 51 for the O2 and SF6
discharge. See text for detailed explanation of each data set. The last colum notes which
integration method was use, either the FCCv02.vi, LV, or the areaXY, EP.
S p e c tru m
4.9(a)
4.9(b)
4.9(c)
4.9(d)
46
0.30
0.64
0.29
0.27
47
0.21
0.17
0.46
0.15
m /z Ratio
48
49
0.25
1.0
0.24
1.0
1.0
0.31
1.0
0.21
50
0.03
0.02
0.04
0.04
51
0.05
0.01
0.04
0.05
Fraction
m /z 51
0.027
0.005
0.019
0.029
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F it Method
LV
LV
IP
IP
95
Table 4.7: Literature values of the enthaplies of formation for NS+ and
Experimental A H f Theory
Species
(kcal/mol)
(kcal/mol)
CH3S+
245.0 ± 0 .5 °
244.8'
CH2SH+ 211.5 ± 2 .0 “
211.7'
CH2S+
244.50 ± 2 .0 6
245.0' 211.7* 213.5e
NS+
294.25c
a) Ref.23
b) Ref.25
c) Ref.26
d) MP2 calculations from Ref.24
e) MP4(SDTQ) calculations from Ref.24
f) Values from unspecified method, reported in Ref.25
or H2CSH+ relies on the A Hj values, see Table 4.7, of these species being very similar
the A v a l u e of CH2S+ .
If CH2S+ is present, then there is no reason for H3 CS+ or
H2CSH+ not to be present.
As has been mentioned before, COF+ is often observed in
fluorocarbon discharges as a by product of the etching of the S i0 2 cell wall.
As with
most of these peaks, there is a significant probability that several species contribute to
the observed signed. W ith the peak at m /z 48 almost certainly being SO+ , the peak at
m /z 49 is most likely HSO+ , although FNO+, and 30SiF+ could also be present.
The apparent increases of the m /z 49 intensity with the addition of CO, should be
carefully considered.
At first it seems th a t some component may be increased by the
presence of the CO, until one considers the findings of Sparrapan et a/.,1in th a t CO
reactions with SF6 ionization products produce SO+. Comparison of the ratios of m /z 48
to 49 in Table 4.6 when CO is added to the discharge (entries 8 and 9) to th a t when CO is
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96
absent (entries 3 and 4) shows th at the signal for m /z 49 relative to th at for m /z 48 signal
actually decreases upon CO addition. From these observations we believe th at the m /z
49 peak is indeed a combination of two or more species and that the HSO+ concentration
does increase with the addition of CO, but th at the other contributing species are not
enhanced.
The addition of H2 to the discharge had the immediate effect of reducing the overall
signal intensity, as shown in Fig. 4.10, with the apparent intensity of the m /z 48 peak
decreasing by a factor of four. Upon shutting off the flow of H 2 , the discharge chemistry
returned to the baseline state within one minute. Because of the dram atic decrease in the
intensity, it is not possible to determined the effect that H2 has on the relative abundance
of SF+ .
We can say th at it is unlikely that a discharge seeded with H 2 will produce a
significant quantity of SF+.
The studies of O 2 , H2 and CO substitution in SF6 + Ar discharges, failed to produce
any reasonable conditions th at enhance the concentration of SF+ to a level th at would
justify a microwave search.
4.4
Argon and Oa Discharges
Following the SF6 discharge investigations, strong signals at m /z 44 were observed in
O 2 -+* Ar discharges.
Based on the reactants used in the SFg studies, several potential
species could be reasonably expected to correspond to the m /z 44 signal, including CS+ ,
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97
60 50 -
850
900
950
1000
Chart Position
(a)
250
200
-
?
150 -
—
100 -
50 ~
1050
1100
1150
1200
Chart Position
04
Figure 4.10: Digitized chart strip traces for segments of the H2 addition study. The spec­
trum in (a) was taken immediately following the admission of H2 to the system, and the
spectrum (b) was taken immediately prior to the admission of H2 into the system. Each
spectrum shows two sweeps of m /z ratio range of 45-55. The discharge had a current
of 700 mA and a pressure of 43.5 mTorr. The gas mixture used for spectrum (a) was
composed of 40 mTorr argon, 2.3 mTorr SF6, and 0.3 mTorr H2.
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98
120
100
80
CO
-e
&
CO
ca>
60
40
20
0
20
30
40
50
60
70
80
90
m/z Ratio
Figure 4.11: The spectrum of the 16C>2 + Ar discharge used as a control for the l8 0 2
isotopic study of an unidentified line a t m /z 44, thought to be SiO+. The discharge
current, voltage and pressure were 825 mA, 825 V, and 44 mTorr, respectively. The
original gas m ixture was composed of 34 mTorr argon and ~ 7 mTorr 0 2.
N2 0 +, CC>2 , and SiO+ .
Previous attem pts a t production of SiO+ in this laboratory
have been limited by the deposition of S i0 2 on the chamber wall and on the surface
of the electrodes, prohibiting the attainm ent of a sufficiently stable discharge to allow a
microwave search to be pursued. In light of this, the possibility, however small, th at SiO+
was being produced by serendipitous means, warranted a more detailed investigation.
The chemical composition of the species corresponding to the m /z 44 peak was deter-
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99
160
140
120
't/T
'£ 100
ZD
-e
80
’co
&
60
tz
40
Cb
CD
20
0 ^ ii
10
i i | ii i r | i m i | i i i i | i i i i | i i i i | i r r r j n t i | i i i i | i i i i |
15
20
25
30
35
40
45
50
55
60
m/z Ratio
Figure 4.12: This is the spectrum of the lSO ^ Ar discharge used to identify the species at
m /z 44. It was thought th at this peak could be SiO+ , but this test showed th at is was
CC>2 . One can see the change in the intensity pattern in the region of m /z 44 to 51,
created by l80 substitution. No appreciable signals were observed above m /z 60. The
discharge had a current of 900 mA, a voltage of ~ 900 V, and a pressure of 44 mTorr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Table 4.8: R elative intensities, to m /z 44, of peaks in th e m /z 44-51 range of 16C>2 and 180 2
seeded A r discharges.__________________________________________________________________
m /z ratio
44
45
46
47
48
49
50
51
Relative to 44
ltio 2
I8 0 2
1
1
0.227
1.43
1.17
1.43
1.72
0.223
0.093
0.462
0.104
0.177
0 .2 1
0
0.577
0.169
Fraction
Relative to 51
A l8Oo
l80 2 ltt0 2 ratio A:B
16o 2
0.129 0.449
0.287 -0.320 1.73
5.92
0.029 0 . 1 0 0
1.32
0.292 -0.071 0.39
0.184 0.042
0.55
4.412 0.142 2.48
0.151 0.207
2.73
0.727 -0.057 2.03
0.184 0.047
3.946 0.138 2.48
0.62
0 .2 2 2
1.05
0.079
2.789 0.142 2.98
0.027 0 . 0 0 0
0 .0 0
0.027 0.36
0.074 0.076
1 .0 0
0.980 -0 . 0 0 2 1 .0 0
mined using isotopic substitution. Introduction of the
by feeding
and
18C>2
18 O 2
into the discharge gas mix.
18 O
substituent was accomplished
Spectra of both O 2 in natural abundance
enhanced discharges are shown in Figs. 4.11 and 4.12. In these studies the mass
spectrum between m /z
10
and ~ m /z 80. was recorded in
the resolution of the spectra.
10
m /z increments to improve
Following the acquisition, the spectra were converted to
bitm ap files, digitized, and combined, following the procedure outlined in Section 4.2.6.
Relative intensities of the peaks in the 44-51 region are referenced to m /z 44 in both
studies, and the values are summarized in Table 4.8.
Addition of
18 0 2
to the discharge leads to a significant change in the distribution
and intensities of the peaks in the mass spectrum. The relative intensities of the peaks
a t m /z 44, 46 and 48, in the enriched discharge spectrum, show an intensity pattern of
7:10:10. This intensity pattern suggests th at there are secondary sources of oxygen in the
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101
system, and th at it is unlikely that the species arising from m /z 44 is a mono-oxygenated
compound, leaving C O J as the most likely species.
The corresponding species for the
m /z 48 peak was thought to be SO+, prior to the addition of l8 0 2. Based on the l8 0 2
spectrum, the m /z 48 line is assigned unambiguously to be SO+. The other most likely
candidate for m /z 48, is O j, but the lack of strong signals at m /z 52 and 54 in the
spectrum rule out this option, leaving only SO+.
180 2
The m /z 50 peak is undoubtedly a
combination of 34 SO+ and Sl8 0 + .
Isotopic substitution proves that the species at m /z 44 is CO 2 and not SiO+ or N2 0 +.
The source of C O J is uncertain, but given the discharge chemistries, i.e., Ar + SF 6 +
CO, th at had been used recently within the chamber, a likely source is from deposits on
the wall.
O ther possible sources include carbon released by the plasma attacking the
Teflon insulation used around the electrode, or contaminants from stopcock grease in the
manifold used to introduce the gas to the discharge chamber, although this is thought to
be very unlikely, or from an unidentified leak in the system.
4.5
Neon Discharge Study
Mass spectra taken of neon only discharges, Fig. 4.13, show a strong signal at m /z
40. Given the strength of the signal, we wanted to know if the species was Ar+ or N eJWe wanted to determine the reproducibility and the current dependence of the signal at
m /z 40. The spectra in Figs. 4.14, 4.15, and 4.16, correspond to high, moderate, and low
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102
o -i
2
-
0
20
40
60
80
100
120
140
180
160
m/z Ratio
o -I
2
-
M
10
15
20
r
25
30
35
40
45
m/z Ratio
Figure 4.13: Neon background spectrum with high discharge current. This was the spec­
tru m where the unknown m /z 40 signal was first clearly identified and was taken prior
to the other neon study spectra. The peak a t m /z 40 was thought a t th a t time to be
^ N e J . The discharge had a current of 1175 mA, a potential of 650 V, and a pressure of
35.11 mTorr.
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103
current neon discharges, respectively. Neon isotope abundance require th at
isotopomers
20 Ne22 Ne, 22 Ne 20 Ne,
and
22 Ne2
44 with intensity ratios of 1:0.34:0.01.
20 Ne2
and the
to produce a peak pattern at m /z 40, 42 and
The lack of a strong signal at m /z 42 in any of
the spectra precludes the presence of a neon dimer.
Since the species at m /z 40 could not be
20 Ne2 ,
the only logical choice was Ar+, but
the only source of Ar was the trace amount that remains present in the neon gas after
purification. W hen the ionization processes of neon and argon are considered, both the
presence and the intensity of the observed m /z 44 peak is consistent with Ar+ formed
from trace argon in the neon.
The ionization rate of neon or argon by the impact of an electron can be expressed
by
O
wO
j
/
I
< E)
^
F (E )d E
(4.4)
^ th r e s h o ld
where <r(E) is the electron energy dependent electron impact ionization cross section, and
F(E) is the electron energy distribution function. The limits of integration are from the
ionization threshold to infinity. The relative ionizations of argon and neon can be found
from
f <rAr( E ) M F ( E ) i E
k At
15.8
v
f <rttc( E ) M F ( E ) d E
21.6
v
The threshold energies of argon and neon27 are 15.76 eV and 21.6 eV, respectively.
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(4.5)
104
•0 -i
•0.14 -i
•
•6
0.12
-
0.10
-
•
S-
-0.08 -
“
0.06 -
e
ac
-
040
42
44
46
48
50
52
m/z Ratio
•0.04 -
•
0.02
-
0.00
11ftIIfTtTl|
iliiffliiiili^niiiiHiiiiliiiilfn'niiiiiiiiiviiiiiiniiiiifiiiiiiii
20
60
40
80
100
120
140
160
180
m/z Ratio
•0.14
0.12
•
0.10
•
•0.06
i
-0.04
•
0.02
0.00
10
15
20
25
50
m/z Ratio
55
60
Figure 4.14: Mass spectrum of Ne discharge at high current. This spectrum was taken on
the same day as Figs. 4.15 and 4.16. The large signal at m /z 40 was at first thought to
be due to 20 Ne20Ne cluster. The lack of an appreciable signal at m /z 42 is an arguement
against this assignment. Although argon had been flowed through the system a short
time prior to this experiment, all the pertinent gas lines and regulators had been pumped
out. T he discharge had a potential of 1100 V, a current of 975 mA, and a pressure of
39.8±0.1 mTorr. The pressure of neon before plasma initiation was 34.7±0.1 mTorr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
•6
•0.12
■s
■0.10
■4
$
•2
*5
•0.08
e
f
•0.06
1c=
•0.04
42
44
46
48
m/z Ratio
SO
52
•0.02
iHiiffnnili^imniTniimiptfiiiniiTmriiiiiimTrni'iimiiii
0.00
20
40
80
100
120
160
140
180
m/z Ratio
•
0.12
-
0.10
-
•
■0.04
-
0.02
-
•
0.00
\T ¥ ll|im f f lTm
1 f fi mn ii|i
0
10
20
40
50
70
90
m/z Ratio
Figure 4.15: Mass spectra of the moderate current Ne discharge. As in the high current
case (Fig. 4.14) 20 Ne-F, 22 Ne+ and 20Ne20Ne are very intense and there is no appreciable
signal at m /z 42. The discharge had a current of 500 mA, a potential of 1125 V, and a
pressure of 39.6 ± 0.1 mTorr. The gas mixture was composed of 34.7±0.1 mTorr Ne.
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106
•3 -
-2
-
0
-
1
—1—i—1—i—r—t—1—i—1—I
42
80
100
44
120
46
48
m/z Ratio
140
50
160
52
180
m/z Ratio
•5 -
•4 -
1
. '3 “
IT
1
-2 -
fji
O
i i'ThTH ti i i i ri i
10
20
30
40
50
m/z Ratio
FfV'WiI
60
70
80
90
Figure 4.16: Mass spectra of the low current Ne discharge. As in the high current case
20 Ne+, 22 Ne+ and m /z 40 (Fig.4.14) are very intense, but there is no appreciable signed
a t m /z 42. The signal in the m /z 44-52 range decreased dramatically. This is not
unexpected, as less contaminants are being scrubbed off the wall, because of the lower
current. The discharge had a voltage of 650 V, a current of 150 mA, and a pressure of
36.1±0.3 mTorr. The gas mixture contained only neon a t 34.7±0.1 mTorr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
Table 4.9: Electron impact ionization for argon and neon assuming an electron temperature of
4 eV.
_______________________________________
^thresh ~ 1000 eV 22.5 -1 0 0 0 eV
(xlO-17 cm 3 /s)
&At
fcjVe
Ar:Ne
1 .6
(xlO-17 cm 3 /s)
0.49
0 .0 2 2
0 .0 2 2
72
22
The Maxwell-Boltzmann distribution function for an electron is
F iE )= ^
{
w
T
^
■
<«>
Equation (4.5) can now be used with Eq. (4.5) to determine the relative ionization.
The cross sections for the electron impact ionization of neon and argon to their singly
charged states were determined by Rejoub et al.2s for electron energies ranging from
the ionization threshold to 1000 eV. The cross section functions are shown in Fig. 4.17.
Using the appropriate cross section function and Eq. (4.4), we numerically determined the
electron impact ionization for neon and argon atoms, assuming an electron temperature
of 4 eV. These values along with the relative ionization values are tabulated in Table
4.9. Based on the ratio of the ionization rate constants, we would expect th at a sample
containing only ~
1%
as much argon as neon will produce a similar number of ions from
electron impact ionization.
Although the disparateness between the ionization of neon and argon is quite large,
this alone is not sufficient to account for the large Ar+ signals observed in the neon
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108
3.0
2.5
CNJ
CO
1.5
1.0
0.5
0.0
0
200
400
600
800
1000
Electron Energy (eV)
Figure 4.17: The electron energy dependent cross section functions for electron impact
ionization of argon (—), and neon (.....). These curves were obtained by performing a
cubic spline interpolation on the original d ata reported by Rejoub et al.2s
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109
discharge.
W ith its much larger ionization potential, a neon ion can ionize an argon
atom in a charge transfer reaction,
Ne+ + Ar —►Ar+ + Ne
,
(4.7)
th at has a rate 29 of 6.2 x 10~ 15 cm 3 s“ l . Even though this rate is quite small compared
with the charge transfer reactions of argon with various fluorocarbons, Section 5.5, the
argon ions lack the energy to ionize the neon molecules, and the reaction in Eq. (4.7) is
always unidirectional. In a pure neon discharge there are a few channels available for the
Ar+ to be neutralized, e.g., electron ion recombination, and the Ar+ concentration will
eventually increase until it reaches a steady state condition, but the percentage of argon
in the Ar+ state will be quite large.
The number of electrons with 21.6 eV or more energy in a distribution with an electron
tem perature of ~ 4 eV is very small (Fig. 4.18).
T he strongest m /z 40 signals are
observed at high discharge voltages. The most intense signal (Fig. 4.14) relative to the
apparent intensity of the m /z 20 line, is observed in a high current, ~ 1 A, high voltage
(1100 V), discharge.
In this study we have determined th at the mystery peak at m /z 40 is indeed Ar+, and
th at in positive column neon discharges the effects of contamination are exacerbated by
the high ionization potential of neon, simplifying the concentration of these ions. In future
studies using neon, every effort should be made to reduce the potential for contamination,
so th at more control can be gained over the chemistry.
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110
0.006
0.005
0.004
0.15
^aT 0.003
0.002
0.001
0.10
0.000
Electron E nergy (eV)
0.05
0.00
o
5
10
15
20
25
30
Electron Energy (eV)
Figure 4.18: The distribution of electrons as a function of electron energy, assuming an
electron tem perature of 4 eV. The function was generated using Eq. (4.6). The region
between 14 to 24 eV is shown in the inset. The probability of electrons have an energy
of 21.6 eV is considerably less than having and energy of 15.6 eV.
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Ill
CHAPTER 5
Mass Spectrometric Studies of Fluorocarbon and SiF4 Discharges
5.1
Introduction
Presented in this chapter are mass spectrometric characterization studies of CHF 3 ,
CF4, and SiF 4 containing discharges. The fluorocarbon discharges were investigated in
an attem pt to determine favorable discharge conditions for the production of CHF 2 • The
SiF 4 study was conducted prior to the line broadening measurements on SiF+ to determine
the current dependence of SiF+ in positive column discharges.
5.2
Introduction to Fluorocarbon Discharges
As a replacement for other ozone reactive fluorocarbon gases, trifluoromethane is
im portant in semiconductor etching processes. Many studies have investigated the com­
position and chemistry of CHF 3 , discharges30-35 using a variety of techniques, including
mass spectrometry and optical spectroscopy. These studies have shown CHF^ to be one
of the principal ionic products produced in CHF 3 discharges.
In addition to the CHF 3
discharges, CHF^ has also been observed in CF 4 discharges.2
This reported favorable
discharge chemistry and a relatively large dipole moment2 of ~ 3 D make the C H F J ion an
excellent candidate for microwave studies. Even when initial considerations are favorable,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
the true test of viability for a candidate ion is how the value of the predicted absorption
coefficient compares with the spectrometer sensitivity ,36 as detailed in Section 6.29. As
the absorption coefficient is dependent on the fractional abundance of the ion in the dis­
charge ,36 considerable effort was devoted to the maximizing the fractional abundance of
CHFj in the discharge. Mass spectrometry was used to quantify and monitor the CHF^
abundance as discharge conditions and feed gas composition were varied. Studies of the
cationic composition of both CHF3 and CF4 based discharges were carried out.
5.3
Carbon Tetrafluoride
Several experiments were performed to determine the optimum conditions for CHFj
production in CF 4 discharges.
These experiments focused principally on how the frac­
tional abundance of CHF^ depended on the CF 4 concentration, although the effects of
variation of the discharge current and gas flow rates were also considered.
The spectra in Figs. 5.1, 5.2, and 5.3 are from a concentration variation experiment
and were originally recorded on chart strip paper in overlapping increments of
10
m /z
width. The chart recordings were digitized using the methods detailed in Section 4.2.6.
Production of CHF^ in a 1:15 carbon tetrafluoride to argon discharge was noted by
Petrm idil 2 a t a total pressure near 80 mTorr.
This high pressure discharge condition
was not replicated as these high pressures tended to produce a very noisy discharge,
unsuitable for microwave studies. The experimental conditions are listed in the caption
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114
500
400
C/3
300
■e
<c
200
100
20
30
40
50
60
70
80
90
m/z Ratio
Figure 5.2: A mass spectrum of cationic species sampled from a CF 4 + Ar discharge, where
the ratio of CF4:Ar was 0.14. The discharge had a pressure of 24.4±0.3 mTorr, a current
of 675 mA, and a potential of 950 V. The initial pressures of CF 4 and argon, were 2.8
mTorr and 20 mTorr, respectively. There is an apparent increase in the signal above 70,
compared with the spectrum in Fig. 5.1, and a decrease in the relative intensity at m /z
28, 29 and 47.
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115
250
200
C/J
'sz
=D 150
•e
<
100
c
50 -
20
30
40
50
60
70
80
90
m/z Ratio
Figure 5.3: As the ratio of CF 4 to Ar continues to increase, CF4:Ar = 0.20, there continues
to be a decrease in the signal around m /z 28-29, relative to the m /z 40 peak. T he m /z
40 peak is assigned to be Ar4". There is still a strong signal at m /z 85, which we assign
to SiFg- arising from the etching of the discharge chamber walls. We also see a signal at
m /z 69, which we attribute to C F j. The discharge had a current of 675 mA, a potential
of 950 V, and a pressure of 18.4 mTorr. T he gas mixture was composed of 3 mTorr CF 4
and 15 mTorr Ar.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
for each spectrum.
The overall mechanism for the formation of C H F j ions in a CF 4 discharge has not
been established.
Literature sources30 provide the heat of reaction for the formation of
CHF^ from CF 3 , the principal ionization product of a CF 4 discharge, and CHF 3 , Eq.
(5.1a) to (5.1c).
There are, however, no values available for the formation of CHF 3
from hydrogen and CF 3 . To provide a reasonable estim ate of the energetics the heat of
reaction for hydrogen with C F J was calculated using heats of formation, as given in Eq.
(5.1a):
e + H + CF 3 —►CHF 3
CF 3 + CHF 3 — ►CHF£ + CF4.
e + H-t- 2 CF:J--+CHF£ + CF 4
A tfrin = -1292 kJ/m ol
(5.1a)
A H = -50 kJ/m ol
(5.1b)
AH rxn = -1342 kJ/m ol.
(5.1c)
If the energetic calculations are correct, then the formation of C H FJ in a CF 4 discharge
will be a very favorable process. These calculations are supported by the findings of
Petrmichl ,2 who in his studies of CF 4 discharges, found th at the optimum discharge gas
mixtures for production of CHF^, were composed of CF 4 with a trace of hydrogen. The
values of the fractional abundance of CHF^ measured in our CF 4 discharges are given in
Table 5.4. As can be seen, the fractional abundance obtained are all very low.
High density fluorocarbon discharges, within S i0 2 cells, exhibit oxygen contamination
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117
of the discharge arising from the etching of the surface .31 Petrmichi2 also reported th at
concentrations of oxygen containing species such as 0 +, COF+ and COj , were dependent
on the concentration of CF4 in the discharge.
Because of the poor resolution evident in the spectra, the integrated areas were found
using the FCCv02.vi method.
In most cases the line is fit to a lognormal line shape.
In some cases the peak could not be fit using a Gaussian, a Lorentzian, or a lognormal
model function.
When this occurred, the curve was fit to the stun of two overlapping
lognormal functions, from which the area was determined. Values of the integrated area
determined using the single lognormal function were typically within
10%
of the double
lognormal function determination. The only exception was the m /z 51 peak of the 0.20
CF 4 to Ar ratio experiment, where the difference was ~25%.
Both the integrated and
relative intensities (to m /z 69) are listed in Table 5.1 .
The effect of CF4 concentration on fluorocarbon cationic fractional abundance is
shown for selected species in Fig. 5.4.
In general, increases in CF4 abundance, with
the exception of the m /z 30 and 31 values, lead to increases of the intensity. The m /z 31
peak was originally thought to correspond to CF+, but the change in the fractional abun­
dance w ith increasing CF4 concentration is opposite to th at which we expected, based on
observed fluorocarbon species. Other potential species with these m /z values would be
HNO+ or CH30+ for the m /z 31 peak, and NO+ or CH20+ for the m /z 30 peak.
As shown in Fig. 5.5, the changes observed in the m /z 44 intensity as CF 4 concentra-
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118
Table 5.1: R elative intensities to C F 3 and fractional abundance of selected peaks for th e C F 4
and A r concentration study.
l/z
28
29
30
31
32
33
34
35
43
44
50
51
65
Intensity Relative to m /z 69
CF4: Ar Ratio
0.14
0 .1 0
0 .2 0
Fractional Abundance
CF4: Ar Ratio
0.14
0 .1 0
0 .2 0
33.09
36.15
7.71
16.90
8.33
8.72
2.90
0.132
0.144
0.031
0.067
0.033
0.035
2.50
2.39
1 .1 1
2.31
9.65
0.96
3.24
0 .0 2 0
0.023
0.008
0.024
0 .0 1 2
0.025
0 .0 1 1
2.70
0.95
2.49
1.14
0.81
2.40
0 .8 8
2.09
0.23
1.06
0.038
0.004
0.013
0.030
0.009
0.026
0 .0 1 1
0 .0 1 0
0.028
0.023
0 .0 0 2
0.013
1 .1 0
1
0.027
0.026
0 .0 1 2
2 .8 8
66
67
69
1.77
2.04
0.69
2.15
1
1
0 .0 1 2
0 .0 1 2
0.004
0 .0 1 1
0 .0 1 1
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119
0.06
0.05
oc 0.04
CO
•o
c:
=3
-O 0.03
CO
c
■§ 0.02
co
LL.
0.01
0.00
0.10
0.12
0.14
0.16
0.18
0.20
Carbon Tetraflouride Fraction
Figure 5.4: Plot of the fractional abundance of selected peaks observed in CF 4 and Ar
discharges as a function of the CF4:Ar ratio. Selected peaks are: m /z 30 •, m /z 31 □ ,
m /z 50 A , m /z 5 1 EB, and m /z 69 ®. Identified species are CF^, C H FJ and C F^. The
peak at m /z 31 was thought to be CF+, but the inconsistent intensity response to CF 4
concentration as compared with other CF+ species argues against this assig n m e n t.
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120
0.06
0.05
8
c
ca
■o
c
.O
0.04
0.03
CO
c
€co
0.02
li-
0.01
0.00
0.10
0.12
0.14
0.16
0.18
0.20
Carbon Tetraflouride Fraction
Figure 5.5: Comparison of the changes of relative intensity between CO 2 and the uniden­
tified species from Fig. 5.4. Plotted are the fractional abundance for m /z 44 (•), m /z 31
(□ ), and m /z 30 (A). As can be seen, the trends in the d ata are quite similar, suggest­
ing th at the unidentified species are chemically similar to CO^, with likely species being
H2 CO+ and H 3 CO+
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121
tion increases follow the same trend as those of m /z 30 and 31. The m /z 44 peak is almost
certainly COJ (Section 4.4), and so it is reasonable, based on the supplied reactants, that
m /z 30 and 31 correspond to H2 CO+ and HaCO4", respectively.
The possibility that
HNO+ and NO+ are also produced cannot be ruled out, especially when the m /z 49 line
could be attributed to FNO+.
Use of CF4 as a reactant for producing CHFj in low pressure discharges was found
in the above experiments not to be practical. W ith ~2% of the total cationic signal due
to CH Fj, the probability of observing a rotational transition by microwave spectroscopy
is very small. The studies of CF4 discharges by Petrmichl2 did not quantify the fraction
of CHFJ present, but based on apparent intensities, a larger fraction of the signal can
be attributed to CHFj in his studies than in the present ones.
Comparisons of the
experimental conditions of the previous work with our studies shows th at the principal
difference lies in the pressure of the buffer gas, and perhaps the condition of the cell and
electrode surfaces. This latter point maybe significant. Fluorocarbon discharges are very
efficient at deposition, and films of material quickly accumulate on the surface of the cell
wall and electrodes. Later studies with CHF3 discharges revealed the need to frequently
run O 2 discharges to remove the deposition.
Our inability to run CF4 discharges at
higher pressures successfully was almost certainly due to excessive film build up. A more
detailed effort a t manipulation of CF4 discharges was not pursued, as it was felt that,
based on literature precedent, trifhioromethane discharges offered a greater promise for
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122
the production of C H F j ions.
5.4
CHF 3 Discharges
Production of C H F j in plasma discharges containing trifluoromethane has been well
documented .31-34
Several authors report the CHF 2 species as being one of the principal
ionic products formed in these plasmas .30,32 Studies to determine optimal experimental
conditions for C H F J production in argon and neon buffer gases, as well as in pure CHF 3
discharges, by varying concentration, current, and pressure, were carried out in this work.
5.4.1
Ar and CHF 3
Early studies of CHF 2 production in varied discharge conditions utilized chart strips
for data recording, but when the computer d ata acquisition was implemented selected
experiments were rerun. Spectra obtained from an experiment to determine the effect of
the discharge current on the formation of CHFJ are shown in Figs. 5.6, 5.7, and 5.8. At
low currents Ar+ dominates the mass spectrum (Fig.5.6), and the fractional abundance of
the m /z 51 species is insignificant. The cause of the unusual peak pattern observed for
the m /z 40 peak is unknown. At this time the V3en3e dependent peak splitting problem
had not been solved. The peak splitting is likely due to the plasma potential sampled by
the probe being larger, as compared to ground, th an is typical when the tower electrode is
being used as the anode. A complete discussion of the splitting problem and its solutions
was given in Section 4.3. Lack of clearly resolved peaks anywhere else in the high m /z
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123
•8
-
■6 -
O
•2 -
1 1
i
40
20
m/z Ratio
•8
-
•6
-
•4 -
r^rrrr
20
25
30
35
40
45
50
55
m/z Ratio
Figure 5.6: Mass spectrum of a low current and low pressure Ar + CHF 3 discharge. As
typical, the upper spectrum shows the complete mass spectrum acquired, while the lower
one shows the range of interest, m /z 20 - 55. The ratio of C F J to CHF 2 is 0.81, while the
percent abundance of C H FJ is 2.0%. The initial gas mixture of 1.4 =fc 0.1 mTorr CHF 3
and 15.9 ± 0.1 mTorr Ar, has a CHF 3 to Ar ratio of 0.09. The discharge had a current
of 90 mA, a potential of 750 V, and an overall pressure of 17.3 ± 0.1 mTorr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
range, supports the conclusion that the pattern is an artifact, rather th an a signal that
corresponds to an actual species with m /z 39. For a discharge with CHF 3 concentration
similar to the low current case, but with a moderate current of 400 mA, no appreciable
increase in the relative intensity of other lines relative to Ar'1' ( m /z 40) is observed (Fig.
