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Development of real-time spectroscopic ellipsometry and its application to the growth of diamond thin films by microwave plasma-enhanced chemical vapor deposition

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The Pennsylvania State University
The Graduate School
Department of Electrical Engineering
DEVELOPMENT OF REAL-TIME SPECTROSCOPIC
ELLIPSOMETRY AND ITS APPLICATION TO THE GROWTH
OF DIAMOND THIN FILMS BY MICROWAVE PLASMAENHANCED CHEMICAL VAPOR DEPOSITION
A Thesis in
Electrical Engineering
by
Byungyou Hong
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
May 1996
UMI Number:
9628106
UMI Microform 9628106
Copyright 1996, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
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Ann Arbor, MI 48103
We approve the thesis of Byungyou Hong.
Date of Signature
Christoper
Ihristoper R. Wronski
Leonhard Professor of Microelectronic
Devices and Materials
Chair of Committee
Thesis Co-Adviser
(£UUYV- M
C*4C*T~*
/
M>r>L i> Ml
Robert W. Collins
Professor of Physics and Materials Research
Thesis Co-Adviser
Ap*& i, n%
^—''Russell F. Messier
Professor of Engineering Science and Mechanics and
Materials Research
AfrnV \, 1396
S. Ashok
Professor of Engineering Science
/*£-~yS&&
4f~'/ '*
W
Jei^y Ruzyll
Professor of Electrical Engineering
MayeT
O
Theresa S. Mayer
Assistant Professor of Electrical Engineering
, C/dwtvv^
Larry C. Burton
Professor of Electrical and Computer Engineering
Head of the Department of Electrical Engineering
*
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in
ABSTRACT
Real time spectroscopic ellipsometry (RTSE) based on the rotating polarizer
configuration and a multichannel detection system has been developed and utilized to
investigate diamond thin film growth by microwave plasma-enhanced chemical vapor
deposition (MPECVD) system. The new detection system was investigated in detail. A new
calibration method based on the dc irradiance level was reviewed and the first order
corrections for residual source polarization were introduced.
A detailed study of microwave plasma-enhanced CVD diamond film growth was
undertaken. First, RTSE was used to calibrate c-Si substrate temperature over the range
from 200 to 900 °C under the conditions of diamond film growth. The temperature
obtained by RTSE is characteristic of the surface because the penetration depth of the light
is 220 A. As an application of substrate surface temperature calibration, the diamond
growth rate was determined as a function of the true surface temperature (500 °C<T<800
°C). The maximum possible activation energy for diamond growth over the temperature
range from 500 to 700 °C was ~9 kcal/mol. For the studies of diamond thin film growth, cSi was seeded by abrading the surface with the diamond powder and the various gas
mixtures were used including (1) H2+CH4, (2) H2+CH4+O2, and (3) H2+CO.
It is shown that RTSE is very powerful to study the evolution of the microstructure
and sp2 C content with thickness in nanocrystalline diamond. Using the various conditions
on C-H-0 phase diagram, the effect of hydrogen and oxygen on the structural evolution of
diamond thin film is shown. The substrate temperature effect on diamond film growth is
also discussed. In this thesis study, there is an optimum CO/H2 flow ratio above and below
which the diamond interface quality degrades.
RTSE was applied to investigate the evolution of the properties of a thin film Ni
sample during exposure to the H2 and H2+CH4 plasmas under conditions used to obtain
IV
diamond in the studies on Si substrates. The optical properties of Ni were modified by
diffusion of H and/or C impurities.
V
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
ACKNOWLEDGMENTS
page
vii
xiv
xv
CHAPTER 1
INTRODUCTION
1
CHAPTER 2
REAL-TIME SPECTROSCOPIC ELLIPSOMETRY
4
2.1 Apparatus
2.2 Basic Principle and Theory of Rotating Polarizer Multichannel EUipsometry:
Data Reduction and Calibration
Principles of Data Reduction
Principles of Calibration
2.3 Alignment, Detector Error Correction, Data Acquisition, and Analysis
System Alignment
Detection System Errors and Corrections
Nonlinearity
Image persistence
Data Acquisition
Data Simulation and Analysis
Bruggeman Effective Medium Approximation (EMA)
Least-Squares Regression Analysis
4
CHAPTER 3
3.1
3.2
3.3
3.4
Introduction
Experimental Apparatus and Procedure
Experimantal Methods and Data Interpretation
Application to Diamond Film Growth
CHAPTER 4
4.1
4.2
4.3
4.4
CHARACTERIZATION OF SUBSTRATE TEMPERATURE IN
DIAMOND GROWTH PLASMAS
REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES OF
DIAMOND FILM GROWTH BY MICROWAVE PLASMAENHANCED CHEMICAL VAPOR DEPOSITION (MPECVD)
7
7
18
25
25
29
29
31
33
37
41
45
50
50
52
56
67
73
Introduction
73
Experimental Details
74
Results and Discussion
79
Diamond Films Deposited under Various Conditions on C-H-O Phase
Diagrams
97
Effect of Hydrogen and Oxygen on the Structural Evolution of Diamond
Thin Film
100
VI
Substrate Temperature Effect on Diamond Film Growth
Diamond Growth using Carbon Monoxide (CO) as a Carbon Source
4.5 Investigation of Ni substrates under Diamond Thin Film Growth
Conditions
CHAPTER 5
CONCLUSION AND FUTURE WORKS
REFERENCES
115
122
126
138
143
vn
LIST OF FIGURES
Figure
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
page
Schematic of the real time spectroscopic ellipsometer in the rotating polarizer
configuration used for studies of diamond thin film growth.
5
Schematic representation of the rotaing polarizer ellipsometer using the
Jones formalism.
10
A plot showing the determination of Amjn and Pi for pixel group number 64
using the dc component I0 and phase function 0 measured as a function of
analyzer angle from -6° to 6°.
