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Laser diagnostics of atomic hydrogen and oxygen production in RF and microwave plasma discharges

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Laser diagnostics of atomic hydrogen and oxygen production in
RF and microwave plasma discharges
Preppemau, Bryan Lee, Ph.D.
The Ohio State University, 1993
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
LASER DIAGNOSTICS OF ATOMIC HYDROGEN AND OXYGEN
PRODUCTION IN RF AND MICROWAVE PLASMA DISCHARGES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Bryan Lee Preppemau, B.A., B.S.E.
ft
ft
ft
*
*
The Ohio State University
1993
Dissertation Committee:
Approved by
T. Miller
E. Herbst
T. Gustafson
Adviser
Chemical Physics Program
ACKNOWLEDGMENTS
This dissertation reflects the culmination of many years of endeavor
and I should express my appreciation to those who have contributed in
many ways to enhance my own efforts while in Graduate School. In
addition, I wish also to recognize the support and guidance of those I've
have know professionally throughout the years and from my previous
education. Therefore, I wish to sincerely thank all of those listed below
as well as my parents and family and especially my wife, Mary Post, for
their unending consideration and wisdom.
The Ohio State University:
Dr. Terry Miller
Dr. Harris Kagan
Dr. Jim Dunlop
Angelika Tserepi
Dr. Vish Subramaniam
Dr. Richard Kass
Dr. David Dolson
Tim Cerny
Dr. Suliman Dregia
Dr. Terry Gustafson
Chris Carter
Ken Pearce
AT&T Bell Laboratories
Dr. Richard Gottscho
Advanced Plasma Group. Wright-Patterson Air Force Base:
Dr. Bish Ganguly Dr. Alan Garscadden
Dr. Charles Dejoseph
Dr. Peter Bletzinger
Air Force Institute of Technology:
Dr. Eric Jumper
Dr. William Bailey
Dr. Max Stafford
Dr. David Griffiths
Dr. Ken Davis
Reed College:
Dr. Nick Wheeler
VITA
April 18,1959.......................................................Born - Aberdeen, Maryland
1981.....................................................
B.A.,
Physics, Reed College
Portland, Oregon
1982-1987......................................................Officer, United States Air Force
1984..............................................................B.S.E., Aeronautical Engineering
Air Force Institute of Technology
Wright-Patterson AFB, Ohio
1987-Present..................................................... Graduate Research Assistant
Chemical Physics Program
The Ohio State University
PUBLICATIONS
Absolute H-Atom Concentration Profiles in Continuous and Pulsed RF
Discharges, A. Tserepi, J. Dunlop, B. Preppemau, and T. Miller, J. Appl.
Phys., 72 (7), 2638, 1992.
The Effects of Surfaces on H-Atom Concentration in Pulsed and
Continuous Discharges, A. Tserepi, J. Dunlop, B. Preppemau, and T.
Miller, J. Vac. Sci. & Tech., 10 (4), 1188,1992.
Nucleation and Growth of Diamond on Silicon using Hot Filament CVD, J.
Rebello, D.Straub, V. Subramaniam, E.. Tan, S. Dregia, B. Preppemau, and
T. Miller, Mat. and Manuf. Processes, 6 , 501,1991.
H-Atom Plasma Diagnostics: A Sensitive Probe of Temperature and Purity,
J. Dunlop, A. Tserepi, B. Preppemau, T. Cerny, and T. Miller, Plasma
Chem. and Plasma Process., 11 (4), 1991
hi
Real-Time Monitoring of Low-Temperature Hydrogen Plasma Passivation
of GaAs, R. Gottscho, B. Preppemau, S. Pearton, A. Emerson, and K.
Giapis, J. Appl. Phys., 68 (2), 440,1990.
Enhanced Atomic Hydrogen Concentration Measurements in Radio
Frequency Discharges, B. Preppemau and T. Miller, J. Vac. Sci. Technol. A,
8 (3), 1673, 1990.
Temporally Resolved Laser Diagnostic Measurements of Atomic
Hydrogen Concentrations in RF Plasma Discharges, B. Preppemau, D.
Dolson, R. Gottscho and T. Miller, Plasma Chem. and Plasma Process., 9
(2), 157, 1989.
Rydberg State Stark Spectroscopic Measurement of Electric-Field Profile
in a Glow Discharge, B. Ganguly, J. Shoemaker, B. Preppemau, and A.
Garscadden, J. Appl. Phys., 61 (8 ), 2778,1987.
Adaptations of a Wall-Catalytic Fluorine Recombination Model to FluidDynamic Computations in an HF Laser Nozzle, E. Jumper, P. Wilkins, and
B. Preppemau, J. AIAA, Apr 1987.
Laser-Based Diagnostics of Reactive Plasmas, B. Preppemau and T. Miller,
(Plenum Press, New York, 1993).
FIELDS OF STUDY
Major Field: Chemical Physics
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS......................................................................................ii
VITA.................................................................................................................iii
UST OF TABLES..............................
vi
UST OF FIGURES...............
vii
CHAPTER
I. INTRODUCTION TO LASER DIAGNOSTICS FOR PLASMA PROCESSING
1
A. Scientific and Technological Significance of Plasmas.................... 1
B. Technological Impact of CVD Diamond...........................................4
C. Overview of Plasma Diagnostic Techniques................................... 7
H. THE GEC REFERENCE CELL.......................................................................12
m. DIAMOND CHEMICAL VAPOR DEPOSITION CHEMISTRY........................ 21
IV. EXPERIMENTAL TECHNIQUES...................................................................34
A. Experiment Apparatus....................................................................34
B. H-Atom and O-Atom Concentration Calibration Procedure....... 44
C. Effects of Quenching Upon Concentration Measurements.........50
V. EXPERIMENTAL RESULTS FROM A GEC REFERENCE CELL...................... 85
VI. EXPERIMENTAL RESULTS FROM AN ASTEX DIAMOND REACTOR.......104
APPENDIX A: EXPERIMENTAL QUENCHING DATA......................................127
APPENDIX B: COMPUTER ACQUISITION AND ANALYSIS PROGRAMS.......135
BIBLIOGRAPHY..............................................................................................174
v
UST OF TABLES
Table
Page
1. Comparison of Diamond and Silicon Electronic Properties................ 5
2. Comparison of Measured and Calculated Fluorescence Lifetimes for
Helium Quenching.................................................................................75
3. Comparison of Measured and Calculated Fluorescence Lifetimes for
Argon Quenching.................................................................................. 79
4. Cross-Sections for Quenching of Hydrogen Atoms (n=3)...................82
5. Computed Maximum H-Atom Densities in GEC Reference Cell
vi
92
UST OF FIGURES
Figure
Page
1. The GEC Reference Cell....................................................................13
2. C-H-0 Phase Diagram. Unshaded area is nominal diamond growth
region........................... .........................................................................25
3. Experiment Layout Schematic for H-Atom TALIF.......................... 36
4. Experiment Layout Schematic for O-Atom TAUF..........................40
5. Representative H-Atom TAUF Signal Trace.................................... 42
6 . Titration Assembly........................................................................... 47
7. O-Atom TAUF Titration Curve. Data corresponds to a
concentration of 5.98 x 1015 cm-3. Line is a linear regression
extrapolation for determining the titration endpoint. X-intercept is
7.63 seem of NO2................................................................................... 49
8 . H-Atom TAUF by Photodissociation of C2H2..................................52
9. Nonlinear Dependence of C2H2 H-Atom TAUF Signal. Straight line
represents a linear regression fit to the initial rise of the data
53
10. Inverse Quantum Yield Dependence on Pressure........................55
11. Radiative Lifetime of n=3 State from Photodissociated C2H2 HAtom TAUF............................................................................................ 58
12. Radiative Decay of n=3 Component Levels for 1 Torr Quenching
by H2. Also shown is the Normalized Radiative Rate, R*.................. 63
13. Radiative Decay of n=3 Component Levels for 10 Torr
Quenching by H2. Also shown is the Normalized Radiative
Rate, R*....................................................................................................64
14. Calculated Quenching Curves With and Without Nonradiative
Deexcitation or L-State Mixing and the Total of Both Effects
65
15. Comparison of Calculated and Experimental H-Atom TAUF
Quenching by Acetylene....................................................................... 67
16. Measured Versus Calculated Photodissociated Acetylene H-Atom
TAUF Signal............................................................................................69
17. Low-Pressure Detail of Figure 16. Straight line is from linear
regression fit as shown in Figure 8 ...................................................... 70
18. Measured versus Calculated H-Atom TAUF Lifetime from
Photodissociation of C2H2. Straight Line is from linear regression fit
as shown in Figure 11............................................................................71
19. Comparison Fit of Quenching Model Calculations to
Experimental Quenching of H-Atom TAUF by H2 Gas....................... 73
20. Expanded Horizontal Scale from Figure 19................................... 74
21. Quenching of H-Atom TAUF by Helium. The upper curve is
calculated based on data from Reference 87.......................................76
22. H-Atom TAUF Quenching by Argon. Lower curve is calculated
based on data from Reference 87.........................................................78
23. Quenching by Nitrogen. Lower calculated quenching curve is
based on data from Reference 87.........................................................80
24. Quenching by Oxygen. Lower calculated quenching curve is
based on data from Reference 87.........................................................81
25. GEC Reference Cell Geometric View Factor Correction. Origin is
position of powered electrode..............................................................87
26. TAUF H-Atom Signal Profiles in GEC Reference Cell for Different
H2 Pressures. Power deposited in plasma is 30 Watts........................89
27. Quenching Corrected TAUF Signal Profiles From 26...................90
28. H-Atom Balmer-a Emission Profiles in GEC Reference Cell as a
Function of H2 Pressure........................................................................ 93
viii
29. Interpolated 3-D Mesh Representation of H-Atom Balmer-a
Emission Profiles....................................................................................94
30. Quenching Corrected H-Atom Baimer-ex Emission Profiles
97
31. Quenching Corrected Interpolated 3-D Mesh Representation of
H-Atom Balmer-a Emission Profiles.....................................................98
32. Plasma Current as a Function of H2 Pressure in GEC Reference
Cell.......................................................................................................... 99
33. Total Plasma Voltage and DC Bias as a Function of H2 Pressure in
GEC Reference Cell.............................................................................. 100
34. Comparison of Maximum H-Atom Density and the Product of
Current and Pressure as a Function of Pressure...............................101
35. The ASTEX HPMM Microwave Diamond Growth Reactor
106
36. ASTEX Reactor Geometric View Factor Correction.................... 109
37. Raw Data for H-Atom TAUF Concentration Map in 0.7596 CH4 /H 2
Methane-Based Diamond Growth Plasma.
Xc=l, Xo=0, Xh=0.996..........................................................................112
38. Corrected Data for H-Atom TAUF Concentration Map in 0.7596
CH4/H 2 Diamond Growth Plasma. Maximum H-Atom Density is 3.70
± 0.18 x 1017 per cm 3......................................................................... 113
39. Raw Data for H-Atom TAUF Concentration Map in MethaneBased Diamond Growth Plasma.
Xc=0.451, Xq=0.048, andXH=0.96...................................................... 115
40. Corrected TAUF Data from Figure 39. Maxim um H-atom density
is 5.09 ± 0.93 x 1017 per cm 3............................................................. 116
41. Raw Data for H-Atom TAUF Concentration Map in Acetone-Based
Diamond Growth Plasma. Xc=0.52, Xo=0.32, and XH=0.67..............117
42. Corrected TAUF Data from Figure 41. Maximum H-Atom density
is 2.77 ± 0.28 x 1017 per cm 3............................................................. 118
43. Repeat Corrected TAUF Scan for Conditions in Figure 41........ 119
44. Raw Data for O-Atom TAUF Concentration Map in Acetone-Based
Microwave Plasma. Xc=0.41, Xq=0.42, and XH=0.67......................... 121
45. Corrected O-Atom TAUF Data from Figure 44. Maximum O-Atom
Density is 1.2 ± 0.12 x 1017 per cm 3..................................................122
46. H-Atom TAUF and Stimulated Emission Pumping (SEP) Signals as
a Function of H2/O 2 Mass Flow Ratio in Microwave Plasma.
123
47. O-Atom TAUF and Stimulated Emission Pumping (SEP) Signals as
a Function of Acetone/ 0 2 Mass Flow Ratio
in Microwave Plasma............................................................................124
x
CHAPTER I
INTRODUCTION TO LASER DIAGNOSTICS FOR PLASMA PROCESSING
A. Scientific and Technological Significance of Plasmas
The final decade of the twentieth century is witness to a renewed
impetus
in
our
capability
to
manipulate
chemically
reactive
environments to form novel materials in part based on detailed
theoretical and computational calculations. As these predictions and
models become more elaborate the constant need is to provide
quantitative input data and experimental verification. The rapid advance
of technologies derived from the inter-related fields of chemistry,
physics, and materials science may give the impression that basic
experimental inquiry is perhaps counter-productive or even unnecessary
and
that
these
achievements
are
solely
driven
by
economic
considerations. However, many areas of endeavor suffer from a lack of
basic physical or chemical understanding and are not supported by a
solidly established experimental database. The economic impetus to
advance production techniques and volume is perhaps unfortunately
overshadowing basic research considerations which always provide the
initial stimulus for new technologies.
A recent panel committee on plasma processing of materials
formed under the Plasma Science Committee established by the National
1
2
Research Council agreed with this view and presented as one of their
findings that
The demand for technology development is outstripping scientific
understanding of many low-energy plasma processes. The central
scientific problem underlying plasma processing concerns the
interaction of low-energy collisional plasmas with solid surfaces.
Understanding this problem requires knowledge and expertise drawn
from plasma physics, atomic physics, condensed m atter physics,
chemistry, chemical engineering, electrical engineering, materials
science, computer science, and computer engineering. In the absence
of a coordinated approach, the diversity of the applications and of
science tends to diffuse the focus of both . 1
This course of events is suggested throughout recent work in lowtem perature plasma processing of materials. The use of glow discharge
plasmas to deposit materials or to modify surface structures through
etching processes has been a developing area of technological expertise
since the late 1960's. Now important advances are being made in the use
of plasma etching techniques for producing novel devices such as
quantum interference well surface-emitting lasers and materials such as
light-emitting porous silicon2 while, at the same time, there is poor
understanding of the plasma-surface interface chemistry generated by
reactive ion or neutral bombardment leading to selective anisotropic
etching of the surface atomic components. Beside the etching process,
surface modification by exposure to a glow discharge plasma is
beginning to find use in the modification of composite materials and
metal surfaces and for the critical surface passivation 3 of compound
(GaAs) device interfaces for which no native oxide material exists as in
the case of silicon. Here again there is incomplete knowledge of how the
3
plasma and its components affects the surface state in these
applications.
The purpose of this dissertation is to describe the experimental
techniques
and
results
for
absolutely
calibrated
concentration
measurements of atomic hydrogen and atomic oxygen. Both atomic
hydrogen and oxygen are among the most important reactive species
generated
in
plasma
processing
environments.
Such
absolutely
calibrated measurements provide experimental reference data for a
comparison between our theoretical understanding and computational
modeling of plasma processing systems.
In an effort to provide a secure experimental foundation and
theoretical basis for understanding plasma processing techniques and
systems such as those mentioned above, the plasma processing research
community has in recent years advocated the development of standard
reference plasma processing systems. Measurements in a reference
plasma reactor would allow multiple plasma diagnostic techniques to
characterize
as
completely
as
possible
the
internal
operating
environment of the reactor. By correlating measurements in several
identical reference reactors at different institutions, a standardized
concept of plasma reactor design and operation could be achieved. In
turn, the standardization of diagnostic measurement techniques would
provide reproducible input data and hence improve the ability of theory
and computational programs to predict reactor operating parameters
and to extrapolate the behavior of the standard reactor to either actual
plasma processing production systems or to more innovative and
developmental reactors. In 1988, at a workshop sponsored by the
4
Gaseous Electronics Conference (GEC), scientists and production
engineers discussed the initial conceptual design of a standard reference
cell reactor. The reactor came to be known as the GEC Reference Cell.
Since the final design and manufacturing features were completed in
1989, ten of the GEC Reference Cells have been installed at 6 facilities
around the U.S.
This thesis presents the results of spatially-resolved absolute
concentration measurements for atomic hydrogen and oxygen in two
actual plasma processing systems. Atomic hydrogen concentration
profiles were measured in one of the GEC Reference Cell reactors
installed at Wright-Patterson Air Force Base, Ohio. Measurements were
also made in a commercially built plasma reactor (ASTEX HPMM System)
installed at The Ohio State University which is used for diamond thin
film deposition from a microwave-excited CVD plasma. Measurements of
atomic hydrogen and oxygen concentration profiles were obtained.
B. Technological Impact of CVD Diamond
A recent area of vigorous development involves the deposition of
high quality diamond thin films by enhanced chemical vapor deposition.
Moderate pressure direct current (DC), radio frequency (RF), and
microwave excited glow discharge plasmas are used (among other
methods) to provide energetic dissociation and excitation to a
hydrocarbon gas mixture. The combination plasma and neutral gas
mixture can then be exposed to a variety of hot substrate materials to
nucleate and deposit a material consisting predominately of sp 3 bonded
polycrystalline diamond. The technological impact of the advent of low-
cost readily produced thin film diamond is enormous. Surface
conforming thin film diamond can be made to coat machine tool and
bearing surfaces taking advantage of diamond's inherent hardness. The
excellent thermal conductivity of the diamond atomic structure has been
utilized in the production of diamond heat sinks for use with high
power or high density electronic circuitry. In it's own right, diamond has
valuable electronic properties; several of which are shown in Table 1 in
comparison with those for silicon.4
Table 1. Comparison of Diamond and Silicon Electronic Properties
Property
Resistivity
Breakdown Field
Electron Mobility
Hole Mobility
Saturation
Velocity
Band Gap
Transmutation
Cross Section
Diamond
> 1012 f3-cm
107 V / cm
2000 cm2 / V*s
2100 cm2 / V*s
2x l 0 5 m /s
Silicon
1 05 f3-cm
103 V / cm
1450 cm 2 / V*s
370 cm 2 / V*s
lx l 0 5 m /s
5.50 eV
1.12 eV
3.2 mb
80 mb
With the advantages of low leakage current due to higher inherent
resistivity and breakdown field, larger electron-hole mobilities which
implies improved device operating speed, larger indirect band gap and
radiation hardness, research into the use of diamond thin films is
beginning to spawn a new generation of diamond-based semiconductor
devices.
6
Along with the ambitious application of thin film diamond
technology, there remains the central problem of an incomplete
understanding of just how polycrystalline diamond is produced from a
wide variety of chemical vapor deposition (CVD) environments such as
thermally-activated hot filament reactors, oxy-acetylene flames, low
pressure plasma assisted CVD and high pressure thermal arcs and even
laser-assisted CVD. It is known that each of these systems is capable of
producing polycrystalline diamond thin films under a variety of
conditions with varying growth rates, crystalline texture, and resulting
thermal and electronic film properties. But, several questions remain as
to how these conditions and properties come about:
• Is there one key molecular radical gaseous precursor produced in
diamond CVD systems which leads to surface deposition of diamond
or are there many variants which lead to similar results?
• What is the role of certain atomic species such as hydrogen, oxygen, or
fluorine that are generated during the CVD process and are known to
interact vigorously with the deposition surface?
• Why do so many seemingly varied CVD environments provide
remarkably similar diamond deposition characteristics?
• What influence do the gaseous components of the CVD process have
over the deposition surface crystal orientation and texture?
• And, ultimately, can control of the diamond CVD process be achieved
so as to step beyond polycrystalline or even homoepitaxial deposition
to true heteroepitaxial diamond film growth at productive growth
rates and uniformities.
7
Beyond these questions there are still unresolved issues concerning
the adaptation of diamond's material and electronic properties for
technological applications, but certainly progress in understanding the
answers to the above fundamental research questions will provide a firm
foothold for manipulating CVD diamond as an innovative material into
the twenty-first century.
For CVD diamond deposition, it appears that the highest quality
diamond films (in terms of electronic and material properties) are
produced via microwave plasma enhanced chemical vapor deposition.
As far as application to the semiconductor processing, microwave or
electron cyclotron resonance (ECR) plasma diamond deposition systems
are probably the most readily adapted to current semiconductor
production methods; indeed microwave-based systems are beginning to
find uses in other areas of plasma processing of semiconductor materials
such as reactive ion etching (RIE). However, the techniques discussed in
this thesis may be extended to filament-assisted and flame deposited
CVD diamond systems.
C. Overview of Plasma Diagnostic Techniques
Critical to the development of our understanding of basic plasma
chemistry systems is the parallel development of diagnostic techniques
necessary to study these environments in situ. The current emphasis
now is to develop diagnostics that can be applied towards the difficult
task of discerning the variety and absolute quantity of plasma species.
Because of the short-lived nature of many important species present in
chemically reactive plasmas care must be taken to insure that diagnostic
measurements accurately reflect their relative as well as absolute
abundances and their relationship to the physical plasma parameters.
Currently, plasma diagnostic measurements for plasma-induced
species are derived from three basic approaches. External sampling
techniques such as mass spectrometry or gas chromatography are
capable of generating general survey information about the basic plasma
constituents provided efforts are made to make measurements in as
close proximity to the plasma volume as possible and to in turn reduce
the effect of recombination mechanisms in the external analyzer which
artificially perturb the analysis of the nascent population distributions
for the species of interest. Wu et al have had good success in selfconsistent analysis of reactant species which have been sampled by gas
chromatograph probe at the boundary of a CVD diamond deposition hotfilament plasma .5
A second approach makes use of plasma emission spectrometry to
detect the presence of certain radical species existing in the plasma. The
major drawback of this technique is that it is capable of measuring only
excited state radical distributions. Since these states are typically
generated by electron impact excitation or dissociation, inferences must
be made about the ground state populations for a particular radical.
Often due to the low ( < 1 % ) fractional ionization and electron
tem perature found in electronic processing plasmas, excited state radical
species concentrations are in turn a small percentage compared to the
ground state concentrations. In addition, electron impact excitation and
production cross sections are nonlinearly dependent upon electron
translational energy making production pathways complicated functions
of electron energy distributions. However, plasma emission spectroscopy
can be used to partly determine the degree of dissociation of precursor
molecules by determining what excited state fragments are present and
to determine plasma physical parameters such as electric fields (Stark
broadening) or translational or rotational gas temperatures by analyzing
Doppler widths or resolved molecular rotational emission manifolds .6
The final set of experimental approaches utilize laser-based
techniques. Such techniques currently offer the best procedures for
making non-intrusive in situ measurements of plasma generated ground
state radical concentrations as well as some plasma physical parameters.
By using a single probe beam of light a reasonable degree of spatial
resolution can be achieved in one or more dimensions compared to
either mass spectrometry or optical emission measurements. Laser
spectroscopic probe diagnostics can be further divided into two general
classes. The first class of laser diagnostics consists of those techniques
which make use of nonlinear absorption or multiphoton absorption and
subsequent ionization to detect the sought after atomic, molecular, or
radical species. Coherent anti-Stokes Raman spectroscopy (CARS) and
resonantly-enhanced
multiphoton
ionization
(REMPI)
or
laser
optogalvanic spectroscopy (LOGS) are characteristic of this class of laser
diagnostic. Both CARS and REMPI can provide an excellent means of
detecting a large variety of plasma-generated ground state radicals ,7*8'9
either due to the efficient collection of ionization charge (REMPI and
LOGS) or as in the case of CARS the emitted coherent beam of light is
emitted in a single direction with small divergence and is easily collected
10
with near unit efficiency. However both techniques suffer from
difficulties in calibration and it becomes problematic to place the species
distribution on an absolute scale. Due to the highly nonlinear response
of CARS calibration of these measurements rely on careful control of the
incident beam intensities as well as their overlap in space and time.