5.7). An example of a high current, high CHF3:Ar ratio is shown in Fig. 5.8. Peaks at
m /z 85,
66
and 47, which we assume to be the SiC>2 etching products SiF^, S iF j, and
SiF+ are observed. In addition, the apparent intensity of Ar+ is much lower than in the
other discharge conditions. While present, the signal at m /z 51 is very weak.
Preliminary studies of a 1:6 CHF 3 to Ar discharge at high pressures (approximately
80 mTorr) showed no appreciable C H F j signal.
Attem pts to optimize CHF^ production in argon discharges seeded with trifluoromethane failed to produce a significant CH FJ fractional abundance.
Variation of
flow rates, discharge current, and the concentration of CHF3, failed to produce a set
of discharge conditions where the total fraction of ions due to CHF^ was greater than
*6 %.
Pure CHF 3 discharges were too unstable to allow for successful searches, and an
upper limit of the CHF3:Ar ratio was found to be ~1:2.
Lack of production of CHF 2
in any appreciable abundance shows th a t for our system, CHF 3 and argon discharges are
unsuitable for CHF^ microwave searches.
5.4.2
Ne and CHF 3
Discharges of neon and trifluoromethane were studied after computerized d a ta acqui-
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125
-0.30
•0.25
0.10
■
•0.05
TrmqprPiiin n | ift i| i wi p i ru i
0.00
0
20
40
60
80
100
120
140
n i p i ii p n
160
180
m/z Ratio
-
2.0
-1.5
•1.0
•0.5
0.0
A
11
45
50
55
60
65
70
75
80
85
90
95
m/z Ratio
Figure 5.7: Mass spectrum of a moderate current, low pressure Ar ± CHF 3 discharge.
Complete spectrum is shown above, and a zoom of the m /z 42 - 95 region, below. The
percent abundance of C H F j is 1.9%, and the ratio of m /z 69:51, C F^ to C H F J, is 0.72.
The discharge had a voltage of 900 V, a current of 400 mA, and a total pressure of
18.1 ± 0 .1 mTorr. The gas mixture was 15.4 ± 0 .1 mTorr Ar and 1.6 ± 0.1 mTorr CHF 3 .
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126
1
I
■0.10
•0.05
(nWtW^Wii|mi|iilltTW|Wi|!lii|<W>TIH^iMtliil|WWt<t
0.00
10
20
30
40
50
60
70
80
90
100
110
m/z Ratio
•0.16
•0.14
•
_
0.12
0.10
-
i -0.06
— -0.04
•
0.02
0.00
36
38
40
42
44
46
48
50
52
54
m/z Ratio
Figure 5.8: Mass spectra of a moderate current and moderate pressure Ar + CHF3 dis­
charge. W ith a gas mixture of ~ 12 mTorr Ar, and ~ 9 mTorr CHF3, the CHF3 to Ar
ratio is 0.75. The complete spectrum from 0-200 m /z is shown in the upper spectrum,
while the m /z 30 - 55 is shown in the lower. The percentage fraction of CHF^ is 0.24%
and the ratio of CF 3 to CHF^ is zero. The discharge had a current of 675 mA, a voltage
of 1050 V, and an overall pressure of ~ 24 mTorr.
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127
sition for the mass spectrometer was implemented. Implementation of computerized d ata
acquisition for the mass spectrometer increase the efficiency of both the acquisition and
the analysis of mass spectral data. This allowed us to acquire data sets th a t covered the
entire mass region of the instrument (~ 200 m /z) and sample more conditions.
W ith
this we could make better assessments of the effects of the experimental parameters being
varied. Not only can we now collect a much larger mass range, but we can do it within a
few minutes. This is advantageous, as it helps to minimize systematic, but uncharacterizable, time dependent changes in the system such as deposition on cell walls, pitting of the
electrode surface, and humidity. Effects of the discharge current and CHF 3 concentration
on the chemistry of neon and trifluoromethane discharges are reported here. A discussion
on the relevant chemistry given is also undertaken in Section 5.5.
The d ata for this study is composed of five spectra acquired under different discharge
conditions.
The actual concentration of CHF 3 in any of the discharges can only be
estimated, since small adjustments to the CHF 3 and Ne feed rates were made during the
course of the experiment.
Trifluoromethane pressures of ~2-3 mTorr are present in all
but the last d a ta set, where the flow of CHF 3 was increased and the neon flow was steadily
decreased towards zero.
Spectra 1 and 2, shown in Figs. 5.9 and 5.10, correspond to low pressure ~ 30 mTorr,
m oderate current, ~600 mA, and low pressure, high current,
~ 1
A, conditions, respec­
tively. Peaks a t m /z 85, 51, 47 are evidence th a t surface reactions between radical and
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128
-6
I
-
4'
Q)
3
-2
x
-
^ iriniwuiiiiiiiiiimf ^ i riTWiiiii'iiiiiiiiKiiffffpfffi'i'w
0
40
20
60
80
100
120
140
160
180
m/z Ratio
•
1.2
•
1.0
1
-0.8
^
-0.6
•0.4
0.2
■
40
45
50
55
60
65
70
75
80
85
mil Ratio
Figure 5.9: Mass spectrum of the ions sampled from a moderate current, 588 ± 13 mA, low
to m oderate pressure, 27.9 ± 0 .1 mTorr, Ne ± CHF 3 discharge. The discharge potential
was 750 V. The fractional abundance of the m /z 51 peak is 0.01. The gas mixture was
26 ± 1 mTorr Ne and 2.0 ± 0.5 mTorr CHF 3 for a CHF3:Ne ratio of 0.08. The complete
range acquired is shown in the upper spectrum, while the mass range of 35 to 90 is below.
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129
100
120
140
160
180
m/z Ratio
mh Ratio
Figure 5.10: This is a mass spectrum of a high current, 1 A, low to m oderate pressure,
28.9 ± 0 .1 mTorr, Ne + CHF 3 discharge. The discharge potential was 700 V. The gas
mixture used, 26 ± 1 mTorr Ne and 2.0 ± 0.5 mTorr CHF 3 with a CHF3:Ne ratio of 0.08
The fractional abundance of the observed m /z 51 signal is 0.0074.
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131
•3 -
■e -2 -
20
40
60
120
80
140
160
180
m/z Ratio
•1.4
•
1.0
3 -0.8 -
c
•0.4
0.0 H
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5
70
75
8 0 8 5 9 0 9 5
m/z Ratio
Figure 5.11: The fractional abundance of 0.069 for the m /z 51 line, is the largest value
obtained, from any discharge chemistry. This discharge had current o f425 mA, a potential
of 1450 V, and a pressure of 47.6 ± 0 .1 mTorr. The gas mixture had a CHF3:Ne ratio of
0.05 and absolute contributions of ~ 40 mTorr Ne and 2.0 ± 0.5 mTorr of CHF3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
relative intensity of the Ne+ and C 0 + ( m /z 28) are much closer. The same basic product
ions observed in Fig. 5.11 are also observed here. The intensity of m /z 51 is decreased.
There seems to be a inverse relationship between the intensity of C H F j ( m /z 51) and the
intensity of Ne+. Another notable difference is the loss of resolution, which although not
significant, is noticeable.
The last d a ta set (# 5 ) corresponds to a discharge where the concentration of CHF3
is variable over the course of data collection.
Because of the difficulty in initiating a
pure CHF3 discharge, it was hoped that shutting off the flow of the neon would allow
a pure CHF3 discharge to be obtained for characterization by mass spectrometry. The
spectrum in Fig. 5.13 shows the ion composition at a point when the amount of neon gas
remaining in the discharge was thought to be low. The spectrum in Fig. 5.14 corresponds
to the discharge th a t had an appearance th at was significantly different from observed
Ne
4-
CHF3 discharges, and we assume the gas mixture to be principally composed of
CHF3. Comparison of the spectrum in Fig. 5.13 with the "pure" spectrum in Fig. 5.14,
shows th at the two discharges have very similar chemistry.
In comparing the "pure"
CHF3 spectrum to the other Ne + CHF3 spectra, there is an apparent enhancement of
the signal a t m /z 85, relative to the cluster of peaks around m /z 45. There is also an
apparent enhancement of the H£ species between m /z 1 and 3. The fractional abundance
of m /z 51 is also reduced (Table 5.4).
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133
-4 -
C
K
11111f>111
20
40
60
80
100
PHyWfff^nffWWTf i W| Wl>nffW11| 11Ml| H
120
140
160
180
m/z Ratio
- 1.0
1
0.8
-
• £ -0.4
0.2
•
111
11111111 iH frM fy r 1111111
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5
70
11111 n
75
8 0 8 5 9 0
m/z Ratio
Figure 5.12: This discharge also had a relatively large fractional abundance of m /z 51 at
0.059. As with the best discharge conditions, this discharge had a large potential, 1500
V, a moderate current, 475 mA, but a much larger pressure, 72.0 ± 0.1 mTorr. The gas
mixture also differed significantly, with ~ 70 mTorr of Ne and 2.0 ± 0.5 mTorr CHF3,
or a CHF 3 :Ne ratio of 0.03. As before, the complete spectrum is on top and a reduced
range spectrum is on the bottom .
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134
•3.0
•2.5
•
2.0
•1.5
C
O
><
•
1.0
•0.5
11nI'lfl 11Mnf*i i
20
60
40
80
100
120
140
160
180
m/z Ratio
•2
-
04
30
35
40
45
50
55
60
65
70
75
80
85
m/z Ratio
Figure 5.13: This mass spectrum was obtained from a discharge where the Ne concentration
was being depleted in an attem pt to produce a pure CHF3 discharge. The gas mixture at
the beginning of the experiment was composed of 43 ± 1 mTorr Ne and 3 ± 1 mTorr CHF3.
The discharge had a current of 475 mA, a potential of 1700 V, and a total pressure of
46 ± 1 mTorr. The fractional abundance of the m /z 51 line was 0.032.
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135
-2.5
-
2.0
§
-1.5
rs—j
- 1.0
-0.5
20
40
60
80
120
100
140
160
180
m/z Ratio
•6 -
030
35
40
45
50
55
60
m/z Ratio
65
70
75
80
85
90
Figure 5.14: The "pure" CHF3 discharge obtained by using neon to aid the initiation of
the discharge, and then shutting off the neon flow. The discharge color was used as
an indicator of gas mixture character. W hen the discharge color was observed to be
blue/w hite it was assumed th at the neon had been exhausted and the "pure" spectrum
could be collected. The discharge had a current of 450 mA, a potential of 1675 ± 25 V,
and a n overall pressure of 45 mTorr. The gas mixture used for discharge initiation was
the same reported for Fig. 5.13. The fractional abundance of C H F j is 0.0255.
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136
5.5
Ion Chemistry of CHF3
Electron impact ionization30 of CHF3 produces CHF^, C F J, C F J and CF+, although
which of these is the principal ionization product is a debated point.30,32 Jayaram an et
al,32 also identified CHF+, F+ and CH+ as minor products of electron initiated molecular
dissociation reactions of CHF3.
Formation of the CHF^ ion can occur by electron impact ionization, charge transfer
reactions, or by reactions of CHF3 with ionization products. Electron impact ionization
proceeds by a dissociative mechanism30
e + CHF3 -► [CHF*] + e — C HyF+ + 2e
(5.2a)
e + CHF3 — [CHFj] + e -► C HyFz + e,
(5.2b)
where y can be 0 or 1 and z can have any value between 0 and 3. The neutral dissociation
pathway is strongly favored over the ionization pathway a t low electron energies, (< 20
eV). Ion products formed via the ionization channels are as follows:
CHF3 + e — ► CF£ + H + 2e
(5.3a)
CHF3 + e — ► CHF 2^ -f- F 4* 2e.
(5.3b)
Appearance energies for the reactions in Eq. (5.3) are listed in Table 5.2, along with the
values for C F J and CF't\
The lower appearance energy for C F^ favors it as the principal
ionization product in our discharge.
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137
Table 5.2: Electron impact ionization energies for CHF3
Appearance Energy eV
Ionization Reaction______ Ref (a)
Ref (b)
Ref, (c)
CHF 3 + e — >CFJ+ H + 2 e
13.7
14.14
14.7 ± 1 .0
16.4
14.3 ± 1 .0
15.75
CHF 3 + e — ►CHFJ + F + 2 e
2 1 .2
15.7 ± 1 .0
15.7
-> C F J + F " 4 - H +2e
»,,,
2 0 .2
-> CF+-f F + HF +2e
19.5 ± 1 .0
»»»»
2 1 .6
— C F ++ F 2+ H +2e
(a) Jiao et a /.30
(b) Jayaram an et al.32
(c) Tsuji et al.37_____
W ith low electron energies other reaction mechanisms become increasingly important
to the formation of CHF£. Among these is the halide transfer reaction of the ionization
products 35 with CHF 3 to form CHF^. These reactions include:
C F 3 + CHF 3 — ► CF 4 + CH Fj +•••
C F^+C H Fs
A H = 1 6 8 kJ/m ol
— » CH F++CF3
C H F^ + CHF 3 — ► no reaction
A H = - 5 0 kJfm ol (5.4a)
.
(5.4b)
(5.4c)
Blint et a / . , 38 report the reaction rate for the reaction in Eq. (5.4a) as 2.1xl0 - 9 cm 3 s~l ,
based on IC R studies.
The favorableness of the CF^ reaction with CHF3, coupled with the lack of reactivity
of CHF^ w ith CHF 3 ,30,35 leads to the expectation th a t CHF^ should be present in larger
concentrations th an CF^.
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138
The polar dissociation of CHF3 by the mechanism
H+ + CHF3 — * CH«F J + Hm + F n
a = 0 —2; 6 = 0 —3;m = 2 —a ,n = 3 —6,
(5.5)
has not been shown to produce a significant amount of product.30 In contrast to polar
dissociations, charge transfer reactions with Ar+ play a significant role in the formation
of C H FJ. The reaction has been shown37 to proceed by two channels
Ar+ + CHF3 — ► CHFJ + F + Ar
— ► C F J + H + Ar
(5.6a)
.
(5.6b)
Jiao et al.30 report a product ratio of 3:1 between CHFJ:CHJ, while Tsuji et al.37 report
a branching ratio of 54:46. The formation of CHFJ from the reaction in Eq. (5.4a) also
occurs in the CHF3 discharges. Jiao et al. used electron impact ionization to initiate the
charge transfer reactions, while Tsuji et al. used a microwave discharge to form the Ar+.
Reaction rates obtained from both methods are provided in Table 5.3.
Based on the
reaction rates, we expect th at Ar+ will form CHFJ preferentially over the CFJ product.
We observe a CFJ:CHFJ product ratio of ~ 0.75 in the Ar + CHFJ discharges (Figs.
5.6 and 5.7), which is consistent with the relationship between the reaction rates for the
Ar+ reactions with CHF3 and CF4.
W ith the threshold energy27 for Ar being ~ 15.8 eV, the number of therm al electrons
in a typical discharge that can lead to the formation of Ar+ and CH FJ via electron
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139
Table 5.3: Total reaction rate constants for the formation of C H Fj. The columns represent
the different methods used to produce the ionic reactant. The Ar+ coulmn used ions from a
microwave discharge,37 while the columns labeled e used electrons of the specified energy to
form the ionic reactant.
k ( xlO -10 cm3s - l)
Reaction
Ar+
e (20eV)“ e (35eV)a
1.9 ± 0 .4
CHF 3 + C F J — ►CH FJ
2.1 ± 0 .4
---------CHF 3 + C F J — ►CH FJ
3.9 ± 0 .5
CHF 3 + Ar+ — > CH FJ
20 ± 66
10.3 ± 1.0 10.3 ± 1 .0
CHF 3 + Ar+ — ►C F J
3.5 ± 0 .4
3.7 ± 0.4
6.7 ± 2 .6
CF 4 + Ar+ -> C FJ
a) Ref.30
b) Ref.37
impact ionization channels are roughly the same, within a factor of two. The appearance
potential of C F J has been reported at 15.7 eV by Jayaram an et al.,30 and 14.7 eV by
Tsuji et al.37 Although the formation of C F J is energetically favorable, no C F J signal is
observed. This is consistent with the results of the Ar+ ± CHF 3 charge transfer study of
Tsuji et al. They report only C F J and CH FJ products for the charge transfer reaction.
They do report the formation of C F J when 70 eV electrons are used for the electron
impact ionization of CHF3.
Since we observe no C F J, we assume th at the principal
mechanism of C H F j formation in our argon discharges is charge transfer reactions.
The chemistry of the Ne + CHF 3 discharge is somewhat different than th at of the
argon discharges.
W ith a threshold energy 27 of 21.5 eV, Ne+ is produced less readily
than Ar+ (Section 4.5) but it ionizes other species more efficiently than argon can. The
charge transfer reaction of Ne+ and CHF 3 has been studied by Chau and Bowers,39 using
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140
a drift cell ICR spectrometer. They report a rate constant of 1.86 x 10- 9 cm 3 s - 1 for the
reaction
Ne+ + CHF 3 —►P roducts
.
(5.7)
Comparison of this rate constant with those obtained for the Ar+ + CHF 3 charge transfer
reaction (Table 5.3) shows th at the two rates are essentially equal. Prom this we expect
th at the reactions will produce CH FJ in similar quantities.
The appearance energy of C F J has been reported to be 21.2 eV by Jiao et al.30 Cornu
and Masset40 determined from an electron impact ionization study of CHF 3 , using 70
eV electrons, th at C F J and CH FJ axe produced with branching percentages of 5.2% and
32.9%, respectively. The ratio of C F J :CH FJ production is 0.168. W ith 21.5 eV of energy,
Ne+ is capable of producing C F J from CHF 3 .
we see a small peak at m /z 50, Fig. 5.15.
Indeed, in the Ne + CHF 3 discharges,
Determination of the area of this peak was
made using the FCCv02.vi program, by first fitting the m /z 51 peak and then subtracting
it out.
The resultant peak a t m /z 50 was then fit.
The integrated intensities of the
m /z 50 and 51 peaks were determined to be 0.00139 and 0.01303 area units, respectively.
The ratio of the m /z 50 to 51 areas is 0.11. Although the fit of the m /z 50 peak must
be treated cautiously, the agreement between the ratio from Cornu and Masset and our
measurement suggests th at m /z 50 is C F J.
As with most fluorocarbon discharges, there appears to be a significant amount of
etching of the SiC>2 surfaces.
These processes not only lead to the formation of SiF+,
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141
m/z 50
40
42
44
46
48
50
52
54
m/z Ratio
Figure 5.15: This is the m /z 40-54 range of the spectrum displayed in Fig. 5.11, showing
the small peak a t m /z 50 th at is possibly C Fj .
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142
Table 5.4: Sum m ary o f In teg rated A rea and Fractional A bundance for th e m /z 51 line observed
in fiuorocarbon containing discharges.
Spectrum
5.9
5.10
5.11
5.12
5.13
5.14
5.7
5.6
5.8
Integrated Area Total Area
Area units xlO2
0.253
25.62
-0.089
-12.08
-1.263
-18.32
-18.32
-1.088
-0.709
-22.15
-20.04
-0.511
-1.409
-72.89
-0.575
-28.02
-0.350
-144.69
Fraction of
m /z 51
0.010
0.007
0.069
0.059
0.032
0.026
0.019
0.021
0.002
Percent
Abundance
0.1
0.7
6.9
5.9
3.2
2.6
1.9
2.1
0.2
S iF j and S iF j, but also to the production of CO, CO 2 and COF2 Observation of signals
a t m /z 47, 66, 85 confirm the formation of the S iF j species, while signals at m /z 28, 44
and 66, suggest the formation of the oxygenated species.
5.6
CH FJ Fractional Abundance
Values of the fractional ionic abundance of the C H FJ species for several fiuorocarbon
discharges, obtained from the ratio of the integrated intensity of the m /z 51 peak to the
total signal of the spectrum, are summarized in Table 5.4.
Values for the integrated
intensity are determined using the FCCv02.vi program, while values for the total signal
are determined using the areaXY method or the FC Cv02.vi. See Section 4.2.5 for more
detail regarding these methods.
The moderate current, moderate pressure discharge
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143
conditions from which the spectrum in Fig. 5.11 was obtained, were found to produce the
greatest fractional abundance of C H F j.
Although the positive column glow discharge
mode used in these studies does not produce C H F j in sufficient abundance to justify a
microwave search, it was hoped th at the magnetically confined negative glow mode would
allow for enough additional production of the CH FJ ion for a successful search.
5.7
SiF4 Discharges
Prior to the pressure broadening study of SiF+ a mass spectroscopic study was per­
formed to ascertain the effects of current and various discharge chemistries on the pro­
duction of SiF+ .
The effects of O 2 and H2 contamination on the discharge chemistry
were also investigated. Dependence of SiF+ concentration on the partial pressure of SiF4
was not investigated, as previous work in this laboratory had clearly defined the optimum
SiF4 partial pressure region for microwave studies.2 These conditions are tabulated in
Table 5.5 for both neon and argon buffers.
Extensive studies of the SiF+ ion by R. Petrmichl showed th at the ion is produced
most efficiently in a neon discharge with a low partial pressure of SiF4.
We studied
the effects of discharge current on the intensity of the observed SiF+ concentration by
sampling neon and SiF4 discharges a t low, moderate and high currents. Samples of the
obtained spectra are shown in Figs. 5.16, 5.17, and 5.18, respectively. The spectrum from
high current discharge conditions (~ 1 A) is shown in Fig. 5.16
Clearly identifiable at
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144
•8
-
•4 -
o
'm
lfwl|»Mliw^ ffii|iiii|imm>iTi'"i^niwii|tniipiiiffiW|mfTWii|iHi|Mi
0
20
40
60
60
100
120
140
160
180
m/z Ratio
•8 -
■4 -
O
“ 2-
10
20
25
30
35
40
45
50
m/z Ratio
Figure 5.16: Mass spectrum of high current, low SiF4 concentration, SiF 4 -+- Ne discharge.
The discharge had a current of 1175 mA, a potential of 625 V, and a pressure of 33.8
mTorr. The gas m ixture was composed of 30 mTorr Ne and 1-2 mTorr SiF4
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145
Table 5.5: Summary of the optimum discharge conditions for production of SiF+ in neon and
argon discharges as determined by Petrmichl2
SiF4 (mTorr)
Buffer (mTorr)
Temperature (K)
Current (mA)
Discharge Mode
Argon
~ 0.7
15
95
...
Neg. Glow
Neon
2
36
298
100
Neg. Glow
m /z 20 and 22 are the 20Ne+ and 22Ne+ species. At m /z 40 a peak th at was thought
to be Ne£ was observed. This was quite intriguing, and a separate study (Section 4.5)
to optimize this line in pure discharges was conducted.
From the results of this study
we conclude that the signal at m /z 40 corresponds to Ar+ produced from the trace argon
contamination present in neon gas.
Another interesting peak occurs a t m /z 39, which
the most likely candidate species is F2H+. It has been shown th at F2H+ can be formed
by the reaction41
F 2+ + H2 — ►F2H+ + H.
(5.8)
Although we did not pursue this reaction, it would be an interesting study to see if F2H+
could be produced in sufficient quantity to justify a microwave search.
A theoretical
study using MP4 QCISD(T) theory with the 6-311-H-G(2DF,2PD) basis set by Li and
Hamilton42 determined the structure of the two lowest energy states, lA' and 3A", to be
bent H-F-F. The reported bond lengths and the bond angle are listed in Table 5.6. Based
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146
Table 5.6: The geometries of the 1A” and 3A” states of F2H+ calculated by Li and Hamilton42
using MP4 QCISD(T) methods with a 6-311 -f+G(2DF,2PD) basis set
F-F bond (A)
H-F bond (A)
ZH-F-F (degrees)
lA!
3A"
1.4600
0.9881
100.34
1.7488
0.9434
107.93
on these structures the F2H+ molecule has a Ca geometry, and we can expect it to be a
nearly symmetric prolate top.
A m oderate current (~550 mA), spectrum is shown in Fig. 5.17. Observed species
included 20Ne+ ,22Ne+, Si+, Ar+, SiF+ , SiF^, and SiFg". A dram atic decrease in the m /z
20 to m /z 40 ratio is also observed, compared to the high current spectrum. The SiF+
signal is rather weak, but the S iF j line is relatively strong.
The low current mode ( ~150 mA) spectrum in Fig. 5.18, shows a further decrease in
the apparent m /z 20: m /z 40 ratio, compared to the high and moderate current spectra,
and at this point the ratio is nearly one to one. T he SiF+ signal is increased compared
to the m oderate current case, while the apparent ratio of SiF^ to SiF+ remains fairly
constant. The inset in Fig. 5.18 shows the m /z range around the 22Ne+ peak at m /z 22.
The comparison of this line to the one at m /z 44 shows approximately equal intensities.
This and the constraints of isotopic abundance, strongly argues against the formation of
neon clusters. As is shown in Section 4.5, the m /z 40 peak is Ar+ , so the m /z 44 peak
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147
m ust correspond to some other species. Considering the chemistry of the discharge, and
th a t fiuorocarbon discharges had been recently run in the system, the line at m /z
44
is
most likely C O J or SiO+.
Prom the study of current effects on the intensity of SiF+, it appears that, in a positive
column discharge, a low current, < 150 mA, is optim um for the production of SiF+.
The experiments to determine the effect of O 2 contamination are shown in Figs. 5.19,
5.20, and 5.21, for low, moderate, and high current plasmas. Differences in the spectra
as compared with corresponding discharge current SiF^Ne plasmas are obvious.
The
O 2 seeded discharges are more like the Ne + CHF 3 discharges described in Section 5.2,
w ith the strongest signal at m /z 28, a strong m /z 44 signal and a m /z 51 signal.
It is
believed th a t the oxygen is attacking the materials deposited on the walls of the discharge
cell,2 resulting in the production of species observed in the CHF 3 discharges.
In fact,
trifluoromethane discharges had been studied extensively over the last few' months prior
to this study, with the last experiments conducted only a few days earlier. Variations in
current produces some changes, principally in the relative intensities of the lines in the
m /z 38-55 region.
A loss of resolution, compared with the lower current spectrum, is
observed in the higher current spectrum, but since the high current spectrum was the last
taken, the loss of resolution may be due to the time dependent effect discussed in Section
4.5. Signal in the 1-3 mass region, (H+, H j, and H^), is appreciably greater in the high
current mode th an in the lower current modes.
Considering the apparent strength of the
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148
•3.5
•3.0
•2.5
•
Q>
2.0
-1.5
X
•0.5
o
JkrmrptttfMrff11n11ifpIitrwfi14iijw111inv M
40
20
60
80
100
120
140
160
180
m/z Ratio
•3.5
•3.0
•2.5
•
2.0
•1.5
rp
O
-1.0
■0.5
F*p 1 1 1 1 1 n ^ p i r 11 n fTV*pTt 1 1 | H n i [ i
10
15
20
25
30
35
40
45
1i iV j
50
55
60
65
70
m/z Ratio
Figure 5.17: Mass spectrum of moderate current Ne + SLF4 discharge. The discharge had
a potential of 550 V, a current of 975 mA, and a pressure of 29.83 mTorr. Approximately
30 mTorr Ne and ~ 3 mTorr SiF 4 were used in the gas mixture.
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149
•3.0 -i
•2.5 -1.5
•
2.0
-
•1.5 -
•0.5
o.o -V
E
!
m/z Ratio
-0.5
\ iHi11
0
20
40
60
80
100
m/z Rato
120
140
160
180
.1 5
E
I
o •2 -
■c
ll|llll|llll|B II|llll|l lll| l
40
44
48
52
56
m/z Ratio
60
64
Figure 5.18: Mass spectrum of a low current SiF4 and neon discharge. An expanded view
of the m /z 22 line is shown in the upper right hand corner. This corresponds to the
22Ne+ species. The discharge had a pressure of 32.8 mTorr, a current of 150 mA, and a
discharge voltage of 950 V. The gas mixture used was composed of ~ 30 mTorr Ne and
3 mTorr SiF4.
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150
•5 H
•1.5
■4 •
1.0
■0.5
•2 -
m/z Ratio
iVlll|
0
20
40
60
80
100
m/z Ratio
flf| RHfHHI'fftfpWI nw
11
120
140
160
180
•5 ~ \
■4 -
3
-3 -
•2 -
0
10
20
30
40
50
m/z Ratio
60
70
90
Figure 5.19: Mass spectrum of a N e+ SLF4 +O 2 discharge. Shown are the overall, m /z
0-90, and m /z 36-52 regions. Note the increase in m /z 44, m /z 47, and m /z 51, relative
to the signal observed in the Ne -I- SiF4 discharge. The m /z 85 line corresponds to SiFg .
The discharge had a current of 275 mA, a potential of 1000 V and a pressure of 34 mTorr.
Approximately ~ 1 mTorr O 2 , ~ 3 mTorr SiF4, and ~ 30 mTorr Ne were used.
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151
•5 I
■0.16
■4 •0.14
0.12
■
•2 •
0.10
•0.08
•0.06
m/z Ratio
•0.04
0.02
•
0.00
0
20
40
60
120
80
140
160
180
m/z Ratio
■0.16
•0.14
0.12
•
•
0.10
•0.08
•0.06
~
-0.04
•
0.02
0.00
Q
10
20
30
40
SO
m /z Ratio
60
Figure 5.20: Mass spectrum of a N e+ 0 2 + SiF 4 discharge with moderate current. Note
the enhancement of the SiF£ peak at m /z 85 as compared to the low current case, Fig.
5.19. Also the signal at m /z 49 is stronger as well. The percent of the total signal for the
m /z 44 peak is ~ 2.4%. The discharge had a potential of 1000 V, a current of 500 mA,
and a pressure of 34 mTorr. The gas mixture was approximately 1 mTorr 0 2, 3 mTorr
SiF4, and 30 mTorr Ne.
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152
•0.25
0.12
■
•
0.10
■0.08
0.20
•
•0.15
-
-
0.02
0.00
•
0.10
m/z Ratio
•0.05
0.00
■171|Tlt1V
0
20
40
60
80
160
180
mil Ratio
•0.25
•
0.20
•0.15
,-S* -0-10
•0.05
0.00
0
10
20
30
40
50
60
70
80
mil Ratio
90
Figure 5.21: Mass spectrum of a Ne+C>2 + SiF4 discharge with high current. Note the
loss of intensity for the SiF^ peak at m /z 85 as compared to the low current case (Fig.
5.19). The discharge current was 1050 mA, the potential 950 V and the pressure 33.1
mTorr. The gas m ixture used was composed o f : ~ 1 mTorr 0 2, ~ 3 mTorr SiF4, and ~
30 mTorr Ne.
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153
signal at m /z 44 and the reactant gases present in the discharge, there is a real possibility
th a t SiO+ was being formed. A preliminary determination of the fraction of total signal
from m /z 44 was made by using the areaXY method, after baseline subtraction using
the MS Baseline.vi from the suite of d a ta analysis programs described in Section 2.4 and
Appendix A..