23
Schematic of RTSE and MPECVD systems: top view (left) and side view
(right).
27
l-(oc2+P2) vs. photon energy for different nonlinearity correction factor £.
The best one was assumed to yield the minimum ll-(a2+(32)l.
30
Normalized photon counts as a function of pixel group number derived
from thesesuccessive exposures for the situation in which a shutter is closed
during the second exposure. The counts levels for the second and thied
readouts are shown after normalization by the count level from the
corresponding pixel groups of the first readout. The constant values vs.
pixel group occur when the shutter is fully closed or fully open throughout
the associated exposure time. The residual counts near zero at the end of the
third readout originate from image persistence.
32
Detection system image persistence correction, Crp, arising from the
observed photon count level along the abscissa.
34
Repetitive measurements of the ellipsometric angles at 2.5 eV for a stable,
opaque Cr film, selected from the full spectroscopic data sets. For (a), the
multichannel ellipsometer was used in the slow (2.56 s)/(10 s)
acquisition/repetition mode and for (b), in the fast (64 ms)/(5 s)
acquisition/repetition mode. S.D. denotes the standard deviation for the
measurements.
36
General n-medium structure used in the analysis of ellipsometric data on
multilayered samples. The index j ranges from 0 to n+1 for the media
(including the ambient medium and substrate), and from 1 to n for the
layers. The complex dielectricv function and thickness for the jth layer are
designated as e(i) (0<j<n+l) and dj (l<j<n), respectively.
38
Real (top) and imaginary (bottom) parts of the effective complex dielectric
function of a composite material consisting of the randomly-mixed diamond
and glassy carbon.
43
vm
2.11
(a) The assumed physical structure and (b) the corresponding optical model
for a sample consisting of a surface roughness layer and bulk layer. In this
application the pseudo-dielectric function is used for the substrate, i.e.,
£sub=<£Sub>> an(* m e SUfface roughness is simulated by a mixture of
diamond/void with 0.50/0.50 volume fraction, dj (j=s, f) and £j (j=a, s, f,
sub) denote the thicknesses and the dielectric functions of each layer,
respectively.
47
Deposition system and multichannel spectroscopic ellipsometer employed to
monitor microwave plasma-enhanced CVD of nanocrystalline diamond thin
films in real time.
53
3.2
ASTeX microwave plasma-enhanced chemical vapor deposition system.
54
3.3
Real (<ei>) and imaginary (<£2>) parts of the room temperature pseudodielectric functions measured by ex situ spectroscopic ellipsometry for three
separate c-Si substrates, which were (1) unseeded, (2) seeded, and (3)
seeded and annealed at the diamond deposition temperature of 785 °C.
57
Real (ei) and imaginary (£2) parts of the dielectric functions of c-Si
measured at different temperature by real time spectroscopic ellipsometry.
59
Critical point analysis used to determine the amplitude, transition energy,
phase factor, and broadening parameter from the Ei transition in single
crystal Si substrate.
62
The difference between the true temperature obatined by ellipsometry,
Teliips. and that obtained by other methods, Tjndic> including a thermocouple
embedded within the substrate holder (lines and open points) and a
pyrometer (filled points).
64
The broadening parameter T, associated with Ei transitions in Si as a
function of the true surface temperature of the substrate as determined from
analyses similar to that of Fig. 3.5. A result (dashed line) from the literature
is included for comparison with that of the present work (solid line).
66
The microstructural evolution, deduced by real time spectroscopic
ellipsometry and plotted vs. time, for a sequence of five depositions
performed on the same Si substrate at different temperatures. The
temperature values indicated here are characteristic of the film surface and
have been determined by the calibration of Fig. 3.6. dj are the bulk (j=b)
and surface roughness (j=s) layer thicknesses. In addition, fsp2,b» fsp2,s>
fV)b, and fV)S are the volume fractions of sp2 C (sp2) and void (v) in the
bulk (b) and surface roughness (s) layers.
68
Increase in diamond mass thickness, deduced by real-time spectroscopic
ellipsometry and plotted vs time, for a sequence of five depositions
performed on the same Si substrate at differnet temperatures as determined
by the calibration of Fig. 3.6.
70
3.1
3.4
3.5
3.6
3.7
3.8
3.9
IX
3.10
Mass deposition rate of diamond as a function of true temperature obtained
from the sequence of five nanocrystalline diamond film depositions shown
in Fig. 3.8.
71
Atomic force microscopy (AFM) image of a diamond-seeded Si substrate.
The bright spot on the upper boundary of the image appear to be a diamond
particle remaining from the seeding procedure.
75
4.2(a) Ex situ SE data (<ei>, <E2>) for the diamond seeded substrate at room
temperature along with the best fit calculated result employing the one-layer
optical model shown in the inset. This model stimulates a structure that is
completely disordered throughout the penetration depth of the light, with a
roughness layer on the surface. LRA shows that the layer thickness d is 152
A and the void volume fraction fv is 0.66.
76
4.2(b) Ex situ SE data (<Ei>, <£2>) for a diamond-seeded substrate measured at
room temperature after annealing to the deposition temperature of 785 °C.
Also shown is the best fit to the data using the two-layer optical model given
in the inset. This model stimulates a recrystallized bulk region with a
roughness layer on the surface. The amorphous component in the surface
layer accounts for a reduced Si grain size near the surface.
77
4.1
4.3
4.4
4.5
4.6
4.7
4.8
Real part (ei) of the dielectric function of diamond at different temperatures.
The imaginary part £2 is zero over the photon energy range from 1.5 eV to
5.0 eV.
80
Real (ei) and imaginary (£2) parts of the dielectric functions of optically
polished glassy carbon measured with RTSE at different temperatures along
with a data at room temperature from the literature (Williams and Arakawa,
1972).
81
Typical RTSE data collected during the diamond film growth, shown in the
form of the psudo-dielectric function.