REMPI and LOGS in particular are difficult to calibrate due to interactions
of the laser ionization electron with the surrounding plasma medium
resulting in an undetermined electron multiplication factor.
The second class of laser-based plasma diagnostics consists of laser
absorption spectroscopy and laser-induced fluorescence (UF). While laser
absorption spectroscopy may not provide a suitable dynamic range in
signal sensitivity and laser-induced fluorescence, which is usually
radiated isotropically, does not enable efficient signal collection, they are
perhaps more manageable when one attempts to calibrate such
measurements and often they can provide better signal to noise ratio
than other techniques.
Tunable infrared diode laser absorption spectroscopy has been used
to measure absolute concentrations for a number reactive hydrocarbon
radical species produced in methane-based deposition plasmas .10
Calibration of laser absorption measurements is achieved by using a
detailed knowledge of the molecular spectroscopy for the radical of
interest; including molecular band strengths, partition functions, spin
degeneracy's, transition energies, and path length.
Laser-induced fluorescence is beginning to be used to make
absolutely calibrated radical species concentration profiles within lowtem perature processing plasmas. Previously LIF has been used for
11
measurements on stable molecular species and metastables ,11 positive
and negative ions ,12 and for plasma physical parameters such as the
local electric field .13 By use of two-photon absorption from the ground
state of an atom many light reactive atoms such as H, C, N, O, S, Cl, and F
could conceivably be detected by UF measurements in situ in processing
plasmas. In the course of research performed for this dissertation, twophoton allowed laser-induced fluorescence (or TAUF) diagnostics have
been developed for calibrated concentration measurements for two of
the most important ground state atomic species, atomic hydrogen and
oxygen. This dissertation describes these measurements and their
practical application.
The remainder of the thesis is organized as follows: Chapter Two
will briefly describe the development and design of the GEC Reference
Cell, as well as the diagnostics performed to date on this system. Chapter
Three will briefly review the historical development of diamond chemical
vapor deposition and then describe what is currently known about the
gas-phase plasma chemistry leading to diamond deposition. Chapter
Four will describe the experimental techniques used to determine
absolutely calibrated concentration spatial profiles for atomic hydrogen
and atomic oxygen. Having discussed the experimental methods, Chapter
Five will describe the results of experimental measurements in an actual
GEC Reference Cell system. Finally, Chapter Six details the results of
measurements of atomic hydrogen and oxygen concentrations in an
ASTEX microwave diamond growth reactor.
CHAPTER n
THE GEC REFERENCE CELL
The Gaseous Electronics Conference Reference Cell (known as the
GECRC) concept was initially conceived in 1988. A workshop dealing with
preliminary design proposals for a standard reference cell plasma
processing reactor was held during the 41st Annual Gaseous Electronics
Conference (GEC) at the University of Minnesota in Minneapolis in
October 1988.14 The workshop attendees were asked to review several
preliminary design proposals for the reference plasma system. Upon
extended discussions a consensus was reached on developing a radio
frequency (RF) excited parallel plate electrode plasma reference cell
operating at 13.56 MHz. The following March of 1989, another workshop
sponsored by SEMATECH was held in Austin, Texas.15 At this workshop a
committee of representatives from the plasma processing community
reviewed comments from forty other plasma processing researchers
regarding the initial design proposal formulated at the previous
conference. Upon review of these comments the committee then
finalized the GECRC design and determined the need to have four of the
reactor systems built by industrial suppliers to test the GECRC design.
The basic configuration for the system is shown in Figure 1 in cross
section.
12
13
Cooing Wator
Metal Hold-down Ring
O-RIng Seal
Gas Feed
Top Insulator
Ground Shield
Top Electrode
Shower Head
Top F langt^
Main Viewing Ports
t.
Bottom
Electrode
Bottom Flange
Manifold for
flowing gas
operation
Port tor High
Vacuum
Pump-oul
f
\
Ground Shield
Bottom Electrode
Annular Pump-out
Connection
Figure 1. The GEC Reference Cell
14
Since that time on the order of ten GECRC's have been installed and
are operating at research organizations throughout the U.S. at
institutions such as AT&T Bell Laboratories, IBM, National Institute of
Standards and Testing (NIST), Sandia National Laboratories, the
University of Michigan, the University of New Mexico, and WrightPatterson Air Force Base. International interest in the standard reference
cell concept has increased with researchers in France, Germany, and
Taiwan planning to purchase the GECRC system. Japan is developing a
separate reference cell design.
The basic configuration of the GECRC as mentioned is shown in
Figure 1. The cell is a UHV stainless steel chamber with a volume of
approximately 12.9 liters, comparable in size to standard production
plasma processing reactors. The 4 inch diameter water-cooled electrodes
used are made of aluminum with an adjustable (optional) interelectrode
spacing nominally set at 1 inch. Provisions were made in the design to
allow for other electrode materials such as stainless steel. The electrodes
are insulated from the rest of the assembly by either alumina or teflon
insulators. Surrounding the electrode insulators are grounded guard
rings or shields which serve to help confine the plasma discharge to a
cylindrical region between the electrodes of diameter approximately
equal to the electrode diameter as well as to reduce sputter etching of
the insulator material.
Vacuum pumping is accomplished through connection of the main
chamber to a lower pump-out chamber. Slots in the flange interface
between the two chambers serve to minimize angular variations in gas
pumping speed around the main chamber volume. The chamber is
15
typically pumped with a 300 liter per second turbomolecular pumped
backed on the foreline by a diaphragm roughing pump. The GECRC is
designed to have a pump down base pressure of 10'? Torr and has low
conductance because the pump-out manifold does restrict pumping
speed. Typical gas flow rates are 10-100 standard cubic centimeters per
minute (seem) and operating pressures range from 50 milhtorr to several
Torr.
Access to the main chamber is provided by eight in-plane viewports:
two 8 -inch ports, two 6 -inch ports orthogonal to the 8 -inch ports, and
four 2.75-inch ports intermediate between the larger ports. Longitudinal
optical access to the inter-electrode volume can be achieved through any
of these ports while complete radial or lateral access can only be
accomplished through the largest ports. The window material is
nominally high-grade vacuum port glass or for the measurements
discussed in this thesis two of the 2.75-inch viewports were made of
Supersil-1 fused silica.
The reactor chamber is typically filled with ultra-high purity
research grade gases such as argon, helium, or hydrogen adjusted to
specified flow rates by electronically controlled mass flow controllers. An
electronically actuated throttle valve at the inlet to the turbomolecular
pum p provides pressure selection and stabilization. Either electrode of
the GECRC can be grounded and the opposite excited by frequency/pulse
generator and RF power amplifier configuration either with or without
the use of an in-line matching network.
Upon assembly and initial operation of five of the GECRC's, a
program of electrical characterization was initiated. The electrical
16
characterization diagnostics were discussed at a conference session
during the 42nd Annual GEC held at Palo Alto, California in October
1989.16 By the time of a separate workshop meeting hosted by
SEMATECH of the GECRC design committee held in July 1990 at Dallas,
Texas it had become apparent that electrical characterization and
comparison between the few then operating GECRC's was not
straightforward. This meeting established stringent procedures to make
the required current and voltage measurements. The first public
comparison of electrical data from six reference cells from five
installations were presented at the 43rd Annual GEC held at the
University of Illinois at Champaign-Urbana in October 1990.17
Initially, the electrical diagnostics were to be comprised of
measurements of current and voltage waveforms for the amplitudes and
phases of the first five harmonics (Fourier components) of the excitation
frequency and the associated DC bias for specific applied peak-to peak
voltages across the electrodes and at various pressures of argon. It
quickly became apparent that a direct comparison of electrical
measurements between plasma reactors was complicated by seemingly
minor variations in the external circuitry associated with both the
measuring probe instruments and the power electronics. Variations were
to be expected between cells with differing electrode and insulator
materials, but, remarkably, even minor variations in power amplifier
output impedances at higher harmonics of the excitation frequency led
to variations of as much as 20 percent in harmonic amplitudes and
phases and as much as 40 percent variation in developed DC bias in the
volume of the plasma.
17
For those experienced with RF parallel plate discharge operation,
the complexity of these results was surprising and implied that the
relatively simple assumptions describing the equivalent circuit for both
the reactor chamber and the external circuitry had to be more carefully
considered. Furthermore, the sensitivity of the electrical behavior of
supposedly exactly similar reactor systems would force those modeling
plasma processing reactors by the use of computers to rethink their
assumptions regarding the influence of the external circuitry. The final
effect of these measurements was to demonstrate that for commercial
plasma etching systems, the choice of power supply equipment and
networks,
grounding,
cabling,
would
strongly
influence
the
reproducibility of system-to-system design and operation, impacting on
the actual plasma voltage, current, and DC bias and hence in etching
performance and the degree of anisotropy of etched profiles as well as
potentially the etching chemistry at the plasma-surface interface.
With the problems regarding electrical characterization and
correlation having been clarified, researchers began to branch out into a
variety of other diagnostic measurements on the GECRC. In 1990, the
first reports on measurements of optical emission profiles from argon
discharges in the GECRC appeared .18 The following year saw an
enormous increase in the number and types of experiments being
performed on the GECRC. 19 These experiments fell into three categories.
The first involved more refined electrical diagnostics, which were more
precise impedance measurements over a wide frequency range leading
to a detailed consistent description of the GECRC in terms of an
improved equivalent circuit model. In addition, a low-pass filter circuit
18
was developed for the input power feed to the cell which eliminated the
sensitivity of plasma operating conditions to the external circuitry .20
The second category of experiments were those performed to
estimate plasma species' distributions and concentrations. Experiments
have now encompassed measurements of electron densities, n e, in argon
and helium discharges by microwave interferometry, helium metastable
spatial density profiles by optical absorption, time-resolved optical
emission studies, and ion kinetic energy distributions by quadrupole
mass spectrometry. While practically none of these experimental results
has yet appeared in publication, the intent to use the GECRC as an
platform for reference diagnostic experiments is well established.
A third category of experiments represents the first attem pts to
relate the reference capability of the GECRC to practical production etch
processes by running CI2 and C^/HBr etching discharges in a reference
cell and observing the etching parameters and rates for the etching of
silicon. The results demonstrated were consistent with etching rates and
profiles from production systems.
Soon after the initial development of the idea for a standard
reference plasma system, researchers working in plasma modeling began
to develop computer codes to simulate the GECRC. By 1991, results were
presented at the GEC for a variety of computational approaches to
modeling the reference cell. Along with the development of computer
codes, a concerted effort has now been to compare the computational
results with experimental measurements from the GECRC. Some debate
has insued over whether or not the GECRC can be successfully modeled
as a one-dimensional system. The computer codes used are currently
19
only capable of predicting some plasma parameters such as electron
densities and energy distributions, voltage and current at the plasma,
and electric fields internal to the plasma. Preliminary comparison of
extrapolated emission profiles based on computational results and
known excitation cross-sections with measured emission profiles seem to
indicate that a one-dimensional modeling approach may be sufficient.
Measured emission profiles show little radial variation across the
diameter of the electrodes. Determining whether one-dimensional codes
are reasonable is important because of the computational complexity
and expense of higher-dimensional codes.
Some researchers feel that while there is some scientific interest in
measurements in a RF parallel plate electrode system such as the GECRC,
the industrial uses of plasma processing are now focusing on the use of
microwave-based electron cyclotron resonance (ECR) or Helicon21 source
plasmas and thus measurements
on a parallel plate
electrode
configuration are beginning to be outmoded. The advantages, however,
of using a system such as the GECRC are the generally simple design and
the
ability of researchers using the GECRC to correlate their
measurements with the large amount of experience and literature that
has been accumulated over the past several decades regarding the
diagnostics and operation of parallel plate plasma processing reactors. A
solid understanding and ability to predict, design, and control precisely
a parallel plate reactor's environment as in the GECRC should provide a
firm basis for extending the scientific (versus empirical) design of more
innovative plasma processing systems.
20
Support for continued advances in diagnostic measurements and
refinement in computational models for the GECRC is strong. In
particular, those developing computer models are now being asked to
incorporate excitation and production cross-sections and mechanisms
for plasma species in addition to electrons such as ions and neutral
species and to include the interactions of all plasma species with the
electrode surfaces. The aim of computer modeling is to predict absolute
concentration profiles of the most important plasma-generated species.
At the same time, experimentalists are striving to develop diagnostic
techniques to measure ion and neutral populations and distributions
produced in the GECRC and to place these measurements on a absolutely
calibrated scale rather than just a relative basis. Part of the work
reported in this dissertation describes such absolutely calibrated
measurements in a GECRC for concentration spatial profiles of neutral
atomic hydrogen produced in the simple RF H2 discharge.
CHAPTER m
DIAMOND CHEMICAL VAPOR DEPOSITION CHEMISTRY
The deposition of diamond from a gaseous medium was first
described in 1956 in a technical report discussing the 1952-3 work of
William G. Eversole at Union Carbide Corporation .22 Eversole's lowpressure vapor deposition of diamond on diamond seed crystals
predates the process for growing industrial grade diamonds at high
pressure developed by General Electric Company in 1954 and is most
certainly the first known instance of man-made diamond growth.
Eversole patented the process in two U.S. patents in 1958.23 Parallel
efforts at diamond synthesis also took place in Sweden (1953) and more
notably in the U.S.S.R in 1956. The work in the Soviet Union was directed
by B. Derjaguin whose work successfully culminated in the low-pressure
deposition of diamond without the use of seed crystals. The work was of
course published in Russian and was not known internationally until
translated reviews began to appear in the late 1960's and early 1970's.24
Work on low-pressure diamond synthesis was continued through
the 1970's by both the Russian researchers 25 and now American
scientists. John Angus and his group as Case Western Reserve University
improved upon methods of homoepitaxial vapor deposition of diamond
onto natural diamond powder using various hydrocarbon gas mixtures
and were the first to describe the critically im portant etching of
21
22
graphitic carbon by supersaturation of atomic hydrogen .26 Along with
low-pressure synthesis, ion beam deposition of diamondlike carbon was
first achieved in 1971.27 The early results with low-pressure diamond
synthesis resulted in inhomogeneous films which grew at commercially
impractical growth rates of less than 0.1 pm per hour, however this work
provided the initial experimental motivation for the explosion of work
on diamond CVD which began the early 1980's.
Deposition of faceted polycrystalline diamond thin films without
the use of seed crystals from hot filament and plasma-assisted CVD was
conclusively demonstrated by researchers at the National Institute for
Research in Inorganic Materials in Japan in 1982-83.28 The diamond
grown by these processes were typified by the criteria later established
for characterizing diamond growth:
• The film can be characterized as having a definite crystalline
morphology and texture observable by either optical or electron
microscopy.
• The deposition product has a clearly defined diamond crystalline
structure identified by x-ray or electron diffractometry.
• Using a Raman spectrometer, the film has a single first-order line
centered at 1332 c m 1 shift.
There has been much initial enthusiasm over CVD diamond because
of the dramatic increase in diamond film growth rates; making the
general CVD process for diamond applications at least conceptually
possible. Work on CVD diamond continued throughout Japan with
several hundred patents gained to date. Research on diamond CVD
expanded internationally since 1982 as it became quickly apparent that
23
for a modest outlay in capital equipment anyone could produce CVD
diamond. The original methods of hot filament-assisted and microwave
plasma-assisted diamond CVD have been improved upon and additional
techniques have also been developed. The approach of using ion beams
for deposition has continued for either slow homoepitaxial growth on
natural diamond or for preparing nucleation sites on substrate materials
via ion bombardment .29 In 1988 journal papers appeared describing the
use of atmospheric pressure oxy-acetylene torches for diamond
deposition .30 The films grown in this manner have very high growth
rates («100 fun/hr) and good crystalline quality, but are prone to
nitrogen incorporation from ambient air entrainment and have poor
uniformity and void defects. Extending the ideas of high tem perature high pressure deposition, several researchers have used therm al arcs
(also known as plasma torches) to deposit diamond at very high growth
rates on the order of 1 m m /hr .31 Homogeneous diamond growth has
even been demonstrated directly from the gas phase and as a result of
laser excitation of gas mixtures .32*33.34 Further reviews of diamond CVD
technology can be found in several current journal articles .35-36-37-38
Since diamond growth from the vapor phase has been produced in a
variety of CVD processes, several observations regarding the gas phase
chemistry can be made which in turn generate some questions. First, an
energetically activated gaseous medium is required to generate the
necessary gas-phase diamond precursors. As of yet, merely the presence
of a heated substrate in a simple gas flow of neutral low-temperature
precursor gases is not sufficient to yield diamond growth; and there is
no published data to suggest a high-temperature substrate can generate
24
diamond. The current evidence suggests that dissociation and/or
activation of the precursor gases must be accomplished by either using
the addition of electrical energy as in plasma-assisted CVD or the
addition of thermal energy to the gas phase chemistry as in the cases of
hot-filament-assisted or combustion-assisted CVD.
Secondly, in reviewing the literature on reported methods of CVD
diamond growth, one is struck by the wide variety of gas mixture
compositions used to deposit diamond. Bachman et al have written an
excellent review article tabulating most of the known diamond
deposition gas mixtures as well as the corresponding deposition
m ethod .39 In addition, using the stated gas mixtures given by various
researchers, they determined the atomic fractions of carbon, hydrogen,
and oxygen atoms and then related the predominant precursor atomic
fractions leading to diamond growth to a specific region in a ternary C-HO phase diagram. A simplified presentation of the given in Reference 37
is shown in Figure 2. The axis scales of this diagram are fractions given
by
*< = ( C 7 0 ) '
x' = j £ c r
X ° =
WW)
(1)
where C, H, and O denote the atomic species concentrations. Thus, a gas
mixture which gives diamond deposition from a microwave plasma such
as 500 standard cubic centimeters per minute (seem) H2 , 50 seem CH4 ,
and 20 seem O2 has atomic fractions
X c = 0.555, X H = 0.960, XQ= 0.032
which corresponds to datapoint #47 in the previous reference.
Figure 2. C-H-0 Phase Diagram. Unshaded area is
nominal diamond growth region
26
Beyond obviously needing a carbon-bearing precursor, it has been
apparent for some time that a superabundance of atomic hydrogen, or
oxygen, or even perhaps a halogen such as atomic fluorine m ust be
present at the deposition gas-surface interface .40 Three reasons for this
requirement can be advanced. First, it is known some atomic species
react more readily with sp2-bonded or graphitic carbon than with
diamond-bonded carbon and hence more rapidly etch away the non­
diamond carbon that has been deposited. Secondly, the presence of the
non-carbon atomic species may promote the sp 3 bonding leading to
diamond or may terminate the dangling carbon surface bonds in such a
m anner as to enable an advancing growth front. Finally, the non-carbon
atomic species may play a role in the gas phase chemistry to help in the
production of a suitable diamond deposition precursor species.
We now review the previous work on measurements of gas phase
species which are thought to be active in the chemistry of the diamond
CVD process. To date the consensus among researchers working with
diamond CVD is that one of the following radicals or molecules, CH3,
CH4 , C2H2 , or C2H4 is probably the reactive precursor to diamond growth
from the gas phase. Among these species, the methyl radical alone or a
combination of methyl radicals and acetylene molecules seem to be the
most likely candidates as derived from a variety of indirect observations
and reaction kinetic calculations. Besides the need for a hydrocarbon
precursor, it has long been know that a supersaturation of atomic
hydrogen is required to achieve predominately sp3-bonded carbon
deposition. The role of atomic oxygen is also thought to be im portant in
that enhanced deposition rates and diamond film quality are observed
27
when oxygen is added to a CVD system either as O2 or as part of a larger
hydrocarbon complex.
Some concentrations of gas-phase species in plasma CVD (also in
filament-assisted CVD) can be ascertained by mass spectrometry, optical
emission studies, resonantly-enhanced multiphoton ionization, and
laser-induced fluorescence. All of these techniques have been applied to
the study of the diamond CVD for either plasma-assisted or filamentassisted deposition. Emission studies of plasma-assisted diamond CVD
from a methane-hydrogen gas mixture have shown increased emission
from atomic hydrogen and radicals such as CH as one increases the
applied excitation power, while CARS measurements of H2 and CH4
concentrations show a corresponding depletion .41 These observations
are indicative of a high degree of molecular dissociation. Optical
emission can also show the presence of carbon monoxide, C2 and OH
radicals, and carbon atoms depending upon the gas mixture used. As
such, even given the small amount of observed species which
predominate in emission, experience with the kinetics of combustion
chemistry suggests that there are many reactive pathways in diamond
CVD plasmas which provide an involved reactive chemical environment
made even more complex by the presence of ionic species.
Modelers of the diamond CVD process use chemical kinetic
computer codes to attempt to predict concentrations of possible
diamond growth precursor species. However, several of these precursors
C2H2 , C2H4 , and CH3 do not emit in the plasmas and hence cannot be
detected by optical emission measurements. Instead some researchers
have used either infrared laser absorption, mass spectrometry, or REMPI
28
in an effort to detect them and assess their absolute or relative
concentrations. Davies and Martineau have measured concentrations of
CH4, CH3, C2H2, C2H4, and C2H6 in methane CVD plasmas by using IR
laser absorption.42 While their measurements were performed at lower
pressures than typically used for diamond CVD form plasma (~ 1 Torr
versus > 1 0 Torr) they show that the concentration of methyl radicals
depends linearly with increasing electron current in the plasma,
decreases with pressure at constant current, and is enhanced by the
addition of molecular hydrogen. Furthermore, enhanced diamond
deposition rates were
observed with increasing
methyl radical
concentration. The stable molecular species, CH4, C2H2 , C2H4, and C2H6
have been shown to have concentrations which are roughly independent
of plasma current or power. These results suggest the methyl radical is
necessary for diamond CVD given the dependence on growth rates with
increased methyl radical concentration.
The CH3 radical and excited-state carbon atoms have also been
detected using REMPI by Celii and Butler in a hot filament-assisted
diamond CVD system.43 Under conditions of saturated electron
collection, REMPI measurements for the methyl radical can be made
linearly proportional to the concentration. The measurements are not on
an absolutely calibrated basis, but do provide a linear response which
can used to make relative measurements as a function of gas mixture
ratios or distance from the filament. The relative CH3 concentration was
found to be only slightly dependent on filament temperature, but
strongly dependent on CH4/H2 feedstock ratio in the range from 0.5 to
296 CH4. The presence of excited state carbon atoms could not be
29
ascribed to the dissociation of the CH3 or CH4 . It was also postulated that
the REMPI atomic carbon signal could be due to photolysis of aromatic
carbon complexes by the probe laser as the signal did not vary in the
same manner as the CH3 response to operating conditions. These
measurements have not yet been extended to plasma-assisted CVD
systems.
Gas chromatography or mass spectrometry can be used both with
filament-assisted and plasma-assisted diamond CVD. Wu et al. results
using a gas chromatograph show that for filament assisted CVD, CH4 is
converted into C2H2 as the major stable molecular species, the
interconversion rate increasing with filament tem perature .44 Other
hydrocarbons such as C2H4 and C2H6 (reaction intermediates) were
measured at nearly two orders of magnitude smaller concentrations than
CH4 or C2H2. Recently Hsu at Sandia National Laboratory has adapted a
molecular beam mass spectrometer to a microwave plasma-assisted
diamond deposition system .45-46 This system is capable of determining
mole fractions at the entrance to a quartz probe tip placed at the
boundary of the plasma. The species measured were H, H2, CH3, CH4 , and
C2H2
for
a
measurements
methane-hydrogen
Hsu
surmises
gas
that
mixture.
the
neutral
Based
on
species
these
relative
abundances and concentrations are very similar to those found in
filament-assisted thermal CVD below 196 CH4 percentage and thus the
CVD diamond deposition process is dictated primarily by neutral
chemistry. The role then of the plasma is to produce greater amounts of
atomic hydrogen by dissociation of H2 than can be achieved by filament
30
decomposition and hence a greater supersaturation of H-atoms at the
growth surface.