The SiO+ percentage of the total signal, 2.4% for the moderate current
O 2 + Ne + SiF 4 discharge (Fig. 5.20) is not sufficient to justify a microwave search, but
more in-depth studies of the SiF 4 and O 2 discharge chemistry may elucidate a favorable
chemistry for the SiO+ species.
Besides the addition of O 2 the effects of added H2 were also considered. Spectra in
Figs 5.22 and 5.23 show the effects of added H2 . Addition of H2 seems to enhance the
production of SiF+ species. Resolution problems seen in the spectrum are thought to be
due to material build up on the extraction element.
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154
•8 - I
•3.5
•3.0
•2.5
■IQ
•6 -
•1.5
- 1.0
•0.5
m/z Ratio
iVfWfff
0
20
40
60
80
100
11111>1111111'lWfiTW11irPfTffiii
120
140
160
160
m/z Ratio
•8 -t
•6
-
0
10
20
30
40
50
m/z Ratio
60
70
80
90
Figure 5.22: Mass spectrum of a low to moderate current N e+ SiF4+-H2 discharge. Poor
resolution is believed to be due to build up of m aterial on the surface of the extraction
element. The spectrum is dominated by the S iF j signal at m /z 85, with signal also for
S iF j (m /z 66) and SiF+ (m /z 47). The discharge current was 275 mA, discharge voltage
1150 V, and the pressure 51.3 ± 0.1 mTorr. The gas mixture was composed of ~ 35
mTorr Ne, ~ 3 mTorr SiF4, and ~ 0.5 mTorr H 2 .
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155
•0.16
•5 -
a -4 -
■0.14
•
0.12
0.10
■
§
-0.08
m/z Ratio
•0.06
•0.04
•
0.02
TnTftTTTffRWfTfTTpiTfTITW
0
20
40
60
80
100
120
140
160
m/z Ratio
•0.16
•0.14
•0.12
«
-0.10
•0.06
•0.04
•
0.02
0.00
0
10
20
30
40
SO
m/z Ratio
60
70
80
90
Figure 5.23: Mass spectrum of a moderate current Ne-t- SiF4+H 2 discharge. It appears
th a t the formation of SiF^ (m /z 85) is reduced compared with the low current case (Fig.
5.22). O ther SiF£ species also appear to have reduced intensities. The discharge had a
potential of 1150 V, a current of 500 mA, and a pressure of 50.8±0.2 mTorr. The gas
mixture was ~ 35 mTorr Ne, ~ 3 mTorr SiF4, and ~ 0.5 mTorr H2.
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156
CHAPTER 6
Microwave Searches
6.1
Introduction
Characterization of molecular ions using microwave spectroscopy has been an ongoing
labor for almost 30 years. Much of the initial efforts were directed towards characteriza­
tion of ionic species believed to exist in the interstellar medium,15 and this remains one
of the principal driving forces of current research.
Molecular ions are also observed in
other environments of more practical importance, particularly within the plasmas used to
etch semiconductor surfaces. Several studies have shown strong correlations between the
ionic composition of the plasma and the type of processes occurring at the semiconductor
surface.31-33 Use of microwave spectroscopy as a diagnostic tool in the optimization of
etching discharges, requires th at there exist, within the discharge, a species for which
observable transitions are known.
Determination of the rotational spectra, and where
possible the spectroscopic constants, of molecules known to exist within etching discharges
is another aim of our work. Microwave spectroscopy allows for very precise and accurate
structural determinations of molecules, with the uncertainties in determined values some­
times due to the limits of precision in determined values of the fundamental constants, e.g.,
h. These high accuracy/high precision structures and spectroscopic constants provide an
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157
excellent reference for evaluating the accuracy of computational models and methods.
While a number of molecular ions have been characterized using microwave spec­
troscopy, these have been primarily diatomic, linear, symmetric top, or slightly asym­
metric tops, where one, two, or three light atoms create the asymmetry.
The observed
species are shown in Tables 6.1 - 6.4. No asymmetric top molecular ions where the asym­
m etry is strong, or nearly symmetric tops where heavy, non-hydrogen, atom(s) create the
asymmetry, have been successfully studied with microwave spectroscopy.
To date only
one molecular anion, SH- , and its deuterated form have been reported .3 In this chapter
efforts to determine the transition frequencies of two true asymmetric tops O j and CH FJ
are described.
Finally, a comparison of the predicted absorption coefficients
7
of SiF+ and CHF 2 is
made to assess the potential for successful microwave characterizations of asymmetric top
ions.
6.2
Asymmetric Tops
A top is asymmetric when none of the principal moments of inertia are equal to each
other, Ia < h < Ic. The magnitude of the molecular asymmetry can be described using
asym metry parameters, such as Ray’s asymmetry param eter given by
2B - A - C
K
A -C
'
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(
^
158
Table 6.1: Diatomic cations observed by microwave spectroscopy. References are given for spec­
troscopic characterizations and do not represent all studies o f a given cation. The year o f the first
reporting is given in the Year column.
Species
Year
Reference
36A rD'
1983
43
3HA rD '
1983
43
A rD'
1983
43
c r
1986
44
ccr
1975
45
GeF'
1990
46
pcr
1991
47
SiF'
1990
48
49
SO'
XcD'
1991
50
XeH"
1991
50
Table 6.2: Linear molecular ions observed by microwave spectroscopy. References are given for
spectroscopic characterizations and do not represent all studies o f a given cation. The year o f the first
reporting is given in the Year column.
Species
Year
Reference
Species
Year
Reference
D,gB F
1987
[51]
HCO'
1975
[53],[54],[60],[61]
D“ BF'
1987
[51],[52]
HCS*
1981
[62], [63]
DC 180'
1981
[53]
HCCCNH'
2000
[64]
DCO'
1981
[53]-[55]
HNCCN'
1991
[65],[66]
DNT
1981
[56]
H15NCCN'
1992
[67]
DOC'
1986
[57]
HNCI3CN'
1992
[67]
H,UBF~
1987
[51],[52]
HN,3CCN'
1992
[67]
H "B F'
1987
[51],[52],[58]
HNCCMN '
1992
[67]
HI3CO '
1981
[53]
HOC'
1982
[68],[69]
HC‘rO"
1983
[59]
N,H'
1976
[56],[70]-[72]
HCtaO*
1981
[53]
NCCCNH'
2000
[64]
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159
Table 6.3: Symmetric top molecular ions reported to date. References are given for spectroscopic
characterizations and do not represent all studies o f a given cation. The year of the first reporting is given
in the Year column.
Species
Year
Reference
CHjCNH'
2000
[64]
D ,cr
1998
[73]
H:CT
1988
[74]
HjCM-
1985
[73],[75],[76]
HjS-r
1997
[77]
HOCS*
1998
[78]
[79],[80]
SDj"
34SD}‘
[80]
1999
Table 6.4: Asymmetric top molecular ions reported in literature. References are given for spectroscopic
characterizations and do not represent all studies of a given cation. The year of the first reporting is given
in the Year column.
Year
Reference
C2H3-*-
1992
[81]
DOCO-t-
1994
[82]
H,l5COH+
1995
[83]
H,COH*
1995
[84]
H:D+
1984
[85],[86]
HOCO+
1982
[78], [82]
D,COD+
1997
[84]
ArD,H+
1999
[78],[82]
ArDj-t-
1987
[78], [87]
ArH}-r
1987
f—
00
Species
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160
Here A, B and C are the rotation constants of the molecule, and the values of the asym­
metry param eter k range from -1 for a prolate top to 4-1 for a oblate top.
As with the
symmetric top the quantum numbers J and M are good, but because there is not constant
component of the angular momentum along any molecule fixed direction in an asymmetric
top, the quantum number K is no longer useful in specifying the state. The K quantum
number can be use to describe the cases where the asymmetric top approaches the prolate
(K - 1) or oblate (Ki) limit. These "pseudo" quantum numbers are often given using the
following relationship
t
= K -i —Ki
.
(6.2)
The Hamiltonian for the rigid rotor asymmetric top is given by
H —A P \ + B P \ 4- C P l
where
,
(6.3)
A = /i2 / ( 87 r2/ a) and the Pa , Pb , and Pc are the angular momentum operators.
For ease of calculations the Hamiltonian is often expressed as a function of k and called
the reduced Hamiltonian . 18,88
This form of the Hamiltonian is
H = i( A + C)P2 + i( A - C')W(k)
H(K) = P \ + KP l - P l
.
(6.4a)
(6.4b)
The wave functions of the asymmetric top are linear combinations of the symmetric top
wave functions
=
51
K
*
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(6*5)
161
As a consequence, the Hamiltonian of the asymmetric top is expressed in matrix form,
and the energy levels are found by solving the secular determinant
|E
(
k
) -
IX\ = 0
.
(6 .6 )
T he energy levels obtained from Eq.( 6 .6 ) and Eq. (6.4) are given by
E
Numerical values of
E jr
=
±{A + C ) J ( J +
l)
+ h2 ( A - C ) E J r ( K )
.
(6.7)
(k) are listed in tables found in the literature . 18,88 The reduced
Hamiltonian and energy are only one method for finding the energy levels of the asym­
metric rigid rotor, other methods are described in detail by Gordy and Cook ,88 as well as
Townes and Schawlow . 18
The assumption th a t the location of the nuclei with respect to each other is fixed
is of course not valid.
Zero point energies of molecules ensure th at the nuclei within
a molecule are always in motion, changing the moments of inertia and consequently the
rotational energy. Corrections for the vibrational rotational interaction are given by
+ i)
(6.8a)
= Be - £ a f(v i -h i )
(6 .8 b)
Ay = A e -
53
i
By
i
Cy
= Ce - £ a ? (Vi + £)
t
•
(6 .8 c)
T he a , values are the vibration-rotation interaction constants for each of the vibrational
modes within the molecule, and ut- are the vibrational quantum number of the state of the
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162
ith vibrational mode. More detailed discussions on the relationship between vibrational
and rotational motion is given by Gordy and Cook .88
In addition to distortions of the molecular geometry from vibrations there are distor­
tions arising from centrifugal forces produced by the rotation of the molecule itself.
It
is beyond the scope of this work to describe in detail the theory of centrifugal distortion,
but, a brief summary of the theory relative to asymmetric molecules will be presented.
The general form of the Hamiltonian for a semi-rigid non vibrating rotor is88
W = 53
a
+ ~r 53 TafasPaPpP-yPs + 6®52 Ta0l6er>PaP/3P-y PePr,
^
(6.9)
The distortion constants r a^ s are defined88 for a harmonic potential model of the restoring
force as
where (
is an element of the m atrix inverse to the m atrix of force constants fa, and
M
The
(6 . 10)
>
ij
i r ) ,
(6-u)
•
term is the partial derivative of the a/3 element of the of the reciprocal moment
of inertia tensor with respect to the internal coordinate i ?,-.88
Centrifugal distortion
constants are obtained from linear combinations of the r values, but are dependent on
the form of the Hamiltonian and the representation used for the axes .88
From the Hamiltonian in Eq. (6.9), the W atson asymmetric top reduction can be
used to create a reduced Hamiltonian, for asymmetric rotors. This reduction corrects for
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163
Table 6.5: A sym m etric selection rules
Dipole Component A A '-t
Ha 0
0, ±2, ±4...
fib 0
±1, ±3...
fic________________ ±1, ±3...
&Ki
±1, ±3...
±1, ±3...
0, d:2, ±4...
indeterminacy in calculating the r a^ s values from experimental d a ta .88
The details of
the reduction and the resultant Hamiltonian are beyond the scope of this work, but more
details can be found in Gordy and Cook .88 We mention the A reduction to provide context
for the ASROT 89 program input.
This program, used to calculate the energy levels
and rotational transitions of asymmetric tops, utilizes the W atson asymmetric reduced
Hamiltonian and the Ir representation. The Ir representation assigns the x, y, z axes to
the b, c, and a principal rotation axes, respectively. It is im portant to ensure th at the
centrifugal distortion coefficients are in the proper form to prevent erroneous output.
W ith three unequal moments of inertia an asymmetric top may have components of
the dipole moment along each principal axis. Transitions of a n asymmetric top are typed
and selection rules determined by the corresponding dipole moment component. The
three types of possible transitions and the corresponding selection rules are tabulated in
Table 6.5.
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164
6.3
O 3 Studies
Characterization of a molecular anion by microwave spectroscopy has long been a prize
sought by microwave spectroscopists and the subject of much effort in this laboratory .2
While S. Civis et al.3 have reported spectral lines of SH“ and SD~ in the submillime­
ter region, no molecular anion has been characterized solely by microwave spectroscopy.
Previous to their reporting of the SH” and SD“ transitions, a search was begun in this
laboratory to find the spectral lines of the O 3 molecule.
Several factors, both experi­
mental and theoretical, favored O 3 as a candidate ion.
Mass spectroscopic studies of
O 2 discharges by Petrmichl.2had shown th at O 3 was a principal ionic component of the
discharge.
Since only a single gas, O 2 , would be required, the presence of contaminant
species would be small, and the principal contaminant species, O 3 , was expected to be
observed only in the ground state.
The absence of contaminant species, it was hoped,
would lead to a condition where few competing lines would be observed. The high level
ab initio calculations of Peterson et a /. 90 and the spectroscopic constants derived from
them would minimize the propagated uncertainty in the transition frequencies calculated
using these values and reduce the search region. Ozonide is not expected to have a hyperfine structure and spin statistics leads to half of the lines being absent, which further
simplifies the spectra.
6.3.1
Theoretical
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165
T able 6 .6 : Sum m ary o f th e experim etnally an d theoretically determ ined stru c tu re of O 3 .
Method
Re (A)
0e(deg)
Reference
Exp.
1.36 ± 0 .0 2 111.7 ± 2 .0 a
Exp.
1.34 ± 0 .0 3 112.6 ± 2 .0 b
CASSCF 1.363
115.6
c
CASPT2 1.361
115.3
c
CCDS(T) 1.376
115.0
c
CCDS(T) 1.357
115.6
c
CASSCF 1.3723
115.36
d
Corrected 1.3572
115.36
d
a) Photoelectron study Ref.91
b) Photodetachment study Ref92
c) Ref. 103
d) Ref.90___________________________________
Ozonide has been studied both experimentally and theoretically. Experimental stud­
ies have included photoelectron ,91 photodetachment,92,93 IR in noble gas matrices ,94"96
IR and Raman studies of alkali metal ozonides,97,98 and Raman studies of aqueous O j
The studies by Arnold et a l91 and Wang et al92 determined the bond length and
bond angle using Franck Condon factor analysis.
These values are listed in Table 6 .6 .
Theoretical studies have predicted the electron affinity, 100 the geometry and vibrational
frequencies,9 0 ,101-103 and the electron spin g factors . 104,105 Of these studies, only Peterson
et al.90 provide spectroscopic constants.
The equilibrium geometries from Table
6 .6
were used with MOMIRT, a Fortran pro­
gram, to calculate the body centered rotational constants for the given molecular geom­
etry.
The obtained equilibrium rotational constants were then corrected for vibration-
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166
Table 6.7: Sum m ary of th e ro tatio n al constants for equilibrium geom etries. Values rep o rted in
this table are those used in predicting th e rotational sp ectru m o f O 3 an d are not reflective of
th e precision of th e m easurem ent. C om parison of th e CA SSCF(cor) an d C A SPT 2 values shows
th a t uncertainties are : A A « 400 MHz, A B ~ 70 MHz, an d A C « 60 MHz.
A* (MHz) Be (MHz)
90018.68
12009.69
11937.31
89609.68
89842.56
11876.12
87425.16
11691.38
89152.57
12061.11
81313.69
12471.46
85738.24
12711.51
a) Peterson et al.90
b) Borowski et at.103
c) Arnold et al91
d) Wang et al.92
Ce (MHz)
10597.66
10534.03
10489.53
10312.31
10623.85
10813.02
11070.24
K
Method
-0.9644 CASSCF (cor)
-0.9645
CASPT2
-0.9651
CASSCF
-0.9642
CCDS(T) a
-0.9634
CCDS(T) c
Exp
-0.9530
Exp
-0.9560
Ref
a
b
b
b
b
c
d
rotation interactions using the a values reported by Peterson et al.90 The equilibrium
and vibrational dependent rotational constants are listed in Tables 6.7 and
tively.
6 .8 ,
respec­
The geometries used were selected to illustrate the sensitivity of the rotational
constants to variations in the molecular geometry.
Table 6.9 lists the calculated rota­
tional constants from the experimentally obtained structures of O 3 .
Also reported is
the uncertainty in the rotational constants propagated from the reported errors in the
experimented structure.
6.3.2
Theoretical Spectrum
W ith the spectroscopic constants from Peterson et a/ . 90 (Table 6.10) the energy levels
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167
Table 6 .8 : R otation C o nstants corrected for ro tatio n /v ib ratio n interaction.
A (MHz) B (MHz)
90137.68 11906.69
89728.68 11834.31
89961.56 11773.12
87544.16 11588.38
89271.57 11958.11
81432.69 12368.46
85857.24 12608.51
a) Peterson et a l90
b) Borowski et a im
c) Arnold et al.91
d) Wang et al92
C (MHz)
k
Method
10487.81 -0.9644 CASSCF (cor)
10424.18 -0.9644
CASPT2
CASSCF
10379.68 -0.9650
10202.46 -0.9642
CCDS(T) a
10514.00 -0.9633
CCDS(T) c
Exp
10703.17 -0.9529
10960.39 -0.9560
Exp
Ref
a
b
b
b
b
c
d
Table 6.9: Values of th e propagated uncertainty for th e ro tatio n constants calculated from ex­
perim entally determ ined stru ctu res o f O j
Ae (MHz) Be (MHz) Ce (MHz) Ref.
a
81300
12500
10800
370
a
2400
320
290
a
4400
140
85700
12710
b
11070
380
b
2600
330
4700
290
b
150
(A), A d = ± 2.0 (deg)
Constants
AR
Ad
Constants
AR
Ad
A R = ±.02
a) Arnold et al.91
b) Wang et al.92
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169
Table 6.10: Spectroscopic constants used in calculating the 0 3 transition frequencies, as reported
by Peterson et a/.90
Constant
Ae (cm-1)
Be (cm-1)
Ce (cm-1)
A j (MHz)
A JK (MHz)
A * (MHz)
Sj (MHz)
8k (MHz)
/*( D)
Constant
3.0027
0.4006
0.3535
0.0144
-0.0296
4.823
0.0024
0.1140
-1.115
a f (MHz)
nA
a2 (MHz)
a 3 (MHz)
o f (MHz)
a ? (MHz)
(MHz)
(MHz)
nc (MHz)
q2
oP
3 (MHz)
-245
-1333
1267
62.3
42.4
99.3
31.3
93.0
91.8
In the Hamiltonian, the Na are the components of the rotational angular momentum,
the SQ are the components of the electron spin angular momentum, and the ea are the
components of the spin rotation tensor. We have included up to the quartic term s in the
centrifugal distortion portion, and up to the quartic term for the spin-rotation interaction.
The presence of the unpaired electron will result in a doublet for each N value.
W hen electron spin is present, in the molecule, the quantum numbers change meaning.
The symbol J now denotes the angular momentum from all sources, rotational angular
momentum is symbolized with the letter N, and the electron spin by S. This relationship
can be expressed
J = N + S.
(6.14)
Effects of the vibration-rotation interaction can be included by correcting the rotation
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170
constants as in Eq. (6 .8 ). The C^v geometry of O 3 forces the dipole moment to lie along
the b axis (symmetry axis), allowing only b-type transitions.
Selection rules are given
in Table 6.5. O ur early calculations of the rotational spectrum of O 3 were for the rigid
rotor model using the Fortran program MODTOP. Although centrifugal distortion is an
im portant factor, the structure of an asymmetric top spectrum is such that, by choosing
the correct K_i series, centrifugal distortion effects can be minimized by searching for Q
branch transitions of low N value.
This is shown in Fig. 6.1. Here the K_i =1 and
K_i =2 series have low N transitions near 230GHz and 390 GHz, respectively.
While
the regions immediately near these frequencies are not favorable for searches with our
instrument, the K_i series does have relatively low N transitions in the prime search
region of 250 - 280 GHz, making the search practical.
Even a t low N, the uncertainty
in the rotational constants, neglect of the centrifugal distortion effects, and the rotation
vibration interaction terms, combine to create an uncertainty in the calculated transition
frequencies th at requires large search regions to maximize the potential for finding a line.
In cases such as this, the close spacing of the Q branch lines helps. Even if there is a
significant shift in the frequency, the density of lines is such th a t there is a good probability
of finding a t least one transition in the search range. This is illustrated in Fig. 6.2, which
shows the effects of the variation of the molecular geometry on the spectrum. Even when
the band head is shifted by 50 GHz, as it is between the spectrum for the K _!=2 series
arising from the structure reported by Arnold et al.9l and the spectra of the K _i
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=2
171
50
40
□
ffl
30
©□
□©
20
10
0
200
250
300
350
400
450
500
Transition Frequency (GHz)
Figure 6 .1 : T he Q branch spectrum for O 3 predicted using the spectroscopic constants
reported by Peterson et al.90 The K_i series visible are the K_i = 0 (0)> = 1 (©), = 2
□ , and = 3 (EH). Frequency values were calculated with the A reduced Hamiltonian and
the Ir representation using the program ASROT .89 All rotational constants were corrected
for vibration-rotation interaction effects, and centrifugal distortion was accounted for up
to the quartic level. Effects on the spectrum due to spin statistics of the equivalent
oxygen atom s have been included.
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172
40 -
□£> ffl
□®
CO
®
Z
250
300
350
400
450
500
Transition Frequency (GHz)
Figure 6 .2 : The spectra of the K _i=2 series for selected theoretical and experimental
structures of O 3 . Structures were determined experimentally 91 (o) , and theoretically:
(ffi) CASSCF 90 , (©) CASSCF , 103 (DJCCDST . 103 Spectra calculated using the same
methods as for Fig. 6.1.
series from the structures determined by CASSCF 90
103
and CCSD(T ) 103 computations,
the line spacing is such th at a search region of ± 3 GHz, about either band head, should
contain a t least one line.
Because O 3 has no nuclear spin, there will be no nuclear quadrupole or magnetic hyperfine structure. As a simplification, and considering the uncertainties already present,
we have not included the effect of the electronic spin angular momentum in the spectra.
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173
The spectra show the predicted center frequency of the spin doublet.
For open shell molecules like O 3 the interaction of a magnetic field and the electronic
spin angular momentum causes a breakdown in the degeneracies of the M states.
A
transition arising from an open shell molecule may be split into multiple components.
This is dependent on the nature of the interaction of the microwave electromagnetic and
the applied static magnetic fields with the molecule.
In a weak field, two types of components are observed, which correspond to the allowed
changes in M. For the case AM =0, the magnetic field is parallel to the direction of the
microwave E field88 and the component is labeled a || component. For the case where the
magnetic field is perpendicular to the microwave E field, AM = ±1, and the component
is labeled a J_ component. 18,88
The magnitude of the frequency shifts of the || and the _L components is given by
v = v 0 + ( gj2 —g jx) M H ^
( || component)
(6.15)
and
u = vQ+ [(]gj2 - gJl)M2 ± gjt\
( J_ component),
(6.16)
where g j n is the molecular factor for a given state, fi0 the Bohr magneton, H the magnitude
of the magnetic field, and vQthe unperturbed transition frequency 18
Non-linear molecules with electron spin are equivalent to linear molecules with electron
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174
spin and are in a E state . 18 The g factor for molecules of this type is given by 88
gj
( 9 ,\ J{J + 1) + S (S + 1 ) - N {N + 1 )
K2 /
J ( J + 1)
sgr\ J (J + 1 ) + N (N + 1 ) - S(S + 1 )
V2 I
J (J + 1 )
(6.17)
where g3 is the g factor for the electron spin, gr is the g factor for molecular rotation
along. Equation (6.17) can be simplified. W ith values of g3 =2.002 and of gr « 10-4, the
second term is negligible and is discarded. For O 3 the total electron angular momentum
is 1/2. Using this and the definition of the total angular momentum (Eq. 6.14) we obtain,
9j =n +± = ^
(6.18)
and
9j = n - i
1001
-
■
(6 *i 9 )
For a molecule with electron spin angular momentum, the strong transitions obey the
relationship A N = A J .
W hen we apply this rule we see th a t A gj in Eqs. (6.15) and
(6.16) goes to zero for the Q branch (A N = 0) transitions. Thus || components will not
be perturbed a t all, and in the J_ case the line will be split into a doublet. T he R branch
transitions (N-+N -I- 1) will have a A gj term th at can be expressed as
1-001
S j"A,+i ~ (AT + i ) (JV + | )
1
’
and
1.001
—
TTt
1\ ( \ T , i\ >
-i - (AT-J)
(AT+ i)
& 9 j =n - ±
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(6.21)
175
Table 6.11: Summary of the factors used in estimating the magnitude of the perpendicular
Zeeman effect for a molecule with spin angular momentum but in a S state or for an asymmetric
top with angular momentum. Values of A nu assume Q branch transistions, A N = 0.
Constant
N
10
S
1 /2
H (Gauss)
100
At/ (MHz)
~ 13
^ = 1.39967 MHz18
3
1 /2
100
~ 40
where N is for the initial state. The splitting pattern is now dependent on the M term
of the lower state, and we will see many lobes for high J states. For both the Q and R
branches, the Zeeman effect will decrease rapidly with N. The doublet splitting of the Q
branch will further simplify the identification of the transitions of O 3 .
The magnitude of the splitting, of a Q branch transition, for the perpendicular case
can be estim ated using Eqs. (6.16), (6.18), and (6.19). If we assume a 100 G magnetic
field and N values of 3 and 10, the line will be split into a doublet with a separation of
~ 80 MHz and ~ 26 MHz, respectively. The values used in the calculation are listed in
Table 6.11.
6.3.3
Experimental Work
Determination of the spectral regions to search was made by using the structure and
spectroscopic constants calculated by Peterson et al.90 using CASSCF ab initio methods.
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176
A region containing low N, Q branch transitions was chosen to minimize the effects of
centrifugal distortion and to provide closely spaced peaks so the probability of finding a
line would be maximized.
Lines from the
= 1 series were chosen as the principal
targets, because many were predicted to be in the optimum range (240 - 270 GHz) of our
spectrometer. In all searches liquid nitrogen cooling of the discharge cell was used. A
typical tem perature of ~ 90 K was obtained.
A summary of the experimental conditions used in each of the three searches is pro­
vided in Table 6.12.
The final search was in a negative glow discharge with magnetic
confinement. O ther higher pressure searches were attem pted, but discharge noise made
acquiring spectra extremely difficult.
While noise can be averaged out, this requires a
significant increase in d ata acquisition time. A low noise spectrum is created by averag­
ing around 50 scans, and from start to finish, it takes between 4 to 5 minutes to sweep
a 10 MHz region for an effective scanning rate of ~ 2 MHz/min.
Weak lines or noisy
conditions can lead to scan counts of 200 or more, with just the data acquisition for each
scan taking about 3 seconds, the total acquisition tim e increases from around five minutes
to over ten. At the 2 MHz/min. effective scanning rate, the total scanning time needed
to sweep a 3 GHz region is ~ 25 hours. Of course the ratio of scanning time to time in the
laboratory is, unfortunately, much smaller than one. When this is kept in mind, a noisy
discharge can prevent a reasonable search from occurring, even if satisfactory spectra are
able to be obtained by extensive signal averaging.
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177
Table 6.12: A summary of the experimental conditions used for the three primary searches
conducted for O3 . The first search required nearly two months to complete, the second was
actually two searches over the 89.0-90.5 GHz region and required a month, while the last search
took only two weeks.
Search
1
2
GDFa Range (GHz)
89.0-90.5
79.5-83.0
T hird Harmonic (GHz)
328.5-249.0 267.0-271.5
Fourth Harmonic (GHz) 318.0-332.0 356.0-362.0
Fifth Harmonic (GHz)
397.5-415.0 445.0-452.5
Pressure (mTorr)
~33
~32
Current (mA)
~ 60
~ 60
~ 1100
- 1100
Vo(V)
~ 95
~ 95
Temperature (K)
Magnetic Field (Gauss)
a) The source or Gunn diode frequency
3
89.0-90.5
267.0-271.5
356.0-362.0
445.0-452.5
~ 17
~ 17
~ 1600
~ 95
200
One failure of our studies was the lack of mass spectrometric optimization of the O 3
signal in the discharges. At the time of the searches problems with the operation of the
mass spectrometer prevented proper use of the instrument, and it was decided to forgo
the mass spectrometric optimization. Conditions used were based on the studies of O 2
discharges by Petrmichl .2
The assumption th at similar conditions will produce similar
chemistry is not valid. As has been shown in this work, the dynamic nature of discharge
chemistry prevents the experimentalist from creating a set of standard conditions for
studying a particular ion.
To be of any benefit mass spectroscopic optim ization must
occur every tim e the search is conducted, and if the experimental design, ie , no magnetic
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178
confinement, will allow, during the search.
6.3.4
Results
Our searches and subsequent analyses found over a hundred unique lines, most of
which correspond to ozone species. More than 40 unassigned lines have been found within
the search region. Surprisingly, over 70 unique ozone fines arising from six different ozone
forms, including excited vibrational states and isotopomers, have been identified.
Advances in computer technology have increased the accessibility to spectral databases
never before enjoyed, which has proven a key in working with systems where the potential
for many competing fines is high. The Submillimeter, Millimeter, and Microwave Spectral
Line Catalog,110 m aintained by the Jet Propulsion Laboratory, is readily accessible via the
internet and offers a user friendly browser for d ata retrieval. W ith over 300 species, the
database, while it does not contain all the species observed by submilfimeter, millimeter
or microwave techniques, provides a first, and sometimes only, step in the assignment of a
newly observed fine. This ability dramatically simplified the search for O 3 , where many
lines arising from excited vibrational states in preliminary tests showed transient behavior.
The identification of these fines using the database saved the effort of further testing to
determine ionic character. The JP L catalog does not report only observed fines, b u t also
reports predicted transitions based on experimentally determined spectroscopic constants.
Many of the assignments for fines we observed correspond to calculated transitions th at
have not been experimentally observed.
Details of the program used to calculate the
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179
spectra have been given by Pickett.111 The precision of the database values is either the
reported experimental uncertainty, from the literature, or a 95% confidence level110 for
those lines th at are predicted by the fitting program. The program used to calculate the
predicted frequencies neglects the high level centrifugal distortion effects and does not
account for mixing of closely separated states.110 These omissions introduce systematic
error into the predicted frequency values.110 A summary of some of the assigned lines,
organized by species and state, are listed in Tables 6.13 to 6.19. Unassigned lines are
listed in Tables 6.21 and 6.22.
Our experimentally obtained frequencies of the assigned ozone transitions are compiled
in Tables 6.13 to 6.19.