82
Evolution of microstructure during MPECVD diamond film growth,
deduced from an analysis of RTSE data. This film was grown to a bulk
thickness of 2140A. The substrate surface temperature, plasma power,
pressure, and CH4/(CH4+H2) gas flow ratio were 785 °C, 500 W, 7 Torr,
and 1%, respectively.
84
(a) One-layer and (b) two-layer optical models used to simulate diamond
film growth in the nucleation and coalescence/bulk growth regimes,
respectively. The compositional parameters
(fsp2, fv) and (fSp2,b» fv,b) are
the independent volume fractions of sp2 C and void in the nucleating layer
of the one-layer model and the bulk layer of the two-layer model,
respectively.
85
Unbiased estimator of the mean square deviation a obtained in a leastsquares regression analysis of RTSE data collected during the deposition of
Fig. 4.6. Here a one-layer model is assumed, and the abrupt increase in a
X
indicates nuclei are beginning to make contact to form a bulk layer. Thus,
for t>15 min a two-layer model must be used (see Fig. 4.6).
87
The physical thickness for 8<t<15 min and the diamond mass thickness for
0<t<15 min as a function of time during diamond deposition. This film is
the same as that enlarged in Fig. 4.6.
89
The void volume fraction (fv) vs. thickness in the nucleation regime for a
diamond film prepared with a substrate temperature of 785 °C and a
[CH4]/{[CH4]+[H2]} flow ratio of 0.01. These results were obtained using
a one-layer model of the nucleating film, consisting of diamond, sp2 C, and
void. The solid line is the best fit result based on a model of hemispheroidal
nuclei as shown in the inset.
90
AFM image of a 350 A thick microwave plasma CVD diamond film
deposited with a 1% [CH4]/{[CH4]+[H2]} gas flow ratio, a surface
temperature of 785 °C, a plasma power of 500 W, and a total pressure of 7
Torr.
92
Atomic force microscopy (AFM) image of the 2150 A thick microwave
plasma CVD diamond film of Fig. 4.6 deposited with a 1%
[CH4]/{ [CH4]+[H2]} gas flow ratio, a surface temperature of 785 °C, a
plasma power of 500W, and a total pressure of 7 Torr.
95
First-order Raman spectrum of a microwave plasma CVD diamond film
deposited with a 1% [CH4]/{[CH4]+[H2]} gas flow ratio, a surface
temperature of 785 °C, a plasma power of 500W, and a total pressure of 7
Torr. The sharp feature at 1333 cm-1 is indicative of crystalline diamond,
while the feature between 1450 and 1550 cm-1 is attributed to disordered
sp2-bonded carbon. The peak centered at 1355 cm-1 is attributed to
microcrystalline graphite.
96
High-resolution cross-sectional transmission electron microscopy (HRXTEM) image which shows the interface region between the c-Si substrate
and diamond film. The deposition condition parameters were as follows:
1% [CH4]/{[CH4]+[H2]} gas flow ratio, 500W plasma power, 785 °C
surface temperature, and 7 Torr total pressure.
98
4.15(a) C-H-O phase diagram for carbon film growth which is divided into the three
distinct regions of non-diamond growth, diamond growth, and no growth.
99
4.9
4.10
4.11
4.12
4.13
4.14
4.15(b) Enlarged hydrogen-rich sector of the C-H-0 pase diagram.
4.16
Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond
films prepared with different atom-volume flow ratios XH/Z =
[H]/{[H]+[C]}: (a) 0.972, (b) 0.986, and (c) 0.995 which correspond to
6%, 3%, and 1% CH4 in (H2+CH4), respectively. The growth rates are
30.0, 43.2, and 30.7 A/min for 6%, 3%, and 1% CH4 in (H2+CH4),
respectively.
101
102
XI
4.17
4.18
4.19
Volume fraction of sp2-bonded C plotted as a function of bulk thickness for
nanocrystalline diamond films prepared with different atom-volume flow
ratios XH/z = [H]/{[H]+[C]}: (a) 0.972, (b) 0.986, and (c) 0.995 which
correspond to 6%, 3%, and 1% CH4 in (H2+CH4), respectively.
103
Raman spectra measured for the samples deposited under different C atom
fractions, 1%, 3%, and 6% CH4 in (CH4+H2). Other conditions are the
same for all samples including a surface temperature of 785 °C; a plasma
power of 500W; and a total pressure of 7 Torr.
105
Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond
films prepared with different atom-volume flow ratios (Xc/z> Xo/Z) =
([C]/{[C]+[0]}, [0]/{[0]+[H]}): (a) (1.00, 0.00), (b) (0.50, 0.03), (c)
(0.33, 0.06), and (d) (0.20, 0.10).
107
4.20
Volume fraction of sp2-bonded C (left scale) and void (right scale) as a
function of bulk layer thickness, showing the effect of controlled additions
of O2 in (H2+CH4). The sp2 C fraction in the film is suppressed, so that the
film quality improves with increasing O atom fraction. For these
depositions, X H /z = [H]/{[H]+[C]} was fixed at 0.97 [6% CH4 in
(H2+CH4)].
108
4.21
Raman spectra measured for the samples deposited under (Xc/z» Xo/z)
values of (a) (1.0, 0.0); (b) (0.50, 0.03); (c) (0.33, 0.06); and (d) (0.20,
0.10). Other conditions are the same for all samples : a surface temperature
of 785 °C; a plasma power of 500W; a total pressure of 7 Torr. In addition,
XH/Z = [H]/{ [H]+[C]} was fixed at 0.97 (6% CH4).