Two
other studies based upon
isotopic
enrichment
of
a
hydrocarbon precursor by enriching with the 13C isotope merit
discussion. D'Evelyn et al. at Rice University performed 13CH4 - 12C2H2
isotopic competition experiments for diamond deposition to determine
which precursor was most effective in promoting diamond growth .47 By
studying the isotopic shift of the 1332 cm*1 Raman line of diamond, their
results demonstrated that methane is ten times more effective as a CVD
diamond growth precursor than acetylene and also by the efficient
interconversion of CH4 and CH3 reacting with H and H2 , the methyl
radical is the indicated growth species. These conclusions were later
reproduced by similar experiments using Raman shift analysis 48
The use of nuclear magnetic resonance (NMR) spectroscopy in
conjunction with Raman isotopic shift studies has been performed to
study the incorporation of ]H and 13C into filament-assisted CVD
diamond films 49 In these experiments 13C was substituted either for the
methyl radical carbon or for the carbonyl carbon in the acetone
precursor for a 22% enrichment in either case. Careful analysis of the
NMR resonance line shapes and line shifts enabled a determination of
the concentrations of iH and 13C in the solid films. The overall
enrichment of 13C in the diamond films was 2296 in accord with the gas
phase enrichment. This agreement was shown to be true for either
isotopic enrichment at the methyl radical or at the carbonyl radical
comprising acetone. The isotopic shift of the 1332 cm *1 Raman line
confirmed this observation. The incorporation of carbon from the carbon
31
attached to the oxygen in acetone has implications for the results
presented in Chapter Six regarding measurements of atomic oxygen
concentrations in a microwave plasma-assisted diamond CVD system.
Plasma-assisted CVD diamond can be grown from a variety of gas
mixtures, all of which provide some amount of atomic hydrogen and
atomic oxygen. High growth rate CVD diamond growth was of course
first demonstrated from gas mixtures of CH4 and H2 or C2H2 and H2.
Since then CVD diamond has been grown from mixtures such as CO-O2H2,50 CH4-Ar-02,51 and H2O with various alcohol's52 to m ention just a
few. In many cases attempts have been made to describe the roles of
atomic hydrogen and oxygen in producing CVD diamond. Comparison of
film crystalline morphologies and other properties as a function of
molecular hydrogen or oxygen content in the gas mixture is the most
common means of inferring the effects of the atomic species. Along with
film properties comparison, some investigators have use plasma
emission or mass spectrometry to try to deduce the influences on gas
phase chemistry.
Initially attention was focused on the action of atomic hydrogen in
CVD plasmas .53 Next, additions of rare gases were seen to partially
promote film quality and growth rates .54*55 Starting in 1987,56 the
addition of oxygen was shown to have dramatic effect on the range of
gas mixture ratios of hydrogen to hydrocarbon over which diamond
could be grown as well as a general reduction in substrate deposition
temperature. Over the past few years, several research groups have
reported on the influence of atomic hydrogen and oxygen in their
deposition processes, again, either by examining film properties or by
32
analyzing relative species concentrations measured as intensities taken
from mass spectrometry .57-58.59.60.61-62
To summarize the current understanding of the roles of atomic
hydrogen and oxygen in plasma-assisted diamond CVD, the following
points can be made:
• H atoms, primarily produced by electron impact dissociation in
the plasma, readily diffuse to the growth substrate and act
preferentially to etch sp2-bonded (graphitic) carbon at the growth
surface.
• In addition, H atoms may react with CH4 in the gas phase to
produce methyl radicals.
• Not only will H atoms act as a surface etchant, but may help
terminate carbon surface bonds.
• O atoms may act in a similar manner to H atoms to etch non­
diamond surface complexes.
• O atoms can react preferentially with certain hydrocarbons such
as C2H2 , hence freeing up more atomic hydrogen to interact at
the surface.
• O atoms are not present in large concentrations compared to H
atoms. This is because they easily react with hydrocarbons and
are trapped, particularly when CO is formed.
To date H atoms have only been detected and their concentrations
m easured in filament-assisted diamond CVD. H atom concentrations
have been inferred from CARS detection of H2 concentration and
tem perature measurements assuming translational and rotational
tem perature equilibrium between H and H2 at a constant total
33
pressure .63 Two photon laser-induced fluorescence has been used to
determine H atom concentrations near heated filaments in hydrocarbonH2 gas mixtures, though without the presence of a deposition substrate
surface .64-65 Typical H atom concentrations are 1-3 x 10 14 cm'3. No in
situ laser diagnostic measurements for H atoms or 0 atoms have as yet
been performed in plasma-assisted diamond CVD systems.
The importance of making absolutely calibrated concentration
profile measurements of both H atoms, and when they occur, O atoms is
readily apparent. Chapter 4 will describe the experimental techniques
used for such measurements in a plasma and Chapter 6 will describe
data measured during actual microwave plasma-assisted diamond CVD.
CHAPTER IV
EXPERIMENTAL TECHNIQUES
A. Experiment Apparatus
The use of the laser as a powerful spectroscopic tool has introduced
the laser probe diagnostic to plasma discharge research as a means of
making in situ, localized, and temporally precise measurements on a
variety of chemical plasma parameters, including electric fields ,66 gas
species temperatures and velocities 67 and concentrations .68 Important
to all varieties of low temperature plasma discharge environments are
the presence of atomic species usually generated via electron impact
dissociation of larger parent molecules. The atomic species present in
plasma discharges can be generated with considerable translational
energies and have either excited state or ground state chemical activity
relative to other species in the discharge or surfaces. The capability to
measure relative populations or absolute concentrations of atoms in
plasmas can provide information on one of the dominant active species
in chemical plasmas.
Laser-induced fluorescence (LIF) has been used to observe several
atomic species important to plasma processing, including carbon ,69
chlorine ,70*71 fluorine ,72 hydrogen ,73 nitrogen ,74 oxygen,75-76-77-78 and
sulfur .79 Our research has focused on measuring ground state atomic
hydrogen and atomic oxygen by two-photon absorption ILF (TALIF) in RF
34
35
discharges for both the spatial profile dependence and temporal
behavior.80
Measurement of atomic ground state populations in
discharges is important for two main reasons. First, as in the case of
hydrogen, the use of hydrogen-bearing or hydrogenic plasmas are
im portant for semiconductor processing applications such as amorphous
silicon deposition from silane (SiH4) discharges, as previously mentioned
for H2 discharge passivation of GaAs, and for H2/CH4 discharge etching
of InP 81 and now for the production of novel materials such as diamond
thin films by plasma-assisted chemical vapor deposition. Certainly,
atomic hydrogen is known to be the dominant reactant species produced
by these discharges, so that measuring H-atom production is useful for
modeling and design control of these processes. Likewise, detection of
ground state atomic oxygen is important for understanding a variety of
oxygen-based discharges; such as O2-CF4 discharge etching of silicon.82
Secondly, it is often the case that the TAUF or UF techniques for
hydrogen and many other atoms require the use of a probe laser with a
wavelength shorter than the tunable transmission cutoff of KDP at 217
nm .83 Although this makes the atomic detection technically more
difficult, we have successfully demonstrated the TAUF technique for
hydrogen using both Raman shifting in H2 gas and sum-frequency
generation (SFG) in a beta-barium borate crystal (BBO) to reach the 205
nm wavelength required.
1. Laser System Configuration
A schematic of the general experimental scheme used for the TAUF
H-atom detection is shown in Figure 3. The schematic layout shows a RF
36
FREQUENCY
GENERATOR
DISCHARGE
GATE
Nd:YAG
LASER
532 nm
1Q-SWITCH TRIGGER
RF POWER
AMPLIFIER
MATCHING
NETWORK
615 nm KDP CRYSTAL
MIXER
DYE LASER
-Q
DICHROIC
MIRROR
6
615nm
TIME DELAY
GENERATOR
1
307 nm
-o -B -p '
I ] BBO CRYSTAL
GATE
fr-
POLARIZATION
ROTATOR
205 nm
E S II
PELUN-BROCA
PRISM
SIGNAL
TO CELL POSTTION
TRANSLATION
STAGES
REACTOR CELL
DIGITIZER
IBM-AT
COMPUTER
X-Z STAGE
CONTROLLER
Figure 3. Experiment Layout Schematic for H-Atom TAUF
37
reactor cell power supply system, the 205 nm generating laser system,
and the associated acquisition and control electronics. The laser light
generation configuration will now be described and the acquisition
electronics are discussed in the following section.
The TAUF transition for atomic hydrogen is from the ls 2S1/ 2
ground state to the 3 d 2D 5/ 2 ,3/2 and 3s2 Si/ 2 excited states at 97492 cm '1.
Both excited state levels are populated due to the energy level
degeneracy in hydrogen for different angular momentum states and due
to the two-photon absorption selection rule of Al = 0, ±2. The transition
requires two 205.14 nm photons to excite the atomic ground state. The
TAUF transition has also been observed in deuterium at 97519 c m 1 in
the course of this research.
The excited state is weakly populated by the discharge impact
kinetics due to a rapid (~15 nsec) radiative lifetime. Thus, the TAUF
excitation can be expected to populate effectively the upper state
provided sufficient photon density is available given the small twophoton absorption cross-section.
TAUF measurements for H-atoms can be performed using a high
pressure H2-filled Raman cell or by sum-frequency mixing (SFM) in a
beta-barium borate (BBO) crystal. For our purposes the use of SFM with a
BBO crystal is preferred since SFM generates far more 205 nm light. The
light generation scheme depicted in 3 was used in all but our initial
experiments. The probe laser is generated by pumping a Quanta-Ray
PDL-2 dye laser with the second-harmonic 532 nm output of a QuantaRay DCR-2A Nd:YAG laser operating at 20 Hz. The dye laser operates with
Exciton Sulfurhodamine 640 dye at 615 nm. The dye laser output is
frequency doubled using a Quanta-Ray WEX KDP crystal providing an
output of 7 m j/pulse at 307 nm and a residual 14 m j/pulse at 615 nm.
Upon exiting the WEX system, the polarization of the 307 nm beam is
rotated to coincide with the polarization of the 615 nm beam. Both
beams are collimated with a 3:1 telescope and combined via a dichroic
mirror. The collinear, collimated beams are input to the BBO crystal
manually angle tuned to provide SFG at 205 nm. The input beams spot
size diameter is 3 mm. The SFG output from the BBO crystal can be as
high as 800 microjoules/pulse with careful alignment and overlap of the
two input beams. The output pulse energy is carefully m easured against
a newly calibrated Molectron Model J3-05 Joulemeter. Using the BBO SFM
technique gives over ten times the output of the H2 Raman shift
technique. The conversion efficiency of BBO at this wavelength has been
quoted as high as 12 % in the literature and the efficiency of our system
was measured at 11 % which is predominantly dictated by the input
beam's profile quality and alignment. Upon leaving the BBO crystal the
residual input pump beams are dispersed by a Pellin-Broca prism and
beam dumped. The TAUF probe beam is tightly focused by a quartz lens
through a Supersil 1 quartz window into the discharge reactor of
interest.
Detection of O-atoms by TAUF is accomplished by utilizing a twophoton transition from the 2p 3P2 ground state to the upper excited
3p3p2>i i0 states upon absorption of two 226 nm photons. The
fluorescence decay between the 3p3P states and the intermediate 33S}
excited state is observed at 845 nm. The lowest energy (J”=2) fine
structure component of the ground state is selected as the lower state
39
for the two-photon absorption process. The laser linewidth is sufficiently
narrow to select only this component and also provides the greatest
signal strength due to the inherent population of mainly this level. All of
the upper excited state fine structure levels are populated by the
transition.
The generation of 226 nm photons is similar to the procedure used
to generate 205 nm light; though for the wavelength required the use of
a BBO crystal was unnecessary as KDP conversion was satisfactory. A
schematic of the experimental layout for O-atom TAUF measurements is
shown in Figure 4. Conversion of the dye laser system from one TALIF
measurement to the other can be accomplished in one day, and most
optical components can be left in place to facilitate a rapid conversion.
The 226 nm light is generated by pumping a dye laser filled with a
mixture of Rhodamine 590 and Rhodamine 610 laser dyes solvated in
m ethanol using the 532 nm second harmonic output from a Nd:YAG
laser. The dye fundamental output at 572 nm is upconverted to its
second harmonic at 286 nm using a KDP doubling crystal and
subsequently mixed with the residual 1.06 micron fundamental output
of the Nd:YAG laser in a second KDP crystal. The residual beams were
dispersed and discarded using a Pellin-Broca prism. The 226 nm laser
probe beam was then passed into the reactor through a Supersil 1 quartz
lens and window. Typical laser energy output at 226 nm is 500
microjoules per pulse at 20 Hertz.
FREQUENCY
GENERATOR
DISCHARGE
GATE
Nd:YAG
LASER
532 nm
DYE LASER
1060 nm
572 nm KDP CRYSTAL
MKER
1060 nm
J
'Q-SWITCH TRIGGER
RF POWER
AMPLIFIER
MATCHING
NETWORK
Beam Dump
226 nm
GATE
TIME DELAY
GENERATOR
PELUN-BROCA
PRISM
SIGNAL
TO CELL POSITION
TRANSLATION
STAGES
REACTOR CELL
DIGITIZER
IBM-AT
COMPUTER
X-Z STAGE
CONTROLLER
Figure 4. Experiment Layout Schematic for 0-Atom TAUF
41
2. Signal Detection and Analysis
Our initial refinement of both the H-atom and O-atom TAUF
diagnostic was performed using a small glass discharge reactor that has
a variable gap cylindrical planar electrode design with water-cooled
stainless steel or aluminum electrodes. The discharge load power can be
measured with a high voltage probe and a current loop detector with
output acquired on a digital oscilloscope and multiplication averaged
upon waveform transfer to the IBM-PC. The reactor cell is m ounted on a
stepper motor positioned X-Z translation stage which allows spatial
profile measurements as the cell is translated relative to the fixed laser
probe focal point, as viewed by the fluorescence collection optics.
The excited state fluorescence from the 3d2D5/2t3/2 and 3 s 2Sj/2
levels to the 2 p 2p 3/ 2 ii /2 at the Balmer alpha line (656.3 nm) transition is
detected perpendicular to the primary discharge cell axis and the laser
probe beam with focused collection optics. The TAUF passes through a
10 nm FWHM interference filter centered at 656 nm and focused on the
photocathode of ITT Model 4123 gated photomultiplier tube (GPMT).
Detection of H-atom TAUF is also easily achieved (provided the average
DC current does not exceed the rating of the particular photomultiplier
tube) by using continuous (CW) photomultipliers such as the RCA 1P28
or Thorn-EMI 9659 tubes. O-atom TAUF requires more red-sensitive
tubes, in which case the Thorn-EMI 9659-QB or Hammatsu R928 tubes are
satisfactory.
The signal collected by either a GPMT or CW photomultiplier is fed
directly to the input Tektronix DSA 601 Digital Signal Analyzer or other
similar high-speed digital oscilloscope. The data acquisition, dye
H—Atom
TAUF Signal, m illivolts
35
30
25
HammatBU 02S
PMT Voltage - 700 V
20
15
10
5
0
10 20 30 40
50
60 70 BO 00 100
Time, nanoseconds
Figure 5. Representative H-Atom TAUF Signal
Trace
43
laser tuning, and experiment timing is controlled by a Stanford research
System Digital Delay Generator in combination with an IBM-386
microcomputer. The experiment timing sequence allows for temporallydependent measurements of H-atom TAUF over all relative phases of the
RF discharge driving cycle. The use of a GPMT and a narrow-band
interference filter in the collection optics allows detection of the TAUF
response even in the presence of the bright plasma-induced emission
(PIE). In working with the larger reactor systems it was found that even
using a CW photomultiplier was sufficient provided the anode current of
the tube was carefully monitored and did not exceed the m aximum
rating.
A representative H-atom TAUF signal trace is shown in Figure 5.
The TAUF resonance transition is shown for a typical set of discharge
operating conditions. As shown, the TAUF signal has an excellent
signal/noise ratio, which is typical of the TAUF signal over all phases of
the RF cycle relative to the PIE. The full-width-half-maximum (FWHM) twophoton linewidth of the TAUF resonance is typically 3.5 ± 1 cm '1. The
dye laser linewidth at 615 nm is approximately 0.6 c m 1, as measured
independently by optogalvanic detection of neon and iron transitions in
a hollow-cathode glow discharge lamp. Multiplying this by a factor of 6
(third harmonic of 615 nm times two photons) accounts for the FWHM
linewidth of the TAUF transition.
Note that the associated Doppler linewidth for the two-photon
absorption in hydrogen at a neutral atom temperature of 300-500 Kelvin
is < 1.0 cm '1, which might be expected in the center of the discharge gap
at zero degrees phase angle in the RF current cycle; thus, our TAUF
44
measurements do not have a sufficiently small laser probe linewidth to
measure H-atoms with small translation energies without etalon
narrowing of the dye laser fundamental output.
B. H-Atom and O-Atom Concentration Calibration Procedure.
Having developed a laser diagnostic to detect H or O atoms, it would
be useful to place the number of atoms detected on an absolutely
calibrated scale and determine actual local concentrations of atoms
directly in the plasma. By directing an external source of H or O atoms
into a central position in the volume of a plasma reactor, the TAUF
signal derived from this source can be made to simulate detection of
plasma-generated atoms. The external source of atoms, usually
generated via microwave discharge, provides a steady, reproducible, and
controllable TAUF response. Simultaneously,
small quantities
of
molecules known to efficiently react and combine with the atomic
species can be added and a corresponding decrease in the TAUF signal
intensity can be observed as the atoms are depleted. This reaction or
titration technique can give a reliable means of determining the
concentration of atomic species corresponding to a given amount of
TAUF signal.
Calibration of the fluorescence signal collected by the PMT-Filter
combination was performed using in-situ titration of either the H-atoms
or O-atoms by chemical reaction with NO2.84 For H-atoms the titration
reaction proceeds as
H + N 02 -*0H + N 0
(2 )
with a reaction rate constant of k 298 = 1.3 x 10'10 cm3 s_1 where the rate
constant is given for room temperature (T=298K). There is also a
secondary reaction of OH with H2 given by
H2+ 0 H -> H 20 + H
(3)
with a reaction rate constant k2gg « 1.6 x 10-15 cm3 s 1. However,
provided the ambient H2 concentration remains below 1 Torr (3.3 x 1016
cm-3) this reaction will not appreciably perturb the main reaction. For 0atoms the titration reaction is
O + NO, -» O, + NO
(4)
with a reaction rate constant k2g8 = 9.5 x 1 0 12 cm3 s 1. For both H and O
atom reactions, sufficient mixing time m ust be allowed to insure that the
reactions go to completion. To have a reaction go to 99% completion
implies that the mixing time, t ^ , must be greater than 5 characteristic
reaction times,
t.
In other words, we have that the percentage of
complete reaction is
1 - e~t/T = 1- <T5t/T = 1- e-5 = 0.9932 = 99%
(5)
The characteristic reaction time is the inverse of the reaction rate
constant times the concentration of titrant. For example, in the case of
the reaction in Equation 2, at the point of complete reaction (here called
endpoint) a measured concentration of N02 is used to react completely
46
with an equal concentration of H-atoms. If the concentration of [NO2]
used is 1 x 1 0 15 cm*3 then the required mixing time m ust be at least
tmix > 5 t = 5 (^ 2 9 8 [^ 2 ]) * = 7.7 microseconds
(6)
In the titration assembly described below, the main gas flow rates are
adjusted to reduce the slug flow gas velocity in the mixing zone and
raise the mixing time to approximately 4 milliseconds satisfying the
condition in Equation 6 even for the O-atom titration reaction, which has
an order of magnitude lower rate constant.
The titration assembly is shown in Figure 6 . At the larger inlet a gas
mixture of either H2/Ar or O2 is passed through a microwave discharge
produced by an air-cooled Evenson microwave discharge cavity which
dissociates the molecular gas mixture. The presence of argon helps to
induce complete dissociation. The discharge section is composed of
quartz for both heat resistance and to minimize reactions of the
microwave plasma with the walls. Further downstream, NO2 is
introduced through a glass coaxial tube which passes the gas to a
perforated mixing zone approximately 2 cm in length and 2 cm in
diameter. The inner tube is covered by a Teflon sleeve to reduce the
amount of recombination of H-atoms on the tube surface. The assembly
is placed through a 3/4" diameter (I.D.) Cajon O-Ring fitting welded to a
2-3/4" Conflat copper gasket sealed flange. The Conflat flange is mated
to a port on a given reactor, and the length of the titration assembly
N02 Dnlet
Microwave
Teflon Sleeve
H2 ,0 2 /Ar
Discharge Region
Figure 6 . Titration Assembly
MbdrjgZone
48
allows the exit from the mixing zone to be placed at the center of the
reactor and near the focal point of the probe laser. For a titration
calibration measurement, a steady-state concentration of H or O-atoms is
produced by the microwave cavity discharge source and NO2 is
introduced at known mass flow rates. The TAUF fluorescence is
monitored and recorded manually as a function of addition of NO2 . A
typical titration data curve for O-atom titration is shown in Figure 7.
At the endpoint (minimum observable TAUF signal), the total
pressure in the reactor is recorded. A straight line is least-squares fit to
the first several titration data points and the exact NO2 endpoint mass
flow rate is extrapolated numerically. Combining this information, we
can use the following equation, where at the endpoint
(7)
where [A]0 is the concentration of H-atoms or O-atoms titrated, [NO2J0 is
the concentration of NO2 used, F(N0 2 ) is the mass flow rate of NO2
m easured in standard cubic centimeters per minute (seem), SF is the
total mass flow rates of all the gases used summed together, and P is the
total pressure measured in Torr. The numerical coefficient is used to
convert Torr into number density, per cm3. Titration curves can be taken
for different initial atomic concentrations, PMT gain settings, and probe
laser energy. The calibrations curves correlate an experimental TAUF
signal with a known concentration. Typical uncertainties in the
calibrations are 15% and the minimum detectable concentration is
extrapolated to be 1 0 12 cm*3.
400
9
P = 657 milliTorr
PMT Voltage = 800 V
Laser Energy = 440 /jJoules/pulse
20 seem 0 .
350
300
S* 2 0 0
150
100
[0] = 6 xlO15 cm *
50
0
1
2 3 4 5 6 7 8 B 1
Mass Flow Rate of N0(l seem
0
Figure 7. 0-Atom TAUF Titration Curve. Data
corresponds to a concentration of 5.98 x 10 15
cm'3. Line is a linear regression extrapolation
for determining the titration endpoint. Xintercept is 7.63 seem of NO2.