Where multiple measurements, under similar conditions, were
made the average and standard deviation, er, are reported. Prior to the reporting, the fit
for each line was graded based on how well the least squares fitting routine fit a Lorentzian
or Gaussian line shape model to the experimental data. A feel for how the fits were rated
can be made by considering two weak lines observed in the same spectrum, Fig 6.3. Third
and fifth harmonic baseline suppressions produce the spectra observed in Figs. 6.4 and
6.5 respectively. The line in Fig. 6.4 is well fit, the modulation sidebands are apparent,
and the fit is considered good.
The line in Fig. 6.5, does not have clear modulation
sidebands, and the overall fit is graded poor. The species observed include O3,
0 3 ( 1 0 0 ),
O3(001), O3(010), 10O16O18O ( 0 3 asymlsO) and 160 180 160 ( 0 3 sym180 ).
The isotopomers are present in natural abundance, but many of the frequencies listed
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180
4
2
0
tn
c
Q)
-2
-4
89.532
89.536
89.540
89.544
GDF (GHz)
Figure 6.3: An unfitted spectrum containing three lines: The O 3 (100) 62,4 <— 61,5 at
268,628.3990 MHz (A), the unidentified # 2 line a t 268,616.7188 MHz (B), and the H 0 2
281,27 «— 272,26 line a t 447,677.2208 MHz, (C). The x axis corresponds to the source or
Gunn diode frequency, GDF. The discharge had a current of 16 mA, a potential of 1600
V, and a pressure of 21 mTorr. A magnetic field of 200 Gauss was being applied. The
detector sensitivity was 1 0 fiV.
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181
3
2
&
0
'tn
c
o
•2
•3
268.600
268.610
268.620
Frequency (GHz)
Figure 6.4: Spectrum showing the fit of the # 2 unidentified peak. Spectrum obtained
by three baseline suppressions of the spectrum shown in Fig. 6.3. The intensity axis
has been expanded by a factor of ~ 25, including the effects of the baseline suppression
routine. The lock-in amplifier sensitivity is 10 /iV, and other experimental conditions are
as given in Fig. 6.3. Despite the low signal to noise ratio and the distortion arising
from the influence of the O 3 ( 1 0 0 ) transition to the right, the peak shape is well fit by a
Lorentzian model function and so the fit is considered good.
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182
4 -
>
&
CO
ca>
c=
447.66
447.67
447.68
447.69
447.70
447.71
Frequency (GHz)
Figure 6.5: A fifth harmonic baseline suppression of the spectrum in Fig. 6.3 shows what
appears to be a line near 447,679 MHz. This line can be attributed to the HO 2 281,27
*— 272,26 transition a t 447,677.2208 MHz, as given by the JP L catalog . 110 The fitting
routine cannot fit the spectrum well, and the fit is judged less th an A. This line has
been observed a t least twice, in both cases a magnetic field was present. Experimental
conditions are listed in the caption for Fig. 6.3.
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183
Table 6.13: Summary of observed ground state O3 lines. A comparison with values from the
JPL database110, both observed and predicted, is also provided. A spectrum for the 303,27 <—
302,28 transition is shown in Fig. 6 .8 .
Transition
92,8
83,5
154,12 *— 163,13
367,29 *— 376,32
1 2 4,8
*— 133,11
40s,32 *— 417,35
185,13
194,16
182,16
181,17
202,18
20i,ig
62,4
*
61,5
« - 6lt5
20i,ig *— 20o,2o
303,27 <— 302,28
62,4
*— 282,26
143,11 *— 142,12
283,25
1 2 o,i2
Experiment0
Average Error
244158.42 0 . 0 1
247761.78 0 . 0 1
271091.83
327844.56 0.01
356086.98 0.02
361669.33
239093.28 0.01
248183.44
267266.52 0.01
267266.53 0.02
319996.55 0.01
358199.82 0.01
359649.66 0.01
448876.23 0.04
243453.75 0.03
326900.99
357629.83 0.03
358853.34 0.02
445458.70 0.08
JPL Database
Frequency Error Source6
0.5
E
244158.0
247761.77 0 . 1 2 E
0 .0 2
C
271091.81
327844.63 0.02 C
356087.00 0.03 C
361669.44 0.03 C
239093.26 0.10 E
248183.38 0.12 E
267266.57 0.12 E
267266.57 0.12 E
319996.54 0.12 E
358199.84 0.06 E
359649.68 0.04 C
0.02 C
448876.38
E
0.5
243453.70
326900.99 0.02 C
0.15 E
357629.83
358853.35 0.15 E
445458.66 0.03 C
— I l l , 11
111,11
10o,io
20i,i9 *— 192,18
15i,i5
16o,i6
62,4 < - 5 i ,5
a) This work
b) Experimental (E) and calculated (C) values
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184
Table 6.14: Sum m ary of th e observed O 3 (100) transitions and J P L catalo g 1 1 0 frequency values.
E rrors for frequencies from o u r experim ents represent one stan d ard dev iatio n o r th e difference,
if only two values are available, of th e frequencies. Errors for th e J P L d a ta are th e errors
reported in th e catalog. T h e le tte r C in th e Source column denotes a frequency calculated from
experim entally o b tain ed constants, while th e E denotes a m easured quantity. A spectrum for
th e 6 2 , 4 ♦— 6 1 , 5 tran sitio n is shown in Fig. 6 . 8
Transition
142,12 ♦— 14i ,13
202,18
201,19
122,10 *— 1 2 i,n
83,5 < 92,8
*— 61,5
296,24 *— 305,25
H i ,11 *— 10o,io
62,4
16o,ie <— 15i,i5
132,12 *— 13i,13
303,27 ♦— 32,28
323,29
*—
322,30
Experiment
Frequency Error
238675.68 0.04
244217.44
244404.25
244805.83
268628.39 0 . 0 2
269853.50 0.03
329635.53
356650.49 0.08
358750.87
359073.55 0 . 1 0
360078.38
JPL
Frequency
238675.45
244217.23
244404.12
244806.01
268628.29
269853.84
329635.37
356650.47
358750.88
359073.33
360078.34
Database
Error Observed
0.03
C
0 .0 2
C
0 .0 2
C
0 .0 2
C
0.04
C
0.04
C
0.04
C
0.04
C
0.04
C
0.04
C
0.04
C
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185
Table 6.15: Summary of observed O3 (001) transitions and JPL catalog 110 frequency values.
Errors for frequencies from our experiments represent one standard deviation or half the dif­
ference, if only two values are available, of the frequencies. Errors for the JPL data are the
errors reported in the catalog. The Source column symbol C denotes a frequency calculated
from experimentally obtained constants, while the E denotes a measured quantity. A spectrum
for the 13q,i3 <— 1 2 i,i2 transition is shown in Fig. 6 .6
0
0
T
Experiment
Frequency Error
Transition
192,17 <— 19i,i8 243063.63 0.01
268474.97 0.01
144,11
153,12
12i,i2 270923.38 0.01
13o,i3
322688.44 0.01
102,9
15o,i5 « - 141,14 327699.06
313,28 *— 312,29 358742.56 0.20
360318.93
256,19
265,22
0.01
361659.28
21 i ,2o *— 2 1 o,2 i
18i,i8
17q,17 451044.55 0.03
-
JPL Database
Frequency Error Source
243063.52 0.02
C
268474.44 0.05
C
270923.36 0.04
E
322688.48 0.05
C
327699.18 0.04
C
358742.77 0.04
C
0.04
360319.49
C
361659.22 0.06
C
C
451044.35 0.04
in the tables represent the apparent frequency of a line created by unresolved hyperfine
structure, as shown in Fig. 6.7. It is thought th at this apparent line is a unresolved
16O ir0 160 spin hyperfine structure. In addition to lines from the isotopomers, many lines
from vibrational excited states were observed, and selected spectra are shown in Figs. 6.6
and 6.8
Of the unidentified transitions, two were the most reproducible.
referred to as transition # 1 and transition # 2 .
These lines are
Raw spectra of these lines are shown
in Figs. 3.13 and 6.3. Although both lines were weak, the unidentified # 2 was weaker.
F itting of the spectra shows a marginal S /N of ~ 2.5 for the unidentified # 2 , Fig. 6.4 and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
186
Table 6.16: Observed O3 (010) transitions and JPL catalog110 frequency values. Errors for
frequencies from our experiments represent one standard deviation or half the difference, if only
two values are available, of the frequencies. Errors for the JPL data are the errors reported in the
catalog. The symbole C in the Source column denotes a frequency calculated from experimental
obtained constants, while the E denotes a measured quantity. A spectrum for the 222,20 *—
2 2 i,2 i transition is shown in Fig. 6 .8
Transition
323,29 *— 314,28
16o,i6 - 151,15
32,2 <— 2i,i
72,6 - 61,5
62,4 ♦”* 5 i ,5
162,14 « - 161,15
142,12 ♦- 14i,i3
182,16
*— 181,17
<— 2 2 i,2 i
132,12 *— 13i,i3
28 i ,27
282,26
235,19 *— 244,2o
377,31 *— 386,32
222,20
Experiment
Frequency Error
268204.17
0.05
356421.694 0.018
0.05
359605.80
0.03
445993.46
450038.25
0.05
239861.28
241273.22
243382.32
0.04
268663.71
0 .0 2
358750.88
0.04
359948.80
246551.29
0.08
0.04
268599.05
JPL Database
Frequency Error Source.
268204.31 0.03
C
356421.70 0.02
C
359605.77 0.03
C
445993.40 0.04
C
450037.79 0.04
C
239861.24 0 . 0 2
C
241273.21 0 . 0 2
C
243382.32 0 . 0 1
C
268663.68 0.05
E
358750.88 0 . 0 2
C
359948.79 0 . 0 2
C
246551.40 0 . 0 2
c
268599.21 0 . 0 2
c
Table 6.17: Observed O3 (020) transitions and JPL catalog110 frequency values. Errors for
frequencies from our experiments represent one standard deviation or half the difference, if only
two values are available, of the frequencies. Errors for the JPL data are the errors reported in the
catalog. The symbol C in the Source column denotes a frequency calculated from experimental
obtained constants, while the E denotes a measured quantity.
Transition
161,15
16o,i6
182,16
82,6
*— 181,17
*— 81,7
Experimental
Frequency Error
240619.78
247821.68 0 . 0 1
267852.16
JPL
Frequency
240619.88
247821.86
267852.20
Database
Error Observed
0.06
C
0.05
C
0.07
C
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187
Table 6.18: Observed O3 asym 180 transitions and JPL catalog110 frequency values. Errors for
frequencies from our experiments represent one standard deviation or half the difference, if only
two values are available, of the frequencies. Errors for the JPL data are the errors reported in the
catalog. The symbol C in the Source column denotes a frequency calculated from experimental
obtained constants, while the E denotes a measured quantity.
Transition
202,18 *— 2 0 i,g
7 i ,7 <— 60,6
122,10 *— 1 2 i,n
1 6 9 ,7
16g,8
2 I 2.19
21i,2o
52,3 *— 5i,4
111,10 *— 10l,9
73,5 ♦— 82,6
242,22 ♦— 24i ,23
45s,38
467,39
156,10 *— 146,9
152,14 *— 15i,15
Experiment
Frequency Error
240507.51
240636.52
240727.14 0 . 0 1
244355.21
245795.87
268188.85
268462.31 0 . 0 1
270077.90
270744.18 0 . 0 1
271291.79
357241.70 0.03
358459.84
JPL Catalog
FVequency Error Source
C
240507.47 0 . 0 2
240636.51 0 . 0 2
C
240727.17 0 . 0 2
C
244355.16
C
245795.89 0 . 0 2
268188.86 0 . 0 2
E
268461.72 0 . 1 2
C
270077.90 0.15
E
E
270744.15 0.04
271291.82 0.04
E
357241.56 0 . 1 2
358459.90 0 . 1 2
E
Table 6.19: Observed O3 sym l80 transitions and JPL catalog110 frequency values. Errors for
frequencies from our experiments represent one standard deviation or half the difference, if only
two values are available, of the frequencies. Errors for the JPL data are the errors reported in the
catalog. The symbol C in the Source column denotes a frequency calculated from experimental
obtained constants, while the E denotes a measured quantity.
Transition
202,18 *— 20i,i9
62,45
61,5
7 l ,7 ♦— 60,6
52,4
5i ,5
Experiment
Frequency Error
238716.21
242998.15 0 . 0 1
239965.08
270476.68
_______ JPL Catalog
Frequency Error Source
238716.14 0 . 1 0
E
242998.11 0 . 0 2
C
0
.
1
0
239965.03
E
270476.67 0 . 1 2
E
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
188
10
5
0
-5
-10
90.300
90.304
90.308
90.312
Source Frequency (GHz)
Figure 6 .6 : Unfitted spectrum showing the O 3 (001) 13o,i3 «— 1 2 i,i2 transition (A) at
270,923.3550 MHz and the 16o,i6 *— 15i,is l 6 0 I7 0 l60 spin state transitions near 361,250
MHz. The discharge had a potential of 1500 V, a current of 16 mA ,and an initial
pressure of O 2 a t 22 mTorr. A magnetic field of ~ 2 0 0 Gauss was applied. The cell
wall tem perature was at ~ 85 K. The lock-in amplifier had a sensitivity of 10 fxV. The
modulation used FM side bands at 2.00 MHz, with an AM frequency of 55.555 kHz and
an amplitude of -15 dbm.
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189
2.0
1.8
‘co
e
<x>
1.6
90.3120
90.3125
90.3130
90.3135
Source Frequency (GHz)
Figure 6.7: The line (at A) is composed of transitions of the spin hyperfine structure of
the 16o,i6 *— 15i,i5 l6O l7O ieO transition. Here the quantum number format is N k- uk +1A full description of the transitions is given in Table 6.20. The initial pressure of O 2 was
22 mTorr. The dischrge had a current of 16 mA and a potential of 1500 V. The applied
magnetic field was 200 Gauss. The tem perature was 85 K. The lock-in sensitivity was 10
fiV. A FM side band frequency of 2.00 MHz, and an AM frequency of 55.555 kHz, with
an amplitude of -15 dbm, were the modulation settings.
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190
10
5
>
¥'C/3
C
o
cz
0
-5
-10
89.540
89.545
89.550
89.555
89.560
Source Frequency (GHz)
Figure 6 .8 : A unfitted spectrum showing ozone transitions for three different states. Peak
A is the O 3 (100) 62,4 «— 61,5 transition a t 268628.3831 MHz. Peak B is the O 3 3 0 3 , 2 7
*— 302,28 transition a t 358,199-8247 MHz. Peak C is the O 3 (010) 222,20 *— 2 2 i,2 i tran­
sition a t 268,663.7156 MHz. This spectrum clearly shows the convolution of the three
harmonic ranges into the single source frequency spectrum. A spectrum of this type can
be simplified by using frequency cutoff filters. The pressure was 27 mTorr, the discharge
current was 55 mA, the discharge potential was 930 V, and the tem perature was ~ 90
K. Modulation param eters include 2.0 MHz FM sidebands w ith an amplitude of -16 dbc.
The AM frequency is 19 kHz at a power of -13 dbm.
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191
Table 6.20: Calculated transition frequencies for l6 0 170 16 O hyperfine structure from the JPL
catalog. 110
Frequency (MHz) Ai/ (MHz)
361250.193
0.069
361250.554
0.067
361250.764
0.026
0.026
361250.780
361250.826
0.027
361250.865
0.027
0.066
361250.926
0.028
361250.976
N’ K_i
16
0
16
0
16
0
16
0
16
0
16
0
16
0
16
0
J N” K_i K+l
J
K+i
16 18 15
1
15 18
16 17 15
1
15 17
16 17 15
1
15 16
16
15
1
16
15 15
16 18 15
1
15 17
16 15 15
1
15 14
16 16 15
1
15 16
16 19 15
1
15 18
a reasonable S /N of ~ 5 for the unidentified # 1 in Fig. 6.9. W ith these two unknowns,
and a significant number of intense transitions for vibrationally excited ozone, extensive
effort was made to determine which observed peaks were assignable and which were not.
Assignment of a line begins when it is first observed. A simple test is conducted to
determine if the corresponding molecule could be a transient or a stable species formed
in the discharge. The line is tuned up while the microwave program is running in the
rapid scanning mode, the discharge is then shut off rapidly, and the time decay of the
line intensity is observed. If the line intensity disappears immediately, the corresponding
species exists only within the discharge and is of transient nature, such as an ion or
unstable excited state. If the line intensity drops off slowly, then the molecule is produced
in the discharge but is a stable species th a t persists until pumped away. All ionic species
are transient, b u t not all transient species are ionic, so this test is not definitive.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
192
10
5
&
/%
0
ij v
y
CO
ca>
•5
-10
89560.00
89565.00
89570.00
Source Frequency (GHz)
Figure 6.9: Spectrum of the unidentified line # 1 , in an O 2 discharge, following three base­
line suppressions and vertical scale expansion. The signal to noise ratio is acceptable with
a value of ~ 5. Three fits using a Lorentzian line shape model were made, and average
frequency, linewidth, and integrated intensity values were found to be 268,695.86 ± 0.01
MHz, 0.30 ± 0.03 MHz, and -0.364 ± 0.015 MHz V, respectively. T he lock-in amplifier
sensitivity waslO /iV. The discharge pressure was 30 ± 1 mTorr. the current was 63 ± 1
mA, and the potential 1090 V. T he cell wall tem perature was ~ 85 K. Sidebands for
FM are a t 2 MHz, while AM modulation is a t 21 kHz with -13 dbm power.
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193
next step is to check against the JPL catalog , 110 to determine if the line of interest
was reported in the literature. During the active search period only unidentified lines
# 1 and # 2 were found th at were thought to possibly be due to transient species.
A
series of experiments was performed in an attem pt to provide information on the physical
and chemical properties of the unidentified # 1 species.
unidentified line
# 1
line.
# 2
Because the intensity of the
is so small, it is not suitable for the tests used with the unidentified
After completion of the final search a complete review of all obtained spectra
was made in an attem pt to assign all the neutral lines and find any unidentified lines
overlooked in the initial assignment phase.
Each potential line was graded, using the
method described previously, and where possible assigned.
The remaining lines were
checked for multiple observation, but no lines other than unidentified
# 1
and
#2
were
observed more than once. There are several potential reasons for this including: improper
source tuning, contamination, baseline suppression artifact, and limited scanning.
The
effect of source timing on the signal intensity is shown in Figs 3.5 and 3.7. An improperly
tuned source can result in a weak line being missed altogether. As w ith the case of the
HO 2 line in Fig. 6.5, the line arises from a contaminant and could not be reproduced in
later scans.
A spike in the baseline may result in the creation of an artifact line when
the baseline suppression routine is applied (Section 2.3.4). Until each possible line can
be rechecked, the possibility exists th a t they may be real lines. These unidentified lines
are listed in Tables 6.21 and 6.22.
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194
Table 6.21: Summary of unidentified and non reproduced transitions below a source frequency
of 89500 GHz.
Source Freq. Fit Frequency Intensity Linewidth
(MHz)
(MHz)
(MHz)
MHz V
79886.602
319546.41
-0.074
0.50
79887.601
319550.40
0.67
-0.077
79992.369
319969.48
-0.063
0.50
79992.390
319969.56
0.99
-0.159
80992.916
323971.66
-0.090
0.31
80994.653
404973.27
-0 . 1 0
0.51
81002.792
324011.17
-0.037
0.39
82690.066
248070.20
-0.194
0.31
89073.890
356295.56
-0.054
0.91
89192.214
445961.07
-0.090
0.42
89193.050
445965.25
-0.058
1.45
89193.983
445969.91
-0.104
0.58
89194.482
445972.41
-0.060
0.54
89196.183
0.82
267588.55
-0.262
89196.277
356785.11
-0.128
0.57
89196.355
445981.77
-0.135
0 .6 8
89197.060
445985.30
-0.008
1.03
89197.267
445986.33
-0.078
0.79
89200.731
446003.65
-0.052
1.24
89202.296
267606.89
-0.118
0.27
89206.595
267619.79
-0.197
1.17
89303.128
357212.51
-0 . 0 1 1
0.99
268114.56
-0.131
0.64
89371.521
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195
Table 6.22: Summary of unidentified lines with source frequencies > 89500 GHz.
Source Freq. F it
(MHz)
89510.006
89514.535
89519.250
89520.678
89528.452
89536.339
89537.814
89559.629
89682.614
89682.615
89684.631
89684.636
89692.285
89692.289
89704.083
89776.682
89778.777
89894.534
89917.203
89917.210
89917.512
89983.307
89983.360
90002.491
90180.474
90182.597
90392.897
90397.010
Frequency Intensity Linewidth
(MHz)
MHz V
(MHz)
358040.02
-0.117
0.40
358058.14
-0.673
0.67
-0.114
358077.00
0.54
268562.03
-0.044
0.25
447642.26
-0.036
1.24
447681.69
-0.172
1.29
447689.07
-0.042
0.90
268678.89
-0.035
0.75
448413.07
-0.107
0.46
448413.08
0.52
-0 . 1 2 0
448423.15
-0.072
0.32
448423.18
-0.093
0.38
448461.42
-0.123
0.61
448461.44
-0 . 1 1 0
0.56
358816.33
-0.007
0.59
269330.05
-0.076
0.42
448893.89
-0.026
0.49
359578.14
-0.016
0.83
269751.61
-0.032
1 .1 2
269751.63
-0.025
0.87
269752.54
-0.070
0 .8 6
449916.54
-0.084
1.24
359933.44
-0.082
0.30
450012.46
-0.075
1.39
360 721.90
-0.037
0.60
360730.39
-0.292
1.65
271178.69
-0.052
0.23
451985.05
-0 . 0 2 0
1.04
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196
6.4
The Unidentified Line at 268695 MHz
Of all the unidentified lines observed in the microwave spectroscopic study of oxygen
discharges, the line at 268695 was the most studied. Observed early in the O 3 search, its
assignment has proved elusive. Several different studies were undertaken in an attem pt
to elucidate the identifying properties of the species.
These efforts are detailed in the
subsequent sections.
6.4.1
Zeeman Effect
For an open shell molecule like O3 , the interaction of a magnetic field with the spin
of the electron will split the line. As discussed previously (Section 6.3.2), the application
of an axial magnetic field, using the solenoid magnet, will result in a _L type splitting
pattern.
For an asymmetric top this splitting is expected to be moderate (Table 6.11)
for the Q branch transitions we are considering.
If we use the N = 10 case previously
considered, the splitting pattern would a doublet with a separation from ua of ~ 26
MHz for a magnetic field of 100 Gauss. Searches near the unknown line in negative glow
discharges revealed no clear peaks, especially compared with the main line. From this we
assume th a t the species corresponding to the unknown is most likely not O 3 , but some
other species.
6.4.2
Electric Field Doppler Shifts
An ion in an electric field will be subject to a force dependent on the magnitude and
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197
(B)
Figure 6.10: This diagram shows the effect of an electric field between two electrodes on
the velocity of ions in a glow discharge. Case (A) is referred to as positive polarity and
case (B) the negative polarity. Microwave radiation propagates in the direction of the hu
arrow. Transition frequencies of cations will be blue shifted for case (A) and red shifted
for case (B), while anions will have shifts opposite the cation case.
direction of the field, and on the magnitude and sign of the charge carried by the ion. As
the frequency of absorption is measured a t a fixed point in the laboratory frame, motion of
the ion relative to th at point will introduce a shifting of the observed transition frequency.
As shown in Fig. 6.10, anions in the discharge will experience a force directed towards the
radiation source, when the cathode is opposite to the source (case A). As the detector is
also opposite the radiation source, the force accelerates the ion away from the detector,
resulting in the red shifting of the light.
W hen polarity of the electrodes are reversed,
the transition frequency will be blue shifted. For cations the opposite shifting behavior
will be observed.
Provided the magnitude of the shift is large enough to be observed,
and pressures are kept relatively constant to avoid pressure induced line shifts (Chapter
7), this test can reliably be used to determine the ionic nature of a species, as was done
by Civis et al.3 in their identification of SH~ and SD- .
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198
The movement of an ion within a discharge can be characterized by the drift velocity
of the ion. Using the drift velocity, the magnitude of the Doppler shift can be expressed
as
(6 .22)
where c is the speed of light in a vacuum, va is the center frequency of the undisturbed
line, and v<* is the drift velocity of ion. The drift velocity, in cgs units, is given by
(6.23)
where E is the electric field, D the ionic diffusion coefficient, e the ionic charge, k Boltzm ann’s constant, and T the gas tem perature .8 The diffusion coefficient is related to the
ion mobility K by the Einstein relation
Calculation of the magnitude of the shift requires knowledge of the electric field acting
on the ion, the ion diffusion coefficient, and the translational tem perature.
Using the
measured ion mobility 112 of O j and reasonable estimates of the gas tem perature, pressure,
and the electric field, as listed in Table 6.23, the approximate value of the Doppler shift
of an O j line a t 268,695 MHz is Su — 2.20 MHz.
The Doppler shift studies on this line were conducted by measuring the transition
frequency multiple times at or near ±1000 V. Multiple fits to the same spectra were
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199
Table 6.23: Values used to estimate the magnitude of the Doppler shift that would occur for 0 3
at a frequency fo 268,695 MHz, a pressure of 30 mTorr and a temperature of 85 K.
Dp (cm 2 torr s-1)a
D (cm 2 s - 1 ) 6
K (xlO5 cm 2 V - 1 s-1)
5u (MHz)
a) Bbhringer et of. 112
b) for 30 mTorr
54.0
1800
2.46
T (K)
E (V cm "1)
u (MHz)
85
1
268695
2 .2 0
made, from which the average and standard deviation, a, were determined. As spectra
with a > 0.01 MHz typically had low S /N ratios, it was decided minimize the effects
of noise by rejecting all average frequencies with a > 0.01 MHz.
Pressure dependent
frequency shifts were held constant by maintaining the pressure at 30 ± 4 mTorr.
The
resulting d a ta sets are shown in Fig. 6.11. As one point from the negative polarity data
set seemed to be an outlier, it was tested using Dixon’s Q test at a 95% confidence level
and rejected . 113
The d ata set for the positive polarity is actually made up of several
smaller sets a t slightly different voltages, but the errors introduced by the relatively small
variations in discharge voltage are small.
After filtering the d a ta using the a test, the distribution of the points is quite broad.
It is im portant to determine if this distribution is due to effects of the baseline or if
it is due to a n o m a lo u s dispersion.
In most experiments of this type, we would have
tuned the instrum ent to center the transition on a n extrem a of the baseline to m in im ize
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200
1.1
1.0
fsl
0.9
CO
CO
03
0.8
O
c=
03
3
S ' 0.7
0.6
•800
•400
0
400
800
1200
Discharge Voltage
Figure 6.11: Plot of the frequency residuals for multiple measurements of the unknown
line near 268,695 MHz vs the discharge voltage. Point A corresponds to a point rejected
by Q testing. The frequency residual is found by taking the transition frequency and
subtracting out 268,695 MHz.
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201
the anomalous dispersion effects.
The line near 268,695 MHz was relatively weak and
required significant amounts of signal averaging to acquire a good spectrum. This maHp
it very difficult to m aintain the line at an extrema of the baseline.
Rejection of all the
points th at were not at an extrema would leave too few points for a meaningful analysis.
It was then necessary to include lines not at the baseline extrema, potentially biasing the
analysis. As detailed in Section 3.3, the magnitude and direction of the frequency shift
created by anomalous dispersion is dependent on the sinusoidal function of the baseline.
The direction of the shift is dependent on the portion of the sine function the peak rests
upon.
A line in the positive portion of the sine function should be blue shifted, while
a line in the negative region will be redshifted.
If the effect of anomalous dispersion is
strong, a plot of the subsets defined by the sign of the baseline function should show a
clustering of positive functioned points at higher frequencies and the negative ones a t lower
frequencies.
Most of the other frequency shifts are expected to be systematic, and the
sum of these should produce a uniform shift, so the effects of anomalous dispersion should
be seen. A plot of the d ata segregated as mentioned above is shown in Fig. 6.12. No
clustering is apparent in this plot. Indeed, the measurements from the negative polarity
condition have a near uniform distribution of both subsets from high to low frequencies.
From this we can say th a t there is no anomalous dispersion sufficient to bias the d ata in
a given direction.
Another potential source of frequency shifting is the distortion of the line shape created
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202
0.90
0.88
INI
CO
3
■o
0.86
0.84
'to
d>
OC
Q
)
3
0.82
S'
0.80
0.78
-1200
•800
•400
0
400
800
1200
Discharge Voltage
Figure 6.12: A plot of the upper (ffl) and lower (®) subsets defined by the sign of the
baseline function where the transition is observed. T he upper set corresponds to a
positive baseline function, the lower to a negative baseline function. From the plot there
seems to be no observable dependence of the frequency measurement on the sign of the
baseline function and, hence, on anomalous dispersion.
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203
by the addition of the baseline function to th at of the absorption function.
Although
any effect of this type should be minimized by the baseline suppression routine, a test
similar to th a t done for the anomalous dispersion was performed. In the baseline slope
test, the d ata were divided into five subsets: negative slope, positive slope, negative near
zero, positive near zero, and zero. The peaks in the near zero subsets were those where
there was ambiguity if the slope was truly zero or not. The plot of these five subsets is
shown in Fig. 6.13.
From this plot there is no apparent dependence of the transition
frequency on the sign of the baseline is observed.
The preliminary analysis strongly suggests that the scatter in the d a ta points is ran­
dom, but the two d ata sets have different averages.
It was desirable to know if the
observed difference was real, or if it was simply chance. The noise filtered d a ta set con­
tains 17 elements from the negative polarity and 21 points from the positive polarity sets.
Given the small sample size and the difference in the means of the two sets the Student’s
t-test for two samples assuming unequal variances was performed on the d a ta sets using
the statistical package in Excel 2000.
W hen performing the t test is was assumed th a t the difference observed between the
means of the negative and positive polarity d ata sets was due to chance.
This is done
by setting the null hypothesis value to zero when performing the t test.
If the t stat
value calculated is larger than the t Critical value then the null hypothesis is not correct,
and the difference between the two means is not due to chance.
The t critical value
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204
0.90
0.88
M
OS
0.86
0.84
CO
CD
0C
0.82
<X>
3
O'
Q>
0.80
0.78
-1200
•800
•400
0
400
800
1200
Discharge Voltage
Figure 6.13: A plot showing the lack of frequency dependence on the baseline position of
the measured transition. Five classifications were used to sort the peaks: minus slope
(EB), positive slope ( O ) i minus to zero slope (■), positive to zero slope (•), and zero slope
(-*-). As was expected, there is no clear dependence of the transition frequency on the
sign of the baseline.
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205
Table 6.24: Results of the t-Test: Two sample assuming unequal variance calculations. With a
t stat value greater than the t Critical two tail test the hypothozied mean difference of zero is
not true and the difference between the means of the two data sets is real. This test is for a 95
% confidence level.
Mean
Variance
Observations
Hypothesized
Mean Difference
df
t Stat
P (T < = t) one-tail
t Critical one-tail
P (T < = t) two-tail
t Critical two-tail
Negative Positive
0.8483
0.8322
0.000594 0.000372
17
21
0
30
2.21929
0.01709
1.69726
0.03417
2.04227
is dependent on the level of significance desired.