110
4.22(a) HR-XTEM image showing the interface between the diamond film and c-Si
substrate. A faceted grain is shown on the lower left side and its
approximate diameter is ~250 A. In this case the diamond film was
deposited with (XH/Z, XC/Z, XO/Z) = (0.97, 0.2, 0.1). The plasma power
was 500W; the surface temperature was 785 °C; and the total pressure was
7 Torr.
Ill
4.22(b) HR-XTEM image showing locally-oriented growth of nanocrystalline
diamond grains on the substrate. In this case the diamond film was
deposited with (XH/Z» X Q Z , XO/Z) = (0.97, 0.2, 0.1). The plasma power
was 500W; the surface temperature was 785 °C; and the total pressure was
7 Torr.
112
4.23
Model for diamond growth showing the evolution of sp2 C content under
(a) optimum diamond growth conditions (for example, X H / Z = 0 . 9 7 ,
XO/Z=0.10) and (b) nonoptimum conditions (for example, XH/Z=0.97,
X O /Z=0.00).
4.24
Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond
films prepared with different substrate temperatures.
114
116
xn
4.25
The effect of substrate temperature on the nucleation density. The substrate
is c-Si, the gas mixture is 1% CH4 in (H2+CH4), the total gas flow is 100
seem, the microwave power is 500 W, and the pressure is 7 Torr.
117
The effect of substrate temperature on the evolution of sp 2 C volume
fraction in the diamond film. The substrate is c-Si, the gas mixture is 1%
CH4 in (H2+CH4), the total gas flow is 100 seem, the microwave power is
500 W, and the pressure is 7 Torr.
119
Sp2 C volume fractions vs. the substrate temperature calibrated by RTSE
measurement (a) within the nuclei, (b) within the bulk film after ~300 A of
growth (at the peak in the sp2 C content), and (c) within the bulk film after
2000 A of growth.
120
4.28
Bulk layer growth rate vs. substrate temperature.
121
4.29
The sp2 C volume fraction for different XH/Z values ranging from 0.10 to
0.98 measured just after coalescence. Three sets of result are shown by
circles and triangles.
123
The bulk layer deposition rate for gas mixtures of CO in H2 ranging from
XH/Z = 0-00 to 0.98. Three sets of result are shown as the open and closed
circles and triangles.
125
(A, *P) at 3.0 eV plotted vs. time showing the changes in the raw data for a
Ni substrate as a function of the various processing conditions: (1) heating
from 25 °C to 800 °C, (2) annealing at 800 °C, (3) exposure to a H 2
plasma, and (4) exposure to a plasma of H2 and CH4.
128
The result of So minimization for the analysis of a Ni substrate exposed to a
(CH4+H2) plasma using an optical model consisting of a single layer. A
plot of So vs. the trial overlayer thickness is shown along with a secondorder polynomial fit used to establish the minimum. The minimum occurs
for an overlayer thickness of ~ 193 A.
131
The dielectric function (£i,end» £2,end) corresponding to the overlayer
obtained by the So minimization method in Fig. 4.32. This result is
compared to the bulk dielectric functions of Ni (i) at room temperature from
the literature, (ii) at 800 °C from this study, and (iii) at 800 °C after H2
plasma exposure also from this study.
132
The results of real time analysis of data collected during exposure of a Ni
sample to a H2+CH4 plasma assuming a one-layer growth model. The
dielectric function andfinalthickness of the layer were established using the
So minimization method of Fig. 4.32. Shown here are: (a) the thickness vs.
time, and (b) o vs. time.
133
4.26
4.27
4.30
4.31
4.32
4.33
4.34
xiii
4.35
The dielectric functions (ei,SUb. e2,sub), (e J}, e ^ , (s®, e f), and (e<n), e f)
corresponding to the substrate, first (underneath) layer, second (top) bulk
layer, and an alternative bulk layer.
135
4.36
Results of real time analysis of data collected during H2+CH4 plasma
exposure of a Ni sample assuming a two-layer model: (a) o vs. time and (b)
thicknesses vs. time. The dielectric functions used for the analysis are
(ei,sub, e2,sub), ( e f , e ^ , ( e f , e ^ , and (e f,ef) as shown in Fig. 4.35.
136
XIV
LIST OF TABLES
2.1
Root-mean-square (rms) roughness determined from 10x10 |im atomic
force microscopy (AFM) images along with the roughness layer thicknesses
and 95% confidence limits deduced using spectroscopic ellipsometry (SE).
46
XV
ACKNOWLEDGMENTS
I would first like to express my deepest gratitude to my thesis advisors, Professor
Robert W. Collins and Professor Christoper R. Wronski, for all of their invaluable
guidance, encouragement and support throughout the duration of this work. Their time and
efforts were instrumental in the completion of this work. My special thanks go to Professor
R. Messier for his helpful technical suggestions and assistance. I also appreciate Professors
S. Ashok, J. Ruzyllo, and T. Mayer for serving my committee and reviewing this thesis.
I would like to thank William Drawl for the useful discussions and assistance, and
my thesis work could not have been completed without the help of fellows in ellipsometry
group. In particular, I would like to thank Dr. Ilsin An, Dr. Alan R. Heyd, Dr. Hien Van
Nguyen, Dr. Yiwei Lu, and Dr. M. Wakagi at Hitachi Ltd in Japan.
I am also grateful to my parents, Myun-Hoo Hong and Dong-Ryun Park, my
wife's parents, Hak-Gyun Kim and Suk-Yeon Yoon, especially my father-in-law who had
passed away while I am working this thesis, my wife, Hyejung Kim, my two daughters,
Joanna and Rachel, and my new son, Edward, for their patience, supports, and standing
by me in all my endeavors.
This study was supported by the National Science Foundation (Grant Nos. DMR8957159, DMR-9217169).
1
CHAPTER 1
INTRODUCTION
EUipsometry is a technique used to obtain the dielectric properties of materials in the
optical frequency domain. The technique is based on the measurement of changes in the
state of polarization of a coUimated monochromatic light beam caused by the interaction of
the beam with a physical system consisting of one or more specular, parallel interfaces
between optically dissimilar materials. Because it is purely an optical technique, the
ellipsometry measurement is performed without making physical contact to the sample.