50
C. Effects of Quenching Upon Concentration Measurements
Another
problem
that
figures
predominantly
in
plasma
concentration measurements above 200-300 millitorr is the quenching of
the excited fluorescence state by collisions with the ambient background
gas molecules. Molecular hydrogen, in particular, is known to be a very
efficient fluorescence quenching molecule.85 Reference data in the form
of collisional quenching cross-sections and collisional deexcitation rates
are few and often in disagreement.86 Bittner et al have provided the
most comprehensive collisional quenching cross sections to date in
conjunction with their analysis of atomic hydrogen and oxygen
measurements in low pressure flames.87 These effects have also been
investigated by Goldschmidt in flames.88*89
Since collisional fluorescence quenching effects are noticeable even
at a few Torr total pressure and are very pronounced at higher
pressures, it is necessary to extend the previous work to much higher
pressures. For this purpose photodissociation of either C2H2 or NO2 by
the TAUF laser probe beam is used to generate ground state H or O
atoms respectively. The discussion here will focus on the quenching
measurements for hydrogen atoms. Photodissociation of either acetylene
or NO2 is also useful in determining a geometric view factor correction
which accounts for the variation in solid angle collection efficiency as a
function position of the laser probe beam in a reactor cell; this will be
described in the following two chapters.
The photodissociation of acetylene provides a convenient source of
hydrogen atoms using the 205 nm TAUF laser probe beam. A previous
study of photodissociation of acetylene was completed in the wavelength
51
region 201-216 nm .90 The photodissociation process at 205 nm was
shown to produce solely ground state C2H and H-atoms. The excited
C2H2 predissociative state was also measured in this work to have a
lifetime of 10-20 picoseconds, which implies that over the lifetime of this
state the molecule can suffer practically no deexcitation collisions even
up to ambient pressures of 100 Torr. Thus, collisional deexcitation of the
predissociating acetylene can be neglected as a mechanism which could
perturb these quenching measurements.
One might expect, given the same concentration of C2H2 and
photon flux density, the photodissociation process should yield a H-atom
concentration independent of the pressure or the identity of other gases
present, provided the gas environment is optically thin to the probe
laser. Our measurements in a static cell pressurized with acetylene have
shown that the system will remain optically thin below ~5 Torr. For the
other gases used here, the absorption at 205 nm can be determined from
the literature or by experimental observation and none were shown to
absorb at this wavelength. By having a fixed concentration of acetylene
and by raising the ambient pressure by slowing adding a foreign gas, the
variation in the fluorescence signal can be examined to test for optical
opacity.
An obvious first step would be to examine the effect of acetylene
pressure on the fluorescence itself. The H-atom TAUF signal response as
a function of acetylene pressure is shown in Figure 8 . The signal is
produced as the total PMT current response across 50 Ohms integrated
over a 100 nanosecond gate, giving units of nanovolt seconds. After an
initial linear rise, the photodissociation-generated TAUF signal begins to
TAUF Signal, nVs
Acetylene Photodissociation
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
1
2
3
4 5 6 7 8 9
CaH2 Pressure, Torr
10 11
Figure 8 . H-Atom TAUF by Photodissociation of
C2H2.
5.0
d
4.0
3.5
d
a
J
30
2.6
3o
S
*a
0.5
4
0.0
0.0 0.1
0.2 0.3 0.4 0.5 0.0 0.7 0.0 0.0
1.0
CjHjj Pressure, Torr
Figure 9. Nonlinear Dependence of C2H2 11Atom TAUF Signal. Straight line represents a
linear regression fit to the initial rise of the
data.
54
saturate below 1 Torr ambient pressure. An expanded view for lower
pressures of acetylene is shown in Figure 9. The straight line in this
represents a line fit by linear regression over the initial linear rise in the
TALIF signal. Clearly at pressures above 150 milliTorr, the TALEF signal
response deviates strongly from a linear process which would depend
solely on acetylene concentration. The quantum yield in this experiment
can be defined as the ratio of the actual TAUF signal data to the value
predicted by the straight line fit from the lower pressure data. A plot of
the inverse of the quantum yield is shown in Figure 10. A linear
regression fit straight line to the data is also shown and gives excellent
agreement with the data. In this case, the inverse of the quantum yield
follows a dependence know as the Stern-Volmer formula 91 where the
quantum yield, Q, is given by
where P is the pressure and C0 is a constant. We can take the inverse of
the Stern-Volmer formula and write
(9)
Therefore, a plot of the inverse of the quantum yield versus pressure of
the quenching gas should, by the Stern-Volmer formula, yield a linear
relationship. In the case of Figure 10 the constant found from the slope
of the straight line is Co=3.053 T o rr1. The constant CQ can next be
related to a quenching rate constant for the foreign gas.
35
30
25
u
20
1
s
or
0 1
2
3 4 5 6 7 8 9
CgHg Pressure, Torr
10 11
Figure 10. Inverse Quantum Yield Dependence
on Pressure.
Since we can write
(1 0 )
where
[N q ]
is the concentration of quenching foreign gas, x is the
radiative lifetime of the state being quenched , and kQ is the quenching
rate constant. Equation 8 can be rewritten to give
[We ] x (3.3x10 X(,cm-'Torr ')Px~ (iMO^cnC'Torr-') r
We can initially chose for x the statistical average natural lifetime
of the
n=3
excited state
of atomic hydrogen which is
10.2
nanoseconds .92 Substituting this value into Equation 9 we find a rate
constant of kQ = 9.07xl0'9 cm 3 s 1 for quenching of the H-atom
fluorescence by acetylene.
The product
[N q ]
times kQ is the quenching collision frequency,
Zq ,
which can be written as
ze=[A
reK=,roiK]v
( 12 )
where v is the relative collision velocity of the hydrogen atom fragment
(after photodissociation) to background gas molecules and
c
2q
quenching cross-section. We can solve for o 2 q in terms of kQ giving
is a
57
For the moment, let us consider a velocity, v, which is the maximum
photodissociation-induced velocity the hydrogen atom can have after the
photodissociation process, and calculate a quenching cross section. The
photodissociation-induced velocity can be measured by analyzing the
Doppler profile of the photodissociated acetylene H-atom TAUF
transition .93 The velocity measured is 7123 m /s which corresponds to a
tem perature of 4100K. Using this velocity in Equation 11 gives a
quenching cross-section for acetylene quenching of n=3 H-atoms of
,
kQ (9.07xl0-9c m V )
L = 4,1x10
o2 = _e = .L-----------n\
123x10 cm/s)
cw
Besides affecting the overall TAUF signal strength as a function of
pressure, the apparent radiative lifetime of the atom is also influenced.
Figure 11 shows the lifetime dependence of the H-atom n=3 state as a
function of background acetylene pressure. The lifetimes were
determined by fitting
a single exponential decay to
digitized
fluorescence waveforms detected with Thorn-EMI 9659-QB and acquired
from the digital oscilloscope. Data were fit up to the 9096 level after the
initial onset of the fluorescence signal. The contribution from the laser
probe pulse temporal width is 5 nanoseconds and the minimum
resolvable level for lifetime measurements is estimated to be 6
nanoseconds. From a linear regression fit, as shown in the figure, at very
low pressures the radiative lifetime approaches 14 ± 1.5 nanoseconds.
This value is larger than the statistical average lifetime of the n=3 state
58
16
14
ioa
it
m
o
i03
IId
10
6
6
0
20
40
60
80
100 120 140
160
180
CjjHj, Pressure, milllTorr
Figure 11. Radiative Lifetime of n=3 State from
Photodissociated C2H2 H-Atom TAUF.
59
mentioned earlier. The explanation for the observation are the three
angular momentum states of the n=3 level are not equally populated. As
described before, due to the selection rules for such a two-photon
absorption transition only the L=0 and L=2 states and not the L=1 state
are populated. In addition, the two-photon absorption cross-sections to
the s and d state are different. The ratio of the d-state absorption crosssections to that for the s-state is 7.56.94 Since the laser linewidth is wider
than the energy separation between each L-state, this means that ~1296 of
the n=3 population is contributed by the s-state and the remaining 8896
is contributed by the d-state. The natural radiative lifetime of the d-state
is 15.6 nanoseconds and 159 nanoseconds for the s-state. Thus, most of
the observed lifetime for the n=3 level in this experiment at low pressure
is contributed by the d-state.
It is also reasonable to expect that collisions could perturb the
distribution in the angular momentum states after the initial population
by the laser. This redistribution or mixing of the angular momentum
state populations can have two effects. First, there would be variations in
the contributions to the radiative lifetime of the Baimer-« fluorescence
from each of the three states. And secondly, since the p-state could then
be populated by mixing, not only does the fluorescence channel 3p-2s
become available, but the 3p-ls fluorescence channel in the vacuum
ultraviolet then allows for a loss of fluorescence from the Baimer-«
transition.
Therefore, collisional quenching of the excited state fluorescence
can be thought of as having two mechanisms. The first would be an
overall nonradiative (n level) deexcitation of the excited state atom. The
60
second mechanism would involve the mixing of angular momentum In­
state populations within an n-level. A simple model utilizing these
mechanisms can be described by the following set of coupled decay rate
equations which describe the time development of the n=3 angular
momentum L-state populations after initial population by the laser
probe:
^ L = - A,J 7 + A r e ( " - + * e ) + 3 A T e * . ( A r . + J V J )
v "p
/
(15)
where Ns, Np, and
are the populations of the different s, p, and d
angular momentum states,
Nq
is the concentration of quenching
molecules, and k ^ and kQ are rate constants associated collisional
population mixing of the angular momentum L-states and nonradiative
deexcitation of the entire n-level respectively. If we assume the mixing
between different L-states have equal rate constants, then the integer
coefficients account for the statistical weighting of the L-states
degeneracy's by the number of mj sublevels. The right-hand side of each
rate equation has two parts. The leftmost term is for population loss and
the right term is for population gain. Loss occurs by natural fluorescence
or by mixing to other angular momentum states or by nonradiative
61
dexcitation. and gain for a level occurs by mixing contribution from the
other states.
This set of coupled rate equations can be solved numerically by a
Runge-Kutta differential equation routine written in Fortran .95 The
initial conditions are given by the initial L-state distributions which are
population by the laser. The time development of the L-state populations
are shown for two different foreign gas pressures in Figures 12 and 13.
The calculations are normalized with respect to the initial overall
population of the n=3 energy level. Also displayed is a normalized
radiative rate which is related to the time history of the total population
of the n=3 level. A radiative rate from the n=3 level can be defined as
R (,)= L N'(,)+L N r( /) + £ * ,( ,)
rtp
T‘
(16)
where fs, fa, and fa are the branching ratios for fluorescence decay from
each L-state of the n=3 level to lower n-levels. For the s and d states, each
decay to a single lower state in the n=2 level. The p-state however, can
decay not only to the 2s state, also to the Is level. The branching ratio,
fa, can be calculated as the ratio of the transition probabilities for the
transitions 3p-2s and 3p-ls 96 This gives a branching ratio for fa of
0.1183.
The radiative rate in Equation 16 can be normalized to the initial
radiative rate at time t=0. At time t=0, only the s and d states are
populated and so the initial radiative rate, R0, is calculated as
62
882
t .3
rd
1.59xl0_7s
1.56x10
7 _ -l
= 5.73x1 O'5
*s
Thus, the normahzed radiative rate, R* can be given by
R0
(,.75*10-4^1.59x10
W, s
V
5.4x10 s
1.56x10 a’j
^l g j
Figure 13 shows at the higher pressure (10 Torr) the p-state has
more contribution, while the s-state decay is unchanged and meanwhile
norm ahzed radiative rate decays much more quickly. The exchange of In­
state populations can be checked in the numerical calculation output by
artificially increasing the natural radiative lifetime for all three states to
very large values (effectively turning off fluorescence) and by setting the
rate constant Icq, for nonraditive deexcitation to zero. Calculated
numbers for pressures above a few hundred milhtorr the populations of
the L-states have equilibrated in the percentages: 11.1196 in the s-state,
33.3396 in the p-state, and 55.55% in the d-state. The ratio of these
percentages is just 1:3:5; as expected by the statistical weighting given by
the nij degeneracy's of each L-state. Since the contribution from the sstate population goes only from 11 .8 % to 11 . 11 %, one can again see that
the principal exchange of L-state populations occurs between the p and d
states. Trapezoidal integration of the normahzed radiative rate (Eq. 18)
with respect to time gives the quantum yield of the Baimer-«
fluorescence. The integration time is 100 nanoseconds which reflects the
integration gate temporal width in the experiment. The numerical
program used can repeat this process for different pressure of the
quenching foreign gas. Figure 14 shows the resulting quenching curves,
for given k ^ and kQ, both with and without the contribution of
Normalized n=3 Populations and Radiative Rate
1.0
0.9
0 .B
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
25
30
Time, nanoseconds
Figure 12. Radiative Decay of n=3 Component
Levels for 1 Torr Quenching by H2. Also shown
is the Normalized Radiative Rate, R*.
Normalized n=3 Populations and Radiative Rate
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Time, nanoseconds
Figure 13. Radiative Decay of n=3 Component
Levels for 10 Torr Quenching by H2. Also shown
is the Normalized Radiative Rate, R*.
1.0
0.0
0.B
1.90 z 10
cm /■
Quantum Yield
0.7
No Nonradiative Deexcitation
0.4
0.S
No L-State Mixing
0.2
0.1
Sum
0.0
0
2
4
6
B
10
12
14
16
18
20
Pressure, Torr
Figure 14. Calculated Quenching Curves With
and Without Nonradiative Deexcitation or In­
state Mixing and the Total of Both Effects.
66
mixing and or collisional deexcitation. As one can see from the figure,
nonradiative deexcitation is the dominant contribution to the quenching
process. However, by adding to the calculation the effect of L-state
mixing, the variation of the angular momentum state populations also
provides some discernible effect.
A further extension to the numerical program is to include the
described computational model as a subroutine in a nonlinear-leastsquares fitting program. Quenching data taken in the laboratory is used
as input to the program which then fits the model and the
corresponding mixing and deexcitation rate constants to the data. Rate
constants were converted to cross-sections by using Equation 13. Figure
15 shows a comparison of the fitting program results and experimental
data for the "self-quenching" effect by C2H2 itself on the H-atom TALIF
quantum yield. The best fit to the data required only a single
nonradiative deexcitation cross-section and no mixing cross-section. The
deexcitation cross-section, ctq, was calculated to be 8.87±0.2 7 x 10*15
cm2. If both mixing, 0 ^ , and deexcitation, oq, cross-sections were used
the values calculated were 8.03±4.12 x 10‘15 cm 2 and 0.42±2.22 x 10' 15
cm 2 respectively.
The error in the calculated mixing cross-section would imply this
value was not statistically significant and could not be adequately
determined. For some of the gases discussed later, it was found that for
those
with
larger
nonradiative
deexcitation
cross-sections,
a
determination of the mixing cross-section often gave larger uncertainties
in the calculated values. It is probable that for gases which are more
1.0
0.0
0.0
0.7
sII
I
or
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
0
10
11
CaHg Pressure, Torr
Figure 15. Comparison of Calculated and
Experimental H-Atom TAUF Quenching by
Acetylene.
68
effective
nonradiative
quenchers
(acetylene
having
the
largest
deexcitation cross-section measured to date), a determination of the
mixing cross-section is more uncertain because of the dominance of the
nonradiative mechanism. It will be shown later that for gases which are
not as effective in nonradiative deexcitation, particularly helium, the
effect of a mixing cross-section is readily apparent.
Using the single calculated deexcitation cross-section, a
TAUF
signal response can be predicted as a function of acetylene pressure.
Figure 16 shows a comparison between the original data from Figure 8
and the predicted signal. Over a large range of pressure the agreement
between the calculated signal and the data is excellent, Only above ~3
Torr does the calculated curve predict a slightly larger signal than is
observed. One explanation is that the model does not take into account
the onset of optical opaqueness near 5 Torr of acetylene as was
previously mentioned. As our use of acetylene as a photodissociated
source of H-atoms is accomplished at 100 milliTorr, this discrepancy can
likely be ignored. Figure 17 further demonstrates the agreement between
the calculated result and the data in the low pressure region.
The measured n=3 lifetime data can be compared to the model
calculation as shown in Figure 18. Displayed is the original measurement
data, a linear regression fit to the lifetime data (as before in Figure 11),
and calculated lifetimes derived by fitting a single exponential decay to
the normalized radiative rate, R*; in the same manner as the original
measurements were determined. The calculated lifetimes he weh within
the error bars of the measurements with a slight curvature as a function
of pressure as compared to the linear regression line. The extrapolated
69
5. 0 r*2 4. 5 I
4. 0 -
no
d 30 '
H
I 80I
!
101
3
io I
i
CL.
*>
I
0. 5
0.0
0
1
2
3
4
5
6
7
8
0
10
11
CjHj, Pressure, Torr
Figure 16. Measured Versus Calculated
Photodissociated Acetylene H-Atom TALIF
Signal.
70
s.o
4.0
3.5
fl 3.0
%
A 2.6
I
2,0
I
15
&
3 i-o
«
0.5
I
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 O.B 0.9
i.O
CjHj Pressure, Torr
Figure 17. Low-Pressure Detail of Figure 16.
Straight line is from linear regression fit as
shown in Figure 8 .
16
14
iea
i>
12
10
3
n
II0
B
6
0
20
40
60
80
100 120 140
160
160
CgHj Pressure, milliTorr
Figure 18. Measured versus Calculated H-Atom
TAUF Lifetime from Photodissociation of C2H2.
Straight Line is from linear regression fit as
shown in Figure 11.
72
natural lifetime at zero pressure is 15.6 nanoseconds in good agreement
with the natural lifetime of the n=3 d-state.
Quenching data can be taken using other gases and the computer
program used to calculate quenching curves and rate constants or crosssections. However, given the partial pressure of acetylene present,
Equation 15 m ust be modified to account for the "self-quenching" by
acetylene. Addition of a constant term to Equations 15 is straightforward
since there is a constant 130 milliTorr partial pressure of acetylene with
a fixed quenching cross-section. As shown in Equations 19 the constant
term is only added to the loss term of the right-hand-side of each
individual equation:
- + M 8* - + *») + * 42*10 V 1 + V - . K
VTs
dN
dt
jl =
J
+ *«)
^
t
- N b - + ^ e ( 6 ^ + ^ ) + 3.42xl075-' +3 NQk ^ ( N s + N d)
pv tp
dN]d _
= -N a dt
K*d
+
+* c ) + 3.42*107r ' +5Nak ^ ( N . + N „ )
(19)
Figures 19 and 20 show a comparison of experimental quenching
data for quenching by molecular hydrogen with the calculated
quenching curve. Two sets of experimental data were combined to
comprise the figures. As shown in Figure 20 with an expanded
horizontal scale the agreement of the calculated quenching curve with
the data is very good.
73
0.65
0.60
0.55
0.50
0.45
|
0.40
^
0.35
I
0.30
9
0.25
0.20
0.15
0.10
0.05
0.00
0
10 20 30 40 50 60 70
HB Pressure, Torr
80
90 100
Figure 19. Comparison Fit of Quenching Model
Calculations to Experimental Quenching of 11Atom TAIJF by H2 Gas.
74
0.6S
0.60
0.55
0.50
0.45
2
1
0.40
0.35
0.30
or
0.25
0.20
0.15
0.10
0.05
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Hg Pressure, Torr
Figure 20. Expanded Horizontal Scale from Figure
19.
75
Figure 21 shows the results for quenching of H*atom TAUF by
helium.
Shown
are
the
averaged
experimental
data
and
the
corresponding calculated quenching curves. The upper curve in the is
the calculated quenching curve using only nonradiative quenching and
the cross-section reported by Bittner et al for quenching by helium .97
The experimental data differs significantly from this calculated curve
suggesting their lower pressure (up to 7 Torr) data was not sufficient to
determine the appropriate cross-section value.
Calculation of the mixing and dexcitation cross-sections fitted to the
helium data show the calculated deexcitation cross-section to be a factor
of 24 smaller than the corresponding mixing cross-section. The
dominance of the mixing cross-section would suggest a large change in
effective radiative lifetime of the n=3 energy level due to mixing. Table 2
shows measured effective lifetimes as a function of helium pressure.
Also shown are lifetimes calculated using the cross-section reported by
Bittner and lifetimes calculated by our two cross-section model.
Table 2. Comparison of Measured and Calculated
Fluourescence Lifetimes for Helium Quenching
He Pressure,
Torr
0 .0
1.5
3.0
4.5
6.0
7.5
(measured)
12.7 ns
12.1 ns
11.8 ns
11.7 ns
11.7 ns
11.3 ns
x (Bittner)
11.3 ns
11.1 ns
10.9 ns
10.7 ns
10.5 ns
10.3 ns
x (New Model)
11.3 ns
6.8 ns
6.5 ns
6.3 ns
6.2 ns
6.1 ns
t
76
0.65 r
0.60
0.55
0.50
0.45
|
0.40
0.35
I
0.30
0.20
0.15
0.10
0.05
0.00
0
10
20
30
40
50
60
70
60
00
100
He Pressure, Torr
Figure 21. Quenching of H-Atom TALIF by
Helium. The upper curve is calculated based on
data from Reference 87.
77
As can be seen from the table there is actually very little change in
radiative lifetime over the given range of helium pressure. While by
using Bittner's cross-section for helium quenching the agreement is
within about one nansecond, for the current calculations there is nearly
a factor of two in difference. One explanation for the discrepancy is that
presence of acetylene has interfered with the mixing of L-states by
helium. As mentioned before, around pressures of 100-200 milUTorr of
foreign quenching gas L-state mixing has nearly reached statistical
equilibrium. Though a cross-section for mixing by C2H2 could not be
reliably determined here, it is very likely that acetylene is also very
effective in promoting L-state mixing. Thus, given a partial pressure of
acetylene of 100 milUTorr used in these experiments, there may be
already nearly complete mixing of the L-state populations so that the
addition of helium does not discernibly contribute to this effect.
The small lifetime variations would make the determination of
quenching cross-sections based on lifetime measurements very difficult.
This is the m ethod used by Bittner et al in their measurements using the
same photomultipher tube as for the present measurements. Their
quenching cross-section is a factor of three smaUer than the present
colhsional deexcitation cross-section measurement. The difficulty of not
observing significant lifetime variation during heUum quenching while
at the same time the overall quenching behavior is reproduced by the
current model suggests the exact mechanism for colhsional m ixing by
helium could stiU remain unclear.
By selecting another rare gas like argon, which is larger and heavier
than helium, there should be an increase in the quenching effect and the
78
0.65 r
0.60
0.66
0.50
0.45
g
0.35
1
0.30
or 0.26
0.20
0.15
0.10
0.05
0.00
0
10
20
30
40
50
60
70
60
00
100
Ar Preaaure, Torr
Figure 22. H-Atom TALIF Quenching by Argon.
Lower curve is calculated based on data from
Reference 87.
79
cross-sections. Figure 22 shows quenching
data
and
calculated
quenching curves for quenching by argon. Again, the lower calculated
quenching curve is based on data published by Bittner et al in Reference
87. Lifetime variation was observed in the case of argon quenching as
shown in Table 3 in for the same range of pressure as for the helium
measurements. The measured fluorescence lifetimes varied from 12
nanoseconds down to 3 nanoseconds at higher pressures.
Table 3. Comparison of Measured and Calculated
Fluorescence Lifetimes for Argon Quenching
Ar Pressure,
Torr
0.0
1.5
3.0
4.5
6.0
7.5
x (measured)
12.3 ns
8.0 ns
5.7 ns
4.4 n s
3.0 n s
3.2 ns
x (Bittner)
11.3 ns
5.9 ns
4.0 ns
3.0 n s
2.4 n s
2.0 ns
x (New Model)
11.3 ns
6.1 ns
4.8 ns
4.1 n s
3.5 n s
3.1 ns
Now in the case of argon quenching we have better agreement in
comparing the calculated versus measured radiative lifetimes; with the
results calculated by use of the previously measure cross-section now
being significantly lower. In both cases for helium and argon quenching
the
lifetime
data
has
been
corrected
for
a
5
nanosecond
laser/instrum ental contribution. Thus, it would appear for gases such as
argon and other molecular gases that the radiative lifetime of the n =3
level would rapidly drop to levels where variations in the lifetime would
be unresolvable from instrumental contributions.