Our calculations used a 95% level of
confidence, or a 5% line to test against, and the results are summarized in Table 6.24.
The t sta t value was determined to be 2.22. This is greater than the t critical value of,
2.04. This difference is statistically significant and suggests there is a real frequency shift.
While this test indicates that the shift is real, we have not determined what is causing
the shift.
6.4.3
Composition Tests
If it is suspected th a t the unknown species is a result of contamination, the suspected
contaminant is adm itted to the system in a controlled fashion. The dependence of the line
intensity is monitored, and the effects are noted. The premise behind this experiment is
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206
th a t a small amount of contaminant is involved in the synthesis of the unknown species,
and th at by varying the amount of potential contaminants the intensity will vary in a
systematic fashion. The response of the intensity to the addition of the contaminant will
provide information on the chemistry occurring in the discharge
Effects of N 2 on the line intensity were investigated by adm itting various amounts of
air into the system. Although not pure N2 gas, the other m ajor constituent of air, 0 2, is
not a contaminant in this case. The small percentage of air th at is neither 0 2 or N2 is
so small as to be negligible.
The plot in Fig. 6.14 shows the relationship between the
pressure of added air, as determined separately from the 0 2 pressure, and the intensity
of the unknown line. No effect is observed until the pressure is approaches 5 mTorr. At
this pressure the magnitude of the intensity appears to increase. Noise in the discharge
prevented the uncertainty of the point from being determined, so it must be considered
carefully and should not be relied upon as a clear indicator of the chemistry occurring in
the discharge. This is especially true with the ambiguous results obtained from the CO
addition experiment, Fig. 6.15. The results are suggestive th a t the unknown is dependent
on N2 either in its formation chemistry or as a constituent.
The apparent decrease in
the intensity a t ~ 1 mTorr is most likely due to the lack of precision in determining the
correct value of gas added, due to outgassing following the shut off of gas flow. W hen CO
is added to the system, no effect is observed, except an increase of noise in the discharge.
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207
1.2
1.0
0.8
N
=
0.6
CO
cQJ
0.4
0.2
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
(mTorr)
Figure 6.14: Plot of the integrated intensity of the unidentified line a t 268,695 MHz as a
function of N 2 pressure. Error bars represent one standard deviation. Unstable discharge
conditions prevented us from recording enough spectra, at 6 mTorr of N2 , to determine
the uncertainty.
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208
0.7
0.6
Intensity (MHz V)
0.5
0.4
0.3
- o >
0.2
0.1
0.0
0
2
4
6
8
10
12
14
16
CO (mTorr)
Figure 6.15: Effect on the integrated intensity of the unidentified line a t 268,695 MHz of
the addition of CO. Error bars represent one standard deviation.
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209
16 -I
14
-
12
-
10
-
>
IM
2
8
-
4
-
IT
t=
a>
c
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
H 2 (mTorr)
Figure 6.16: Effect of H2 addition to the discharge on the integrated intensities of the
unidentified line at 268,695 MHz A , the 62,4 —> 61,5 O3 v l transition at 268,628.29 MHz
©, and the 2 2 2,20 —*22i,2i O3 (010) transition a t 268,663.72 MHz □ .
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210
The experiment where H2 was added to the system is a bit more revealing. In this
experiment, the unknown line, and two known lines arising from the O 3 (101) and the
O 3 (010) species, were studied.
It is extremely interesting to note the real decrease in
the intensity of the two ozone lines without a corresponding decrease in the intensity of
the unknown (Fig. 6.16).
From this, it can be stated with some confidence, th at the
unknown is not ozone.
6.4.4
Summary
None of the tests clearly supports an assignment of the unidentified line to an O3
transition.
unlikely.
The possibility, however, cannot be entirely dismissed, b u t it is extremely
Reproducibility of the line argues against a species derived from a surface
contaminant, especially given the cleansing effects of O 2 discharges .2
Considering the
effects of adding H 2 and N 2 to the discharge mix and the transient nature of the line the
species is likely a closed shell, excited state of a nitrogen containing compound.
6.5
CHFj
Mass spectroscopic studies of CHF 3 discharges show th at the CHF^ ion is produced
readily and in large fractional abundance .30-33 While our studies did not show the large
reported CHF^ abundance (Section 2.4) the observed abundance was thought to be suffi­
cient in the non magnetically confined discharge, th at a magnetically confined discharges
would have a C H F j fractional abundance large enough to provide reasonable transition
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211
intensities.
6.5.1
Preliminary Studies
Unlike O 3 the amount of rotational spectroscopic relevant information for C H FJ
extant in the literature is very sparse. Even ab initio studies were limited to principally
one study by Dearden et al.,lu which was performed using Hartree-Fock (HF) and MollerPlesset (MP2) methods and the 6-31G* and 6-31G** basis sets. Inspection of the values
obtained by Dearden et al., listed in Table 6.25, reveal a great amount of variance. It
was felt th at a new structure optimization calculation, using a more suitable program
and higher theory, would provide a more accurate structure from which to estim ate the
rotational constants and subsequently define a suitable range for microwave searches. The
structure for CHFj was recalculated by D. Olszewski, 115 at CCSD(T)/cc-pVDZ theory
assuming Civ symmetry using the MOLPRO program.
Based on the new structure
CHF^ is found to be a slightly asymmetric prolate top, k = —.96. As Dearden et al. did
not report a dipole moment and the MOLPRO calculation produced only an optimized
structure, a M P2/6-31G(d,p) calculation using Gaussian 94 was performed, and a dipole
value of 3.05 D was obtained. This value was used to estim ate transition intensities.
W hen an asymmetric top possesses a C 2V axis, the dipole must be directed along th at
axis. The dipole is directed along the C-H axis, which is coincident with the B rotational
axis, and the rotational transitions are b-type. Selection rules for a b-type transition are
AAT_i = ±1, ± 3, ± 5 ,... and AK+i = ±1, ±3, ± 5 ,.. .
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212
Table 6.25: Results of CCSD(T)/cc-pVDZ structure optimization calculation using MOLPRO
and assuming C21 / symmetry.
C-F (A)
Theory
1.2170
HF/6-31G*
1.2172
HF/6-31G**
1.2427
MP2/6-31G*
1.2424
MP2/6-31G**
1.2386
CCSD(T) / cc-pVDZ
114
a) Prom Dearden et al.
b) Reference115
C-H (A )
1.0798
1.0816
1.0925
1.0883
1.1052
ZFCF (deg)
118.04
117.90
118.24
119.19
118.306
ZHCF (deg)
120.98
121.05
120.88
120.41
120.847
Reference
(a)
(a)
(a)
(a)
(b)
Once the rotational constants were calculated, the values could be used with the
ASROT program to predict the rotational spectrum. Centrifugal distortion terms were
estim ated by using the reported centrifugal distortion constants116 for HBF2, which is
isoelectronic with CHF 2 • Transition frequencies were then calculated, accounting for the
centrifugal distortion up to the quartic terms. Estimations of the absorption coefficients
(Section6.6.1) were made prior to the search. These values were obtained using estimated
CHF 2 fractional abundance values.
This was necessary, as it is impossible for us to
sample the magnetically confined discharges using our mass spectrometer.
Given the small relative abundance of the CHF 2 ion observed in the discharge, any re­
alistic hope of observing the transition would be within a magnetically confined discharge,
where signal intensities of some ions have been enhanced dram atically compared to the
signal intensities observed in non magnetically confined discharges.2 Initial estimates of
the gamma coefficients are shown in Fig. 6.18 as a function of tem perature.
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213
50
o=
Q
40
30
ffl-
20
10
0
250
300
350
400
450
Transition Frequency (GHz)
Figure 6.17: The Q branch of the predicted C H F j spectrum using the spectroscopic con­
stants in Table 6.26. Several K” series are found in this region: K”= 0 (©), K”= l (EB),
K”=2 (* ), K”= 3 ( O ) , and K” = 4 (□).
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214
2.0
-]
o
X
>0.5 -
0.0 - I
80
120
160
200
240
280
320
360
400
Temperature K
Figure 6.18: Values of the absorption coefficient for the 113)9 —* l l 2,io transition as a
function of tem perature. Two fractional abundance values are considered, f3 = 0.15 (®)
and /3 = 0.05 (EB). In the temperature range where our instrum ent was able operate
without condensation of the CHF3 gas, ~ 200 K, the y values are very small. Comparing
these values w ith the sensitivity thresholds of the spectrometer, these lines are near the
limits of detection.
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215
Table 6.26: Summary of Predicted CH Fj spectroscopic constants and the estimated centrifugal
distortion constant values from HBF2 . The uncertainties in the rotational constants created by
various errors in the bond length and bond angle are also provided.
Value
Constant
81922
A (MHz)
11760.9
B (MHz)
10284.46
C (MHz)
Dj (kHz)®
9.931525
Djk (MHz)® -0.127330851
D k (MH z)® 2.411650449
dj (kHz)®
1.90608
dK (kHz)®
44.639097
/i (D)
3.05
a) Reference 116___________
6.5.2
Effects of Structure Uncertainties
Bond Length
Bond Angle
Combined
+0.001 A
± 0 . 0 0 1 ± 0 . 0 1 + 0 . 0 1 -0.01 +0.05
-0 .0 1 °
±140
+1400
-24
+80
-160
+11
±18
+190
- 1 .0
-5.9
+ 2 .0
-17
±16
+160 +0.63
- 1 .2
-3.3
-16
Experimental
The search region was selected based on the desire to have a large concentration of
peaks and low J values. Inspection of Fig. 6.17 showed th at the K” =2 branch in the 352.5
to 357.5 GHz range (Fig. 6.19) would be ideal. Following the establishment of the search
region several initial studies showed th a t a pure CHF 3 discharge could be maintained if
the negative glow mode and magnetic confinement were used.
As determined by mass
spectrometric characterizations (Section 5.2), the C H F j signal was highest in Ne and
CHF 3 discharges, but no study of pure CHF 3 discharges was possible, because of a lack
of stability.
Given the limited fractional abundance of ~
6%
obtained under the best
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216
30
25
20
15
10
5
0
352.5
355.0
357.5
Transition Frequency (GHz)
Figure 6.19: The predicted Q branch spectrum of CHF£ in the search region 352-358 GHz.
The observed series are the K” = 2 (* ) and the K” =1(EE). Numbers offset from the symbols
correspond to the J ” level.
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217
conditions, and considering the ion chemistry of CHF 3 discharges, it was decided that a
pure CHF 3 discharge in the negative glow mode would most likely provide the greatest
concentration of C H FJ •
The first search covered the GDF range between 88,700 and 89,600 MHz. Many lines
were observed, with one of the principal species being CHF 3 . A symmetric top, CHF 3 has
transitions th at are characterized by K intensity pattern, where due to the equivalency
of the fluorine atoms, every line corresponding to a K” value divisible by three is more
intense, by a factor of three, than the immediately adjacent K lines. An example of this
is the J= 16 —►17 CHF 3 transition, as shown in Fig. 6.20, where the K splitting and
the intensity characteristics are plainly obvious.
a m ajor complication.
The presence of CHF 3 transitions is
The spectral regions covered by the J = 16 —►17 transition is
nearly four times a typical scan range, in the unmultiplied source frequency frame. These
strong lines often obscure small lines, as is illustrated by comparing the intensity of the
line near GDF 87,905 with th at of the adjacent CHF 3 lines.
Because of the large number of observed lines and the relatively few third harmonic
CHF 2 lines expected within the search region, see the 240 - 270 GHz portion of the
spectrum in Fig. 6.17, it was decided to focus on the region where the fourth harmonic
lines (352-358 GHz), were expected by filtering out the third harmonic.
Although the
sensitivity of the instrument is reduced (Section 3.2), the removal of the third harmonic
lines greatly simplified the spectrum and allowed for a much larger search region to be
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218
2
[ 1i 1i 1i '1 II 1i '1 i1 i1 || i1 i1 i1 1i |I »m» i1 i1 || 1i i11i i1 I| i1 i1 i1 i1 fr tt rr ti ii || i1 rt i1 rr || i1 1i i1 17
r f i1 m
i i i1 || i1 i1 i1 i1 ||
m
1
0
’tn
c
'1
03
-S
-2
•3
.4
.......................1
..................................... 11 I
1 1
1 11 1
1 1T
1 T
r 11 1« 1111 11 11 11 1111 II 11 11 11 11 1i 11 11 11 11 I1 11 11 1i 11 111« 11 1«»1 l1 ■1 ■1 .............
I ....................
»
87.90
87.91
87.92
87.93
87.94
87.95
Source Frequency (GHz)
Figure 6.20: This is the J = 16—>17 transition of CHF 3 with a K’ = 0 transition frequency
estim ated to be 351,638.54 ± 0.15 MHz. Notice the spikes in the spectrum. Even
though the cell had been recently cleaned, there is extensive noise. A ttem pts to reduce
the sparking were unsuccessful, and pure CHF 3 discharges were observed to have excessive
noise.
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219
covered.
As an aid in assigning lines, a catalog of stable neutral lines in the 88,700-89,600 MHz
GDF region was created, by searching with only CHF3 present and no discharge.
region was searched with and without the third harmonic being filtered out.
The
Although
many lines observed when a discharge is present will not be observed in the gas, enough
of the lines are present to provide a first source for cross checking a newly observed line.
Several experimental difficulties are encountered with CHF 3 discharges. The most
im portant of these is the problem with deposition. It does not take long for the system
to develop a brownish film on the glass walls and to have significant deposition of material
on the electrodes, as well. The deposition occurs to such an extent th at it is possible to get
significant CHF 3 signal in a pure Ar discharge, where the source of the CHF 3 is from the
deposited m aterial (Fig. 6.21). Deposited m aterial on the interior surfaces of the cell, and
particularly the electrodes, create serious problems in the microwave search. As material
is deposited on the surface of the electrode, the resistance increases and it takes a larger
voltage to obtain the same discharge current. Eventually, if left uncleaned, the electrode
is unable to initiate a discharge. During the deposition process, it is not uncommon to
have excessive sparking in the discharge. This sparking produces RF radiation observed
in the spectra as spikes, see Fig.6.20. Scrubbing with an O 2 discharge, can clean most of
the deposits off, but eventually the vacuum system must be opened up and cleaned.
The final search used a filter to remove the third harmonic, resulting, as expected, in
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220
4
2
0
c
Q)
-2
-4
89655.00
89660.00
89665.00
89670.00
89675.00
89680.00
Source Frequency (GHz)
Figure 6 .2 1 : Spectrum of the J= 12—+13 transition of CHF 3 near 268,971 MHz, obtained
from CHF 3 liberated from the surface of the discharge cell by a pure Ar discharge. The
pressure in the discharge was 26.4 ± 0.2 mTorr, and the gas was composed principally
of argon. The discharge voltage was 1200 V, the discharge current was 550 mA, and the
tem perature was 296 K. The lock-in amplifier scale is 10 /iV, and the time constant was
3 mS.
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221
a greatly sim plified spectrum , w ith few lines being observed.
A fter prelim inary testing
two lines rem ained promising: one near 89,690 MHz and th e other near 88,943 MHz, as
shown in Figs. 6.22 and 6.23, respectively.
A ssum ing th a t th e unidentified lines were part o f a series, an additional line was
sought. U sing th e difference betw een the source frequencies o f the tw o unidentified lines
the final search w as extended to cover the frequency range betw een 87,900 MHz to 88,635
MHz. Several lines were found in this range w ith only one line, at 88623.250 MHz, being
considered a good candidate
6.5.3
Line A ssignm ents
M ost o f the lines observed could be assigned using either the JPL catalog 1 1 0 or other
literature sources. T he line at 88,623 was determ ined to be part o f a grouping o f neutral
lines.
A m biguity o f th e original transient test on th is cluster, did not rule out the
possibility th at 88,623 was a transient species.
T he neutral character o f this line was
determ ined by com parison o f the series o f peaks near 88,623 MHz to a series o f neutral lines
near a 88,065 M Hz source frequency having a very sim ilar distribution . Observed lines
are listed in T able 6.27 w ith the assignm ent, where known. W hen m aking the assignm ents
the possible fragm entation products o f CHF 3 were considered. T hose products considered
were: CH F 2 , C H F, CF 2 , COF 2 , and C F. O f th ese no transitions for CF are expected to
be w ith in th e spectral range o f th e search , 1 1 8 and no spectral patterns consistent w ith
the extensive hyperfine structure o f CHF 2 were observed.
A ssignm ents for th e COF 2
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222
10
5
&
"co
c=
03
0
•5
-10
89685.00
89690.00
Source Frequency (GHz)
Figure 6 .2 2 : O ne o f the in itially unidentified lines observed in a pure CHF 3 discharge.
T his line was determ ined to be the 6 2 , 5 to 5 ^ 4 o f COF 2 , at a frequency o f 358784.81 MHz.
T his spectrum is an average o f 70 scans w ith one 4th harm onic baseline suppression and
a vertical expansion o f 0.5. T he lock-in am plifier sen sitivity is 5 fiV w ith a tim e constant
o f 3 m s. Discharge current, potential, pressure and tem perature, are 8 mA, 1700 V,
14.4 mTorr, and 295 K, respectively. T he negative glow m ode is sustained by an applied
m agnetic field o f 250 G auss.
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223
>
CD
•0.5
•
1.0
u —
88940.00
88945.00
88950.00
88955.00
Source Frequency (GHz)
Figure 6.23: T he second o f th e in itially prom ising lines th at spurred th e search from 87,900
MHz to 88,635 M Hz. T h is line was later identified as the 2 8 3 , 2 6 - 2 7 3 , 2 5 CF2 line at
355,775.1582 M Hz. T he discharge had a pressure, voltage, current, and tem perature o f
12.3 mTorr, 1875 V , 9 m A , and 200 K, respectively. T he applied m agnetic field had
astrength o f 250 G auss. T he lock-in am plifier sen sitivity is 5 fiV.
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224
4
2
>
¥'co
0
c
03
C
•2
-4
88620.00
88625.00
88630.00
88635.00
Source Frequency (GHz)
Figure 6.24: T he spectral pattern observed near 88,623 MHz. T his pattern m atches a
pattern observed for a series o f C H F 3 lines near 88,065 MHz. B ased o n th e sim ilarity,
the lines are though to be an unspecified C H F 3 transition. T he third line is near 88,624
MHz G D F.
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225
Table 6.27: Sum m ary of lines observed in a C H F 3 negative glow discharge in th e source range
of 87.9 GHz to 89.8 GHz w ith th ird harm onics filtered out.
Source
Frequency0
89633.914
89761.156
89863
87905.109
88943
89429
89669
89661
89680.203
89688.508
F it
Frequency 0
358535.27
358684.54
359452.65
351620
355775.19
357716.75
358679.11
358645.17
358720.72
358754.03
Au
0.612
0.511
0.658
0.453
0.501
0.415
0.491
0.670
Species
NA
NA
NA
c f2
c f2
c f2
c f2
c o f2
c o f2
c o f2
Literature
TVansition
Frequency 0
351620.28*
355775.16*
357716.74*
358679.34*
358645.17°
358720.94°
358754.81°
301,30 - 29 i ,3o
2 8 3 , 2 6 - 273 , 2 5
274i24 - 264,23
153,12 - 152,13
52,3 - 4 i ,4
143,11 " 142,12
62,5"5l,4
a) A ll frequency values are in units o f MHz.
b) C alculated from th e constants reported by D eLucia 1 1 7 using A SR O T . 8 9
c) Frequency and assignm ents from the JPL 1 1 0 database.
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226
lines were based on m atches m ade to entries in th e JPL catalog . 1 1 0
T he CF 2 frequencies
were calculated from th e C F 2 spectroscopic constants reported by D e Lucia 1 1 7 using the
ASROT program.
Transitions from CHF 3 are easily identified by there K inten sity pattern and th e broad
range o f the K series.
Several transitions were observed am ong th ese were th e J = 12
—> 13 and the J = 13 —> 14.
6.5.4
Conclusions
Several searches o f pure CHF 3 negative glow discharges, over th e G unn diode fre­
quency range o f 87.9-89.7 GHz and som e other lim ited ranges centered about 87.6 and
90.6 GHz, were conducted.
T hese searches included all harm onics, th e fourth and fifth
harm onic, and the neutral background (no discharge).
A lthough m any lines were ob­
served, none o f the unidentified lines, based on linew idth considerations, were thought
to offer enough prom ise to warrant further investigations. T he linew idth considerations
were used, because at th e tim e it was assum ed th at linew idths o f ionic species would be
broader than those o f neutral species. W hile th is is generally true, th e linew idth function
has been shown to be com plex and dependent on th e rotational sta te o f th e m olecule,
so a sim ple elim ination o f lines using linew idth is not valid (C hapter 7).
G iven th is
fact, further searches for CHF^ m ay prove successful, if several criteria are m et.
First,
th e system m ust be as free as possible from sources o f contam ination to m inim ize loss
o f C H F j through secondary reactions.
Second, a m ore efficient control m echanism for
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227
th e LN2 cooling m ust be developed that w ill allow th e system to operate right above the
point w here C H F 3 condenses out and signal is lost. Third, b etter spectroscopic constants
are required, so the m ost appropriate search region can be utilized. Finally, as m any o f
the observed lines th at are transient m ust be identified, if possible, so th at more effort
can be focused on the more prom ising lines.
6 .6
T he A sym m etric Top Challenge
In a m olecule th at is an asym m etric top, the degeneracy o f the K quantum number is
broken, and the number o f potential energy levels increases accordingly. For a sym m etric
top, changes in th e K quantum number are forbidden, and w hile the asym m etric top does
not have a true K quantum number, changes in th e K _i K i pseudo quantum numbers are
allow ed.
Thus the number o f allow ed transitions o f an asym m etric top is greater than
th at o f a sym m etric to p and th e population o f any given sta te w ill be lower. W hile m any
experim ental m ethods can be used to reduce the im pact o f th e lower populations, including
cooling th e discharge, we have not y et observed a rotational transition o f an asym m etric
top m olecular ion w ith a heavy atom , i.e., non-hydrogen, creating the asym m etry. G iven
th e effort th at has been expended, it w as felt th at a evaluation o f th e su itab ility o f our
experim ental approach was necessary to determ ine under w hat conditions an asym m etric
top m olecular ion could be observed.
In th e past w e have been forced to estim ate th e number density o f th e ion o f inter­
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228
est. W ith th e im plem entation of com puterized d ata acquisition and analysis for th e mass
spectrom eter, we can now determ ine the fractional abundance of the ion o f interest w ith
a greater precision, and we believe to a greater accuracy. An attem pt to provide a quali­
tative m easure o f the system response was undertaken by first calculating the absorption
coefficient for SiF + . U sing fractional abundance values based on mass spectrom etric mea­
surem ents, m easured linew idth, and th e frequency, th e absorption coefficients o f predicted
strong C H FJ transitions and the J = 6-7 SiF+ transition were calculated.
T he CHF 2
transitions had frequencies sim ilar to th e SiF + and a range o f rotational states. W e then
com pare th e
7
values and relate this to the intensity o f the SiF + line. From th is we can
make a qu alitative assessm ent o f the probable inten sity o f th e CHFJ transition. T his of
course assum es th at all other factors upon which th e absorption is dependent are equal.
6.6.1
C alculation o f
7
T he feasibility o f a microwave search for a m olecular ion is dependent on the ab ­
sorption coefficient
7
for the given transition exceeding the sen sitivity threshold o f the
spectrom eter . 3 6 T he peak absorption coefficient can be w ritten 1 8
_
7
8 *>Nf
3ckT A v
’
(
'
where N is the number density o f the ion o f interest, / the fraction o f ions in the lower
sta te o f th e transition, (/x^ l2 is the square o f the dipole m atrix elem ent for the transition,
uQ is the center frequency o f the transition, Au th e h alf w idth at half m axim um . Values
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229
of
7
required for d etection are dependent on the sen sitivity o f th e detector, frequency
range, discharge stability, and the duration o f the averaging tim e . 3 6
T he fraction o f the
population o f m olecules in a given sta te is / = / v / r where f v is th e fraction o f th e sam ple
in th e given vibrational sta te
v
and
/ r
is th e fraction in the lower rotational sta te R. A t
the relative low tem peratures used in these studies /„ =
/B
(2 J + l ) e - ^
£ (2 J +
and
1
/ r
is given as follows:
'
*•
'
J
A bove T = 100A
th e re la tio n sh ip k T / h »
A
is g en erally v alid , 1 8 a n d E q . (6.26) c a n
b e e x p re s s e d a s
/ . - ( 2J+ l)e-/‘^ ( A ) 3,
(6.27)
where A , B and C are th e rotational constants for an asym m etric top m olecule and W is
the energy o f th e lower sta te . 1 8 For a diatom ic the fraction
/ fi=
2
/ r
is given by
(J + l ) ^ |
(6.28)
or
where E q. (6.28) is for the high tem perature lim it . 3 6
T h e num ber o f ions o f the desired typ e are given by 3 6
N = Nion(3,
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(6.30)
230
where N toJl is th e to ta l ion concentration and /3 is the fraction o f th e tota l th at corresponds
to the desired species. Su bstitu ting Eq. (6.30), and the definition o f / and /„ into Eq.
(6.25), we obtain
.....
7
~
3<*TA i/
'
l
)
T he square o f the dipole m atrix elem ents for an asym m etric top m olecule is given
by 1 8
= 2.7 +
1
’
^6 ‘32^
where S is th e transition strength. Values for S were taken from th e output o f th e ASROT 8 9 program . For th e diatom ic case
(6.33)
T ransitions selected for use are listed in Table 6.29.
From F ig 6.17 the selected CHF^
transitions are am ong th e closest to the 267,320 GHz frequency o f the SiF+ transition.
In addition to th e lines close to th e SiF+ line, two other lines had
com parison o f high J and low J states.
7
values calculated for
Fractional abundance o f SiF+ ,0.16, and CHFJ
,0.069, were determ ined from th e SiF 4 N e discharge m ass spectrum show n in Fig. 6.25
and from th e CH F 3 N e discharge m ass spectrum show n in F ig. 5.11, respectively. Values
used in the calcu lation o f
7
are listed in Table 6.28.
For the case o f CHF^ nuclear spin statistics m ust b e taken into account, w hen deter­
m ining
7
, as there are tw o equivalent fluorine atom s. T he CHF^ m olecule shows a 1:3
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231
C
03
"£
)\u\miflWw 11Attwrifii if flfti 11
20
40
60
80
100
120
140
160
i*rHt*
180
m/z Ratio
Figure 6.25: M ass spectrum o f th e ions sam pled from a SiF 4 discharge in the positive
colum n m ode. T his spectrum was acquired at th e sam e tim e as th e microwave spectrum
from w hich th e u and Au values used in the SiF+ were obtained.
Table 6.28: Values used in
Param eter
P
A v (MHz)
Njon
M CD)
A (MHz)
B (M Hz)
C (MHz)
a) see text
b) ref. 1 1 9
c) ref4 8
7
calculations for CHF ^ an d SiF+
CHF+
0.069
0.6280
5E10
3.05“
81972“
11761“
10284“
SiF+
0.16
0.6280
5E10
3.386
19168“
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232
Table 6.29: Comparison of 7 values for CHF^~ and SiF+
7
Frequency (M Hz)
Species
Transition
270542.12
475,43 >—466,40
CHF 2
CHFJ
270438.39
2 6 3 ,2 3 - 2 6 2 , 2 4
266881.54
CHF 2
235,18 —>226,17
457391.51
454,41 —>455,40
CH Ft
CHF£
276588.56
2 i ,1 —>32,2
267 320.977(22)6
SiF+
6 —>7
a) values 7 < 1 0 9 cm l set to zero
b) From Petrm ich et al. 1 2 0
S
7.129
20.721
3.270
7.129
2.667
10
300 K
0.000927
0.0502
0.00813
0.0175
0.0245
5.17
r 6 cm - 1
100 K
0 “
0.0567
0 .0 1 0 2
0 .0 0 0 1
0.228
46.5
statistical w eight ratio betw een rotational states o f K _i K +i sym m etry ee,
00
4 K
0 “
0 “
0 “
0 “
143.6
29065
and oe, eo,
respectively . 1 8 , 8 8
6.6.2
Com parison of Predicted
R esults o f th e
7
7
Values for SiF+ and CHFj
calculations show th at th e relationship betw een th e rotational distri­
bution, the line strength and tem perature, is the single m ost im portant, non instrum en­
tation, factor in determ ining th e success o f a microwave search. C om paring th e
listed in Table 6.29, o f the
2
i,i —>3 2 , 2 and
2 6 3 ,2 3
7
values,
—>2 6 2 , 2 4 transitions o f C H Fj shows, that
despite a factor o f ten betw een th e two line strength values, the
7
values are on ly a factor
o f two different. In addition, a high J sta te reaches a m axim um pop ulation th at is much
sm aller than is possible for the low J sta te, causing maximum
7
values o f th e high J sta te
to rem ain sm all com pared to those o f th e low J sta te. It appears th a t, dependent on the
m olecule, J values greater than ten or so have very little probability o f being found w ith­
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233
out significant tu ning and signal averaging. T his is especially true for those lines w ithin
a fourth or fifth harm onic region where the
7
values o f weak observable lines are orders of
m agnitude larger than th ose for C H FJ in Table 6.29 (Section 3.2). A search should have
the m ost accurate spectroscopic constants possible, and the absorption coefficients for all
poten tial lines should be calculated for a tem perature region near th e condensation point.
T his w ill enable an evaluation o f th e m ost prom ising lines and lim it th e w ide search re­
gions, and m ost im portantly show which, if any, fourth harm onic lines can reasonably be
expected to be observed. In searches for m olecules like C H F j, where there are significant
neutral m olecules th at can cause cluttering o f the spectrum , and filtering is absolutely
essential, the knowledge o f w hat transitions should be observed is o f critical im portance.
T he com parison o f th e SiF + and C H FJ spectra and related
7
values, when considered
in conjunction w ith th e transition distribution predicted for C H F j strongly suggests that
the potential for observation o f CHF^ transitions is sm all.
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234
CHAPTER 7
Theory and Applications of Linebroadening
7.1
Introduction
Line broadening m echanism s are im portant to the interpretation o f rem ote sensing
data obtained from th e study o f planetary atm ospheres, in the stu d y o f th e collisional
relaxation o f m olecules w ithin th e interstellar medium, and as a probe o f th e interm olecular forces betw een th e species o f interest and colliding partner. T he pressure broadening
o f neutral m olecules has been studied extensively , 1 2 1 - 1 2 6 but to date pressure broadening
stud ies o f m olecular ions have been lim ited to a single m olecular ion, HCO +
.8 , 1 2 7 -1 3 1
Here
the results o f th e first pressure broadening stu d y o f th e J = 6 -7 transition o f th e SiF+ ion
are reported and discussed.