EUipsometry is used most extensively in the reflection mode for studies of specular
surfaces, interfaces and thin films. The measurement capability is not limited by adverse
environments that may surround the sample such as plasmas, reactive gases, and liquids.
Thus, ellipsometry measurements can be performed in situ and in real time during thin film
growth or surface processing.
Since the introduction of small, inexpensive microcomputers over the last two
decades, a number of automatic ellipsometers have been developed. The common feature of
these instruments is the capability of much faster measurements than was previously
possible with the traditional manual null ellipsometer (Aspnes, 1988; Collins and Vedam,
1993). As a result, two new measurement capabilities have emerged: real time ellipsometry
and spectroscopic ellipsometry. More recently, the development and application of the
optical multichannel analyzer detection system made possible real time spectroscopic
ellipsometry measurements. The Ellipsometry Group at Penn State University has
developed the first instrument for real time spectroscopic ellipsometry (RTSE) using a
2
multichannel detection system which is controlled by computer (Collins and Kim, 1990; An
and Collins, 1991). With the multichannel detector, this new generation of spectroscopic
ellipsometer can collect one pair of ellipsometric spectra, each consisting of 111 data points
over the photon energy range from 1.5 to 4.5 eV, in a minimum time of 32ms. The
application of the multichannel detector, namely a silicon photodiode array, to ellipsometry
rather than the more conventional photomultiplier tube detector implies that errors specific
to the array need to be characterized and corrected (An and Collins, 1991; An et al., 1991;
Nguyen et al., 1991; An, 1992; An et al., 1992).
This RTSE system can be used in a variety of applications for in situ monitoring of
thin film and surface processes while they occur, yielding both fundamental properties of
the thin film materials and information about the processes under measurement (Cong et
al., 1991a; Heyd et al., 1991; An et al., 1992; Hong et al., 1994). In addition, it is now
becoming possible to use real time feedback in order to control film thickness, film and
surface composition, and surface temperature, for example. In this work, we have applied
RTSE to monitor the growth characteristics of diamond thin films. We show that RTSE is a
very useful tool for characterizing the evolution of the nanocrystalline diamond thin film
structure for films grown under adverse conditions, specifically the high microwave plasma
power, high gas pressure, high temperature, processing environments.
This thesis can be divided into two major subjects: (i) the development of our
second-generation RTSE and (ii) its applications to diamond thin film growth.
In the first part, the basic principles and theory of ellipsometry are explained. In
addition, the systematic errors of the photodiode array detector used for RTSE are
characterized, and the correction procedures are discussed. These errors include
nonlinearity and image persistence. Based on this error characterization, the entire system is
configured for optimum performance.
For the second part of the research, the RTSE instrument was attached to a
3
microwave plasma-enhanced chemical vapor deposition (CVD) system with ports oriented
for optical access. When Si substrates are used, a calibration procedure has been developed
to obtain accurate temperatures of the diamond film/substrate surface under the various
deposition conditions. This approach has been applied to all diamond thin film experiments
for improved control over the growth process. In addition, for diamond films prepared on
seeded Si substrates under different conditions, the time evolution of the nuclei, bulk, and
surface roughness layer thicknesses during the nucleation, coalescence, and bulk growth
processes is determined from the RTSE data. The thickness evolution of the void and
optically-absorbing non-diamond carbon (sp2 C) volume fractions in the nucleating and
bulk layers are also determined. Along with these RTSE studies, results from a number of
other different measurements are also shown, including pyrometry, scanning electron
microscopy, cross-sectional transmission electron microscopy, atomic force microscopy,
and Raman spectroscopy.
Based on the interpretations of the RTSE data collected using different mixtures of
CH4, H2, and O2, the C-H-O gas phase diagram depicting the non-diamond growth,
diamond growth, and no-growth regions (Bachmann et al., 1991) has been better
understood, and the important experimental observations are reported in this thesis.
Additional diamond thin films were grown using (CO+H2) as a source gas. Such
experiments scanned along the CO line which connects the midpoint of the C-O side with
the H vertex on the C-H-O phase diagram. The experimental results are presented for
different (CO+H2) gas mixtures and compared with results obtained using the CH4, H2,
and O2 gas mixtures. Finally unseeded Ni was investigated as a substrate for diamond
growth using (CH4+H2) under a standard set of diamond deposition conditons. This
preliminary work has set the stage for future studies of diamond growth using other
substrates besides seeded silicon.
4
CHAPTER 2
REAL TIME SPECTROSCOPIC ELLIPSOMETRY
2.1. Apparatus
The real time spectroscopic ellipsometer used in this thesis research employs the
rotating polarizer configuration as shown in Fig. 2.1. It also employs an optical
multichannel analyzer (OMA) (EG&G Model 1461 Detector Interface with EG&G Model
1463 Detector Controller) which is based on a 1024-pixel silicon photodiode array detector
(EG&G Model 1412). This detector has a saturation count level of 2 14 and single-pixel and
full-array read times of 16 us and 16 ms, respectively, in a normal scanning mode in which
every pixel is read out. The detector controller also provides the special scanning capability
called "grouped scanning". Grouped scanning gives the user the ability to increase the
effective sensitivity of the detector to incident light but at the expense of spectral resolution
of the system. For all experiments in this thesis, the photodiode pixels are grouped by 8 in
order to increase the signal-to-noise ratio. Thus, each scan contains 128 spectral points. In
this mode, the single-pixel group and full-array readout times are 35 jxs and 4.5 ms,
respectively. For the ellipsometer developed as part of this thesis, the rotation frequency of
the polarizer is 15.6 Hz, and the minimum acquisition and repetition times are half the
rotation period or 32 ms for a single pair of 128-point ellipsometry spectra. The potential
photon energy range of measurements spans from 1.47 to 6.03 eV. Because of the weak
output of the Xe light source and the reduction in efficiency of the detector and
spectrograph grating above ~4.5 eV, the actual useful spectral range of the instrument is
To Multichannel
Detector
Input Fiber
Adaptor
From
Light
ource
Fig. 2.1 Schematic of the real time spectroscopic ellipsometer in the rotating polarizer configuration used for studies of
diamond thin film growth.
oi
6
from 1.47 to -4.5 eV. At the lowest photon energy of 1.47 eV a single eight-pixel group
intercepts a photon energy band 0.009 eV wide; at the mid-range and highest energies of
3.0 eV and 4.5 eV, the corresponding values are 0.036 eV and 0.080 eV, respectively.