80
0.85
0.60
0.66
0.50
■0
£|H
0.46
0.40
fj 0.35
0.30
I
1 0.25
or
0.20
0.16
0.10
\
0.05 -
4 -U
o.oo L
10
20
30
40
SO 60
70
60
00
100
N_ Pressure, Torr
Figure 23. Quenching by Nitrogen. Lower
calculated quenching curve is based on data
from Reference 87.
0.66 r
0.60
0.56
0.50
Quantum
meld
0.46
0.40
0.35
0.30
0.25
0.20
0.15
0.10
O.OS
0.00
0
10
20
30
40
50
60
70
60
00
100
08 Preiaure, Torr
Figure 24. Quenching by Oxygen. Lower
calculated quenching curve is based on data
from Reference 87.
82
Table 4. Cross-Sections for Quenching of Hydrogen Atoms (n=3).
Quenching Gas
Present
Bittner et al
Measurements
Measurements
(x 10 ’15 cm2)
(x 1 0 '15 cm2)
o -2 q
He
=
0.10 ±0.004
<r2Q = 0.035 ± 0.020
<r2mix = 2.43 ± 0.13
<t 2 q =
0.66± 0.03
cr2Q = 1.8 ± 0.20
Ar
o-2mix = 0.94 ± 0.10
ct2 q
h2
<j 2 q =
= 4 .3 3
c 2h 2
6.5 ± 1.0
± 0.01
ct2 q
■ 10.9 ± 0.43
ct2 q
=
^m ix = 0.25 ± 0.08
<t 2 q =
02
9.23 ± 0.16
cr2mix = 0.69 ±0.19
o -2 q
n2
=
3.21 ±0.31
10.2 ± 0.39
o^mix = 0.86 ± 0.36
<72 q =
8.87 ±0.27
<j2q = 22.0 ± 1.6
83
Quenching by two diatomic molecular gases was also investigated.
Figure 23 shows quenching data and calculated quenching curves for
quenching by nitrogen. Quenching data and calculated quenching curves
for quenching by oxygen are shown in Figure 24. As for argon quenching
the lowest curves are calculated based on quenching cross-sections from
Reference 87. Table 4 summarizes the calculated cross-sections and
compares them with the cross-sections from Reference 87. There is
rough agreement for the nonradiative collisional deexcitation crosssection,
oq ,
for hydrogen between the two sets of m easurements within
a factor of 1.4. As already discussed, our measurement of the
nonradiative collisional dexcitation cross-section for helium is a factor of
three larger. For argon, our measurements give a cross-section which is a
factor of three smaller than Bittner's result. Measurements for nitrogen
and oxygen give cross-sections are approximately a factor of 2.5 to 3
smaller than the previously measured cross-sections.
Most
of
the
previously
determined
cross-sections
would
overestimate the amount of collisional deexcitation quenching. One
reason may be the difficulty of measuring lifetimes to determine
quenching cross-sections over a large range of pressure. As the pressure
increases the signals can become very small and the lifetimes will
approach the response time of the photomultiplier tube. It is interesting
to note the previous measurements of H-atom TALIF quenching were all
made below 7.5 Torr.
The model developed herein allows for an extension of the
interpretation quenching measurements over a broader range of
pressures than previously performed. The model adequately describes
84
most quenching behavior as well as fitting quenching cross-sections for
various gases. By determining the role of quenching in reducing
fluorescence
yield from
the
H-atom n=3
excited
state,
TAUF
concentration profiles can now be corrected for this effect.
Having developed techniques to measure Hydrogen and Oxygen
atom concentrations, the next two chapters give experimental results
from making such measurements in two commercially available plasma
reactor systems.
CHAPTER V
EXPERIMENTAL RESULTS FROM A GEC REFERENCE CELL
In 1990 a GEC Reference Cell was assembled from commercially
supplied components at the Advanced Plasma Research Group, WrightPatterson Air Force Base (WPAFB), Ohio. After the initial stages of
assembly and equipment checkout, a series of electrical characterization
experiments based on discharges through Argon and Helium were
performed. These measurements were made in conjunction with
electrical measurements being made at other facilities around the United
States equipped with the GEC Reference Cell. In the Summer of 1992, the
first ground-state atomic species density measurements performed in a
GEC Reference Cell were accomplished in the WPAFB GECRC. The
techniques for H-atom detection discussed in the previous chapter were
used to derive the results which are presented here.
Generation of the TAUF probe beam for H-atom detection was
accomplished in the manner described in Chapter 4. The hydrogen atom
TAUF probe beam was introduced into the reactor cell through a
Supersil 1 Quartz 2.75" diameter viewport, parallel to the 4" diameter
aluminum electrode surfaces. The probe beam exited the cell through an
identical viewport. Translation of the laser probe beam relative to the 25
millimeter interelectrode gap was accomplished by using a computercontrolled AeroTech stepper motor translation stage to which was
85
86
attached a quartz prism periscope. Minimum step resolution was 10
microns, but typically step sizes down to 200 microns were all that were
required to achieve reliable H-atom concentration profiles. The collection
optics assembly consisted of two plano-convex lenses between which a
narrow band (10 nm FWHM) filter centered at 656 nm was placed. The
assembly was focused on the center of the reactor cell through one of
the 6 " diameter glass viewports. No translation of the collection optics
synchronous with the laser probe beam was required or attempted.
The output of the collections optics was loosely focused on the
photocathode of a Hammatsu R928 photomultiplier. The output of the
photomultiplier anode was preamplified and then fed to either a digital
oscilloscope or to a Princeton Applied Research Boxcar Integrator and
then the integrated output was digitized in a digital multimeter
connected to a Hewlett-Packard personal computer through an IEEE-488
bus cable. TAUF signal acquisition was controlled by computer as a
function of stepper motor-controlled laser probe position. The signal
could be normalized to variations in the laser energy, by monitoring the
energy with a Molectron J3-01 Joulemeter detector whose output was
again digitized by a digital multimeter. The normalization with respect
to laser probe energy was calculated as the square of the variation since
two photons are required for the TAUF transition.
Calibration of the TAUF response in the GECRC was performed
using the same titration assembly described in Chapter 4. The assembly
was m ounted on one of the 2.75 inch Conflat flanges and extended into
the middle of the reactor volume. Concentration calibrations were
performed over a range of laser intensities and PMT voltage settings.
87
3.0
Raw Data, and Polynomial Fit
|
2.5
d
$u
2.0
£
u l.S
I
0
$0)
1
&
Normalized Fit to Raw Data
0.0
0
2
4
8
B 10 12 14 16 IB 20 22 24
Interelectrode Position, mm
Figure 25. GEC Reference Cell Geometric View Factor
Correction. Origin is position of powered electrode.
88
To correction for variations in solid angle collection efficiency as a
function of laser probe beam position between the electrodes, the
reactor cell is filled with acetylene to 1 Torr and the photodissociated
TAUF signal is recorded with the discharge off as a function of laser
probe beam position. Figure 25 shows the raw correction data, a linear
regression curve fit to the data, and final form where the regression
curve fit values have been normalized to unity. The periodic variation in
the data and regression fit resulted from the combination of fixed
collection optics and interference with the focused photocathode spot by
the dynode grid structure of the side-viewing photomultiplier. The
correction factor was truncated close to the electrodes to avoid a unduly
large corrections due to the occultation of the laser probe beam by the
electrode surfaces.
H-atom TAUF concentration profiles were collected for variations of
discharge conditions due to RF power and reactor pressure. Over the
range of parameters investigated the most dramatic changes were seem
as a function of discharge pressure. Figure 26 shows TAUF profile data
collected for pressures ranging from 0.3 to 5 Torr for a total deposited
discharge power of 30 Watts. The driven electrode is at the origin. The
data was acquired every 200 microns and averaged for 50 laser shots at
10 Hertz. The data has also been corrected by the data from Figure 25 by
dividing geometric view factor into the raw data. The median values for
the profiles start at low values for low pressures and then reach an
apparent maximum at approximately 1 Torr and then declining again at
higher pressures. The slope of the data would appear to be roughly flat
except at the higher pressures where a distinct slope is observable.
0
4
B
12
16
20
24
28
Interelectrode Poeition, mm
Figure 26. TAUF H-Atom Signal Profiles in GEC
Reference Cell for Different H2 Pressures. Power
deposited in plasma is 30 Watts.
90
16
a
oi
14
3 Torr
12
10
5 Torr
'O
B
1 Torr
g
t
u0
6
1o
ri
»
or
4
2
0
0.5 Torr
0.3 Torr
4
B
12
16
20
24
2B
Interelectrode Position, mm
Figure 27. Quenching Corrected TALIF Signal
Profiles From 26.
91
These H-atom concentration profiles were corrected for the
influence of quenching on the TAIIF quantum yield by dividing the
profile at a given pressure by the associated quantum yield calculated
from the model presented in Chapter 4. The quenching corrected
profiles are shown in Figure 27. Now it becomes apparent that the slope
of the data is much more dramatic at higher pressures as well as there is
a shift in the maximum concentration to 3 Torr instead of 1 Torr. These
observations can be correlated with emission measurements as described
below.
Based on in-situ titration calibration of the TAUF signal from the
GECRC, the TALIF signals observed can be used to calculate absolute
hydrogen atom concentrations generated in the Reference Cell plasma.
Table 5 shows the maximum H-atom densities as a function of pressure
both before and after correction for the influence of fluorescence
quenching. Also shown is the percentage dissociation fraction calculated
as the ratio of the corrected maximum H-atom density over the
particular total pressure of H2 in the reactor. The maximum between 1-3
Torr in the concentration profiles corresponds over fifty percent
dissociation of the H2 gas.
To the eye, the visible emission from the H2 plasma in the GECRC is
asymmetric with a much stronger visible negative glow region after the
cathode sheath near the driven electrode. This asymmetry correlates
with the variation in TAUF concentration
profiles as a function of
pressure. Balmer-« emission from the n=3 level was profiled as a
function of H2 pressure in the reactor at the same RF power level. A 100
micron slit was placed in front of the combination of interference filter
Table 5. Computed Maximum H-Atom Densities in GEC Reference Cell
H2 Pressure
Integrated
Signal
H-Atom Density
(x 1 0 16 cm-3)
Fluorescence
Q uantum Yield
Corrected
H-Atom
Density
(x 1 0 16 cm’3)
Dissociation
Fraction
(Torr)
(Volts)
0.3
0.70
0.110
0.39
0.28
28
0.5
1.00
0.155
0.28
0.55
33
1.0
1.75
0.271
0.16
1.69
51
3.0
1.60
0.262
0.06
4.37
44
5.0
0.75
0.116
0.04
2.90
18
(%)
C
ND
3
H—Atom. n=3 Emission
Signal, (a.u.)
3.0
0.7 Torr
2.5
1.5 Torr
2.0
1.5
0.3 Torr
Torr
1.0
0.5
7 Torr
0.0
0
5
10
15
20
25
Interelectrode Poeition, mm
Figure 28. H-Atom Balmer-a Emission Profiles in
GEC Reference Cell as a Function of H2 Pressure.
Emission
Intensity
(a .u .)
94
Ixxictolc®tro d* PO **00- “ “
Figure 29. Interpolated 3-D Mesh Representation of H-Atom
Baimer-a Emission Profiles.
95
and photomultiplier used for the TAUF measurements and the assembly
m ounted on a computer-controlled stepper motor translation stage. The
emission profiles as a function of position and reactor pressure are
shown in Figures 28 and 29. Figure 28 shows two-dimensional plots of
the emission profiles, while Figure 29 shows a three-dimensional
interpolated mesh representation of the profiles presented in the
previous figure.
Both Figures 28 and 29 show a general asymmetric behavior, sloping
down from the driven electrode. The slopes of the profiles are more
pronounced in the emission profiles as compared to the TAUF
concentration profiles shown earlier. This can be expected since
electron-impact dissociative excitation of H2 which generates excited
state H-atoms mainly occurs in or near the electrode sheaths where the
electrons can gain sufficient energy by acceleration through the sheath
potential drop. Given the short radiative lifetime of the n=3 state the
electron impact-produced atoms do not diffuse uniformly through the
interelectrode gap before they radiate. Ground-state H-atoms, on the
other hand, do not readily recombine in the gas phase and they diffuse
throughout the bulk plasma; generally recombining only on the walls or
electrodes .98 This makes for a more uniform profile of ground-state Hatoms as detected by the TAUF diagnostic.
At lower pressures two peaks are seen in the emission profiles near
the driven electrode. The one further out into the plasma is due to the
contribution from electron impact dissociation discussed above. The
peak which is more proximal the electrode surface is thought to be
caused by H+ and H2+ ions colliding with the electrode surface and
96
generating fast H-atoms. The fast H-atoms are then backscattered and
collide with H2 in the cathode sheath. The collisions have sufficient
translational energy to dissociatively excite the H2 molecules leaving
excited state H-atoms which emit. Similar observations have been made
in the case of low pressure direct current (DC) hydrogen discharges."
Electrons should not play a role since electrons leaving the cathode have
to cross the cathode sheath region before they generally have sufficient
energy to cause this type of process.
As the pressure increases the sheath regions contract and the two
peaks observed at lower pressures coalesce into one and there appears to
be a maximum in the emission profiles near 1 Torr. Again, as in the case
of the TAUF concentration profiles, these emission profiles can be
corrected for the influence of collisional quenching on the fluorescence
quantum yield. Figures 30 and 31 are the emission profiles from Figures
28 and 29 corrected as a function of pressure for variations in quantum
yield.
In both figures the asymmetry in emission profiles is very
pronounced at the higher pressures. This behavior correlates well with
the behavior of the TAUF profiles shown in Figure 27. Overall there is
increased production of ground-state and excited-state hydrogen nearer
the driven electrode for the higher pressure discharges.
Another set of observations which help to validate both the TAUF
and emission profile data are electrical characterization measurements
for plasma current and voltage. Figure 32 show the measured total
current through the plasma as a function of pressure. The effects of
external impedance were carefully evaluated using an equivalent circuit
97
18
0« 16
4
1.5 Torr
* 14
’a
1
12
3 Torr
8 10
•X
■
B
M
II 6
d
a 4
7 Torr
I
w
0.3 Torr
2
0
0.7 Torr
0
5
20
Interelectrode Position, mm
Figure 30. Quenching Corrected
Baimer-« Emission Profiles.
H-Atom
7
8
pres««*e* 'torT
Figure 31. Quenching Corrected Interpolated 3-D Mesh
Representation of H-Atom Baimer-ex Emission Profiles.
99
1.0
0.9
0 .B
0.7
0.6
0.5
« 0.4
0.3
0.2
-
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Preiaure, Torr
Figure 32. Plasma Current as a Function of H2
Pressure in GEC Reference Cell.
100
700
650
600
550
500
450
400
o 350
> 300
250
200
150
100
Total Plaama Voltage
Plasma DC Bias
50
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Pressure, Torr
Figure 33. Total Plasma Voltage and DC Bias as a
Function of H2 Pressure in GEC Reference Cell.
12
12
11
10
9
B
7
6
S
4
3
2
1
0
0
1
3
4
Hg Preaiure, Torr
2
6
6
0
Figure 34. Comparison of Maximum H-Atom
Density and the Product of Current and Pressure
as a Function of Pressure.
102
model of the GEC Reference Cell and deconvoluted from the plasma
current data .100 A maximum in the plasma current is observed at
approximately 3 Torr pressure of H2. This maxim um coincides with the
observed maximum in plasma emission and ground-state H-atom
concentration as measured by the TAUF diagnostic. The shows a
reproducible local m axim um in the plasma current about 0.75 Torr
which may correlate with a maximum production of fast H-atoms near
the
driven
electrode
as
observed
from
the
plasma
measurements. However, the mechanism for enhancing
emission
electron
production and hence the current by electron avalanche multiplication
in this region is not readily apparent.
Measurements of the total plasma voltage and plasma DC voltage
bias are shown in Figure 33. Over a range of several Torr the total
voltage drop across the plasma is roughly constant near 600 Volts. The
plasma DC bias exhibits more variation ; ranging from 50 to 200 Volts.
The large plasma DC bias again demonstrates that the hydrogen plasma
is very asymmetric since such a large bias of approximately 20 percent
on average would induce the plasma to behave partially in a DC
discharge-like manner . 101 The source of the bias and overall asymmetry
of the discharge in the GECRC is due to the effect of unequal electrode
areas between the top driven electrode and the bottom electrode .102 The
bottom electrode effectively has a larger surface area due to the presence
of the grounded guard ring and other reactor surfaces.
An interesting comparison may be made between the pressure
dependence of the maximum H-atom density as measured by TAUF and
the pressure dependence of the product, I x P, plasma current times
103
pressure. The comparison is shown graphically in Figure 34. For
pressures below about 2 Torr the H-atom density follows the increase of
the I x P parameter; indicating the production of H-atoms is roughly
linearly proportional to the product of current and pressure in the lower
pressure regime. Above 2 Torr, the H-atom density reaches a maximum
and then decreases; diverging from the product of I x P. As seen from
Figure 32 the current has also saturated in this pressure region
suggesting the source of H-atoms due to electron impact dissociation has
diminished; possibly due to electron cooling by collision.
The plasma current and voltage measurements reported here are
the first observed for the GEC Reference Cell and a H2 plasma and in a
system which is of industrial scale. At this point the H2 plasma is in
principle the most understandable system that currently exists,
measurement of ground state atomic concentrations along with
dissociation fraction has determined the majority of the neutral species
within the discharge. Practically all important plasma species densities
can now be measured or inferred from developed experimental
techniques; including electron densities by microwave interferometry, H
and H2 concentrations by TAUF, and detection of H* ions by laser
photodetachment measurements. The H2+ and H3+ ion densities and
production regimes remain to be investigated. However, given the nearly
complete list of measured plasma species as well as other plasma
parameters such as current and voltage characteristics it may now be
possible to develop a complete and self-consistent model of the simple
hydrogen glow discharge.
CHAPTER VI
EXPERIMENTAL RESULTS FROM AN ASTEX DIAMOND GROWTH REACTOR
Starting in January 1992, a high-power microwave plasma diamond
deposition reactor system was constructed at the Ohio State University
Laser Spectroscopy Facility. Most of the component parts comprise the
ASTEX HPMM Microwave Plasma Source. Figure 35 shows a basic
schematic drawing of the HPMM system. The main microwave radiation
source is a 1.5 kiloWatt magnetron power generator. The microwaves are
propagated through rectangular waveguides and coupled to the
cylindrical plasma chamber through a TEqi to TMqi mode symmetric
coupler. The microwave radiation is then passed through a quartz
vacuum window into the reactor volume. Tuning elements are also
provided to effectively match the forward microwave power deposition
and minimize reflected power back to the magnetron power head.
At the bottom of the reactor chamber is the gas pumping manifold
and the heater substage assembly. The system is pumped by a 18 liter
per second chemically resistive Krytox oil roughing pump. A base
pressure of 1 miUiTorr can be reached with this pump. In addition, the
entire chamber can be pumped by a compound turbomolecular pump
down to 10‘7 Torr to help remove water vapor and other outgassing
products.
104
105
The heater sub stage assembly consists of a water-cooled radio­
frequency antenna coil powered by 3.5 kilowatt RF power generator. The
RF antenna radiation is absorbed in a graphite susceptor heating
element. The RF radiation then heats the graphite to temperatures
approaching 1000 degrees Celsius. The heating stage is 5 inches in
diameter and can accommodate up to a 4 inch diameter diamond growth
substrate; typically a 3 inch diameter semiconductor-grade silicon wafer.
The entire heating stage can be positioned vertically inside the plasma
chamber by means of an adjustable motor drive. By using the motor
drive positioning of the heated wafer substrate allows for some control
of exposure of the substrate to the plasma.
The ASTEX HPMM system is capable of generating a microwavesustained plasma from about 10 to 100 Torr. Gases are added to the
chamber through a gas dispersion ring on the vacuum side of the quartz
plasma window. Gas mixtures are controlled by calibrated electronic
mass flow controllers and the chamber pressure is m onitored by a 100
Torr range capacitance manometer (Baratron). The pressure in the
chamber is controlled to less than one percent fluctuation via a
electronically-controlled throttle valve assembly in a feedback loop with
the pressure readout of the capacitance manometer.
For the experiments described here the operating conditions for
from the plasma were maintained at constant values and only the gas
mixtures were varied to optimize the diamond deposition process. The
microwave power deposited to the chamber was 1200 Watts with
practically no reflected power measured. The heater assembly was
positioned at the midpoint of the chamber as measured by an electronic
106
Symmetric
Plasm a
Coupler
— 36.5----------------------"
Directional
Coupler
3 Stub
T u n e r^ n
S u ftA
Circulator /
I I
tDum m y
I
'L o aad
dl
f l .
ity=wD=i3
—
Ujmjiutr
II
Power
Head
■ ^ -M a g n e t# !
Rapid-load_ I t
---- ►
Door
©
=111.
Heater level
'Optional 2nd Magnet
^ Tabletop level
58,.5"
‘ 8 in o.d.
Conflat flange
‘Pumping and
instrumentation ports
tt
LI
.M otor Drive
‘for height
adjustment
45" min.
above floor
29"
Heater
Matching
Network
Figure 35. The ASTEX HPMM Microwave Diamond Growth Reactor
107
position monitor on the motor drive assembly. The heater stage
tem perature was maintained at 830±1 °C as m onitored by a
thermocouple placed on the back side of the graphite susceptor block
which was in a feedback loop with the heater stage RF power generator.
The chamber pressure was kept constant at 40 Torr and a maximum gas
load of 600 standard cubic centimeters per m inute (seem) was passed
into the reactor. Under these conditions a plasma ball of approximately 4
inches in diameter forms in the middle of the chamber. Diamond is
deposited directly under the plasma bah. Diamond deposition was
confirmed by use of surface Raman laser spectroscopy and by scanning
electron microscopy (SEM). However, in what follows no descriptive
analysis of the materials deposited will be given, partly because this
research is still ongoing and also because the focus here is on the gas
phase laser diagnostics and chemistry. The diamond deposition gas
mixtures used will be described in further detail later in the text.
Due to the physical dimensions of the diamond deposition system,
the TAUF laser probe beam was introduced into the reactor chamber by
means of a quartz prism periscope to accommodate the height of the
apparatus. Two stepper motor-controlled translation stages positioned
the laser probe beam relative to one of the 2.75" Conflat Supersil 1
quartz viewports. One translation stage controls the vertical position
and the other the horizontal position with respect to the window. Close
to the viewport where the laser probe enters, a second set of two stepper
motor-controlled translation stages was placed to control the positioning
of the final quartz focusing lens to focus the TAUF probe in the central
vertical plane of the reactor chamber. Both sets of translation stages
108
were under computer control and synchronously stepped in unison to
translate the laser probe beam across the quartz viewport in two
dimensions.
The TALIF fluorescence was collected at right-angle to the direction
of the laser probe by a combination of narrow-band interference filter
and focusing lenses as describe previously. The collected fluorescence
was detected using either Thorn-EMI 9659 or Hammatsu R928
photomultiplier tubes.