Early theoretical work predicted m olecular ion line w idths o f 20-30 tim es as large a
th ose observed for sim ilar neutral m olecules 1 3 2 , 1 3 3 due to the long range nature o f the
m onopole-dipole or m onopole-quadrupole forces.
Anderson et a / . , 1 3 1 however, showed
th at line w idths o f m olecular ions are com parable to or slig h tly larger th an the line
w idths o f sim ilar neutrals. Gudem an , 8 in further studies o f HCO+ pressure broadening,
com pared rate constants obtained from his m easurem ents w ith calculated L angevin rate
constants. From th is com parison, G udem an concluded th at, w hile the m onopole-induced
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235
dipole interaction w ill not change th e rotational state o f the ion , 1 3 4 it w ill produce a
collisional broadening cross section such th a t th e broadening follows th e Langevin m odel.
Buffa et a / . , 1 2 7 , 1 2 8 have shown that collisional broadening o f ions does not follow the
Langevin m odel, but rather th at th e largest relaxation effect arises from th e interaction
betw een th e dipole o f the ion and the dipole induced in the neutral by the ionic charge.
T hey base their conclusions on th e success o f an extension of th e A nderson 1 3 5 -T saoC urnutte 1 3 6 (ATC) approxim ation, using a dipole-m onopole-induced-dipole interaction
potential, in predicting the collisional broadening parameters o f HCO+ in argon.
Our
m easurem ents o f the line broadening o f J = 6 -7 transition o f SiF+ by argon and neon
provide pressure broadening inform ation, as w ill be shown, th at support th e findings of
Buffa et al.
W e have im plem ented a convolution m ethod developed by P ickett9 for extracting the
pressure dependent line w idth param eters from spectral data.
T his allow ed us to de­
term ine pressure broadening param eters to a higher level of precision, as com pared to
those obtained by Gudeman 8 and others 1 3 1 in previous line w idth studies in th is labora­
tory. Our im plem entation o f P ick ett’s m ethod was validated by th e excellent agreem ent
o f th e line broadening coefficient obtained for th e self broadening o f th e J= 21-22 tran­
sitio n o f OCS, as com pared w ith available literature values. P ick ett’s m ethod and our
im plem entation o f it are described in d eta il below.
T h e conclusions readied by G udem an were influenced greatly by th e lack o f preci­
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236
sion in th e HW HM values.
T he values o f th e collisional bim olecular rate constants, kc,
determ ined from his m easured pressure broadening coefficients had uncertainty ranges
th at included th e Langevin rate constant, for th e specific discharge conditions. W ith our
more precise m easurem ents, we have been able to show that the kc values on ly agree w ith
the Langevin values for specific com binations o f tem perature, collisional partner, and the
rotational sta te o f the ion. We have also been able to use the theoretical m odel o f Buffa
et a/ . 1 2 8 to obtain theoretical T values th at agree well w ith experim ent.
T he observed
line broadening behavior in our system s follows the general trends predicted by Buffa et
al.
7.2
T heory o f Line Broadening
T he broadening o f a spectral line can arise from several sources: pressure broaden­
ing, collisions w ith the walls o f the cell, saturation broadening, D oppler broadening, and
m odulation effects. In our studies, the m ost im portant forms o f broadening are, Doppler
broadening, m odulation broadening, and pressure broadening.
D oppler broadening arises from the m otion o f a m olecule parallel to th e direction
o f propagation o f th e electrom agnetic radiation being absorbed . 1 8
T he expression for
D oppler broadening is
A t/ = —\ / ^ ^ - l n 2 = 3.58lxlO '7 J^~ru ,
c V m
VM
(7.1)
w here m is th e m ass, M the m olecular w eight in g /m o l, u the resonant frequency, k
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237
is B oltzm ann’s constant, and T the tem perature in K . For transitions in the 300 GHz
region, at 100 K, and for a typical m olecular w eight o f ~ 5 0 g /m ol, th e Doppler linew idth
is ~ 1 5 0 kHz.
M odulation o f the signal also causes broadening of the line. T h e m agnitude o f the
broadening varies, but it is typically betw een tw o or three tim es th e m odulation fre­
quency . 1 8 In our experim ents, m odulation broadening is usually on the order of 40 - 60
kHz.
Pressure broadening is much more difficult to account for theoretically.
A lthough
collisional line broadening can be m odeled using both im pact theory and sta tistica l m eth­
o d s,18, 1 3 7 im pact theory provides the m ost correct description o f broadening in the pressure
range in w hich our experim ents were conducted . 18
T h e use o f im pact theory in studying collisional broadening o f microwave lines be­
cam e possible because o f the work by A nderson . 1 3 5 , 1 3 7
In his theory o f line broadening,
A nderson was th e first to consider the nonadiabatic processes associated w ith collision
induced transitions. T his theory was later enhanced by T sao and C u m ette 1 3 6 , 1 3 7 and is
known tod ay as ATC theory.
T he ATC theory makes several assum ptions.
1. T h e duration o f collision is sm all com pared w ith the tim e betw een collisions.
2. C ollisions are binary.
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238
3. T ranslational m otion is treated classically.
4. Spectral lines m ust be well resolved.
B ased on these assum ptions and the sim plification o f straight line trajectories, An­
derson, using th e spectral intensity , 1 3 7
/
+oo
dt 0 (f)el4(a,o_w)
( 7 .2 )
•OO
and a correlation function o f the form
0 (f) =
,
(7.3)
obtained th e lin e shape function
8 n 2 Nipit
a “
3ckT W
l2
2
A i/
v {u - ua - A i/ S ) 2 + At/ 2 •
Here
N i is th e number o f absorbing particles, targets, per unit volu m e
p, is the fraction o f these m olecules in th e lower state,
\Pij \2 is th e square o f the dipole m atrix elem ent,
v is th e frequency,
Au is th e HW HM,
A ua is th e sh ift in resonance frequency, and
v 0 is th e resonance frequency.
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,
,
(7,4)
239
T he linew idth and shift are given by th e expressions 1 3 7
27tAi/ =
2nA vs =
Nivno'n + N 2 Vi2 a 'l2
(7.5a)
NiVncr'li + N 2v i 2 cr" 2 ,
(7.5b)
where a ' and a" are th e real and im aginary portions o f th e collision cross section, and vu
and V12 are th e m ean relative velocities betw een the absorber ( 1 ) and th e pertruber (2 ).
T he collision cross section can be expressed as
a = H 2*S{b)db
Jo
,
(7.6)
where b denotes th e im pact parameter, or the distance o f closest approach o f th e colliding
partners.
T he collisional operator, S(b), is a w eight factor th at indicates th e effectiveness o f
a collision in disturbing the absorption or em ission o f a m olecule.
T he m agnitude o f
S(b) is dependent on th e quantum states interacting and the nature o f th e interm olecular
potential. A sum o f com plex and real com ponents, S(b) can be expressed
S ( 6 ) = S\(b) + S 2 {b) .
T he first order term ,5^(6),is im aginary and contributes to th e frequency
(7.7)
sh ift.
Colli­
sion induced frequency shifts arise from adiabatic changes o f sta te.W ith m ost collisions
betw een m olecules having sufficient energy to cause nonadiabatic changes in the sta te
o f a m olecule, collision induced frequency shifts are a weak effect in rotational spec-
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240
troscopy . 1 8 , 1 3 7
T h e real portion o f the collisional operator,
8 2
(b ), relates to the nonadia-
batic processes and contributes to the linew idth.
T he interactions betw een the colliding m olecules can be classified based on th e value
of
8 2 (b).
collision.
If
8 2 (b)
< 1, th e collision is weak, w hile values o f
In th e case o f the strong collision, the
approxim ated.
8 2 (b)
8 2 (b)
>
1
indicate a strong
is not w ell defined and is usually
A nderson 1 3 5 addressed th is in this original work and provided three
approxim ations w hich sim plify the calculation o f cr. T he approxim ation usually em ployed
sets all th e
8 2 (b)
> 1 equal to one.
T his corresponds to th e loss o f coherence betw een
initial and final conditions w hen strong collisions occur.
function goes to on e is the cutoff im pact param eter
60
T he b value where the
5 2
(6 )
• U sing th e bQ value in Eq. (7.6),
and neglecting th e Si(b) term , we obtain
a
=
7t 6q
+ I °° 2itS2 (b)db .
Jb,
(7.8)
D
The evaluation o f th e cr expression is detailed by B im baum . 1 3 7
T he pressure broadening
expression used in Eq. (7.5a) does not account for th e distribution o f velocities, but rather
averages over th e distribution by using th e m ean relative velocities.
T he form o f S(b) is dependent on th e interaction potential betw een the colliding pair.
Two o f th e interactions betw een an ion and neutral perturber are th e m onopole-induced
dipole interaction and th e dipole-m onopole-induced-dipole-interaction.
For an ion of
charge q, and a perturber w ith polarizability a, th e m onopole-induced-dipole poten tial is
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241
o f the form
q2a
Kn =
2
(7.9)
r4
The dipole-m onopole-induced-dipole potential is
Vd =
2
qafi cos 6
(7.10)
where the // is the dipole, cos 6 is the angle betw een p, and th e interparticle axis, and r
is th e interparticle distance.
T he dipole-m onopole induced dipole potential is used by
Buffa et a / . 1 2 7 , 1 2 8 in their extension o f ATC theory to m olecular ions.
Buffa et a / . 1 2 7 , 1 2 8
have extended the basic ATC theory by including the velocity
distribution for b oth straight and curved trajectories.
Pressure broadening and line
shifting are found using,
poo
r + is = n
J
Jo
poo
d v v f ( v ) I dbbP(b,v)
Jo
where n is th e density o f th e perturbing gas at
B oltzm ann distribution o f relative velocity.
1
,
(7.11)
Torr pressure and f(v) is the M axwell-
T he function P(b,v) corresponds to S(b),
and is defined 1 2 8 by
R eP (M )
=
Im P(b, v )
=
2 t?
2
h2
S i ( • ' r i K W J i i J ' ) i2 + £ i ( • « i i « W
. J'
)
iij')
(7.12a)
J'
S I (•'/lltWOIIJ') I2 - S I
J')
(7 42 b )
where K(u;) is th e Fourier transform o f the assm ned dipole-induced-dipole interaction
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
242
potential
+00
? (» ) = /
d t« “ - 2n ^ ”
* (t>
.
(7.13)
—o c
T he m atrix elem ents in Eq. (7.12) can be found exactly using straight line trajectories or
num erically if curved trajectories are used . 1 2 8
Use o f straight line trajectories yields the
following expression for the m atrix elem ents:
I( J / I H W ) | | / ) p -
—
*
+
+ 1 6 9 + 8 |" 3 + * *
m
• (7 -l4 )
Here, k = ujjj>b/v, wj j > = {Ej> —Ej)/fr, a is the polarizability o f the perturber, and fxJJt
is the dipole m atrix elem ent.
We have w ritten a program to calculate the m atrix elem ents using Eq. (7.14). These
values are used to calculate the P (b,v) term using, Eq.
(7.12a).
We assum e ideal
behavior o f the gas w hen calculating the number densities and use the rigid rotor m odel
to determ ine th e energies o f the states in each m atrix elem ent. W hen calculating P(b, v),
we im pose th e strong interaction lim it, P(b, v) = 1 for
6
<
6
0.
We have calculated the pressure broadening coefficients T, for HCO+ , and SiF+ using
both neon and argon collisional partners. T he results o f these calculations are shown in
Tables 7.1 and 7.2.
T he results o f our calculated values agree well w ith Buffa et a/ . 1 2 8
for the Langevin broadening [Eq.(7.15)], and th e J = 0-1 transition o f HCO+ .
As the
J level increases, our values begin to deviate from those reported by Buffa e t al.
Our
calculations differ from Buffa et al. in th at we do not account for any possible differ-
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243
Table 7.1: A summary of experimental and theoretical values reported for the pressure broaden­
ing coefficients of HCO+ by Ar and Ne in literature and in this work. All units are MHz/Torr.
The theoretical values were obtained using ATC theory assuming straight line trajectories and
accounting for the distribution of relative velocities. In our calculations we used B = 44594
MHz131, values of 20 g/m ol, 40 g/m ol and 29 g/m ol were used for Ne, Ar and HCO+ , respec­
tively. The dipole moment of 3.91 D 1 2 8 was also used.
_________________ Argon_________________
Experim ental0
T heoretical
Line
77 K
77 K° 77 K 6 100 K 6
0 — 1
21.49(21)
2 1 .0
20.9
18.1
1 — 2
15.4
17.51(19)
17.2
17.5
3—4
1 0 .2
10.7
14.56(7)
9.9
10.42(40)
5.4
4.5
5.2
7—8
Langevin
14.6
14.6
1 1 .2
a) R eference 1 2 8
b) T his work.
ence in relaxation arising from the degenerate M states.
N eon
T heoretical
77 Kb 100 K 6
13.2
1 1 .1
11.7
1 0 .0
7.6
8.5
5.0
4.7
6 .6
8 .6
Buffa et a / . , 1 2 7 , 1 3 8 have shown
th at the M dependence o f th e linew idth can influence the relaxation.
D espite the large
discrepancy betw een our calculated values and those o f Buffa et a l . , 1 2 7 , 1 2 8 the m agnitude
o f this discrepancy com pared w ith difference betw een calculated and theoretical values
is sm all (Table 7 .1 ).
T he predicted values o f T show the pressure broadening becom es
sm aller as both th e angular m om entum and th e tem perature increase.
Several other treatm ents have been developed which attem pt to address som e o f the
assum ptions m ade in th e ATC theory. Besides th e inclusion o f curved trajectories in the
ATC m ethod, several capture m odels have also been em ployed in m odeling th e collisional
broadening.
C apture m odels assum e a com plete loss o f correlation betw een th e initial
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244
Table 7.2: Sum m ary o f th e pressure broadening coeffients T calculated for SiF+ using ATC
th eo ry and accounting for th e distrib u tio n of relative velocities. We used a B„ value of 19096
M H z,120 m olar masses o f 47 g/m ol, 40 g /m o l an d 20 g/m ol for SiF+ , A r an d Ne, respectively.
T he value of th e dipole m om ent was 3.38 D . 1 2 0 All units are in M H z/T orrr.
Line
0 -> 1
1 — 2
3—4
5—6
6 — 7
7 —8
Langevin
77 K
21.9
19.7
14.9
11.5
1 0 .2
9.2
12.9
Argon
90 K 100 K
18.5
19.8
16.9
18.0
13.2
13.9
10.5
10.9
9.4
9.8
8 .8
8 .6
1 1 .0
9.9
130 K
15.5
14.4
11.7
9.5
8 .6
7.9
7.6
77 K
13.1
12.4
1 0 .6
9.1
8.4
7.8
7.9
and final sta tes o f the ion or no relaxation at all.
Neon
90 K 100 K
11.7
10.9
1 1 .2
10.5
9.7
9.2
8.4
8 .0
7.8
7.5
7.3
7.0
6 .8
6 .1
130 K
9.0
8.7
7.8
6.5
6 .1
4.7
T his is the condition assum ed in
the Langevin m odel, where a potential barrier m ust be crossed in order for a reaction
to occur.
T his barrier is a com bination o f the energy stored in the angular m otion o f
th e collision pair and an isotropic interaction potential.
T he Langevin m odel uses a
charge-charge-induced-dipole potential, from which the collisional broadening expression,
/ a
\ 1 /2
rt = « * ( - )
is obtained . 1 2 8 T he values o f
,
(7.15)
for both th e argon and neon conditions used in th e ATC
calculations are tabulated in Tables 7.1 and 7.2. T he decrease in th e T values predicted
by Eq. (7.15) is due to th e change in the d en sity o f th e gas as th e tem perature increases.
In T able 7.2 we can see th at the argon broadening at J — 6 — 7 is actu ally sm aller than
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245
the Langevin lim it, w hile th e neon broadening values are larger than the Langevin lim it.
S tatistical adiabatic channel m odel (SACM ) theory 1 3 9 has been applied to studying
pressure broadening , 1 3 0 providing the ability to include the anisotropic term s o f the po­
tential, and hence, to m odel rotational effects. Liao and H erbst1 3 0 have created a hybrid
m ethod th at replaces the standard ATC cutoff, S(bQ) =
1
, w ith a capture effect dependent
cutoff . 1 2 8
T he various m odels used vary in their accuracy o f predicting th e rotational sta te
dependence o f th e line broadening effect. Buffa e t a l . , 1 2 8 in a stud y o f HCO+ broadening
by Ar, show th at th e accuracy o f the m ethods is highly dependent on the J sta te o f the
m olecule. A t low J th e straight trajectory ATC treatm ent is surprisingly accurate, but it
begins to fail badly as the J level increases, while the curved trajectory ATC does w ell over
m ost o f th e range. T he hybrid m ethods do fairly well over the m any rotational levels, but
the capture m odels fail badly at low J. Each o f the m odels, excepting th e ATC m odel
w ith straight trajectories, reach a lim it at the higher J levels th at corresponds to the
Langevin value.
E ventually all o f the m ethods, except ATC w ith straight trajectories,
reach th e Langevin lim it in calculating I \
T he values o f T reported in th e literature
th at have been experim entally obtained, however, continue to decrease. A t th is tim e the
origin o f th is discrepancy is not clear.
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246
7.3
M ethods o f Line W idth D eterm ination
Studies o f pressure broadening in this work use line w idths obtained from tw o m ethods.
T he direct m ethod uses a m odel line shape function and a non-linear regression m ethod to
fit th e experim ental line shape to the theoretical m odel. Param eters for th e HW HM and
the transition frequency are obtained from th is procedure. P ick ett’s m ethod, so nam ed
because it was developed by H. M. P ickett , 9 takes a low pressure spectrum , convolutes it
w ith a Lorentzian function dependent on line w idth and line shift param eters, and fits the
obtained function to the experim ental data, using a non-linear regression m ethod. N et
lin e broadening and shifts due to pressure effects are obtained.
7.3.1
D irect M ethod
A lthough details o f th e direct m ethod are available elsew here , 1 0 a brief overview of
th e procedure is necessary for proper com parisons o f th e direct and P ick ett m ethods.
T he direct m ethod is em bedded into th e M icrowave.for program w ritten by W oods. 6
T his program controls th e microwave spectrom eter and allows for analysis o f th e obtained
spectra. T he fittin g routine o f th e direct m ethod, allow s the user to fit up to three peaks
w ith in a user defined interval, using either a G aussian or Lorentzian line shape m odel.
T he user is the required to define th e baseline by selecting representative segm ents and
th e order o f th e polynom ial function to b e used to fit the baseline.
O nce th e baseline
param eters are selected, th e user defines th e m axim um and th e HW HM o f each o f the
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247
10
5
C
CA
0
•5
267.310
267.320
267.330
Frequency (GHz)
(a)
10
5
0
•5
*10
267.310
267.320
267.330
Frequency (GHz)
(b)
Figure 7.1: P lo ts o f th e SiF + J = 6 —+ 7 transition at P = 52.4 ± 0.3 mTorr. B oth th e
direct m ethod w ith a Lorentzian m odel (a) and th e P ickett m ethod (b) have been used.
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248
peaks to be fit. U sing the selected param eters, th e program fits the d ata to th e selected
line shape m odel by a least squares regression, returning values for the HW HM, linew idth,
and the integrated intensity.
W hile th e direct m ethod provides a good fit in m ost cases, there are som e potential
sources o f errors.
O ne o f the m ost critical is the lack o f th e ability to fit a Voight line
shape m odel. T he Lorentzian m odel is accurate in th e pressure region where collisional
broadening is dom inant ( > 5 0 mTorr) and the G aussian m odel is accurate where pressure
broadening is negligible ( < 1 0 mTorr). T he Voight lin e shape allow s for an accurate fitting
in th e pressure region, 10 < P < 50 mTorr, where neither the Lorentzian or G aussian
m odels are com pletely accurate.
For weak lines low signal to noise ratios often introduce significant error in the de­
term ined values o f th e HWHM. In addition, other effects such as source broadening and
w all broadening are also not accounted for by th e line shape m odel.
It m ust be noted,
however, th at source and wall broadening are expected to be m inim al because the design
o f th e instrum ent.
7.3.2
P ick ett’s M ethod
A m ethod for determ ining the effects o f pressure on line w idth and transition frequency
separate o f other pressure independent param eters was developed by P ickett9. P ick ett’s
rationale is sim ple. A low pressure spectrum w ill contain all th e inform ation for pressure
independent effects, including Doppler broadening and com plications from th e m odulation
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249
■SI
I
s
£
•
0.2
0
10
20
30
40
SO
60
70
80
90
100
110
Pressure (mTorr)
Figure 7.2: Com parison o f the HWHM values, At> (□ ), and the Pickett broadening para­
m eters, w (O ), obtained for the neon broadened J = 6 —►7 transition o f SiF + . T he data
points are from th e neon 1 experim ent. For the purposes o f com parison, th e P ickett w
values are p lotted against the absolute pressure instead o f the A p values norm ally used.
A s can be seen th e scatter in the d ata is dram atically reduced by use of P ick ett’s m ethod
over th e direct m ethod.
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250
schem e used, contained in the high pressure spectrum .
T his assum es th at th e sam e
instrum ent is used, and the only changes in th e experim ental param eters m ade are those
o f pressure.
B y convoluting th e low pressure reference spectrum w ith a L orentzian line
shape function dependent only on the pressure related param eters o f line w idth change w
and line shift change s, a theoretical m odel w ill b e obtained w hich is fit to a high pressure
spectrum , via a non-linear regression, to obtain th e optim ized values for w and s.
Several research groups have utilized P ick ett’s m ethod w ith great success 1 2 7 , 1 2 8 Indeed
use o f P ick ett’s m ethod results in dram atic im provem ent in the quality o f th e pressure
dependent d ata com pared w ith that obtained using the direct m ethod.
An excellent
exam ple is found in th e application o f both m ethods to the neon broadening o f the J = 6 -7
transition o f SiF+ , shown in Fig. 7.2
7.4
P ick ett’s C onvolution M ethod
7.4.1
Im plem entation o f P ickett’s M ethod
In th e lim it o f low radiation the power absorption (<r0) and dispersion (<Tb) cross
sections can b e expressed and obtained from
/
/
OO
S ( t , P ) cos 2 -Kutdt
(7 .16a)
o
OO
S ( t , P ) s m 2 m ddt
,
o
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(7.16b)
251
where S(t, P) is the impulse response function at a time delay t, v is the frequency of the
incident radiation , and P is the pressure . In the case of the isolated line S(t, P) has the
form
S(t, P ) = S(t, 0 )e( - 2’rr« + 2 ^ p t) ^
(7 17)
where T isthe pressure broadening coefficient and rj is the line shift coefficient. This is
for a pure gas, whereas for a mixture of gases, an exponential term likethe right-hand
side of Eq. (7.17) would be present for each component.
In the use of this method we
assume th at there are no other components except the sample gas which will be present
in the low pressure spectrum and as such will be included in the S(t, 0) term. Use of the
S(t,P) with the Fourier transform convolution theorem yields
/
+oo
P')L{u — u',P — P #) dv’ P > P /
,
( 7 . 18)
— OO
where
•
(7.19)
The above equations are suitable for use with <ra or a^, or with the combination of the two.
Equation (7.18) is used as the basisfor the convolution of a low pressure reference profile
with a Lorentzian profile to obtain the absorption profile for a given higher pressure P.
The experimentally determined cross section is
a> , P ) = /
(t(i/ , P)F{u - v')dv'
.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 7 .20)
252
The function F{u —i/) is the response of the spectrometer system to a cr function absorp­
tion at uQ. If F{v — u') is assumed to have unit area and Eq (7.20) and Eq (7.18) are
combined, the experimental cross section becomes
o*{v, P ) = j °° ax{y\ P ,)L(i/ - v ' , P - P>)dv> .
(7.21)
OO
This equation applies when F ( v —Uq) is only dependent on the frequency difference over the
range of the w idth of current function L. To ensure the restriction on F{v — vQ) is kept,
the spectrometer must be rim under constant spectral resolution, and when frequency
modulation is used the depth of modulation must be kept constant for all spectra to be
compared.
The effects of reflections off the cell window have been considered by Pickett,9 and he
concludes th at the method presented here will be valid if the mixture of the absorption
and dispersion profiles does not change significantly over the w idth of the line.
Implementation of Pickett’s convolution method requires several conditions be met.
The low pressure reference spectrum and one or more higher pressure broadened spectra
must have the same number of steps and step size 8v, the modulation parameters must
be kept constant, and the reference spectrum should return to the baseline at either end
of the scan.
For digital spectral d a ta with a uniform frequency step pressure widths and line shifts
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253
are obtained using the following discreet analog of the convolution integral in Eq. (7.21):
Aw2
=
Rk
2 , IY •
u\k +I s 12
+ a+
3
fc=l
w 2 + [u - «)&'
]2
1
(7.22)
where B? are the elements of the calculated high pressure spectrmn, R* are the elements
of the low pressure reference spectrum, w and s are the line width change and line shift
change parameters.
The step size between successive points in both the reference and
high pressure spectra is noted by 8u. Other symbols are A, the scaling factor for intensity,
and the baseline correction terms a and b. Values for A, w, s, a and b are determined using
a non-linear least squares fit of Eq. (7.22) to the experimental values
B j
.9
A Labview program, LPBExtract lie, was created to perform the convolution and
non-linear least squares fitting. Program proceeds in the following sequence.
1. Initial "best estimates" for w and s are made by the user. Default values for A, a
and b are also supplied.
2. Improved values for A, a and b are determined using a linear least squares procedure
with the values of w and s held fixed.
3. Values for the points, Bj, are calculated using the best estim ate values for w, s, A,
a, and b.
4. New values for w, s, and A are determined using a non-linear least squares fit to
the values of the
and the derivatives.
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254
5. Steps 2-4 are repeated in an iterative process until the A x 2 value of the fit is reduced
to a specified threshold.
The double determination of A allows for a more rapid convergence of w and s to their
final values.
The fitting portion of LBPExtract Ilc.vi, Pickett Method II. vi, is a sub program based
on a National Instruments supplied routine that uses the Levenberg-Marquadt algorithm
to perform the non-linear regression. Chi squared minimization is used to determined
completion of the fitting process . Typically a A x2 value of 0.001 is selected as the cutoff
value. Although smaller A x2 values can be used, it has been found th a t the improvement
in the fit parameters is minimal and does not justify the extra time required to complete
the fitting process. The program works quite well, except when the pressure broadened
spectra have a small signal to noise ratio, or when the reference spectra does not meet the
baseline requirements. A more in depth explanation of LB PExtract Ilc.vi can be found
in Appendix C..
7.4.2
Potential Errors
The presence of sidebands arising from modulation and baseline suppression imposes
a limit on the initial values of s. T he effects of selecting too large of a value for s, are
shown in Fig. 7.3. Here the fitting m ethod has converged on the sidebands, resulting in a
fit th a t makes no sense at all. The limits for initial values were determ ined using Pickett’s
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
255
10
5
>
¥
'(O
c:
OJ
c
0
•5
-10
267310
267320
267330
Frequency (MHz)
Figure 7.3: The baseline suppressed spectrum (----- ) is shown with the fit spectrum (—)
superimposed. W ith an initial value of s = 2.00, the algorithm has settled on one of
the modulation side bands 4.0 MHz away from the main line. Input and output fit
parameters are listed in Table 7.3.
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256
Table 7.3: Initial and final parameters used in the fitting of the spectrum shown in Fig. 7.3 by
the Pickett method.
Fit Parameters
Value
Initial Fit
1.00 -3.77
A (xl0“ l )
w (xlO-2 MHz)
1.00 4.57
s (MHz)
2.00 3.93
a (xlO-2)
1.00 -7.06
b (xlO-4)
1.00 2.63
method with spectra from the argon 3 experiment, and varying a single initial parameter,
either w or s, over a representative range, large to very small, and noting the effects on
the fitted values of the parameters. The effects of the initial s value on the fitted s value
and the mean square error (m.s.e.) obtained from the fits are shown in Fig.7.4, while the
effects of both the initial s and w values on the fitted values of w are shown in Fig.7.5.
Based on this study, it is suggested th a t the user keep the initial values in the ranges of
0.1 < s < 0.5 MHz and 0.1 < w < 1.0 MHz, to prevent either errors in the shift, s, or
broadening, w, parameters.
7.4.3
Scale Effects
D ata files exported from the Microwave.for program (Section 2.3) correspond to the
spectrum as displayed by the program a t the time of exporting, and do not contain infor­
m ation regarding scale expansion or detector sensitivity
Thus a weak, noisy spectrum
can appear to have the same intensity as a strong, low noise spectrum, Fig. 7.6. Ideally,
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257
14 -i
12
-
10
-
8
-
.
4
-
1
2
-
0-00
CD CD
•2 4
0.0
0.5
1.0
1.5
2.0
2.5
Initial s Value (MHz)
(a)
4.0 -i
3.5 3.0 2.5 -
2.0
-
0.5 -
CD CD
0.0 - ° °
■0.5 H
0.0
0.5
1.5
1.0
2.0
2.5
Initial s Value (MHz)
(b)
Figure 7.4: The effect of the initial values of s on the final fitted value of s and m.s.e.
(A x2 < 0.001). As can be seen initial values greater than « 1.9 MHz lead to significant
errors in the determined values of s (a) and in the m.s.e. (b). To avoid errors in the
fitting parameters the initial values of s should be restricted in the range of 0.1 < s < 0.5
MHz.
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258
60 50 -
o
40 - (
CD 0 0
30 -
f
%
20 *
1
10 0 •10 -
V
0.0
“1
0.5
1-----------1—
1.0
1.5
—r
“i
2.0
2.5
Initial s Value (MHz)
(a)
42 1
40 -
o oo
38 J
36 -
¥"g 34 *
I
E
32 -
30 -<
28 -
1-----------1—
2
3
Initial w Value (MHz)
W
Figure 7.5: (a) This plot shows the effect of the initial value of s on the pressure broadening
param eter w. The values of s > 2 cause serious errors, as the Pickett fitting program
fits the sidebands instead of the main line, as in Fig. 7.3. (b) The effect of the initial
value of w on the final fitted w value is shown in this plot. Except a t very small w (<
0.1 MHz) the initial value of w has no effect on the fitted value of w.
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259
10 I
>
&
'tn
c
a>
c
89100
89105
89110
89115
Gunn Diode Frequency (MHz)
Figure 7.6: Comparison of the unsealed data spectrum (—) and the low pressure reference
spectrum (-----) using the raw data as outputted from the microwave.for program. As a
consequence of the lack of scaling information, the noise relative to the reference spectrum
is greatly exaggerated.
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260
10 - i
>
0 a>
c:
-5 -
89100
89105
89110
89115
Gunn Diode Frequency (MHz)
Figure 7.7: T he reference spectrum (-----) and the d a ta spectrum (—) shown in Fig. 7.6,
have been corrected for sensitivity and scaling effects. The noise level of the d a ta spectrum
is now shown in the proper relation to the reference spectrum.