White light having a spectral range from the near IR to the near UV is generated by
a 75 W Xe arc lamp (L2174, Hamamatsu Co.) and is linearly polarized by the rotating
polarizer. The rotating polarizer incorporates a calcite Glan-Taylor prism, which in contrast
to a quartz Rochon prism, does not exhibit optical activity effects. The linearly-polarized
incident white light beam reflects from the sample, and the polarization state of each of its
spectral components is changed. The changes in the polarization state imposed by the
sample are analyzed by a calcite Glan-Taylor prism-type fixed analyzer. Therefore, the
optical activity coefficients of both the analyzer and polarizer, YA a n d YP vanish. The
transmission axis of the analyzer is fixed at 30° with respect to the incidence plane of the
sample in order to minimize detector background noise and inherent fluctuations in light
flux (Aspnes, 1974b). After passing through the fixed analyzer, the beam is collimated by
interface optics (Instruments SA, Inc.), is dispersed by a spectrograph, and impinges onto
the surface of the 1024-pixel Si photodiode array detector. For the spectrograph, an
imaging instrument (Model CP 200, ISA Division Jobin-Yvon) is used in order to generate
a flat focal plane (25 mm width x 8 mm height) where the photodiode array is placed. The
grating is used in the spectrograph at 200 grooves/mm, and a resulting dispersion of 25
nm/mm. A slit width of 0.25 mm was chosen, yielding an approximate resolution of 6.25
nm. This fixed wavelength resolution leads to a photon energy resolution of 0.011,0.045,
and 0.010 eV at the lowest, mid-range, and highest photon energies of 1.5, 3.0, and 4.5
eV, respectively. These values are to be compared with the resolution established by the
grouped detector of 0.009, 0.037, and 0.084 eV. Thus, the resolution of the system is
limited by the slit width and the slit width can be decreased) if improved spectral resolution
is needed.
7
Because a grating is used in this spectrograph, not only is a first-order reflection
generated (which contains the data of interest), but also zero, second, and higher orders.
The intensities of third and higher orders can be considered negligible. However, the
strong non-dispersive zero-order reflection generates a weak background of stray light over
the entire array surface, and the second-order partially overlaps thefirst-orderspectrum so
as to degrade the accuracy of the ellipsometry data at long wavelengths (low energies). The
stray light caused by the zero-order reflection can be reduced by inserting baffles in the
proper positions within the spectrograph. To prevent the second-order spectrum from
overlapping thefirst-orderspectrum, a very thin (0.0066 inch) long-passfilterwith a cutoff
wavelength of A,cutoff (429.05 nm) is attached directly in front of the photodiode array.
Thus, the filter is mounted so as to cover all pixels intended to accept wavelengths longer
than A,cutoff since these wavelengths are transmitted by the filter. With this technique, the
filter can absorb the second-order which has X < Xcutoff without blocking the pixels of the
detector intended to accept the first-order wavelengths X < A,cutoff- Finally, the detector
output is read by the detector controller and transferred to a computer. As discussed in
greater detail below, each detector output consists of the integrated photon counts since the
last detector read out.
2.2.
Basic
Principle
and
Theory
of
Rotating
Polarizer
Multichannel Ellipsometry: Data Reduction and Calibration
PRINCIPLES OF DATA REDUCTION
In ellipsometry, the change in polarization upon reflection is measured as a ratio of
the reflected to incident polarization states (Muller, 1973; Azzam and Bashara, 1977). First,
however, we decompose the incident (i) and reflected (r) electric fields into parallel (p)
8
components and perpendicular (s) components to the plane of incidence. Next the complex
reflectivity ratio p which is the ratio of the reflected to incident polarization states can be
defined by
E
a
rp /E ip_ rp_
En/E,is
exp
i**-**j
(2.1)
In this equation, 8 p (8S) is the phase change of the p (s) electric field component upon
reflection, Ej (Er) is the incident (reflected) electricfield,and rp (rs) is the Fresnel amplitude
reflection coefficient parallel (perpendicular) to the plane of incidence. The two ellipsometry
angles, *F and A are defined as
^ = tan-!
(2.2a)
and
A = op-8s.
(2.2b)
Thus,
p = tan*F eiA.