As for the measurements in the GEC Reference Cell, is necessary to
correct for variations in the fluorescence collection efficiency as a
function of laser probe beam position. In this instance, however, the
geometric view factor correction was obtained in two d im e n s io n s instead
of one as for the case of the GECRC profiles. Figure 36 shows the raw
data for the view factor correction measured by filling the reactor with 1
Torr of acetylene (no plasma) and profiling the photodissociationinduced TALIF signal. One hundred percent reflects the largest signal
recorded. As shown in the figure, the circular outline of the quartz
viewport can be seen as well as the top of the heater stage and wafer
substrate which limits the circular region near the bottom of the outline.
The TALIF signal is strongest to the right of the which reflects the fact
that as the laser probe beam rasters horizontally is then closer to the
side with the collection lenses and photomultiplier. There is an
asymmetry about the horizontal centerline of the which results from
vignetting due of the collection lens assembly and tilt adjustment of the
collection optics to better view the plasma ball which forms in the
reactor.
109
Figure 36. ASTEX Reactor Geometric View Factor Correction
110
Measurements at each stepped position was averaged for 32 shots
of the pulsed laser. The position resolution used here is 1 mm in both
dimensions. Finer stepped resolution could be obtained down to 100
microns, but the time required to make such detailed measurements
became several hours over which the laser energy was apt to fluctuate
significantly. The position resolution used in the measurements
described here represent the best compromise between resolution and
laser stability.
The raw data shown in Figure 36 is normalized to a range of zero to
one hundred percent in TAUF response. To correct the actual TAUF data
acquired from different diamond growth plasma, the data at each point
was divided by the percent factor given at the corresponding point in the
view factor correction profile. The corrected data in tu rn is normalized
to a 100 percent scale. The m axim um concentration of H or O-atoms for
a specific is presented in the caption. All data shown in the following
figures was collected using over a period of 11 days after initial
measurement of the view factor correction. This was done to insure that
any systematic or inadvertent change to the optical alignment of the
laser system was minimized. All the measurements were accomplished
using a Thorn-EMI 9659 photomultiplier operating at either 500 or 600
volts. The low voltage used was necessary to reduce the average anode
current below the maximum rating for this photomultiplier. Laser pulse
energy was stabilized at 225 microjoules per pulse as measured by a
Molectron Joulemeter. The data presented here has the background
contribution from plasma-induced emission and thermal radiation of the
heater stage subtracted.
Ill
Figures 37 and 38 show uncorrected and corrected TAUF
concentration profile maps for a methane-based diamond growth gas
mixture consisting of 0.7596 CH4 in H2 (500 seem) or in terms of atomic
fractions Xq=1, Xq=0, and XH=0.996. This corresponds to a position in
the lower left vertex of the C-H-0 phase diagram shown in Figure 2. This
gas mixture is a standard mixture used for depositing diamond in hot
filament and plasma-assisted diamond CVD systems. The maximum 11atom density is calibrated at 3.37 ± 0.16 x 1015 per cm3. However, at a
pressure of 40 Torr in the reactor chamber, the fluorescence is strongly
quenched. Since the gas mixture is nearly 100 percent hydrogen, we can
use the results from Chapter 4 for quenching by H2. This corrects the
calibrated concentration by a factor of 110 to a maximum of 3.70 ± 0.18
x 1017 per cm3. Thus, approximately 11.2 Torr out of 40 Torr total H2
pressure or - 28 percent is hydrogen atoms.
In Figure 37 most of the uncorrected TAUF signal comes from the
upper region of the 2-D profile. Upon correction the TAUF signal
response is much more uniform over the volume sampled in the reactor.
Variations in H-atom density are on the order of 1596. The correction of
the raw TAUF data is even effective to within ~1 mm of the heater/wafer
surface. At 40 Torr concentration gradients into the wafer are expected
to occur over a length of a millimeter or less.
Figures 39 and 40 are uncorrected and corrected TAUF profiles for
a diamond growth mixture were oxygen has been added. For this
experiment Xc=0.451, Xo=0.048, and XH=0.96. This mixture corresponds
to a position further towards the C-0 line in the phase diagram and is
denoted point #48 in Reference 39. The maximum H-atom density
112
Figure 37. Raw Data for H-Atom TAUF Concentration Map in
0.75% CH4 /H 2 Methane-Based Diamond Growth Plasma. Xc=l,
Xo=0, Xh®0.996.
113
Figure 38. Corrected Data for H-Atom TAUF Concentration Map in 0.7596
CH4/H 2 Diamond Growth Plasma. Maximum H-Atom Density is 3.70 ±
0.18 xlO 17 per cm3.
114
measured for this data after correcting for quenching by H2 is 5.09 ±
0.93 x 1017 per cm 3 or approximately 3996 dissociation H2 gas. This
concentration is a factor of ~1.4 larger than the previous mixture. A
comparison between Figures 37 and 39 shows the second mixture to give
a stronger overall TAUF signal, though the corrected data shows the 11atom density to be as uniform as before.
Beside growing diamond from more standard gas mixture of
methane, hydrogen, and oxygen, experiments were also performed using
acetone as the hydrocarbon source. Figure 41 shows uncorrected TAUF
data for a diamond growth gas mixture of acetone vapor and oxygen.
The conditions for diamond growth (9.76 seem acetone and 8.65 seem
0 2) give Xc=0.52, Xq=0.32, Xh=0.67 which is roughly in the middle of the
C-H-0 phase diagram and duplicates point # 23 for diamond growth
from acetone which was also performed by the authors of Reference 39.
Figure 42 is the view factor corrected data from Figure 41. Figure 43
is a second corrected repeat scan taken a few hours later under the same
operating conditions. Both figures show profiles which are different than
Figures 38 and 40. In this instance there are two interesting features
present in these corrected profiles. First, there appears to be a region
corresponding roughly with the center of the plasma ball where there is
approximately 30 percent depletion of H-atoms. Next, further away from
the central plasma location there is a layer of larger H-atom density near
the heated wafer surface. For these profiles the H-atom TAUF signal is a
factor of two larger than the previous plasmas investigated. If we assume
that the mayor quencher in this plasma is 0 2 at a partial pressure of 19
Torr, the quenching correction factor is 25.8. Therefore, the TAUF signal
115
Figure 39. Raw Data for H-Atom TAUF Concentration Map in
Methane-Based Diamond Growth Plasma. Xc=0.451, Xq=0.048,
and Xh=0.96.
116
Figure 40. Corrected TAUF Data from Figure 39. Maximum H-Atom
density is 5.09 ± 0.93 xlO 17 per cm3.
117
Figure 41. Raw Data for H-Atom TAUF Concentration Map in
Acetone-Based Diamond Growth Plasma. Xc=0.52, Xq=0.32, and
Xh=0.67.
118
Figure 42. CoiTected TAUF Data from Figure 41. Maximum H
Atom Density is 2.77 ± 0.28 xlO 17 per cm3.
119
Figure 43. Repeat Corrected TAUF Scan for Conditions in Figure 41.
120
corresponds to a maximum H-atom concentration of 2.77±0.28 x 10 17
per
cm 3 or approximately 8.4 Torr of hydrogen
atoms. This
concentration is remarkable in that all of the hydrogen atoms m ust come
solely from the dissociation of acetone by the plasma.
Oxygen atom TAUF was also used to investigate the acetone-oxygen
diamond growth plasma. However, no oxygen atoms could be detected in
the plasma for the acetone-oxygen mixture ratio used to grow diamond.
O-atoms could be detected at lower percentage of acetone in the plasma;
under conditions which did not lead to diamond deposition. Figures 44
and 45 show uncorrected and corrected O-atom TAUF profile
measurements for a acetone-oxygen-based (5.55 seem acetone and 9.18
seem O2) plasma where Xc=0.41, Xq=0.42, and XH=0.67 which is in the
oxygen-rich no-growth region just below the main diamond growth
region in the C-H-0 phase diagram given in Figure 2. The O-atom TAUF
signal uncorrected for quenching corresponds to a concentration of 1.19
x 10 15 per cm3. The initial partial pressure of oxygen in this plasma is
approximately 25 Torr. Based on preliminary O-atom TAUF quenching
data for quenching by 0 2, the measured maximum O-atom TAUF signal
can be corrected by a factor of 98 giving a maxim um density of 1.2 ±
0.12 x 1 0 17 per cm3.
Two experimental results which may shed some light on the reason
for the lack of measurable O-atom TAUF under oxygen-acetone diamond
growth conditions are shown in Figures 46 and 47. In both cases O-atom
TAUF was monitored as a function of gas mixture ratio. In addition,
stimulated emission pumping (SEP) can also be observed from the Oatom TAUF diagnostic in the direction of the laser probe beam .103
121
Figure 44. Raw Data for 0-Atom TALIF Concentration Map in
Acetone-Based Microwave Plasma. Xc=0.41, Xq=0.42, and
Xh=0.67.
122
Figure 45. Corrected O-Atom TAUF Data from Figure 44,
Maximum O-Atom Density is 1.2 ± 0.12 x 1017 per cm3.
40
30
Signal, millivolts
30
SEP
30
30
10
TAUF
10
0
0
0.0 0.3 0.0 0.0 1.3 1.0 1.0 3.1 3.4 3.7 3.0
M an Flow Ratio
Figure 46. H-Atom TAUF and Stimulated
Emission Pumping (SEP) Signals as a Function
of H2/O 2 Mass Flow Ratio in Microwave Plasma.
124
40
SEP
o
TAUF
0.0
0.2
0.4
0.6
0.6
1.0
1.2
1.4
1.6
Mm Flow Ratio
Figure 47. O-Atom TAUF and Stimulated
Emission Pumping (SEP) Signals as a Function
of Acetone/ 0 2 Mass Flow Ratio in Microwave
Plasma.
125
A thin glass slide which blocks the transmission of the 226 nm
probe light with low UV fluorescence is placed after the exit quartz
viewport and the highly directional SEP fluorescence continues to pass
on through a narrow-band 845 nm
interference filter
and is
subsequently detected by a Hammatsu R928 photomultiplier. Thus, both
the TAUF and SEP signals can be monitored simultaneously.
Figure 46 shows the response of O-atom TAUF and SEP as a function
of H2 to 0 2 mixture ratio in a microwave plasma at constant 40 Torr
pressure. Both the TAUF and SEP signals are appreciable over a large
range of mixture ratios up to nearly 3 to 1 H2 to 0 2. Both signals have
somewhat of a similar behavior in that there is a relatively gentle decline
in the signals at higher mixture ratios. The fact that TAUF signal
response follows the same functional behavior as the SEP signal
especially at higher mixture ratios indicates the TAUF signal is not
significantly perturbed by the presence of SEP emission.
The curves in Figure 47 both demonstrate a drastically different
behavior as one increases the acetone to oxygen mixture ratio. At a ratio
of 0.4 there is a sharp drop in both TAUF and SEP signals. The data in
Figures 44 and 45 was acquired at a mixture ratio of 0.6 where some
signal from both diagnostics is still observable. In the case of diamond
growth the mixture ratio is around 1.2 where the signals have declined
into the background.
The qualitative difference between the results from the mixture
ratio measurements and also from comparing H-atom versus O-atom
TAUF measurements in the acetone-oxygen diamond growth plasma was
also confirmed by plasma emission measurements. In this case a
126
Photometrix CCD camera monitored the plasma emission through the
narrow band interference filters used to detect H-atom (656nm) or 0atom (845 nm) TAUF.
In the case of hydrogen atoms emission was clearly seen by the CCD
camera and was localized to the boundary of the plasma ball seen visibly
with the eye. This would suggest that the H-atom emission was
generated by electron-impact excitation from electrons generated in the
plasma.
For oxygen atoms no emission was detected by the CCD camera
system. Careful adjustments in exposure and contrast were used to
enhance the possibility of detection of the emission, but no observable
emission was found. This measurement coupled with the results of
TAUF measurement for O-atoms suggests that no free atomic oxygen
was present at levels which could be discerned.
The fact that atomic oxygen could not be detected either by TAUF
or plasma emission measurements in the case of the acetone/ 0 2 -based
diamond deposition plasma is also in accord with the mass spectrometry
measurements discussed in Chapter 3. In those measurements no atomic
oxygen and O2 were detected in the gases flowing out of the reactor. The
hypothesis is that oxygen reacts with carbon or some hydrocarbon and is
very effectively trapped in these plasma. The effect of excess carbon
removal by oxygen capture would seem to enhance the preferred type of
carbon or hydrocarbon form required for higher quality diamond growth
at the surface. Calibrated UF measurements for carbon monoxide in the
plasma
may
help
to
clarify
this
mechanism
by
determining
concentrations of CO and hence the amount of removal of free oxygen.
APPENDIX A
EXPERIMENTAL QUENCHING DATA
127
C2H2 Quenching
Input Data File to MNV.EXE
63 1 2
3.2D-15
5.0D-16
0
1
0.005
0.0068
0.94566
0.93698
0.92984
0.93597
0.94015
0.94101
0.95083
0.95388
0.91758
0.91452
0.89036
0.87137
0.79074
0.67337
0.62685
0.6486
0.65265
0.63883
0.63663
0.63905
0.64203
0.6312
0.62208
0.60602
0.60102
0.58936
0.57425
0.5543
0.53484
0.58095
0.5721
0.5366
0.53913
0.50985
0.502
0.47486
0.46146
0.44027
0.0101
0.0151
0.0211
0.0275
0.0302
0.0354
0.0408
0.0463
0.0503
0.0536
0.0655
0.1025
0.1115
0.115
0.1207
0.1255
0.1335
0.141
0.153
0.161
0.171
0.182
0.192
0.203
0.211
0.225
0.234
0.243
0.251
0.28
0.291
0.303
0.32
0.336
0.357
0.386
0.412
0.449
0.49
0.513
0.555
0.702
0.762
0.818
0.881
0.93
1.016
1.063
1.11
1.22
1.44
1.71
1.91
2.42
2.94
3.93
4.93
6.92
7.06
10.49
.00000D+00
.00000D+00
.50000D-15
.00000D+00
.OOOOOD+OO
•00000D+00
.00000D+00
.00000D+00
63
1
2
0
1
1
1
0.4299
0.40934
0.3952
0.37791
0.36539
0.32235
0.30172
0.2875
0.27296
0.26593
0.24888
0.23884
0.22957
0.21219
0.18538
0.1607
0.14701
0.11848
0.099231
0.075431
0.061199
0.043962
0.042354
0.028565
H2 Quenching #1
Input Data File to MNV.EXE
47 1 2
ID-14
ID-15
0
0.99167
0.099
0.77143
0.2
0.59945
0.302
0.47949
0.403
0.41812
0.498
0.36601
0.602
0.32589
0.702
0.29211
0.798
0.26374
0.9
0.23727
0.998
0.22777
1.098
0.2152
1.198
0.20206
1.3
0.19116
1.398
0.18167
1.497
0.1709
1.598
0.16676
1.695
0.15763
1.796
0.14914
I.898
0.14475
2.9
0.10369
3.901
0.080543
4.903
0.065131
5.901
0.056449
6.911
0.048937
7.906
0.04346
8.904
0.039449
9.893
0.03634
II.922
0.02777
13.942
0.025264
15.932
0.023518
17.922
0.020071
19.972
0.018564
21.972
0.017433
23.912
0.017037
25.952
0.013664
27.972
0.013461
29.912
0.013135
34.992
0.011906
40.042
44.962
49.982
59.982
69.962
80.062
89.972
99.952
.00000D+00
.00000D+00
.50000D-15
.00000D+00
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
47
1
2
0
1
1
1
10
0.00925
0.0091859
0.010166
0.0073714
0.0054026
0.0048758
0.0043895
0.0018099
130
H2 Quenching #2
Input Data File to MNV.EXE
41 1 2
ID-15
ID-15
0
1.00000
0.061
0.152
0.295
0.378
0.47
0.587
0.90293
0.66890
0.50748
0.44055
0.38718
0.33998
0.31209
0.28677
0.28023
0.20602
0.18586
0.17181
0.15865
0.14572
0.10982
0.086545
0.083156
0.069675
0.061892
0.057406
0.045459
0.040152
0.036884
0.035791
0.030620
0.028248
0.026769
0.029038
0.028081
0.027725
0.028389
0.020875
0.019125
0.019208
0.014412
0.013075
0.011217
0.012358
0.686
0.788
0.883
1.081
1.271
1.47
1.679
1.889
2.883
3.875
4.891
5.908
6.881
7.896
8.906
9.899
11.931
14.011
15.991
17.911
19.951
22.001
24.061
26.061
28.111
30.151
34.961
40.011
50.061
60.081
70.311
79.961
90.161
0.0093256
99.861
0.0083197
.00000D+00
.OOOOOD+OO
.50000D-15
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
41
1
2
0
1
1
1
10
He Quenching
Input Data File to MNV.EXE
59 1 2
ID-15
ID-15
0
1
0.0665
0.1645
0.277
0.37
0.469
0.571
0.663
0.765
0.8524
0.7857
0.7258
0.7063
0.868
1.071
1.273
1.477
1.671
1.868
2.071
2.266
2.493
2.689
2.871
3.057
3.268
3.462
3.695
3.92
4.378
4.408
4.906
5.46
5.884
6.385
6.883
7.375
7.847
8.415
8.876
9.543
9.851
11.872
0.68
0.6595
0.6503
0.647
0.635
0.637
0.6346
0.6206
0.6295
0.6144
0.6239
0.6495
0.6105
0.6255
0.5975
0.6317
0.6245
0.6179
0.6089
0.5852
0.5986
0.5774
0.5774
0.5331
0.5311
0.5565
0.5005
0.4853
0.4796
0.4725
0.4915
0.4804
0.4874
0.4529
13.877
15.867
17.892
19.887
24.371
27.895
30.876
34.376
39.862
44.885
49.872
54.862
59.871
64.967
69.872
74.887
79.962
84.867
94.842
99.871
.OOOOOD+OO
.OOOOOD+OO
.50000D-15
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
59
1
2
0
1
1
1
10
0.4207
0.4149
0.3824
0.3781
0.3345
0.2877
0.2936
0.2782
0.258
0.243
0.2332
0.2249
0.2155
0.2046
0.1991
0.192
0.1892
0.1847
0.1754
0.1712
At Quenching
Input Data File to MNV.EXE
33 1 2
1.74D-15
0.61D-15
0
1
0.081
0.449
0.5563
0.658
0.757
1.813
0.911
0.829
0.704
0.649
0.679
0.537
0.474
0.394
0.364
0.321
0.293
0.279
0.253
0.248
0.209
0.182
0.165
0.151
0.108
0.087
0.075
0.063
0.0556
0.049
0.045
0.041
0.038
0.037
0.036
0.035
0.035
0.035
2.8
3.861
4.854
5.854
6.822
7.88
8.842
9.83
11.834
13.87
15.85
17.88
35.29
39.79
44.78
49.81
54.8
59.8
64.8
69.8
74.8
79.8
84.8
89.8
94.8
98.8
.OOOOOD+OO
.OOOOOD+OO
.50000D-15
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
33
1
2
0
1
1
1
10
N2 Quenching
Input Data File to MNV.EXE
50 1 2
ID-15
ID-15
0
1
0.067
0.163
0.27
0.372
0.464
0.572
0.675
0.765
0.869
1.064
1.404
1.871
2.29
2.874
3.462
3.904
4.378
4.863
5.376
5.89
6.37
0.9655
0.8191
0.7534
0.651
0.626
0.511
0.477
0.45
0.426
0.303
0.31
0.262
0.227
0.194
0.17
0.154
0.142
0.134
0.125
6.868
0.101
7.378
8.365
8.847
9.35
9.907
11.89
13.88
15.89
17.9
19.9
23.89
27.96
35.36
39.86
44.86
49.65
0.0931
0.092
0.0815
0.0785
0.0714
0.0588
0.0504
0.044
0.0378
0.0332
0.0269
0.0248
0.0229
0.0188
0.0165
0.0147
51.16
54.92
59.87
64.89
69.87
74.86
79.91
84.95
89.97
94.91
99.93
.OOOOOD+OO
.OOOOOD+OO
•50000D-15
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
50
1
2
0.112
0
1
1
1
0.106
10
0.0133
0.0123
0.132
0.0123
0.0118
0.0084
0.0117
0.0105
0.0071
0.0081
0.0091
O2 Quenching
Input Data File to MNV.EXE
69 1 2
ID-15
ID-15
0
1
0.065
0.116
0.163
0.288
0.369
0.511
0.60838
0.85173
1.1165
1.3739
1.6152.
I.8534
2.1145
2.3394
2.618
2.8529
3.1155
3.3871
3.6188
3.8831
4.1165
4.3759
4.6178
4.8452
5.3945
5.8885
6.3718
6.8678
7.3778
7.8665
8.3705
8.9065
9.3768
9.8952
10.374
10.88
II.404
11.884
0.93744
0.84923
0.84055
0.83058
0.62031
0.64715
0.46106
0.3946
0.30033
0.31304
0.24165
0.26448
0.20758
0.2309
0.18677
0.21412
0.17217
0.18561
0.15578
0.17565
0.14793
0.16687
0.13875
0.1688
0.15439
0.14622
0.14069
0.1341
0.13233
0.12633
0.1225
0.11771
0.11822
0.11345
0.10463
0.10434
0.10027
0.102
12.259
12.884
13.374
13.934
14.193
14.404
14.904
15.364
15.864
16.063
18.013
19.873
21.913
23.923
25.903
27.913
29.903
34.943
39.543
44.953
49.573
54.913
59.893
65.563
70.03
79.863
84.943
89.923
94.903
99.933
.00000D+00
.00000D+00
.50000D-15
.00000D+00
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
.OOOOOD+OO
69
1
2
0
1
10
0.09421
0.090805
0.090318
0.091534
0.074485
0.087935
0.084828
0.079662
0.082924
0.063491
0.058779
0.050727
0.047639
0.043123
0.041226
0.038773
0.039314
0.035683
0.029752
0.026752
0.023596
0.021992
0.021323
0.029744
0.027606
0.021453
0.02036
0.019881
0.016059
0.01591
APPENDIX B
COMPUTER ACQUISITION AND ANALYSIS PROGRAMS
135
136
£********************************************************************
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
Program: DIAMSCAN.FOR
This program allows collection of data for spatial
profiling in the ASTEX microwave reactor. This program
does not control the PDL dye laser, but allows collection of
data as a function of the cell position as controled
by the stepping motor controller. The laser m ust first
be tuned to the peak of a transition of interest and
the peak intensity will be recorded versus position.
On the fly geometric viewing correction is an option.
This program contains many of the subroutines
previously written for PDLTEK4.FOR by Tim Cerny.
3-26-91
4-10-92
7-25-92
Geli Tserepi (Early Position Scanning of RF Cell)
Bryan Preppernau (Inital 1-D Scan Version)
Bryan Preppernau
^* * * * * * **************************************************************
$storage: 2
INCLUDE 'FGRAPH.FF
INCLUDE 'FGRAPH.FD'
C********** DECLARE AND DIMENSION VARIABLES *****************
C
DEFINE VARIABLES USED FOR DATA
DOUBLE PRECISION XPOSmON(5000),YPOSITION(5000)
REAL SIGNALDATA(5000)
COMMON/DATAVARS/XPOSmON.YPOSmON.SIGNALDATA
C
SPATIAL SCAN LOOP VARIABLES
INTEGER*2 IXSTART.IXFINISH.IYSTART.IYFINISH.STEPSIZE
INTEGER*2 XDATAPOINTS.YDATAPOINTS.TOTALPOINTS
INTEGER*2 ISDIREC,XMT,YINIT
REAL XSTART.XHNISH.YSTART.YFINISH.MMSTEP
CHARACTER*30 MESSAGE
CHARACTER* 1 RESP
CHARACTER*3 SDIREC1.SDIREC2
CHARACTER*4 DATE
LOGICAL BECHOOFF,BRS232INIT,BDSASET
COMMON/SSCANVARS/XSTART,XHNISH,YSTART,YFINISHISTEPSIZE,
+ XDATAPOINTS,YDATAPOINTS.MMSTEP, SDIREC1.SDIREC2,
+ IXSTART.IXFINISH.ISDIREC.IYSTART.IYFINISH
C
FILE NAME VARIABLES
INTEGER*2 SRUNNUM, SHOTS
COMMON/SFILEVARS/SRUNNUM,DATE
C
DEFINE VARIABLES USED IN COMMON BLOCK IBGLOBAL
INTEGER RD(15),WRT(15),TEKBD,CNT
£*************
C
ATTAT SCAN LOOP *******************************
INITIALIZE PROGRAMM VARIABLES
BDSASET=.FALSE.