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262
The proper use of Pickett’s algorithm requires th at the signal of the reference spectrum
return to the baseline a t the end of each scan.9 Buifa et a/.127 ensure this requirement is
met by subtracting out the baseline prior to the application of Pickett’s method. In our
treatm ent of data, we suppress, but do not subtract, the baseline. As has been detailed
in Section 2.3.4, and by Piltch,10 baseline suppression can cause deformation of the peaks,
including an increase in the apparent intensity.8 In addition, application of the baseline
suppression routine does not always result in the removal of the baseline. It is important
therefore to ascertain the effects th at these conditions will have on the values determined
by the Pickett method.
The effects of any non-linear baseline functionality remaining in the data sets was
investigated in two separate studies.
In the first study, baseline suppressed and base­
line suppressed/subtracted versions of a single spectrum were prepared and used with
Pickett’s method.
This study sought to determine the effects of non-linearity in the
baseline. The second study expanded on the first, by comparing the d ata sets obtained
from baseline suppression with baseline suppression/subtraction on all spectra from a
given experiment, and determining what effect, if any, these differences would have on the
pressure broadening parameters.
Subtraction of the baseline is accomplished by first calculating the base line function
using the coefficients determined for the baseline function when the spectra is fit using
the direct method. T he direct method fits the baseline to a polynomial function, where
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263
Table 7.5: O ptim ized param eters for Pickett convolution com parison
Fit Param eter
Suppressed
0.1161
0.3158
-0.0270
0.539
A
w (MHz)
s (MHz)
m.s.e (V)
Subtracted
0.1118
0.3300
-0.0270
0.243
A
0.0043
0.0142
0.0000
0.296
the independent variable x is defined by
x = i —m
,
(7.23)
where i is the counter value of the ith frequency point and m is the counter value of the
median point. Calculation and subtraction of the baseline function is accomplished using
the Baseline Removal.vi program.
In Figs. 7.8 and 7.9 the original baseline suppressed
and the baseline suppressed/subtracted spectra and the corresponding Pickett fits are
shown, respectively. Clearly visible in Fig. 7.8, is the non-linearity of the baseline in the
original suppressed spectrum.
Comparison of the fitted parameters, w and s in Table
7.5, shows th at there are small differences in the values, but a significant difference in the
the m.s.e. value.
From this first study it was apparent th at the impact of baseline subtraction on the
pressure broadening parameters needed to be addressed. This was accomplished by using
the spectra from two separate experiments, one argon and neon, and preparing two d ata
sets of w values, corresponding to baseline suppressed and baseline suppressed/subtracted,
from each of them (Figs 7.10 and 7.11).
From these plots, it is readily apparent th at
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264
6
-
4 -
2
-
•4 -
-6
-
•8
-
267.310
267.320
Frequency (GHz)
267.330
Figure 7.8: Spectrum of the J = 6—»7 transition of SiF+in an argon discharge at 57.6 ± 1.5
mTorr and 92 ± 3 K. The spectrum was obtained by applying three third harmonic
baseline suppressions. B oth the supressed spectrum (—) and the Pickett method fit (--) are shown. This spectrum exhibts some non-linearity a t the higher frequency region.
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265
6
4
2
0
c=
•4
•6
•8
267.310
267.320
Frequency GHz
267.330
Figure 7.9: This is the baseline corrected spectrum (---- ) of the spectrum in Fig. 7.8. Also
show is the Pickett method fit (— ). There is some distortion of the suppression induced
sidebands, near 267,328 MHz, which suggests th at the baseline function is not completely
accurate.
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267
0.6
0.5
0.4
0.3
02
0.1
0.0
0
20
40
60
80
100
120
AP(mTorr)
Figure 7.11: Comparison of w values obtained from argon broadened spectra of the J = 6-7
transition of SiF+ with baseline suppression (©) and baseline suppression/subtraction (□)
treatm ents. Although differences do exist, the overall trend is, considering the scatter in
the points, unaffected by non-linear baselines.
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268
many days into a single set. This would require, a single reference spectrum to be used
with all spectra, and a constancy in as many experimental parameters as possible. Since
this cannot be accomplished perfectly, it is very probable that a reference spectrum from
one experiment will not contain all of the necessary non-pressure information required for
use with spectra from other experiments. This would create systematic differences in the
w and s values obtained from the spectra collected in other experiments.
To determine the effect of using a reference file from a separate experiment, the spec­
tra from argon experiment 2 (see below) were fit using Pickett’s method and reference files
from argon experiment 2 and argon experiment 3.
The resulting sets of w parameters
obtained were plotted (Fig. 7.12) and the slope, or T value, and the 95% confidence inter­
val were determined. Comparison of the slopes reveals a difference in the T values, but
the difference is minimal, with both determined values of T lying within the uncertainty
range of each value. The error introduced by using an external reference file should be
minimal, and the combination of d ata sets should introduce no significant error into the
F values obtained from the combined set.
7.4.6
F it Quality
An example of the fit evaluation process can be made using two spectra from the
argon experiment 3.
The spectra in Figs. 7.13 and 7.14 show the difference between a
good fit and a poor fit. These two spectra are very close in pressure, 51.5 ± 0.4 mTorr
and 52.4 ± 0 .3 mTorr, respectively, so we expect very similar fittings. In Fig. 7.13 the fit
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269
IM
n:
0.2
-
0.1
0
20
40
60
80
Pressure (mTorr)
Figure 7.12: Comparison of the w values obtained from using an internal, to the exper­
iment, reference file (□), and an external reference file ( O ) with the Pickett method
analysis of the spectra obtained in the argon 2 experiment. The pressure broadening
param eters are 7±2 MHz/Torr and 8±3 M Hz/Torr for the internal and external reference
files, respectively. The reported uncertainties correspond to the 95% confidence interval.
The comparison of the two data sets shows th a t the error from using an external, closely
related, reference file should not introduce significant error into the determination of T.
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270
(O
ca>
6-1
■6
-
4-
2
267.320
267.324
Frequency (GHz)
-
0*co
cQ) •2
c
-
•4 -
•6
-
267.300
267.310
267.320
267.330
267.340
Frequency (GHz)
Figure 7.13: An example of a poor fit . The raw spectrum (-----), is fit using the direct
method (— ), W hen compared to a similar spectrum (Fig.7.14) the fit has considerable
error. The inset is a magnification of the peak area and shows both the noise and the poor
quality of the fit to good effect. This spectrum was recorded at a pressure of 51.5 ± 0.4
mTorr, a current of 400 mA, and a tem perature of 91 ± 4 K. The uncertainties correspond
to one standard deviation.
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271
267.320
267.324
Frequency (GHz)
3
tfj
C
Q
•8
r i i i I i i i i | i i i i I i i-rr y r r-i i | i i i t
267.300
267.310
267.320
;
i i i i
267.330
|
i i i i
|
267.340
Frequency (GHz)
Figure 7.14: This spectrum is an example where the direct method correctly determines
the HWHM value. The HWHM values obtained from the direct method, 0.5265 MHz,
and the Pickett method, 0.4490 MHz compare very well. Compare this spectrum with the
one in Fig. 7.13. The current of the discharge was 400 mA, the tem perature was 91 ± 4
K, and the pressure 52.4 ± 0.3 mTorr.
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272
near the maximum of the main line is poor, while for the spectrum in Fig. 7.14, the fit in
the peak region is considered good
7.5
Carbonyl Sulfide Pressure Broadening
The verification of our implementation of Pickett’s method, and the determina­
tion of low pressure broadening parameters, i.e., Doppler broadening, was accomplished
by studying the self broadening of carbonyl sulfide.
Long considered a standard in the
field of microwave spectroscopy, OCS has been the subject of many pressure broadening
studies8,122,123,131,140 For our study we chose to use the J = 21—*22 transition of 0 13CS
near 266,669 MHz. This line was chosen because it is near the J = 6—>7 transition of SiF+
and it is sufficiently weak th at optical depth problems should be minimized.18 Transitions
of the parent isotopic species, OCS, are too strong and exhibit effects due to large optical
depth of the absorbing medium.
D ata was acquired using the microwave spectrometer system described previously in
Section 2.3. Pressure readings were taken using a MKS Baratron capacitance manome­
ter, zeroed against pressure readings from an ion gauge. To minimize the effects of OCS
decomposition, outgassing, and leaks in the system, a continuous flow of OCS was main­
tained through the system.
Signal modulation utilized 4.00 MHz FM sidebands and a
19.0 kHz AM frequency.
The determ ination of the Pickett parameters, w and s, was made using a reference
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273
Table 7.6: Literature values for pressure broadening of selected OCS isotopomers
Species Transition
l8OCS“
7 —>8
o 34c s 6 15 — 16
6—7
OCS6
o 13c s c 21 — 22
Ol3CSd 21 — 22
a Ref.8
b Ref122
c Pickett method
d direct method
T (MHz/Torr)
6.22 ±0.22
6.53 ± 0.02
6.54 ± 0.13
6.36 ± 0.16
5.06 ± 0.16
spectrum recorded at a pressure of ~ 2.5 mTorr OCS. D ata spectra were taken in the
pressure range between 2.8 and 107 mTorr, at pressure increments of ~ 10 mTorr up to
60 mTorr, where the increment size increased to ~ 20 mTorr. All spectra were recorded
a t 297 K.
The w values were plotted (Fig. 7.15) as a function of the pressure difference between
the d a ta and reference spectra. Regression analysis of this d a ta determined the value of
the pressure broadening coefficient, T, to be 6.36 ± 0 .1 6 M Hz/Torr for a 95% confidence
level. Comparison of this value with values reported in the literature (Table 7.6) shows
th at our value is consistent with the previously reported values. From this we conclude
th a t our implementation of the Pickett method is correct and th at the values obtained
should be reasonably accurate.
At low pressures, spectral linewidths are very approximately accounted for by a
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274
0.6
0.5
0.4
M
0.3
0.2
0.1
0.0
0
20
40
60
80
100
A P (mTorr)
Figure 7.15: Self broadening of OCS. A plot of the Pickett w parameters obtained from
the spectra of the J = 21 —►22 transition of 0 13CS vs the pressure difference, A P,
between the respective d a ta spectrum and the reference spectrum. The self broadening
coefficient, T, was determined to be 6.36 ± 0.16 MHz/Torr. The uncertainty corresponds
to a 95% confidence interval.
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276
linewidths when using the Gaussian and Lorentzian line shape models, Fig.7.16. Ideally,
one should be able to use the Gaussian model for low pressure spectra and the Lorentzian
model for high pressure spectra and combine the two data sets, but the systematic dif­
ference invalidates this approach. Since we were forced to use a single line shape model
over the entire pressure range, it was necessary to determine which model would produce
the most reasonable direct method results.
This was accomplished by fitting the OCS
spectra using both models, plotting the obtained HWHM values and comparing the over­
all quality of the data. The plots created from the obtained At/ values are shown in Fig.
7.16. The Gaussian d ata has a lot of scatter and appears to have differing responses in
the low and high pressure regions. This is not unexpected, since the Gaussian line shape
is most accurate for low pressure conditions. In contrast to the Gaussian model results
are those obtained from use of the Lorentzian line shape model. In this case there is some
scatter, but overall the data is linear in pressure.
sets produces the T values listed in Table 7.7.
Regression analysis of the two data
In addition to determining the T value
from the complete Gaussian d a ta set, a subset composed of the low pressure points, < 20
mTorr, was also used to determine T. The T value, 10.5±0.3 MHz/Torr, obtained from
the low pressure set is significantly different from the total Gaussian d a ta set.
Our study of OCS self broadening demonstrated th at the Pickett method produces
accurate w values for use in pressure broadening studies. We also show th at the direct
m ethod should use the Lorentzian line shape model for cases where d a ta is obtained in
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277
0.8
-
0.6
-
O'
0.2
-O'
■er
0.4 -
-
0
20
40
60
80
100
Pressure (mTorr)
Figure 7.16: Comparison of the HWHM, At/, values obtained from the direct method with
Gaussian (□ ), and Lorentzian (0)> line shape model functions. Regression fits for the
Lorentzian (— ), Gaussian (—), and the low pressure, P < 20 mTorr, points of the
Gaussian d a ta set (----------), are also shown. T he self broadening coefficients, T, are
5.06 ± 0.16 MHz/Torr, 7.7 ± 0 .6 MHz/Torr, and 10.5 ± 0 .3 M Hz/Torr for the Lorentzian,
Gaussian and low pressure Gaussian d ata sets, respectively
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278
high pressure conditions.
7.6
Carbonyl Sulfide Pressure Dependent Frequency Shifts
The pressure induced frequency shift discussed in Section 7.2 was determined for
the J = 21—>22 transition of 0 13CS. The pressure shift change, s, obtained from the
application of Pickett’s method (Section 7.4) was plotted against the pressure (Fig. 7.17).
Since inspection of the plot suggests that three of the points may be in error, a second
set of points, which excludes these questionable points, was also plotted.
Both sets
had linear least squares fits made to determine the pressure induced line shift parameter
Tj,
with values of —5.6 ± 2.2 xlO -2 MHz/Torr and —5.2 ± 1.5xlO -2 M Hz/Torr for the
complete and edited data sets, respectively. The scatter in the d ata is due to the lack of
complete correction for systematic effects, such as shifting due to anomalous dispersion
(Section 3.3).
Domenech et a/.,141 using HI methods studied the pressure dependent shifting of
the line of the (020) state of OCS over a pressure range greater than five times that
of our study.
From this study they report line shift coefficients 7/, for the P branch
J= 2 2 —>21 transition state of —2.11 ± 0.18xlO -1 M Hz/Torr for an Ar collision partner
and —5.92 ± 0.18xlO -2 M Hz/Torr for a He collision partner. These are a t least of the
same general magnitude as our tentative result for the shifting of a rotational line by an
OCS collision partner.
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279
2 -i
0N
X
-2
-
-6
-
©
3
5
CO
C
!c
CO
©
c
□
-8 -
-10
0
20
40
60
80
100
120
A P ressure (mTorr)
Figure 7.17: Pressure dependent iineshifts of the 0 13CS J = 21 —►22 transition. Two
sets of Pickett’s s parameters, the complete (□), and the edited (•), are plotted. The
edited set was obtained from the complete set by removing suspect points. Regression
analysis of the complete (— ) and the edited (—) d ata sets determined the values of the
pressure shift coefficient rj, to be 5.6 ± 2 x 10-5 M Hz/Torr and 5.2 ± 1.5x 10~5 MHz/Torr,
respectively.
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280
CHAPTER 8
Pressure Induced Linebroadening and Frequency Shifts of SiF+
8.1
Pressure Broadening of SiF+
Prior to this work the only ion th at had been the subject of pressure broadening studies
was HCO+.8,127-131 In this section we present the a study of the pressure broadening of
the J=6-7 transition of SiF+ by neon and argon.
First characterized using microwave spectroscopy by Petrmichl et a/.,120 the SiF+ ion
has a simple spectrum with several lines within the frequency range of our spectrometer.
Additional studies by Petrmichl2 determined the effects of buffer gas, magnetic field and
other parameters on the intensity of various transitions and determined th at the strongest
line, in both neon and argon buffer gas discharges, was the J= 6-7 transition of the ground
state.
W ith a frequency of 267,320.98 ± 0.22 MHz,120 the line is within the range of
the microwave spectrometer and corresponds to a third harmonic of an accessible Gunn
diode frequency.
The presence of a strong line in the optim al frequency range of our
spectrometer, the well characterized chemistry, and the simple structure of SiF+ make
the molecule an excellent subject for pressure broadening studies.
8.1.1
Experimental
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281
An "experiment" is defined as the period of data collection where all spectra collected
can be used with a common reference file and this reference file can be expected to contain
most, if not all, non pressure dependent information.
A "data set" is composed of the
values obtained from the Pickett analysis (w and s) or from the direct method analysis
(Au) of the spectra collected in a single experiment.
In a typical experiment the component gases a t first flowed separately, and the indi­
vidual pressures are recorded.
The gas mixture is then adm itted, and the discharge is
initiated. If the negative glow mode is to be used, the magnetic field is turned on prior to
plasma initiation.
Cooling of the discharge begins shortly after initiation has occurred,
and data acquisition begins once the temperature has reached the desired range.
The
discharge current, pressure, magnet current, discharge voltage, and cell tem perature are
recorded at the beginning, middle and end of the collection period, or run, of a spectrum.
Prom these measurements, average values are calculated and uncertainties are estimated.
A summary of the overall conditions for each experiment is provided in Table 8.1. Mag­
netic field values represent the nominal value used, although actual field strengths varied
somewhat as the current within the solenoid magnet fluctuated.
Studies by Petrmichl,2 suggest th at the linewidth is affected by the presence of an ax­
ial magnetic field, when the discharge is in a positive column mode. Petrmichl attributed
the broadening to an increase in polar products formed more readily in the discharge as
magnetic confinement increases the charged particle density.
Regardless of the mecha-
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282
Table 8.1: Overall Experimental Conditions for Pressure Broadening Experiments of SiF+
Neon Experiment
Property
1
Ne
250
10
2
3
Ne
Ne
Buffer
250
250
Magnetic Field (Gauss)
10
10
Idis (mA)“
Idia (mA)6
Avg. Temp.(K)c
130(6) 102(3) 102(3)
2.5
3.0
4
FM (MHz)
19
19
19
AM (kHz)
-14
-14
-14
Power (dbm)
SiF 4 Pressure (mTorr)
2.34
2.58
1.93
a). Negative glow discharge mode.
b) Positive column discharge mode.
c) Errors are the 95% confidence interval
Argon Experiment
1
Ar
300
7
500
100(4)
4
19
-14
3.4
2
Ar
200
200-1000
96(7)
4
19
-14
1.8
3
Ar
200
4
275-450
92(2)
4
19
-14
1.6-2.4
nism, the broadening of lines in the positive column mode, and not the negative glow
mode, when a magnetic field is present is a potential source of error. This is because the
spectra obtained from positive column discharges will contain additional linewidth infor­
m ation not present in a reference spectrum taken in the negative glow mode.
Several
of the argon studies have reference and low pressure spectra taken in the negative glow
mode, but high pressure spectra taken in a positive column with axial magnetic fields
applied.
The dependence of the discharge current on the pressure resulted in a broad range of
current values for the argon experiments. The typical values of the discharge current are
listed in Table 8.1, with values for both the negative glow and positive column discharges.
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283
The pressures of SiF 4 listed in Table 8.1 correspond to the starting pressures, i.e., the
pressure present in the discharge cell before the plasma initiation and cooling. The actual
partial pressure of SiF 4 is unknown, but a range of values can be estimated. Studies by
Petrmichl2 showed th a t within three degrees of 95 K the vapor pressure of SiF4 is limited
to less than 0.1 mTorr. W ith the exception of the neon 1 experiment the typical average
tem perature for an experiment was between 90 to 100 K. We can expect, therefore, that
the partial pressure of SiF4 is small and th at little self broadening is occurring.
The pressure for each spectrum was determined by averaging the capacitance manome­
ter readings taken a t the beginning, middle and end of the spectrum acquisition period.
It is assumed th at the average of the pressure readings corresponds to the actual pressure
affecting the molecules. This assumption fails, however, when during the spike suppres­
sion step of the preliminary data analysis (Section 2.3), the scan pairs containing the
pressure information corresponding to one of the measured pressures are rejected from
the d a ta set. This may cause a systematic error in the pressure linewidth relationship.
To minimize the error the scan count was noted at the time the pressure readings were
made, and if a large portion of the scans near the pressure reading points are rejected,
the reading is not included in the average.
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284
8.2
Neon Broadening
The pressure broadening of SiF+ by neon was studied in three separate experiments
using both the direct and Pickett methods for analysis.
The neon experiments were
performed prior to our implementation of the Pickett method.
As a consequence the
spectra collected during these experiments are not ideally suited for use with the Pickett
method.
Each experiment has a different FM sideband frequency, 2.0 MHz, 2.5 MHz,
and 4.0 MHz for the neon experiment 1, the neon experiment 2 and the neon experiment
3, respectively.
The different FM sideband frequencies prohibit the use of a common
reference spectrum, and consequently, the sets of the w and s param eters determined
from Pickett’s method, for each experiment, cannot be combined to form a single data set
(Section 7.4). In the neon experiment 3 overlap of the 4.0 MHz sidebands required larger
scan widths. Three scan widths were used: 45, 60, and 75 MHz. This poses no problem
with the direct method, but analysis using Pickett’s method is made very difficult by the
need to correct for the unequal step sizes.
8.2.1
Neon Experiment 1
The first neon experiment was also the first pressure broadening experiment per­
formed, and the 2.0 MHz FM side band frequency selected for this study were found to
be too small. Pressures were varied over a range of ~ 15 mTorr to ~ 110 mTorr a t tem­
peratures near 120 K. The HWHM values, Au, from the direct method and the w values
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285
from Pickett’s m ethod are shown plotted as functions of pressure and A P in Figs. 8.1 and
8.2, respectively.
Comparison of these two plots show quite clearly the effectiveness of
the Pickett method in reducing the scatter in the line width vs pressure plots.
Linear regression analysis of the two d a ta sets yield values for T of 6 ± 2 and 6.4 ± 0 .6
M Hz/Torr for the direct and Pickett methods, respectively. Values for the fit parameters
are listed in Table 8.2.
Careful inspection of the plots in Figs. 8.1 and 8.2 shows th at the low pressure points
fit the trend well and only at the higher pressures (> 50) mTorr is there significant
scattering.
The causes of this scattering are unclear, but it is likely th a t the overlap
of the pressure broadened line with the modulation sidebands is the cause.
In Fig. 8.3,
the superposition of spectra corresponding to differing pressures illustrates the gradual
blending of the sidebands and mainline as pressure increases.
The overlap of the main
line with the side bands will result in an apparent linewidth th at is smaller than the actual
linewidth.
Referring back to the plot in Fig. 8.1, a more random scattering is observed
a t high pressures.
8.2.2
Neon Experiment 2
Results from the direct and Pickett method analysis of spectra taken dining the second
neon experiment are summarized in Figs. 8.4 and 8.5. One ‘edited’ d a ta set was obtained
from each of the two methods by the exclusion of selected points. Points were excluded
from the d a ta sets because of systematic errors th at occurred during the d ata collection
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287
07
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
20
40
60
80
100
APressure (mTorr)
Figure 8.2: The pressure broadening of the SiF+ J=6-7 transition in the neon experiment
1. The w values were obtained using the Pickett m ethod and are plotted against the
pressure difference between the reference and d ata spectra. The discharge was operated
in the negative glow mode, and the tem perature was ~ 130 K. Regression analysis
determined the pressure broadening coefficient to be 6.5 ± 0.6 MHz/mTorr at the 95%
confidence level. The frequency modulation sidebands are a t 2.0 MHz.
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288
6-
2-
c=
■4 -
•6 —
•8 —
89104
89106
89108
89110
89112
Frequency (MHz)
Figure 8.3: This plot shows three spectra from the neon 1 experiment superimposed. The
potential for overlap of the pressure broadened main line w ith the sidebands is obvious.
At 17 mTorr (....), there is a clear separation of the sidebands and the main line. At 66
mTorr (---- ) overlap is beginning to occur, and at 111 mTorr (----- ) the sidebands and
main line are strongly overlapping and the line w idth is narrowed.
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289
1.2
1.0
0.8
.o*
0.6
0.4
0.2
0.0
0
20
40
60
80
Pressure (mTorr)
Figure 8.4: Direct method analysis of the neon experiment 2 data. The HWHM, At/,
values obtained from the direct method from spectra collected in the neon experiment
2 are plotted as a function of the pressure difference, AP, between reference and data
spectra. Regression analysis was used to obtain a T value of 6 ± 3 MHz/Torr. The
exclusion of the single point with a Au value of ~ 1.2 MHz results in a data set th at
yields a T value of 5.1 ± 1.2 MHz/Torr. The fit for the complete d a ta is noted (---- ),
while the edited is (-----). The sideband frequency is 2.5 MHz.
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290
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
20
40
60
80
100
APressure (mTorr)
Figure 8.5: The Pickett method analysis of the spectra collected during the neon experi­
ment 2 resulted a T value of 6.8 ± 0 .6 MHz/Torr. Because of the greater scatter in the
direct method data, there are more points in the Pickett method d ata set. To allow
for comparison, those points corresponding to excluded direct method points, noted (®),
were removed, and the resultant data set yielded a T of 6.3 ± 0.5 MHz/Torr.
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291
Table 8.2: F it p aram eters a n d th e 95% confidence intervals obtained from th e SiF+ broadening
experim ents, neon experim ent 1 an d neon experim ent 2. T h e slope, m an d th e intercept b were
determ ined uisng a linear least squares fit. T h e edited d a ta set was created by th e exclusion of
points w here th e fits were o f poor quality.
Neon
Neon
Neon
Neon
Neon
Neon
D ata Set_______
1 direct
1 Pickett
2 direct
2 direct Edited
2 Pickett
2 Pickett Edited
Fit Parameters
b (MHz) m (MHz/Torr)
0.19
5.9
0.029
6.4
0.24
6.0
5.1
0.271
0.024
6.8
0.042
6.3
Confidence Interval
95%
A6 (MHz) Am (MHz/Torr)
0.12
1.7
0.035
0.6
0.20
2.8
0.084
1.2
0.043
0.9
0.023
0.5
period, principally the loss of correlation between the recorded pressure and the actual
pressure which the spectrum was recorded (Section 8.1.1). Linear regression analysis of
the d a ta sets results in values for T of 6 ± 3 M Hz/Torr and 5.1 ± 1.2 MHz/Torr, obtained
for the direct complete and edited d ata sets, respectively. The Pickett method yields T
values of 6.8 ± 0.9 M Hz/Torr for the complete, and 6.3 ± 0.5 MHz/Torr for the edited,
d ata sets. The fit param eters for the edited and non edited d ata sets are listed in Table
8.2.
8.2.3
Neon Experiment 3
The use of the Pickett’s method in the analysis of the neon experiments, which were
conducted prior to our implementation of it, presented several obstacles. T he principal
difficulties were the different modulation parameters between experiments and the fact
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292
th at spectra w ithin the neon experiment 3 d ata set lacked a uniform scan width. Because
the number of steps in a scan is fixed, increasing the scan w idth will result in an increase
in the frequency increment 8v, and a decrease the resolution of the spectrum.
Since
the direct m ethod does not depend on the relationship between spectra, differences in
modulation and step size, or frequency element, from spectrum to spectrum is irrelevant.
Because of this insensitivity, when the data was collected there was no disadvantage to
modifying the step size between scans, while determining the optim um scan width for use
with the 4.0 MHz FM sideband frequencies. It was determined th at a scan width of 60
MHz was acceptable, but spectra with 45 and 75 MHz scan widths were also acquired.
In order to use the Pickett method the data spectrum and the reference spectrum
must have the same frequency increment, 8u. To ensure th a t all the spectra from neon
experiment 3 had the same step size as the reference file, the d a ta spectra were digitally
re-sampled.
Correction of the step size inconsistencies was slightly different for the 45
kHz and 75 kHz step size spectra. For the 45 kHz spectra, the reference spectrum was re­
sampled at 45 kHz, while for 75 kHz data, each of the individual spectra were re-sampled
from 75 to 60 kHz. Re-sampling was accomplished by using a linear interpolation routine.
Spectra w ith scan widths of 45 MHz and pressures greater th a n 50 mTorr were not used
with either Pickett’s m ethod or the direct method. Above this pressure peak deformation
due to overlapping sidebands causes obvious errors.
A plot of the HWHM values obtained from the direct m ethod analysis of the spectra
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293
1.0
0.8
IM
0.6
0.4
0.2
0.0
0
20
40
60
80
100
A Pressure (mTorr)
Figure 8.6: Direct method analysis of neon experiment 3 for SiF+ pressure broadening by
neon. Regression analysis of the Ai/ values yield a T of 6.7 ± 1.1 MHz/Torr. Rejection
of a single point, (□), changes the T to 6.7 ± 0 .8 MHz/Torr. The reported uncertainties
correspond to a 95% confidence interval.
is shown in Fig. 8.6. Regression analysis of the direct method d a ta yields T = 6.7 ± 1.1
MHz.
In Fig. 8.7, the w values appear to have a systematic shift th a t is dependent on the
original step size. The shift is not due to a systematic difference of the individual spectral
temperatures, as the 45 MHz d a ta has enough tem perature variation th at a tem perature
dependent effect should cause the w or Au values to be more randomly distributed. The
exact cause of the shift is unknown, but could be due to the loss of resolution for the
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294
Table 8.3: Fit results for various subsets of the neon 3 experiment.
Subset Criteria
Pickett w (Complete)
Pickett w (P < 50 mTorr)
direct Au (un-edited)
direct A i/(edited)
a) In units of MHz
b) In units of MHz/Torr
ba
m6
0.04 7.5
0.01 8.7
0.24 6.7
0.24 6.7
Aba Am 6 # of pts.
0.06
1.2
16
0.06 2.1
10
0.06
1.1
17
0.05 0.8
16
larger step-sizes.
The deviation from linearity at higher pressures (Fig. 8.7) has also been reported by
Gudeman.8
Comparison with the neon experiment 1, where overlap of the line and
sidebands is known to occur, and where the tem perature is significantly higher, suggests
th a t the deviation is not due wholly to the overlap of the main line and the sidebands.
This tailing off of the pressure broadening values is also seen in some of the argon data
(Fig. 8.9). The source of this tailing is uncertain. It is possible th a t the peak deformation
created by the application of the baseline suppression routine exacerbates the effects of
overlapping side bands.
It is also possible th at the tem perature dependence of T, as
reported by DeLucia,121,129 and observed in our ATC calculations (Section 7.2) is causing
the line widths to narrow due to some unidentified heating mechanism occurring in the
higher pressure discharge.
Considering the possible effects of non uniform scan widths, d ata from the Neon
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295
0.7 - i
96(4)
0.6
-
0.5 -
104(18)
96(8)
0.4 rsi
2
*
98(7)
0104(9)
0.3 -
102( 10)
0.2
-
121(13)
0
20
40
60
80
100
A Pressure (mTorr)
Figure 8.7: This plot shows the Pickett w values obtained from the collected spectra.
The original experiment was not intended to be used with Pickett’s method and as a
consequence three step sizes, 5v, were used: 45 kHz (□), 60 kHz (A), and 75 kHz (®).
Note the systematic increase in w as the step size is increased. The average tem perature of
the discharge during spectral acquisition is noted by the number above the point with the
standard deviation in parentheses. As can be readily seen, the shift is not tem perature
dependent. Possible sources for the shift are discussed in the text. The T values for
several subsets of the d ata were determined and are presented in Table 8.3.
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296
3 experiment can be grouped into several subsets, some of which are listed in Table
8.3. Linear regression analyses were performed for each of the subsets, and the results
are summarized in Table 8.3. The intercept a,the slope 6, and the values for the 95%
confidence interval are also listed. Individual plots are not provided, but Fig 8.7 illustrates
each subset. Originally, given the general improvement seen when the Pickett method is
applied, it was expected th at neon experiment 3 d ata would be quite a bit better than
the other two neon experiments (Figs. 8.1, 8.2, 8.4, and 8.5).