(2.3)
The light beam passing through the optical system of Fig. 2.1 can be described by
the Jones formalism. This formalism uses vectors to represent the polarization states of the
fully-polarized light beam and matrices to represent the optical elements and coordinate
rotations as shown schematically in Fig. 2.2. Using this formalism, the electric field at the
detector is:
Ed=
Ea
10 cos(A-Ag) shXA-Ag) r p 0
00 -shXA-Ag) cosCA-Ag) 0 rc
cosCot-Pg) -sinCcot-Pg)
sinCcot-Pg) cosCcot-Pg)
0
EQrpCOsCA-A^cosCcot-P^+rgSinCA-AgJsinCcot-Pg)
(2.4)
0
Here, A s is the analyzer azimuth scale reading when the transmission axis lies in the plane
of incidence. -P s is the azimuth of the polarizer transmission axis with respect to the plane
of incidence at t=0, which is defined as the onset of data acquisition by the photodiode
array. This onset is in turn triggered by an encoder mounted on the shaft of the polarizer
motor. The values of A s and P s can be determined by one of three different calibration
procedures (de Nijs et al., 1988; Collins, 1990; An, 1992). The subscripts t and e represent
the orthogonal transmission and extinction axes of the fixed analyzer, respectively. Then,
the observed irradiance Ij at the detector is proportional to the product of the electric field
Ed with its complex conjugate E d *:
WHEJ
=I 0 l+acos2(0)t-Ps)+psin2((ot-Ps)
(2.5)
cos(cot-P s )
-sin(cot-P s )
sin(cot-P s )
cos(cot-P s )
Eo
0
0
0
1 0
cos(A-A s )
sin(A-A s )
0 0
•sin(A-A s )
cos(A-A s )
COt-P
Light
Source
Polarizer
Analyzer
Photo-diode
Detector
Fig. 2.2 Schematic representation of the rotating polarizer ellipsometer using the Jones formalism.
o
11
where
•O4N 2
EopcoftA-Ag) tarpT+tarf^CA-As)
taif^P-tar^CA-As)
a=
(2.6)
(2.7a)
tarfV+tarr^CA-As)'
and
P=
2cosAtarfPtan(A-As)
tan2*? + tan2(A-As)'
(2.7b)
Here a and (3 are normalized Fourier coefficients, I 0 is the average irradiance, and *F and A
are the ellipsometric angles defined previously (-7t<A<7t and 0<*P<7i:/2). From Eqs. 2.7a
and 2.7b, *F and A can be expressed in terms of the two normalized Fourier coefficients, a
and p\ and the analyzer angle A, according to:
cosA =
P
1
\j\-a
tartF=W - ^ tantA-As).
(2.8a)
(2.8b)
These equations are correct for an ideal optical system, however, the major error of
the rotating polarizer ellipsometer is residual source polarization. In an ideal system in the
absence of source polarization, the irradiance transmitted by the rotating polarizer is
independent of its angle and, thus, time-independent. When source polarization is present,
12
the irradiance transmitted by the polarizer oscillates as the polarizer rotates, with an
oscillation amplitude proportional to the degree of polarization of the source flux.
Fortunately, we can simulate the effect of residual source polarization by an extension of
the theoretical Jones formalism of the standard source-polarizer-sample-analyzer system
shown in Fig. 2.1 (Collins, 1990; An et al., 1991; Nguyen et al., 1991). Therefore, Eq.
2.4, which indicates the electric field at the detector, is modified as follows to include the
residual source polarization:
Ed=
10 cosA sinA
= E, 00
-sinA cosA
E
ors
rp0
0 rc
cosP -sinP
sinP cosP
10 cosP sinP
0 0 -sinP cosP
cosS -sinS 1
sinS cosS ie
(pcosA cosP +sinA sinP)[cos(P-S)+iesin(P-S)]
0
(2.9)
where S and e (=1) establish the azimuth and ellipticity of the residual source polarization.
Thus, the effect of a rotating polarizer on a slight partial polarization of the incident light is
assumed to be the same as the effect on a polarization having an ellipticity that deviates
slightly from unity. A' is the actual angle of the transmission axis of the fixed analyzer with
respect to the plane of incidence and is given by A' = A - As, where A and As are the scale
reading and its angular offset from the correct value, respectively. Similarly, the rotating
polarizer angle P' can be written as P' = cot - Ps, where t = 0 is defined as the onset of the
data acquisition as described in the next paragraph, and -Ps is the polarizer angle at this
time. Now, expansion of Eq. 2.9 leads to a theoretical expression of the form:
13
ld(0 = I0{ 1 + a cos[2(G)t - Ps)] + B sin[2(cot - Ps)]
+ a4 cos[4(cot - Ps)] + P4 sin[4(©t - Ps)]},
(2.10)
where the dc component I 0 and the four Fourier coefficients (a, B, (X4, and B4) are
expressed as follows:
lo = [ (1 +4£2)El I r s 12 (tan2 ¥ cos2 A' + sin2 A')]
I (1-e 2 ) tan2Y cos2 A'-sin 2 A'
X[1+
2 (l + e 2) t a b o o s * A'+stf A'
1 (1-e 2 ) tan^cosAs^A'
. ntn
1
^k^u^oo^^A^
a=
j
1+
._ .. .
(2 lla)
-
,
(2.11b)
,
(2.11c)
a
T ( o Y c + PoYs)
Po + Ys
B=
1 +
1
°
O K Y C + POYS)
2(PoYc + a0Ys)
j
,
a4 =
1+
(2.1 Id)
2(aoYc + PoYs)
and
oKYc-PoYs)
P 4 = 2L1
1+
^KYC+POYS)
In these expressions,
•
(2.1 le)
14
tarf^co^A-sirpA
a =
/0 in N
,
(2.12a)
tan^/cosAsin2A
Po=^
5
5-'
taif^WA+shfA
,„ ,„, N
(2.12b)
y c =-^rCos2S,
(1+e2)
(2.12c)
tair^co^A+sir^A
and
Y s =-^-^sin2S.
(1+e2)
(2.12d)
The 4co Fourier components, 0:4 and P4, enter as a result of the modulation of the residual
source polarization by the rotating polarizer. Now, solving Eqs. (2.1 lb) and (2.1 lc) for oc0
and p o and substituting the results into Eqs. (2.8a) and (2.8b) for a, P respectively yields
¥ and A in terms of a, p, yc, and ys.
tan^F = tan(A - As) K /
1 + a-yc+^Ys(PYc-aYs)-iaYc+ $yj
1
1
,
(2.13a)
1 -a+Yc-oYs^Yc-aYsHCaYc+PYs)
and
iYc(aYs-pYc)
2
cosA =
y
[I-^OYC-^B)]
+
P-Ys
-[a-Yc+^Ys(PYc-aYs)]
.