BECHOOFF=.FALSE.
BRS232INIT=.FALSE.
IF (.NOT.BRS2 32INIT) THEN
CALL RS232INTT0 UNITIALIZE COM1 & PORT BUFFER
BRS2 3 2INTr=.TRUE.
END IF
C
INITIALIZE SPATIAL SCAN VARIABLES
IXHNISH=630
IXSTART=0
IYHNISH=630
IYSTART=0
STEPSIZE=315
SRUNNUM=1
SDIREC1=' r
SDffiEC2=' IM'
ISDIREC=2
CALL DSAINTT(TEKBD)! MTIALIZE IEEE BUS
GOTO 4
C
DISPLAY AND CHANGE SPATIAL SCAN PARAMETERS
3 CALL CLEARSCREEN($GCLEARSCREEN)
WRTTE(MOl)
138
101 FORMAT(/////T2 0,'WOULD YOU LIKE TO TAKE ANOTHER SPATIAL
SCAN?'/ /
+
T20/ENTER Y TO CONTINUE OR N TO QUIT \ )
CALL INKEY(RESP)
SELECT CASE(RESP)
CASE (Y, Y)
GOTO 2
CASE DEFAULT
GOTO 1000
END SELECT
C
MANUALLY MOVE THE CELL INTO POSITION
4 CALL CLEARSCREEN($GCLEARSCREEN)
99 WRTTE(M02)
102 FORMAT(/////T20,'DATE (MMDD) ?')
READ(*,'(A4)',ERR=99)DATE
2 CALL CLEARSCREEN($GCLEARSCREEN)
CALL PREPCELLO
1 CALL SSCANPARDISO
CALL SSCANINIT(BECHOOFF)
C
INITIALIZE SPATIAL SCAN DATA AQUISITION
CALL DATAJNIT(TEKBD)
IF (.NOT.BDSASET) THEN
CALL CLEARSCREEN($GCLEARSCREEN)
CALL STRACESEL(RD,WRT,TEKBD,CNT)
BDSASET=.TRUE.
END IF
CALL CLEARSCREEN(SGCLEARSCREEN)
50WRTTE(M00)
100 FORMAT(////T20,'HOW MANY SHOTS TO AVERAGE ?')
READ (V(I3)\ERR=50)SHOTS
CALL DSAAVEG(SHOTS,TEKBD,WRTfCNT)
C
ACQUIRE DATA
CALL CLEARSCREEN($GCLEARSCREEN)
C MOVE STEPPER MOTORS INTO POSITION UNDER COMPUTER
CONTROL
139
XDMTT=MM2INDEX(XSTART)
YINTT=MM2INDEX(YSTART)
CALL INTTMOVER(SDIREC1,SDIREC2.XINTT,YINIT)
K=0
DO J=0,YDATAPOINTS
DO I=0,XDATAPOINTS
MESSAGE='DIG RUN'
CALL S1R2GPIB(MESSAGE,WRT,CNT)
CALL IBWRT (TEKBD,WRT, CNT)
CALL STOPCHECK (WRT,RD,TEKBD,CNT) !MAKE SURE DIGITIZER IS
OFF
CALL COLLECTDATA(K,TEKBD,WRT,RD,CNT)
XPOSITION(K)=XSTART+I*MMSTEP
EFCSDIRECl.EQ.' I-') THEN
XPOSmON(K)=XFINISHT*MMSTEP
END IF
YPOSmON(K)=YSTART+J*MMSTEP
WRITE(*,300) XPOSmON(K),YPOSmON(K),SIGNALDATA(K)
C
MOVE MOTORS AND UPDATE COUNTERS, EXCEPT ON FINAL PASS
IF(I.NE.XDATAPOINTS) CALL SIDEMOVER(SDIRECl,STEPSIZE)
K=K+1
TOTALPOINTS=K
END DO
mSDIRECLEa’ I-') THEN
SDIREC1=' r
ELSEIF(SDIREC1.EQ.' I') THEN
SDIREC 1=' I-'
ENDIF
IF(J.NE.YDATAPOINTS) CALL VERTMOVER(SDIREC2.STEPSIZE)
END DO
message='COND TYP:CONTI'
140
call str 2 gpib (message, wrt, cnt)
call ibwrt (tekbd,wrt,cnt)
message='AVG OFF'
call str 2 gpib (message, wrt, cnt)
call ibwrt (tekbd,wrt,cnt)
CALL ZEROMOVER0
C
STORE DATA
CALL CLEARSCREEN( $GCLEARSCREEN)
450 WRrTE(*,501)
501 FORMAT(//////T2 5'END OF SPATIAL SCAN. OPTIONS:'//Tl5,
+ 'l) SAVE DATA YT15,
+ ’2) CONTTNUE'/Tl 5, 'SELECTION?^
600 CALL INKEY(RESP)
SELECT CASE(RESP)
CASE DEFAULT
GOTO 600
CASE (’2')
GOTO 2
CASE ('1')
CALL FILENAMEO
WRITE(2,299) TOTALPOINTS
299 FORMAT (14)
DO 11=0,TOTALPOINTS-1
WR1TE(2,300) XPOSmON(Il),YPOSmON(Il),SIGNALDATA(Il)
300 FORMAT (3F10.3)
END DO
CLOSE(UNrr=2,STATUS='KEEP')
SRUNNUM=SRUNNUM+1
GOTO 3
END SELECT
1000 CALL OFFINT
STOP
END
C************* prepare cell for a spatial scan *****************
subroutine prepcell ()
141
C
Definitions needed to use clearscreen in a subroutine
integer *2 $gclearscreen
parameter(Sgclearscreen= 0 )
external clearscreen
character*! resp
call clearscreen (Sgclearscreen)
2 0 0 write (*,100 )
100 format ( / / / / / / / T 10,'Please move the cell manually into position.'/
+
T10, 'Touch any key when ready. '\)
call inkey (resp)
return
end
C****** Display and change parameters for spatial scan *************
subroutine sscanpardisO
C
Definitions needed to use clearscreen in a subroutine
integer*2 Sgclearscreen
parameter(Sgclearscreen= 0 )
external clearscreen
C
Spatial file name construction variables
integer *2
srunnum
common /sfilevars/ srunnum,date
real
xstart,xfinish,ystartfyfinish,mmstep
integer *2 stepsize,xdatapoints,ydatapoints
integer *2 ixfinish,iyfinish,mm 2 indexlisdireclixstartliystart
character*3 sdirecl,sdirec2
character*4 date
COMMON/SSCANVARSASTART,XHNISH,YSTART,YFINISH,STEPSIZE,
+ XDATAPOINTS,YDATAPOINTS,MMSTEP,SDIREC 1.SDIREC2,
+ IXSTART.IXFINISH.ISDIREC.IYSTART.IYFINISH
character*! resp, cr
parameter (cr=char(13))
character*30 spatdirtxt(2)
data spatdirtxt / 'Left to right','Right to left'/
xfinish=50
yfinish=50
mmstep=l
1 0 0 xdatapoints=(xfinish-xstart)/mmstep
ydatapoints=(yfinish-ystart)/mmstep
call clearscreen($gclearscreen)
write (*,200 ) spatdirtxt(isdirec),xstart,xfinish,ystart,yfinish,
+
mmstep.srunnum
200 format (/////T20,'Spatial Grating Scan Parameters'//T10,
+ ’a) Scan Direction: '.A30/T10,
+ I d) X-Position Start: '.F9.3,' mm'/TIO,
+ ’c) X-Position Stop: '.F9.3,' mm '/T10,
+ ’d) Y-Position Start: \F9.3,' mm'/TIO,
+ 'e) Y-Position Stop: ',F9.3,' mm '/T10,
+ 'f) Spatial step size: \F9.4,' mm (min.step=.0032mm)'/T10,
+ 'g) Spatial scan rim number: '.I2//T7,
+'ENTER when ready'/T9)
300 call inkey (resp)
select case(resp)
case default
goto 300
case ('a','A')
call sdirecsetO
case Cb'.'B')
305 write (*,310)
310 format (//T10,'Please input the X - starting position in mm: '\)
read (*,'(F8.0)',err=305) xstart
if (xstart.lt.0 .) xstart=-xstart
ixstart=mm 2 index(xstart)
case ('c','C')
315 write (*,320)
320 format (//T10,'Please input the X - stopping position in mm: '\)
read (*,'(F8.0)',err=315) xfinish
if (xfinish.lt.0 .) xfinish=-xfinish
ixfinish=mm 2 index(xfinish)
case ('d'.'D')
321 write (*,322)
322 format (//T10,'Please input the Y - starting position in mm: '\)
143
read (V(F8.0)',err=321) ystart
if (ystart.lt.O.) ystart=-ystart
iystart=mm2 index(ystart)
case ('e'/E')
323 write (*,324)
324 format (//T10,'Please input the Y - stopping position in mm: \ )
read (*,'(F8.0)',err=323) yfinish
if (yfinish.lt.O.) yfinish=-yfinish
iyfinish=mm 2 index(yfinish)
case (T.'F)
325 write (*,330)
330 format (//T10,'Please input the spatial step size in mm: ’\)
read (*,'(F8.0)',err=325) mmstep
if (mmstep.lt.O) mmstep=-mmstep
stepsize=mm 2 index(mmstep)
case Cg’.’G’)
335 write (*,340)
340 format (//T10,'Please input the new spatial scan number:'\)
read (*,'(I2)',err=335) srunnum
case (cr)
return
end select
goto 100
end
£*************** Qjjgogg spatial scan direction *********************
subroutine sdirecset ()
C
Definitions needed to use clearscreen in a subroutine
integer *2 Sgclearscreen
parameter($gclearscreen= 0 )
external clearscreen
real
xstart,xfinish,ystart,yfinish,mmstep
integer *2 stepsize,xdatapoints,ydatapoints
integer *2 ixstart,ixfinish,isdirec,iystartIiyfinish
character*3 sdirecl,sdirec 2
COMMON/SSCANVARS/XSTART,XFINISH,YSTART,YFINISH,STEPSIZE,
+ XDATAPOINTS,YDATAPOINTS,MMSTEP, SDIREC1,SDIREC2,
+ IXSTART,KFINISH,ISDIREC,IYSTART,IYFINISH
character*! resp
call clearscreen($gclearscreen)
write (*,100 )
100 form at(//////T 2 5'Spatial scan direction options7/T15,
+ ’1) Scan from left to right.'/T15,
+ *2) Scan from right to left.'//Tl 5,'Selection?'\)
2 00 call inkey (resp)
isdirec=ichar(resp)-48
select case (isdirec)
case default
goto 200
case (1 )
sdirecl=' I-'
case (2 )
sdirecl=' I'
end select
return
end
^*********************** Construct file nainp ***********************
subroutine filename()
C
Filename construction variables
integer *2 srunnum
character* 17 pathname
character*4 date
character*3 sttus
character* 12 file
com m on /sfilevars/srunnum,date
integer *2 tens
character *2 chsrunnum
character* 1 resp
C
Convert the run number into a string
tens=srunnum /l 0
chsrunnum=char(tens+48)//char((srunnum-10*tens)+48)
file='H Sy/date//chsrunnum //,.DAT
pathname='DATA/7/file
sttus='NEW'
50 open (unit=2, file=pathname, status=sttus, err=400)
return
Error saving data
c
400 write (*,500)
500 form at(//' There is an I/O error saving the data.'/
+
’ Most likely, the file name is already in use.’/
+
' Would you like to overwrite? (Y/N) '\)
call inkey (resp)
select case (resp)
case (T ,V )
sttus=,OLD’
goto 50
case default
call sscanpardisO
end select
return
end
C********* Select signal and calibration signals on DSA 601 *********
subroutine stracesel (rd, wrt, tekbd, cnt)
C
Define variables associated with gpib functions
integer
rd(15),wrt(15),tekbd,cnt
character*30 message
character*30 labtrace
integer *2 i
character* 1 resp
write (*,100 )
100 format (///////T 5,'Please make sure the signal channer/T5,
+ 'is selected. Touch any key when ready. ’\)
call inkey (resp)
C
Query for the selected trace
message='SEL?'
call str 2gpib (message, wrt, cnt)
call ibwrt (tekbd,wrt,cnt)
call ibrd (tekbd,rd,30)
call gpib 2 str (message, rd, cnt)
146
C
Find the trace number
i=l
do while (.not.((ichar(message(i:i)).ge.48).and.
+
(ichar(message(i:i)).lt.56)))
i=i+l
end do
C
Construct command and label trace
labtrace=’LAB TRA7/message(i:i)//’:”SIGNAL"'
call str 2 gpib (labtrace, wrt, cnt)
call ibwrt (tekbd, wrt, cnt)
retu rn
end
C******** Initialize spatial grating scan variables *******************
subroutine sscaninit (bechooff)
character*32 message
logical bechooff
C
Enable communication (E) and zero position counter (Z)
if (bechooff) then
message='EZ'
else
message='EZT'
bechooff=.true.
end if
call strout (message)
!Toggle echo off on first time
return
end
C**************** sen(i averaging information to DSA ***************
subroutine dsaaveg (shots,tekbd,wrt,cnt)
integer *2 shots
C
Define variables used in common block ibglobal
integer
wrt(15)
integer tekbd,cnt
character* 30 message
character*4 inttochar
message='AVG ON;NAVG 7/inttochar(shots)//';COND TYP:AVG’
call str 2 gpib (message, wrt, cnt)
call ibwrt (tekbd,wrt, cnt)
return
end
C********* Convert a string to an ASCII integer array ***************
subroutine str 2 gpib (message, wrt, cnt)
C
Define variables associated with gpib functions
integer
wrt(15),cnt,odd,i
character*30 message
cnt=len_trim(message)
odd=mod(cnt,2 )
i=l
do while (i.le.cnt/2 )
wrt(i)=ichar(message(2*i-l:2*i-l))
!Set low byte
wrt(i)=wrt(i) + ichar(message(2*i:2*i))*256 !Set high byte
i=i+l
end do
if (odd.eq.l) wrt(i)=ichar(message(cnt:cnt))
return
end
check and wait until DSA digitizer is off ************
subroutine stopcheck (wrt,rd,tekbd,cnt)
C
Define variables associated with gpib functions
integer rd(15),wrt( 15),tekbd, cnt
character*30 tekresponse,message
tekresponse=''
do while (index(tekresponse,’STOP,).eq.O)
148
message='DIG?'
call s tr 2 gpib (message, wrt, cnt)
call ibwrt (tekbd, wrt, cnt)
call ibrd (tekbd, rd, 30)
call gpib2str (tekresponse, rd, 14)
end do
return
end
C ***********
initialize tfff. bus and initialize bus variables **********
subroutine dsainit (tekbd)
C
Define variables associated with gpib functions
integer
C
tekbd,v,reos
gpib status, error and count variables
character* 1 resp
C Locate various devices on the GPIB bus
tekbd=ibfind('DSA601')
if (tekbd.lt.0 ) then
write (*,100 )
100 format (//T5'An error occurred opening the DSA 601.7
+
T5'Press CTRL+ALT+DELETE to terminate program.’\)
call inkey (resp)
return
end if
C
Set read statements to terminate when an EOI is encountered
reos=1024
call ibeos (tekbd,reos)
C
Set write statements to terminate with an EOI
v=l
call ibeot (tekbd, v)
return
149
end
C************ Rea(i and convert signal/cal from DSA ***************
subroutine collectdata (k,tekbd,wrt,rd,cnt)
C
Define local variables
integer k
real
areacon
C
Define variables associated with gpib functions
integer
rd( 15 ),wrt( 15),tekbd,cnt
character* 30 tekresponse,message
C
Define variables used for data
double precision xposition(5000),yposition(5000)
real
signaldata (5000)
common/datavars/xposition,yposition,signaldata
message='YTMNS_AREA?'
call str 2 gpib (message, wrt, cnt)
call ibwrt (tekbd, wrt, cnt)
call ibrd (tekbd,rd,30)
call gpib2str (tekresponse, rd, 24)
signaldata(k)=areacon(tekresponse)
return
end
C********** Convert an ASCII integer array to a string **************
subroutine gpib 2 str (message,rd,cnt)
integer
C
i, hbyte, lbyte
Define varibles associated with gpib functions
integer
rd(15),cnt
character*30 message
C
gpib status, error and count variables
odd=mod(cnt,2 )
m essag ed '
i=l
do while (i.le.cnt/2 )
lbyte=iand(rd(i),2 55)
hbyte=rd(i)/256
message( 2 *i-1:2 *i-1 )=char(lbyte)
message(2 *i:2 *i)=char(hbyte)
i=i+l
end do
if (odd.eq.l) message(cnt:cnt)=char(iand(rd(i),255))
return
end
j’**************** Send a string out to Coml ***********************
subroutine strout (message)
character* 3 2 message
character*33 tmessage
integer *2
port / 0 /, sndsta
C
tmessage(l:32)=message
tmessage(33:33)=char(13)
call sndstr (tmessage, port, sndsta)
return
end
q
S t r i l l ^ f r f l lTl C O U ll
subroutine strin (message)
character*32 message
character* 1 bytin, cr
integer *2
ier, il, avail
integer*4
i2, maxwait /1 00000/
cr=char(13)
bytin= ' '
message^ '
ier=l
151
il= l
do while (bytin.ne.cr)
avail=0
i2=l
do while ((avail.ne.l).and.(i2 .1t.maxwait))
call bfstat (avail)
i 2 =i2 + l
end do
call fchchr (bytin, ier)
select case (ier)
case (1)
message(il:il)=bytin
if (ichar(bytin).lt.32) m essage(il:il)=''
il= il+ l
i2=l
case default
write (*,10 ) ier
10 format (' There was an error receiving a byte.'/
+
' The error code is: ’,14)
m essage*''
return
end select
end do
return
end
£******************* initialize the R.S232 port *********************
subroutine rs232init ()
C
Set Coml up for appropriate parameters
n n n
integer *2 baucLrate /4 /, parity / 2 /, stop.bit / 2 /,
+
worcLlength /7 /, comm_port /0 /, rtstat, ier
baud_rate=4 1200
parity* 2
even
comm_port=0 COM1
call stbaud (baucLrate, parity, stop.bit, worcLlength, comm_port,
+
rtstat, ier)
C
Creat buffer to store input
152
call comon
return
end
C********** Move Side Translation Stage Stepper Motors ***********
subroutine sidemover(sdirecl,stepsize)
integer *2 stepsize
character*3 sdirecl
character*4 xstepsize,inttochar
character*32 message
integer i
C
Find leading blanks in converted step size
xstepsize=inttochar(stepsize)
i=l
do while (xstepsize(i:i).eq.'')
i=i+l
end do
C
Step translation stage
message=’C'//sdirecl//xstepsize(i:)//', R'
call strout (message)
return
end
C********** Move Vertical Translation Stage Stepper Motors ********
subroutine vertmover(sdirec2 ,stepsize)
integer *2 stepsize
character* 3 sdirec2
character*4 ystepsize.inttochar
character*32 message
integer j
C
Find leading blanks in converted step size
ystepsize=inttochar(stepsize)
j- 1
do while (ystepsize(j:j).eq.'')
H+l
end do
C
Step translation stage
message='C7/sdirec2//ystepsize(j:)//', R'
call strout (message)
return
end
C***************** initialize Stepper Motor Positions ****************
subroutine initmover(sdireclfsdirec 2 ,xinitIyinit)
integer *2 xinit.yinit
character*3 sdirecl,sdirec2
character*4 xjump,yjump,inttochar
character*32 message
integer ij
C
Find leading blanks in converted step size
xjump=inttochar(xinit)
i=l
do while (xjump(i:i).eq.'')
i=i+l
end do
yjump=inttochar(yinit)
j= l
do while (yjump(j:j).eq.'')
j=j+l
end do
C
Step translation stage
message='C,//sdirecl//xjum p(i:)//' 7/sdirec2//yjump(j:)//', R'
call strout (message)
return
end
C**************** Return Stepper Motors to Zero Position ***********
subroutine zeromoverO
character*9 zmessage
zmessage='CIMO 10 R'
call strout (zmessage)
return
end
C*************** Return Stepper Motor #2 to Zero Position *********
subroutine zeromover2 ()
character*? zmessage
zmessage='CIM0, R’
call strout (zmessage)
return
end
£******************** initialize data arrays *************************
subroutine datainitO
C
Define variables used for data
double precision xposition(5000),yposition(5000)
real
signaldata(5000)
common /datavars/ xposition.yposition.signaldata
integer *2 i
do i=l,5000
xposition(i) = 0.D0
yposition(i) = 0.D0
signaldata(i)= 0 .
end do
return
end
£********************************************************************
C
C
c
c
c
PDLFUN2.FOR
CODE FOR FUNCTIONS
To accompany PDLTEK2.FOR and PDLSUB2.FOR
£********************************************************************
C********** find the first character in a string *****************
integer* 1 function findfirstchar (string)
character *10 string
integer* 1 i
i=l
do while (string(i:i).eq.'')
i=i+l
end do
findfirstchar=i
return
end
C***** CONVERT F10.2 FORMAT TO CHARACTER STRING ***********
CHARACTER* 10 FUNCTION RTOCHAR(Y)
REAL X, Y, XI
INTEGER*2 XTEMP
CHARACTER* 1 C(10)
INTEGER* 1 1, II, FLAG
X=Y !Switch to a working variable not transferred
X1=X-AINT(X) '.Avoid rounding errors-save decimal portion
C
Check for negative value
IF (X .LT. 0.) THEN
RTOCHAR='
.00'
RETURN
END IF
FLAG=0
!Flag to signal first significant figure
C
Convert the figures to the left of the decimal
DO 1=1,7
11=7-1
XTEMP=INT(X/10.**I1) !Pick off leading figure
156
C(I)=CHAR(48+XTEMP) !Convert to a character
IF((XTEMP.EQ.O).AND.(FLAG.EQ.O)) C(I)='' !Use blanks if flag off
IF(XTEMP.NE.O) FLAG=1 !Flag on when 1st figure non-zero
X=X-REAL(XTEMP)*(10.**I1) ISubtract off converted figure
END DO
C
Convert the figures to the right of the decimal
DO 1=1,2
XTEMP=INT(X1*(10.**I)+.01) !Pick off leading figure
C(8+I)=CHAR(48+XTEMP) 'Convert to a character
X1=X1-REAL(XTEMP)/(10.**I) ISubtract off converted figure
END DO
C
Construct entire string
RTOCHAR=C(1)//C(2)//C(3)//C(4)//C(5)//C(6)//C(7)//'.V/C(9)//C(10)
RETURN
END
q************* Convert
4 digit integer to character *****************
character*4 function inttochar(y)
integer *2 x,xtemp,y
character* 1 c(4)
integer* 1 i,il
x=y
do i-1,4
il=4-i
xtemp=x/( 10 **il)
c(i)=char(48+xtemp)
x=x-xtemp*(10 **il)
end do
inttochar=c(l)//c(2)//c(3)//c(4)
return
end
C********* Convert DSA area measure string to a real **************
real function areacon (tekresponse)
character*30
tekresponse
character* 1
csign
integer
mpy, i, imark, il, xmpy, xponent
double precision temparea, power, confactor /-5.0D-11/
157
C
C
C
C
C
C
Initialize variables
areacon=0.