Unfortunately, the error
introduced by inconsistent step sizes limits the usefulness of this d ata set and limits the
accuracy of the broadening coefficients obtained.
8.3
Argon Broadening
Argon discharges produce significantly less intense SiF+ transitions than do neon
discharges.2 To minimize error introduced by the lower signal to noise ratios, multiple
experiments of argon pressure broadening were conducted.
The d ata sets created from
the analysis of the spectra collected in these experiments were combined to produce a
single overall d ata set.
This data set will be referred to as the combined d ata set.
Three experiments are included in the study. Descriptions and analysis of the individual
d a ta sets are included to provide relevant experimental information for each of the points
included in the overall d ata set.
The T values obtained from the individual and the
combined sets are presented in Table 8.4.
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297
Characterization of argon broadening proved far more difficult than for neon broad­
ening. A significant scattering of the data, attributable to the low S /N ratio, is observed.
Additional complications included the need to collect d ata in both the positive column
and negative glow discharge modes.
The discharge switched from the negative glow
mode to the positive column mode a t pressures near 30 mTorr.
W hat effect this may
have had on the accuracy of Pickett’s method is uncertain. The sensitivity of the signal
to tem perature changes, is also another source of error.
Even a shift of a few degrees
from the optimum tem perature was sufficient to significantly reduce the intensity of the
SiF+ signal.
8.3.1
Argon Experiment 1
The analysis of the spectra collected in experiment 1 used a reference spectrum from
with a pressure of 12.94 ± 0.17 mTorr. Values of the broadening parameters of SiF+ by
argon are summarized in Table 8.4. Results from the direct method are shown in Fig. 8.8,
and a large scatter in the d ata points is readily apparent. These points were fit to a linear
function and a pressure broadening value of 5 ± 2 M Hz/Torr was obtained. The Pickett
treated d ata plotted in Fig. 8.9 shows much less scatter and a definite pattern, including
the same kind of deviation from linearity a t high pressures observed previously. Two fits
were made to the Pickett data: one fit to all points in the data set and one to the set of
points with A P < 60 mTorr. The T values determined are 5.7 ± 1.6 M Hz/Torr and 8 ± 2
MHz/Torr, respectively (Table 8.4). All the Pickett method points were convoluted with
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298
1.0
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
120
Pressure (mTorr)
Figure 8.8: A plot of the HWHM values obtained from the direct method analysis of the
spectra collected in the argon experiment 1. The T value was determined to be 5 ± 2
MHz/Torr, with a zero pressure limit of Ai/ of 320 ± 110 kHz.
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299
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
20
40
60
80
100
A Pressure (mTorr)
Figure 8.9: A plot of the Pickett w parameters as a function of the pressure differential
(AP), for the argon experiment 1. It appears as if the pressure broadening levels out at
high pressures. This behavior has also been observed in some of the neon experiment
d a ta sets (Fig. 8.7). The cause of this tailing off has not been determined clearly. To
remove the effects of the tailing off, a second set of data was created by deleting the
two questionable points. Regression analysis determined th at the complete data set (□)
and the low pressure set (•) yield T values of 5.7 ± 1.6 M Hz/Torr and 8 ± 2 MHz/Torr,
respectively. Uncertainties represent a 95% confidence interval.
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300
a reference file from within their own data set.
Argon Experiment 2
A plot of the HWHM values determined using the direct method (Fig. 8.10), shows
a possible change in the broadening behavior around 60 mTorr. Because the number of
points is not sufficient to determine if the change in the slope is real or not in nature, it
was necessary to evaluate the data in the context of the combined argon d ata set. When
viewed in the context of the combined argon d a ta set (Fig. 8.14), the apparent change in
the slope at 60 mTorr is merely an artifact created by the limited number of points and
excessive scatter.
The Pickett method analysis of the spectra acquired in the second argon experiment
produced a set of w values shown in the plot in Fig. 8.11. Because no true reference file
existed in this d a ta set, both the reference file used with the combined set and a high
pressure reference file from within the data set were used with the Pickett method. The
T values obtained are 8 ± 3 MHz/Torr and 7 ± 2 MHz/Torr, respectively.
Use of the Pickett method to analyze the spectra in the argon 2 d ata set is problematic
a t best. W ith no true low pressure spectrum for use as a reference file and the low signal
to noise typical of the argon discharge spectra, it was im portant to determine the quality
of the w values. This was accomplished by superimposing the Pickett fit on the original
spectrum and evaluating the quality of the fit (Section. 7.4.6). Those fits th a t failed to
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0.0
| i r r r t i i i i | i i i i | i i i i | i »r r | i i i i | i i i i | ii i i | i i i i t i i i i \
0
20
40
60
80
100
Pressure (mTorr)
Figure 8.10: A plot of the HWHM values obtained from the use of the direct method with
a set of spectra collected during the argon experiment 2. This d a ta set does not stand
alone well, but all the points follow the overall trend when all the argon experiments
HWHM values are combined to create a single d ata set ( Section 8.3.1).
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302
0.7
0.6
0.5
0.4
M
0.3
0.2
0.1
0.0
•
0.1
0
20
40
60
80
Pressure (mTorr)
Figure 8.11: Pickett m ethod analysis of the spectra obtained in the argon 2 experiment.
The values of w were determined using an internal, to the experiment, reference file
(□), and an external reference file (O )- The pressure broadening param eters are 7 ± 2
MHz/Torr and 8 ± 3 M Hz/Torr for the internal and external reference files, respectively.
The reported uncertainties correspond to the 95% confidence interval.
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303
Table 8.4: Summary of pressure broadening of SiF+ by argon. This table lists the slope T and
the intercept for the regression analyses from the various experiments.
D ata Set
Condition
1
Pickett (< 60 mTorr)
1
Pickett (Overall)
1
Direct
Pickett
2
Direct
2
3
Direct (Edited)
3
Pickett
Combined Pickett
a) Units are in MHz/Torr.
b) Units are MHz.
6°
mb
0.05 8
0.09 6
0.32 5
0.02 6
0.26 7
0.32 5
0.04 9.4
0.06 8.7
95%
A6“ Am6
0.06
2
0.08
2
0.11
2
0.08
3
0.16
3
0.07
2
0.01 0.4
0.02 0.5
reproduce the original d a ta well, particularly in the peak region, were not included in the
Pickett d ata set.
Occasionally, errors in the execution of the Microwave.for program led to erroneous
results. The points th a t are significantly off the line, e.g., the 0.9585 value, are due to
this indeterminate error, and are discarded from the d ata set.
The apparent change in the pressure broadening behavior is not observed with the
Pickett method.
From this we conclude th at the change in the Au trend observed in
Fig. 8.10 is not a real effect.
Although, the Pickett method provides a more plausible
result, the d ata itself is not adequate to reliably determine the broadening effect.
Argon Broadening Experiment 3
In the argon experiment 3, improvements in the approach and execution of the ex-
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304
periment resulted in better quality d ata than was obtained previously.
change in the methodology was greater emphasis on tem perature control.
The principal
Analysis of
the obtained spectra by the direct method resulted in the collection of the HWHM values
plotted in Fig. 8.12.
The two points significantly off the trend set by the remainder of
the points arose from poor fits and were not included in the d a ta set used to determine
the pressure broadening coefficient. Regression analysis determined the value of T to be
5 ± 2 MHz/Torr.
Results from the Pickett method analysis of the argon experiment 3 (Fig. 8.13) spectra
are very good.
The w values plotted in Fig. 8.13 show a clear trend with little scatter,
even the two spectra from which the rejected HWHM values were obtained produced
acceptable w values. The T value determined for this data set is 9.4 ± 0.4 MHz/Torr.
Of all the d ata sets, this one has the largest discrepancy between the Pickett and
the direct method T values. The neon experiments had good agreement, relative to the
argon, between the T values obtained from the two methods.
Two possible sources of
the observed discrepancies were, the distortion of the peak by the base line suppression
routine, and the effects of noise on the accuracy of the fitting algorithm used by the
direct method to determine the HWHM value. The Pickett method should be relatively
immune to effects of the distortion from the baseline suppression routine. Estim ation of
the best and worst slopes obtained from the complete direct method d a ta set provide a
range of possible slope values between 4 and 8 MHz/Torr. From this it is obvious th at
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0.2 -
0.0
1 1 r 11 1 1 1 1 1 | r r i r n i M 1 1 1 1 1 1 1 1 1 i | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0
10
20
30
40
50
60
70
Pressure (mTorr)
Figure 8.12: Plot of the HWHM values obtained, from the direct m ethod for the argon 3
experiment. The fitted line is for all d ata points except the two th at are significantly
off the line. A regression analysis determined the T value to be 5 ± 2 M Hz/Torr. The
zero pressure broadening is 320 ± 70 kHz. The average tem perature is 92 ± 2 K. All
uncertainties represent 95% confidence intervals.
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306
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
60
APressure (mTorr)
Figure 8.13: Plot of argon 3 Pickett method w values vs A P. The reference pressure is
9.24 ± 0.06 mTorr. The pressure broadening coefficient is 9.4 ± 0.4 MHz/Torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
307
scatter, due primarily to noise, is causing the erroneous results of the direct method.
Combined D ata Set
The difficulties in obtaining a good signal to noise ratio for SiF+ lines in argon dis­
charges, prevented enough spectra from being acquired in a single experiment to create a
d a ta set from which an accurate determination of the T value for the SiF+ broadening by
argon could be made. A set of spectra created from the three separate argon experiments
was used with both the direct method, and the Pickett method. Two data sets, one of
HWHM values and the other of w values, were obtained. These two data sets were used
to determine the pressure broadening coefficient.
The direct method analysis results are shown in Fig. 8.14. The two points th at are
significantly off the fine were not included in the analysis.
The remaining points still
show a great deal of scatter, but the scatter appears to be random, so no further points
were discarded.
The T value obtained from the direct method is 5.6 ± 1.0 MHz/Torr.
Using the best and worst fits (Fig. 8.14) we obtain a T value of 6 ± 2 MHz/Torr.
Application of Pickett’s method required each data spectrum to be convoluted with
a common reference spectrum.
The potential for error in using a reference spectrum
from outside of the set of spectra collected during the same experiment was addressed
prior to conducting the analysis (Section 7.4.5). Provided the experimental conditions
were nominally the same, no significant error was introduced.
Once the w values were
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308
1.2 - i
1.0
-
0.8
-
0.6
-
0.4
-
0.2
-
N
0.0 “ |— i—i— i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—p
20
40
60
80
100
120
Pressure (mTorr)
Figure 8.14: Direct m ethod analysis of combined argon d a ta set. The three sets, argon
experiment 1 (A), argon experiment 2 (■), and argon experiment 3 (•), when combined
produce a d a ta set th at yields a T value of 5.6 ± 1.0 MHz/Torr. Some points of the argon
experiment 3 set were rejected and are noted, (O )- The worst fit lines are also shown (- -), and the T value obtained from this method is 6 ± 2 M Hz/Torr.
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309
obtained, the d a ta was filtered to control for various systematic errors.
The effects of
tem perature on the T value is well known, and increasing tem peratures decreases the T
value.
To control for the effects of tem perature all spectra above the tem perature of
>95K were excluded, this resulted in a tem perature range of approximately 5 K. Over a
range of this size the effects of tem perature should be minimal (Section 7.4]). The argon
experiment 1 d a ta set was known to have deviations above pressures of 50 mTorr. Those
points from argon experiment 1 with pressures greater than 50 mTorr were excluded.
T he resulting combined data set is plotted as a function of A P in Fig. 8.15.
The four
points well removed from the main trend, were more closely considered to determine if the
scatter was system atic or random. This was accomplished by judging the visual quality
of the fit (Section 7.4.6) and also considering the m.s.e. values. In all cases the quality
of the fit was poor and the m.s.e. > 0.60, justifying the exclusion from the set. The final
combined and filtered d a ta set was used with regression analysis to determine the T value
to be 8.8 ± 0.4 M Hz/Torr.
8.4
Discussion
Earlier pressure broadening studies conducted in this laboratory8,131 considered the
theoretical line broadening only from the standpoint of the Langevin model. Gudeman8
in particular studied the relationship between collisional rate constants obtained from
pressure broadening coefficients and those predicted using the Langevin model.
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The
310
0.8
0.6
(ZHW) *
oo
0.4
oo
0.2
0.0
0
20
40
60
80
100
APressure (mTorr)
Figure 8.15: Combined argon Pickett method w value d ata set. All Pickett values obtained
using a reference spectrum taken at a pressure of 9.24 ± 0.06 mTorr.
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311
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
20
40
60
80
100
A P ressu re (mTorr)
Figure 8.16: The combined and filtered argon pressure broadening of SiF+ . The points
are from the argon 1 experiment (ffl), the argon 2 experiment (0)> and the argon 3
experiment (□ ). This d ata set was obtained by the rejection of the spectra th at varied
the most from the trend line (Fig. 8.15), in all of which the Pickett algorithm failed to fit
the peaks well. The determined T value is 8.8±0.4 MHz/Torr. The average tem perature
of the discharge was 91.7 ± 0.8 K. Uncertainties in both tem perature and T correspond
to a 95% confidence interval.
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312
uncertainty in his values prevented the exclusion of the Langevin model in use for de­
scribing collisional broadening, and it was concluded th at pressure broadening arose from
the monopole-induced dipole interaction.
Since the time of Gudeman’s study, many additional studies, both theoretical and
experimental, of the pressure broadening of HCO+ have been conducted.8,127-131 These
studies show th at pressure broadening of HCO+ is more accurately modeled when the
dipole-induced dipole interaction is considered as the source of the broadening. A sum­
m ary of the experimental and theoretical T values obtained for the studies of argon and
neon broadening of SiF+ is presented in Table 8.5.
Of the values reported we believe th at T values obtained from the neon experiment 1,
the neon experiment 2, the argon experiment 3, and the combined d ata sets are the most
accurate. These values are listed separately in Table 8.6.
As with Buffa et a/.,127,128 we observe T values well below those predicted using the
Langevin model for our SiF+ and argon broadening study.
At J = 6 —►7 the r exp is
about 18% lower th an the Langevin value. Based on our theoretical calculations (Table
7.2), we expect th a t neon will be close to, but not less than, the Langevin limit.
This
supposition is supported by our Pickett analysis results which show th a t the Langevin
limit is just within or below the error range of the experimental value.
It should be
noted th at the T values determined using the direct method have uncertainties th at keep
us from excluding the Langevin model.
The agreement between the theoretical values
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313
Table 8.5: Summary of the experimental and theorectical T values obtained from the neon and
argon pressure broadening studies of SiF+. The results of the direct (D), the Pickett (P), the
edited direct (De), the edited Pickett (Pe) data sets are presented for the individual and the
combined (CP) experiments.
D ata Set
Neon ID
Neon 2D
Neon 2De
Neon 3D
Argon ID
Argon 2D
Argon 3D
Neon IP
Neon 2P
Neon 2Pe
Neon 3P
Neon 3Pe
Argon IP
Argon IPe
Argon 2P
Argon 3P
Argon CP
r
(MHz/Torr)
6
6
5.1
6.7
9
7
5
6.4
6.8
6.3
7.5
9
5.7
8
6
9.4
8.7
Ar
(MHz/Torr)
2
3
1.2
1.1
2
3
2
0.6
0.9
0.5
1.2
2
1.6
2
3
0.4
0.5
Tca/c
(MHz/Torr)
6.5
7.4
7.4
7.4
9.4
9.6
9.7
6.5
7.4
7.4
7.4
7.4
9.4
9.4
9.6
9.7
9.7
rL
(MHz/Torr)
4.7
5.9
5.9
5.9
9.9
10.4
10.8
4.7
5.9
5.9
5.9
5.9
9.9
9.9
10.4
10.8
10.6
T
(K)
130
102
102
102
100
95
92
130
102
102
102
102
100
100
95
92
93
AT
(K)
11
7.5
7.5
8
8
7
4
9
7.5
7.5
8
8
8
8
7
4
2
Table 8.6: Pressure broadening coefficients for the neon and argon broadening of SiF+
D ata Set
Neon IP
Neon 2P
Neon 2Pe
Argon 3P
Argon CP
r
(MHz/Torr)
6.4
6.8
6.3
9.4
8.7
AT
(MHz/Torr)
0.6
0.9
0.5
0.4
0.5
r C a lc
(MHz/Torr)
6.5
7.4
7.4
9.7
9.7
rL
(MHz/Torr)
4.7
5.9
5.9
10.8
10.6
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T
(K)
130
102
102
92
93
AT
(K)
9
7.5
7.5
4
2
314
and the experimental values, while biased by simplifications made in our calculations, is
generally good.
W hy the pressure broadening coefficients decrease beyond the Langevin limit is un­
certain.128,130
Buffa et al.n& speculated th a t because the energy needed to promote
transitions a t large J states is a significant portion of the translational energy, the failure
maybe due to the invalidation of the assumption that translational and internal degrees
are separable.
They reject this explanation based on the absence of a similar discrep­
ancy for the J= 2-3 transition of HCO+ a t low temperatures, which should occur if the
separation of translational and internal modes were no longer valid. O ur observations of
the neon and argon broadening of SiF+ show th at the energy of the transition is not the
most im portant factor in determining if the pressure broadening will reduce beyond the
Langevin value.
Liao and Herbst130 suggest th at the isotropic potential function [Eq.(7.9)] could draw
a pair of interacting particles to a region where the anisotropic potential [Eq. (7.10)] is
strong enough to cause scattering. This explanation is supported by our comparison of
the argon and neon broadening of SiF+.
We have observed, th at the smaller isotropic
interaction potential of the neon-SiF+ pair parallels a significantly weaker pressure broad­
ening effect, and a much higher J level onset to the Langevin limit compared to argon.
Furthermore, comparison of the calculated T values, for the SiF+ and HCO+ systems,
show th at the effect of changing the polarization of the collisional partner is significantly
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
315
larger than th a t of changing the reduced mass of the collision pair.
8.5
Comparison with the Langevin Model
In a previous work, Gudeman used the monopole-induced dipole interaction of the
Langevin model to describe pressure broadening of HCO+. To allow a direct comparison
of the results obtained by Gudeman 8 for HCO+ pressure broadening with the results
obtained for SiF+ pressure broadening, we will apply the same analysis Gudem an used
on HCO+ to SiF+.
Changes in the rotational level J, occur at a rate defined as the reciprocal of the mean
lifetime r between effective collisions
kcN = -
T
,
(8.1)
kc (cm3 /s) is the collisional bimolecular rate constant and N the number density. Townes
and Schawlow 18 relate the HWHM, A v to the mean time between collisions by
■
<
■
* *
Combining Eqs. (8.1) and (8.2), and assuming ideal gas behavior, A v can be expressed as
a function of tem perature:
•
<8 -3 >
The pressure broadening parameter is
l
d A v _ kc 1
dp ~ 2 x kT '
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
....
(8 '4)
316
where k is the Boltzmann constant. From Eq. (8.4) kc is given as follows:
kc —2n kT *^ -
.
(8.5)
The classical collision cross section is related to kc by
fec = vo
,
(8.6)
where v is the mean relative velocity between two particles of mass m \ and m 2 and is
defined by the Eq. (8)
v2 = 3fcT ( — + — ^
\m i
.
m2 J
(8.7)
Using Eq. (8.7), the classical collisional cross section a, is defined in term s of kc as
o = h = kc \ z k T ( — + — )}
V
L
\ m l
2 .
(8.8)
^ 2 / J
Comparison of the value of the collisional rate constant kc with the Langevin rate
constant fct has been used to provide insight into the nature of the collisional broadening
effect.8,128 The Langevin rate constant is calculated using
kL = 27re
,
(8.9)
where a:(cm3) polarizability of the neutral, and (m is the reduced mass of the ion neutral
collision pair.
Values for kc, k l , <t, and v calculated from the determined d A v/d p (Table 8.5) are
listed in Table 8.7. The polarizabilities for argon and neon used in the Langevin calcu­
lation are 1.6411xl0~24cm3 and 0.3956xl0“24cm3, respectively. 142,143
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317
As with the line broadening study, the kinetic approach shows clearly th a t the neonSiF+ collision rate constants are similar to the Langevin model. The argon rate constants,
however, are much less than that predicted by the Langevin model.
Based on these
observations, we can say that the monopole-induced dipole interaction is not the principal
relaxation effect.
Even with our less conservative error estimates, as compared with
Gudeman (95% confidence interval compared with worst case slopes), we still see the
uncertainties arising from noise limiting the usefulness of the direct method. The errors
in the direct method for our pressure broadening studies of ions are much greater than
those obtained from the Ol3CS study. There is much smaller error in the use of Pickett’s
method, as long as tem perature effects are well controlled.
T he difficulties in tem perature control resulted in a lack of directly comparable neon
and argon kc values.
The tem perature dependence of the pressure broadening value
dA u/dp and in the definition of kc itself make any direct comparison invalid.
Our results agree well with the current models of collisional broadening of molecular
ions.
The consistency of our experimental values with those predicted by theory is
pleasing.
The limited precision of our current measurements and the limited scope of
the J dependence investigations prevent us from gaining a more complete understanding
of the molecular ion line broadening. T he failure of all the current models to predict T
values less th an the T value obtained from a Langevin model, with the exception of ATC
with straight trajectories, remains an im portant point th at needs more investigation. Our
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318
Table 8.7: Pressure Broadening Summary
D ata Set
Neon ID
Neon 2D
Neon 2De
Neon 3D
Argon ID
Argon 2D
Argon 3D
Neon IP
Neon 2P
Neon 2Pe
Neon 3P
Neon 3Pe
Argon IP
Argon IPe
Argon 2P
Argon 3P
Argon CP
fcc:rl 0 10
cm3/s
5.0
4.0
3.4
4.4
3.2
4.2
2.9
5.4
4.5
4.2
5.0
5.8
3.7
4.9
4.0
5.6
5.3
Mc
cm3/s
1.9
T
(K)
130
2 .2
102
1 .0
102
7.5
7.5
1 .1
102
8
1 .6
100
8
1.9
1.3
0.9
0.9
95
92
130
AT
11
0 .6
102
7
4
9
7.5
7.5
1 .2
102
8
1 .8
102
8
1.5
1.5
1.9
0.5
0.4
100
8
100
8
95
92
93
7
4
102
2
V
(cm/s)
480.9
425.9
425.9
425.9
339.9
331.3
326.0
480.9
425.9
425.9
425.9
425.9
339.9
339.9
331.3
326.0
327.8
(h
Aa
fc^xlO10
(* )
cm3fs
43
54
27
37
50
63
41
3.9
3.9
3.9
3.9
6.5
6.5
6.5
3.9
3.9
3.9
3.9
3.9
6.5
6.5
6.5
6.5
6.5
104
93
79
104
94
127
88
113
106
98
117
136
109
145
121
173
161
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22
26
19
40
60
49
49
62
19
14
319
results support the suggestion by Liao and Herbst 130 th at the monopole-induced-dipole
interaction brings the ion and the perturber within a sufficient proximity th at the dipolemonopole-induced-dipole force can be im portant resulting in the broadening of the line.
8 .6
Pressure Dependent Line Shifts of SiF+
Studies of the pressure induced shift in the transition frequency have been focused on
neutral molecules and typically performed using IR spectroscopy (Section 7.2).
In this
section the line shift parameters s, obtained from the Pickett analysis of each of the neon
experiments and the combined set of argon spectra, are used to determine the pressure
induced shift. Plots of the s value dependence on the pressure differential are shown in
Figs. 8.17, 8.18, and 8.19, for the neon experiments, and in Fig. 8.20 for the argon study.
The neon 1 and 2 d ata sets have relatively little scatter and have a definite pres­
sure dependence, w ith pressure frequency shifts
77
of -0.7 ± 0 .3 M Hz/Torr and -1.2 ± 0.5
MHz/Torr, respectively. The uncertainties correspond to a 95% confidence interval, and
most likely over estim ate the accuracy of the values.
Additional fine shift studies will
need to be performed, before these values can be accepted with any degree of confidence.
As these two studies were not performed a t the same tem perature (Table 8.5), the effects
of tem perature on the pressure shift will also have to be considered.
The third neon experiment does not follow the trend th a t is exhibited in the previous
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
320
80
60
40
20
0
-20
-40
-60
•80
0
20
40
60
80
100
A Pressure (mTorr)
Figure 8.17: Regression analysis of the s values obtained from the Pickett method analysis
of the neon 1 experiment. The pressure dependent frequency shift rf is determined to be
0.7 ± 0 .3 MHz/Torr. The average tem perature was 130 K.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
321
100
s (kHz)
50 -
0 -
-100
0
20
40
60
80
A Pressure (mTorr)
Figure 8.18: The lineshift param eter t/ for the neon experiment 2 is determined to be
1.2 ± 0 .5 M Hz/Torr.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
322
neon experiments. Indeed the data points do not appear to follow any trend at all, and no
really useful information can be extracted from the data set. From the plot in Fig. 8.19
it appears th at there may be a dependence of the trend on the size of the frequency
increment used in the acquisition of the spectrum. The 45 kHz step size points appear
to have a negative slope similar to the neon 1 and 2, which were also taken with 45 kHz
step sizes, while the 60 and 75 kHz step size spectra seem to have a positive slope.
The line shift values obtained from the combined argon set are so scattered th at no
real trend can be established. The small signal to noise ratio limits the accuracy of the
line shift studies much more than it does the broadening measurements
Several systematic errors could not be removed from the data, so the results obtained
from this study must be considered qualitative a t best. The principal systematic errors
th at could not be removed are the electric field induced Doppler shift, asymmetries in the
peaks, noise and the loss of resolution when larger scan widths, or step sizes, are used.
The Doppler shift arises from the interaction of the ionic charge w ith the electric field
present in the discharge (Section 6.4.2). The direction of the Doppler shift is dependent
on the charge of the ion and the polarity of the discharge. In these studies our discharge
was used in the negative polarity, which means th at the cathode is near the detector and
th at the positive SiF+ ions will experience a redshift in frequency. The magnitude of the
shift is dependent on the strength of the electric field. In positive column discharges the
electric field is strong enough to cause an appreciable shift in the frequency, while in the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
323
0.08
©
0.06 -j
0.04 -
0.02
IS I
©
0.00
©
(O
m
a
-
0.02
a
•0.04
•0.06
H
•0.08
~f'nT-rt~t n i f i i i m i i i r | i i i i | i i i i | i i i i | i r r r | r i 11 111 1 1 1
20
40
60
80
100
A Pressure (mTorr)
Figure 8.19: The plot of the frequency shift parameter s, as a function of the pressure
differential between the reference and d a ta spectra, for the neon experiment 3 d ata set.
The scatter in the d a ta is too much to determine any reliable pressure shift coefficient.
The three different step sizes are 45 kHz (•), 60 kHz (EB), and 75 kHz (®).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
325
negative glow discharge, the electric field is generally too weak to induce a measurable
shift.
The neon experiments were conducted in the negative glow mode only, so very
little of the observed shift can be due to the Doppler shift.
The argon experiments,
however, contain both the low pressure negative glow and the high pressure positive
column discharges. As a consequence, the Doppler shift contribution to the overall line
shift will not be uniform and we expect th at the higher pressure points will have more
negative s values. The argon experiment plot (Fig. 8.20) shows no discernible dependence
of the s values distribution on the discharge mode, so we conclude th at the Doppler shift
is a t best a minor contributor to the observed scatter.
Another source of error is the shift arising from anomalous dispersion (Section 3.3).
Gudeman8 showed th at centering the absorption line on a maximum of the sinusoidal
baseline will cause the shift to go to zero.
While this remedy works well for constant
tem perature neutral gas studies (no discharge), the cooled discharges used in this study
have been observed to be associated with drifts in the maxima of the baseline.
W ith
the studied transition being somewhat weak, particularly a t the higher pressures, signal
averaging required acquisition times such that it was nearly impossible to obtain spectra
where the transition was centered on the maxima of the averaged scan.
The signal to noise ratio of the spectra in the argon experiment was significantly
less th an in either the OCS study (Section 7.5), or in the neon studies. Excessive noise
superimposed on the peak may increase the uncertainty of the transition frequency, which
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
327
A. Instrumentation: Source Diagram
C19
C18
C17
C20
C21
C2
C22
S25
S9
S16
C15
S 26
S10
C3
C14
S11
C.6
C4
C24
C29
C28
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
_C23
328
nponcm
Description
Company
Scientific
Cl
Pan/Model Number
ZSC2-1
Components Corp
C2
Multiplier Bias Box
Millitech
BMU-1
C3
Frequency Tripler
Millitcch
MU3-W11-1106
C4
Eband Directional Coupler
Hughes
4532JH-1106
C5
10 dB Directional Coupler
Hewlett Packard
W752C
Huges
45775H-1000
Omniyig
C104D
C6
Temp. Compensated
Thermistor Mount Eband
S7
4-8 GHzYig Filter
Miteq
S8
S9
Frequency Source 6000 MHz
S10
Amplifier
S ll
Harmonic Mixer
MXO-WB
MS-540 XE-10(9)
OmniPac
01073
Hughes
47435H-1001
3N-3E
MillimetcrWave
CI2
Dial Calibrated Attenuator
Baytron
C13
Dial Calibrated Attenuator
Baytron
3N-3E
C14
Isolator Eband
Hughes
45I15H-
CI5
Gunn Oscillator
J. E Carlslrom
SI6
Gunn Phase Lock Module
XL Microwave
Model 800A
C17
Control Model
XL Microwave
Model 801
C18
Ailtech 10 MHz reference freq.
Ailtech
CI9
Ailtcch Frequency Output
Ailtech
C20
Function Generator
FlukeTPhillips
PMJ193
Textronix
7603
Hewlett Packard
HP
60-90 Ghz Waveguide Mixer
Textronix
WM490E
Attenuator 6.0t/- 3 dBm
OmniSpcctra
20640-6
OmniSpectra
20640-3
OmniSpcctra
206106
Modulation Source
C21
Gunn Diode output to Scope
C22
100 MHz Reference Frequency
C23
IF Monitor Output
to Spectrum Analyzer
C24
S25
(minature osmfsma))
S26
Attenuator 3.0*/-J dBm
(minature osm(sma))
S27
Attenuator 6.0*7- 3 dBm
(minature osm(sma)>
C28
Spectrum Analyzer
Textronix
494A P
C29
Power Meter
Hewlett Packard
432A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
329
B. Buffer Circuit
Q1
Q2
D2
This is the schematic o f the buffer circuit built by Mike Green and used to interface between the
probe and the voltage follower circuit. The resistors R1-R4 are 1 MO with a power rating o f 4
watts. The resistor, R5, has a 3 MO 1/4 watt rating. Two Power FETs (MTP3N100), Q l and Q2 are
used. The diodes, D l and D2, are 1N4740A 10 V zener diodes. The high voltage is applied at A,
maximum 1500 V, the input signal at B, and the output is read at C.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
330
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