temparea=O.DO
xmpy=l
xponent=0
i=l
do while (tekresponse(i:i).ne.Y) '.Find Y for a reference
i=i+l
end do
i= i+ ll IMovetosign
csign=tekresponse(i:i)
select case (csign)
case (V)
mpy=+l
case
mpy=-l
case default
areacon=-l. IReturn a negative value if a read error occurs
return
end select
Find the decimal point
imark=i+l
do while (tekresponse(imark:imark).ne.7)
imark=imark+l
end do
Convert portion to the left of the decimal point
do il=i+l,im ark-l
power= 1.D1**(imark-il-1)
temparea=temparea+dfloat(ichar(tekresponse(il:il))-48)*power
end do
i=imark+l !Move to the right side of the dec pt
imark=i
Find the E position
do while (tekresponse(imark:imark).ne.,E')
imark=imark+l
end do
Convert the right hand side of the decimal point
do il=i,imark-l
power=l.Dl**(i-il-l)
temparea=temparea+dfloat(ichar(tekresponse(il:il))-48)*power
end do
Round to 5 dec places
temparea=dble(int4((temparea* 1.D5)+. 5))/l.D 5
158
C
C
C
C
i=imark+l !Move to the right side of the E
imark=i
Find the comma position
do while (tekresponse(imark:imark).ne.7)
imark=imark+l
end do
csign=tekresponse(i:i)
select case (csign)
case(V)
i=i+l
!xmpy ok, but increment marker
case('-')
i=i+l
!change xmpy and increment marker
xmpy=-l
end select
Determine the exponent value
do il=i,imark-l
xponent=xponent+(ichar(tekresponse(il:il))*48)*(10**(imark-il-l))
end do
xponent=xmpy*xponent !Put in sign
Combine results; confactor puts value in familiar integrator units
ar eacon=mpy *float((tempar ea* 1.D1**xponent)/confactor)
Check TEK acquire error
if (tekresponse(imark+l:imark+2).ne.'EQ') areacon=-l
return
end
C********* Function to get date and convert to a string *************
character*8 function condate ()
C
C
C
C
integer*2 imonth, iday, iyear, il, i2
character*4 cmonth, cday, cyear, inttochar
Get current date
call getdat(iyear, imonth, iday)
Convert integer format to character*4 variables
cmonth=inttochar(imonth)
cday=inttochar(iday)
cyear=inttochar(iyear)
Remove leading zeroes in the day and month
il=3
if (cmonth(3:3).eq.'0') il=4
12=3
if (cday(3:3).eq.'0') i2=4
Construct string and return
159
condate=cmonth(il :)//'-'//cday(i2 :)//'-'//cyear( 3:)
return
end
C************* convert millimeters to index units ******************
integer* 2 function mm2index (mm)
re a l m m
mm2index=int2(. 5+mm/(3.175E-3))
return
end
convert index units to millimeters *****************
real function index2mm (indx)
integer*2 indx
index2mm=float(indx)* 3.17 5E-3
return
end
160
£*************************************************************************
C PROGRAM TO CONVERT ACQUIRED DSA TEK WAVEFORMS
CFROMIBIC.COM
C Bryan L. Preppernau, Hydrogen Plasma Group
10-19-92
C Tim Cerny contributed Binary String Conversion Algorithms
q
************************** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
$storage: 2
INTEGER
TEKBD,V,REOS
REAL XINCR.YMULT.YZERO
REAL XINCR1.YMULT1.YZER01
CHARACTER*20 FILE
TEKBD=IBFIND('DSA601')
REOS=1024
CALL IBEOS(TEKBD,REOS)
V=1
CALL 1BE0T(TEKBD,V)
CALL CLS
CALL WAVEFORMDATA(TEKBD,XINCRtYMULT,YZERO)
XINCR1=XINCR
YMULT1=YMULT
YZERO1=YZERO
WRITE (*,50)
50 FORMAT (T5,'Please input a filename (include path): ’\)
READ (*,'(A20)') FILE
CALL DATASAVE(XINCR1.YMULT1,YZERO1.FILE)
STOP
END
q ****************
OUTPUT WAVEFORM TO DISK ********************
SUBROUTINE DATASAVE(XINCR1,YMULT1,YZERO1,FILE)
INTEGER*2 NEWCURVE(1029),CURVE(1029),I1,I2
REAL XINCR1.YMULT1.YZER01,CHI,TIME
CHARACTER*20 FILE
OPEN (UNIT=3, FILE='CDAT',FORM='BINARY',STATUS='OLD')
OPEN (UNrr=2, HLE=HLE, STATUS='UNKNOWN')
TIME=0.
DO 1=1,1029
READ(3) CURVE(I)
END DO
DO 1=5,1029
11=IAND(CURVE(I), 16#FF00)
I2=IAND(CURVE(I+1), 16#00FF)
NEWCURVE(I-4)=Il/2 56+12*2 56
END DO
DO 1=1,1024
CHl=YZERO 1+YMULT1*NEWCURVE(I)
WRITE (2/(2E20.5)') TIME,CHI
TIME=TIME+XINCR1
END DO
CLOSE (2)
RETURN
END
*************** COLLECT KEY WAVEFORM QUANTITIES ************
SUBROUTINE WAVEFORMDATA(TEKBD,XINCR,YMULT,YZERO)
INTEGER WRT(15),RD(300),TEKBD,CNT
REAL XINCR,YMULT,YZERO
CHARACTER*300 PREAMBLE
CHARACTER*30 MESSAGE
MESSAGE='OUT TRA1'
CALL STR2GPIB(MESSAGE,WRT,CNT)
CALL IBWRT(TEKBD,WRT,CNT)
MESSAGE='WFM?'
CALL STR2GPffi(MESSAGE,WRT,CNT)
CALL IBWRT(TEKBD,WRT,CNT)
CALL IBRD(TEKBD,RD,600)
CALL GPIB2STR(PREAMBLE,RD,600)
Convert ascii to real
162
CALL MAKEREAL(PREAMBLE,XINCRfYMULT,YZERO)
RETURN
END
C************* MAKE ASCn TO REAL CONVERSION*******************
SUBROUTINE MAKEREAL (PREAMBLE,XINCR,YMULT,YZERO)
CHARACTER*300 PREAMBLE
REAL
XINCR,YMULT,YZERO
OPEN (UNrr=l,STATUS='SCRATCH')
C
Find XINCR value
I=INDEX(PREAMBLE,'XINCR')
11=0
DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.',')
11= 11+1
END DO
WRITE(1,'(A15)') PREAMBLE(I+6:I+Il+5)
C
Find YMULT value
I=INDEX(PREAMBLE,'YMULT')
11=0
DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.V)
11= 11+1
END DO
WRITE(1,'(A15)') PREAMBLE(I+6:I+Il+5)
C
Find YZERO value
I=INDEX(PREAMBLE,’YZERO')
11=0
DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.',')
11= 11+1
END DO
WRITE(1,’(A15)’) PREAMBLE(I+6:I+Il+5)
REWIND 1
READ(1,10) XtNCR,YMULT,YZERO
10 FORMAT(E15.0)
CLOSE (UNIT=1)
RETURN
END
C ************
convert a string to an ASCII integer array *************
subroutine str2gpib (message, wrt, cnt)
C Define variables associated with gpib functions
integer
wrt(15),cnt,odd,i
character* 30 message
cnt=len_trim(message)
odd=mod(cnt,2)
i=l
do while (i.le.cnt/2)
wrt(i)=ichar(message(2*i-l:2*i-l))
!Set low byte
wrt(i)=wrt(i) + ichar(message(2 *i: 2*i))*2 56 !Set high byte
i=i+l
end do
if (odd.eq.l) wrt(i)=ichar(message(cnt:cnt))
return
end
C *************
convert an ASCII integer array to a string ************
subroutine gpib2str (message,rd,cnt)
integer
C
i, hbyte, lbyte
Define varibles associated with gpib functions
integer
rd(15),cnt
character*30 message
C gpib status, error and count variables
odd=mod(cnt,2)
message^ '
i=l
do while (i.le.cnt/2)
lbyte=iand(rd(i),25 5)
hbyte=rd(i)/256
mes sage(2 *i-1:2 *i-1)=char(lbyte)
message(2 *i: 2*i)=char(hbyte)
i=i+l
end do
if (odd.eq.l) message(cnt:cnt)=char(iand(rd(i),255))
return
end
164
PROGRAM N3DECAY
DOUBLE PRECISION XP(5000),YP(3,5000),YSTART(3),DXSAV
DOUBLE PRECISION Xl,X2,Hl,HMINIEPSIP,PV,VELtRADRATE(5000)
DOUBLE PRECISION INTRO,INTRP,aYPOP(3)
COMMON /PATH/ KMAX.KOUNT.DXSAV.XP.YP
CHARACTER*20 FILE
WRITE (*,20)
20 FORMAT (T5,'Please input a filename (include path): ’\)
READ (*,'(A20)') FILE
OPEN (UNIT=2, FILE=FILE, STATUS='UNKNOWN')
DO K=l,6
VEL=9.027D+5
X1=0
X2=lD-7
NVAR=3
YSTART(1)=0.118
YSTART(2)=0.0
YSTART(3)=0.882
YPOP(l)=YSTART(l)
YPOP(2)=YSTART(2)
YPOP(3)=YSTART(3)
H1=5D-10
HMIN=0
DXSAV=(X2-X1)/1000
KMAX=5000
EPS=lD-6
P=(K-1)*1.5
PV=P*3.29D+16*VEL
CALL 0DEINT(YSTART,NVAR,X1,X2,EPS,H1IHMIN,N0K,NBAD,PV)
DO 1=1,4999
XP(I)=XP(I)/lD-09
RADRATE(I)=((YP(l,I)/1.59D-7)+(YP(2,I)*0.1183/5.4D-9)
165
+ +(YP(3,1)/l. 56D-8))/((YPOP( 1) / l .59D- 7)
+ +(YPOP(2)*0.1183/5.4D-9)+(YPOP(3)/1.56D-8))
END DO
DO 1=1 4999
IF(XP(I).LE.100)THEN
C
WRITE(2I,(2XIF12.6,2XtF12.8I2XtF12.8>2X,F12.8,2X,F12.8)')
C + XP(I),YP( 1,D,YP(2,1),YP(3,I)IRADRATE(I)
WR1TE(2,,(2X,F12.6,2X,F12.8),)XP(I),RADRATE(I)
END IF
END DO
INTRP=0
DO 1=1 4999
IF (XP(I+1).LE.100) THEN
INTRP=INTRP+(XP(I+1)-XP(I))*(RADRATE(I+1)
+
+0.5 *(RADRATE(D-RADRATE(I+1)))
END IF
END DO
IF (P.EQ.0) THEN
INTR0=INTRP
END IF
Q=(INTRP/INTR0)
WRITE(*I,(2X,F10.5,2X,F10.6)') P,Q
WRrrE(2l,(2X,F10.5t2X,F10.6)') P,Q
END DO
CLOSE(2)
END
SUBROUTINE DERIVS(Y,DYDX,PV)
DOUBLE PRECISION Y(3),DYDX(3),PV,PA,PAV
DOUBLE PRECISION TS.TP.TD
DOUBLE PRECISION Q,QA,MIX,MXA
TS=1.59D-7
166
TP=5.4D-9
TD=1.56D-8
PA=0.1
PAV=PA*2.97D+22
0=0.035D-15
QA=8.85D-15
MK=0
MXA=0
DYDX(1)=-Y(1)*(1/TS+PV*(8*MIX+Q)+PAV*QA+PAV*8*MXA)
+ +PV*MIX*(Y(2)+Y(3))+PAV*MXA*(Y(2)+Y(3))
DYDX(2)=-Y(2)*(1/TP+PV*(6*MIX+Q)+PAV*QA+PAV*6*MXA)
+ +3*PV*MIX*(Y(1)+Y(3))+3*PAV*MXA*(Y(1)+Y(3))
DYDX(3)=-Y(3)*(1AD+PV*(4*MIX+Q)+PAV*QA+PAV*4*MXA)
+ +5*PV*MK*(Y(1)+Y(2))+5*PAV*MXA*(Y(1)+Y(2))
RETURN
END
SUBROUTINE
ODEINT(YSTART,NVARlXllX2IEPS,Hl>HMIN>NOKINBAD,PV)
PARAMETER (MAXSTP=10000,NMAX= 10,TWO=2.0,ZERO=0.0,TINY= 1.E30)
DOUBLE PRECISION
YSTART(NVAR),YSCAL(NMAX),Y(NMAX),DYDX(NMAX)
DOUBLE PRECISION X,Xl,X2,EPS,HtH lIHMIN,XSAV,HDID,HNEXTlPV
DOUBLE PRECISION DXSAV,XP(5000),YP(3,5000)
COMMON /PATH/ KMAX,KOUNT,DXSAVfXPfYP
DO J=l,5000
XP(J)=1.01D-07
YP(1J)=0
YP(2,J)=0
YP(3,J)=0
END DO
X=X1
H=SIGN(H1,X2-X1)
NOK=0
NBAD=0
KOUNT=0
167
11
12
13
14
15
16
DO 11 I=1,NVAR
Y(I)=YSTART(I)
CONTINUE
XSAV=X-DXSAV*TWO
DO 16 NSTP=1,MAXSTP
CALL DERIVS(YIDYDX,PV)
DO 12 I=1,NVAR
YSCAL(I)=ABS(Y(I))+ABS(H*DYDX(I))+TINY
CONTINUE
IF(KMAX.GT.O)THEN
IF(ABS(X-XSAV).GT.ABS(DXSAV)) THEN
EF(KOUNT.LT.KMAX-l)THEN
KOUNT=KOUNT+1
XP(KOUNT)=X
DO 13 I=1,NVAR
YP(I,KOUNT)=Y(I)
CONTINUE
XSAV=X
ENDIF
ENDIF
ENDIF
IF((X+H-X2)*(X+H-X1 ).GT.ZERO) H=X2-X
CALLRKQC(YiDYDXiNVAR,X,H,EPS,YSCALiHDID,HNEXT,PV)
IF(HDID.ECl.H)THEN
NOK=NOK+l
ELSE
NBAD=NBAD+1
ENDIF
IF((X-X2)*(X2-X1).GE.ZER0)THEN
DO 14 I=1,NVAR
YSTART(I)=Y(I)
CONTINUE
IF(KMAX.NE.0)THEN
KOUNT=KOUNT+1
XP(KOUNT)=X
DO 15 I=1,NVAR
YP(I,KOUNT)=Y(I)
CONTINUE
ENDIF
RETURN
ENDIF
IF(ABS(HNEXT).LT.HMIN) PAUSE ’Stepsize smaller than m inim um .'
H=HNEXT
CONTINUE
168
C
PAUSE ’Too many steps.’
RETURN
END
SUBROUTINE RKQC(Y,DYDXIN,X,HTRYIEPS,YSCALIHDIDIHNEXT,PV)
PARAMETER (NMAX=10,FCOR=.0666666667,ONE=1.(
+
SAFETY=0.9,ERRCON=6.E-4)
DOUBLE PRECISION Y(N),DYDX(N),YSCAL(N)
DOUBLE PRECISION YTEMP(NMAX),YSAV(NMAX),DYSAV(NMAX)
DOUBLE PRECISION X,XSAV,H»HHIHTRY,EPS,HDIDtHNEXT,ERRMAX,PV
PGROW=-0.20
PSHRNK=-0.25
XSAV=X
DO 11 I=1,N
YSAV(I)=Y(I)
DYSAV(I)=DYDX(I)
11 CONTINUE
H=HTRY
1 HH=0.5*H
CALL RK4(YSAV,DYSAVIN,XSAVIHH,YTEMP,PV)
X—xSAV+HH
CALL DERIVS(YTEMP,DYDX,PV)
CAUL RK4(YTEMP,DYDX,N,X,HH,Y,PV)
X=XSAV+H
IF(X.EQ.XSAV)PAUSE 'Stepsize not significant in RKQC.'
CALL RK4(YSAV,DYSAVIN,XSAV,H,YTEMP,PV)
ERRMAX=0.
DO 12 1=1,N
YTEMP(I)=Y(I)-YTEMP(I)
ERRMAX=MAX(ERRMAX,ABS(YTEMP(I)/YSCAL(I)))
12 CONTINUE
ERRMAX=ERRMAX/EPS
IF(ERRMAX.GT.ONE) THEN
H=SAFETY*H*(ERRMAX**PSHRNK)
GOTO 1
ELSE
HDID=H
IF(ERRMAX.GT.ERRCON)THEN
HNEXT=SAFETY*H*(ERRMAX**PGROW)
ELSE
HNEXT=4.*H
ENDIF
ENDIF
169
DO 13 1=1,N
Y(I)=Y(I)+YTEMP(I)*FCOR
13 CONTINUE
RETURN
END
SUBROUTINE RK4(YIDYDX,NIX,H,YOUT,PV)
PARAMETER (NMAX=10)
DOUBLE PRECISION Y(N),DYDX(N),YOUT(N),
+ YT(NMAX),DYT(NMAX),DYM(NMAX)iX,H,PV,HHiH6(XH
HH=H*0.5
H6=H/6.
XH=X+HH
DO 111=1,N
YT(I)=Y(I)+HH*DYDX(I)
11 CONTINUE
CALL DERIVS(YT,DYT,PV)
DO 12 1=1,N
YT(I)=Y(I)+HH*DYT(I)
12 CONTINUE
CALL DERIVS(YT,DYM,PV)
DO 13 1=1,N
YT(I)=Y(I)+H*DYM(I)
DYM(I)=DYT(I)+DYM(I)
13 CONTINUE
CALL DERIVS(YTtDYT,PV)
DO 141=1,N
YOUT(I)=Y(I)+H6*(DYDX(I)+DYT(I)+2.*DYM(I))
14 CONTINUE
RETURN
END
311
400
PROGRAM MNV
IMPUCIT REAL*8(A-H,0-Z)
CHARACTER*20 FUN
DIMENSION X(3 50,1),Y(3 50),RRR(3 50),IB(20),NAR(8),ARR(8)
COMMON/BLK1/B(20),P(20),RE,N,M,K
FORMAT(4F10.2,F12.6)
WR^E(V(A\),), SOURCE FILE: '
READ(*,,(A20),)FUN
OPEN(llFILE=FLIN)STATUS='OLD'lACCESS='SEQUENTlAL')
READ(1,*)N,MIK
WRnE(Y(A\)')' # OF LINES
WRrrE(*,*)N
WRnE(V(A\)')' # OF ASSIGNMENTS = '
WRTTE(V)M
WRrrE(V(A\)')'# OF PARAMETERS
410
415
420
430
450
451
452
WRITE(V)K
READ(1,*)(B(I),I=1,K)
DO 410 J=1,N
READ( 1,*)(X0,I),I= 1,M),Y(J)
CONTINUE
READ( 1,*)(ARR(I),I=1,8)
READ(1,*)(NAR(I),I=1,8)
IF (NAR(4).LT.l) GOTO 415
READ( 1,*)(IB(I),I=1,NAR(4))
CLOSE( 1, STATUS='KEEP')
DO 4201=1,K
WRITE(*,430)1,B(I)
F0RMAT(1X,,B(,,I2,,)=',D12.6)
WRITE(*,451)NAR(4)
FORMAT(lX,' No. parameters held constant = ',15)
IF (NAR(4).NE.O) WR1TE{*,452)(IB(I),I=1,NAR(4))
FORMAT(IX,' They are ’,816)
CALL NLLSQ(Y,X,B,RRR,NAR,ARR,IB,FMT)
STOP
END
Use Subroutine Model in Conjuction with NLLSQV.FOR
171
SUBROUTINE MODEL (F,Y,XIRRR,I,JP)
IMPLICIT REAL*8(A-H,0-Z)
COMMON/Bm/B(20),P(20),RE,N,M,K
DIMENSION Y(3 50),RRR(3 50),X(3 50,1)
DOUBLE PRECISION XP(5000),YP(3,5000),YSTART(3),DXSAV
DOUBLE PRECISION X1,X2,H1,HMIN,EPSIPPIPVIVEL,RADRATE(5000)
DOUBLE PRECISION INTRO,INTRP,SQ,PQ,DQISP,SD1DP,YPOP(3)
COMMON /PATH/ KMAX,KOUNT,DXSAVIXP,YP
VEL=9.03D+5
SQ=B(1)
PQ=SQ
DQ=SQ
SP=B(2)
SD=SP
DP=SP
X1=0
X2=lD-7
NVAR=3
YSTART(1)=0.118
YSTART(2)=0.0
YSTART(3)=0.882
YPOP(l)=YSTART( 1)
YPOP(2)-YSTART(2)
YPOP(3)=YSTART(3)
H1=5D-10
HMIN=0
DXSAV=(X2-XI )/l 000
KMAX=5000
EPS=lD-7
PP=X(I,1)
WRTIE(*t*) PP
PV=PP*3.29D+16*VEL
CALL ODEINT(YSTART,NVAR,XllX2,EPS,Hl.HMIN.NOK.NBAD,
+
p v .sa p a D a sp .sD , d p )
DO 11=1,2000
XP(Il)=XP(Il)/lD-09
RADRATE(11)=((YP( 1,11) / l .59D-7)+(YP(2,11)*0.118 3/5.4D-9)
+ +(YP(3,Il)/1.56D-8))/((YPOP(l)/1.59D-7)
+ +(YPOP(2)*O.H83/5.4D-9)+(YPOP(3)/X.56D-8))
END DO
INTRP=0
n n T1- 1 4Q Q Q
IF (XP(I1+1).LE.100) THEN
INTRP=INTRP+(XP(I1+1 )-XP(Il ))*(RADRATE(11+1)
+
+0.5*(RADRATE(U)-RADRATE(I1+1)))
ENDIF
END DO
IF (PP.EQ.0) THEN
INTRO=INTRP
ENDIF
F=INTRP/INTRO
RE=Y(I)-F
JP=3
RETURN
END
SUBROUTINE DERIVS(Y,DYDXtPVlSQ,PQlDQ,SP,SDfDP)
DOUBLE PRECISION Y(3),DYDX(3),PVIPA,PAV
DOUBLE PRECISION TS.TP.TD
DOUBLE PRECISION SaPCiDaSP.SD.DP.QA
TS=1.59D-7
TP=5.4D-9
TD=1.56D-8
PA=0.13
PAV=PA* 2.9 7D+2 2
QA=8.87D-15
DYDX( 1)=Y( 1)*(-1/TS-PV*( 3*SP+5*SD+SQ)PAV*QA)+PV*(SP*Y(2)+SD*Y(3))
DYDX(2)=Y( 2)*(- 1/TP-PV*(SP+ 5*DP+PQ)PAV*QA)+3*PV*(SP*Y(1)+DP*Y(3))
173
DYDX(3)=Y(3)*(-1/TD-PV*(SD+3*DP+DQ)PAV*QA)+5*PV*(SD*Y(1)+DP*Y(2))
RETURN
END
From This Point Onward Subroutine Model is the same as N3DECAY.FOR
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