(2.13b)
15
a and P in these equations are given in terms of the raw data using the expression
presented below [Eqs. 2.17]. In addition, yc, ys, P s , and As are determined in the
calibration procedure. These parameters will be provided later.
Because the photodiode array used in our RTSE instrument is an integrating
detector, we cannot apply the conventional Fourier analysis method to extract a, P, 0:4,
and P4 as is done when a photomultiplier tube (PMT) is used in the sampling mode.
Instead, Hadamard summation is used to extract the Fourier coefficients (Courdille et al.,
1980; Collins et al., 1991). In our case, this involves integrating the accumulated irradiance
at the photodiode array over each of 5 equal time periods during a single optical cycle (i.e.,
one-half mechanical cycle) of the polarizer. The readout is performed at the end of the time
periods, triggered by the encoder mounted on the polarizer motor shaft. The five integrals
provide sufficient information to deduce the four normalized Fourier coefficients (a, P, 0C4,
P4) as well as the ellipsometry angles Q¥, A).
Next it will be shown how the resulting five readings, Sj (j=l,2,3,4, and 5), can be
manipulated to deduce a, P, (X4, and P4. First Sj (j=l, 2, 3,4, 5) are given by
jj
S j = P Lj(t)d1,
j =1,2,3,4,5
(2.14)
t
where T = & and I d is the irradiance impinging on the detector.
t
I, in turn is given by
'
/
/
/
'
'
Id=I0(l+acos2oot4p sin2cot+a cos4Q)t+P4sin4cot).
(2.15)
16
The coefficients in Eq. (2.10) and (2.15) are related by rotation transformations by 2PS
[(a\ P1)] and 4PS [(o^p^)]:
a = a' cos2P s + P' sin2P s ,
(2.16a)
p = -a' sin2P s + p' cos2P s ,
(2.16b)
and
(X4 = a'A cos4P s + P4 sin4P s ,
(2.16c)
p4 = -a4 sin4Ps + p 4 cos4P s .
(2.16d)
The integrals of Eq. (2.14) represent the photon counts collected during a rotation of the
polarizer by TC/5. Substitution of Eq. (2.15) into Eq. (2.14) and integration yields
_ ' n
n . % > . 71 . TC_> 1
2rc . 2TC ' 1 . 2TC . 2TC '
Si=I (—+cos-=-sm-z-a +sin-?sirHrp + - c o s — s i n ^ a . + - s i i * ^ s i n - ^ p J,
1
ov5
5 5
' n
2% . n
S 2 =I
05
_
fe-cos-^-sin^a
' 7C
5
. TC /
5r
5
5
.
2
5
. 2n . % > 1
5 4 2
TC
. 2TC '
5
5
5
5 r47
\
1 . TC . 2%
+sm-=-sin^-p —^cos-z-sin-r-a --sin^-sin-z-p ),
5
5
2,
4 2,
5
_ .
(2.1/a)
5
4
(2.17b)
1 . 2% '
S 3 =I o (j-sin^a + - s i n y a 4 ) ,
(2.17c)
_ ' TC
2% . TC / . 2TC . TCQ> 1
TC . 2TC ' 1 . TC . 2TC '
S 4 =I (-p-cos-r-sin^a -sin-z-sin^P --cos-^sin-^-a .+;rSinTsin-z-p .),
* ov5
5
5
5
5r 2
5
5 4 2 5
5 r47
and
_„
(2.17d)
17
'
31
Jt .
3t
i
.
31 .
31 '
1
23t .
2ll
'
1
.
2jl .
23t '
S 5 = I o (— + cos vsin —a - sin —sin —p + — cos — sin -=-a4 - — sin —sin - H J 4 ) •
(2.17e)
Solving Eqs. (2.17a-e) yields a' and p", which are the experimentally determined Fourier
coefficients without accounting for the polarizer phase angle correction. These are given by:
a' = 0.5344797 +
1.195133(S 1 - S 2 - S 4 + S5) - 2.672398S3
——-—%
-,
(2.18a)
3d0
and
=
1.2566371CS! - S5) + 2.0332815(S2 - S^
3tIQ
where 7Cl'0= Sj + S2 + S 3 + S4 + S5. One can also solve for a. and P4 and the results
are
, 0.8166123(8! + S5) - 2.1379187(S2 + 84) + 2.6426128S3
a4 =
;
,
3tl
(2.18c)
o
and
/ 2.5132741(S,+S5)-1.5532888(S2-S4)
P =
—
—,
—
-.
(2.18d)
Therefore, the ellipsometry angles *F and A, corrected for the errors due to the residual
source polarization, can be expressed in terms of the raw data Sj (j=l, 2, 3, 4, and 5)
18
through Eqs. (2.13a), (2.13b), (2.16a), (2.16b), (2.16c), (2.16d), (2.18a), (2.18b),
(2.18c), and (2.18d).
PRINCIPLES OF CALIBRATION
Another important component of the ellipsometry measurement, in addition to
determining *F and A, is the calibration procedure. The purpose of calibration is to
determine the polarizer starting angle, Ps, and the azimuth of the analyzer prism, As,
measured with respect to the plane of incidence set by the sample alignment. Calibration
procedures for rotating element ellipsometers and corrections for system imperfections have
been reviewed in detail (Collins, 1990). Among the many calibration methods developed,
residual calibration (Aspnes, 1974a) and phase calibration (de Nijs et al., 1988) are the
most widely used. These methods are based on the principle that a light beam reflected
from the surface of an isotropic material is linearly polarized if, and only if, the incident
beam is linearly polarized and its polarization direction is either parallel or perpendicular to
the plane of incidence. In research reported earlier, these calibration methods were applied
to the multichannel ellipsometer including corrections for errors in the source and
polarization systems (Nguyen et al., 1991). Therefore, instead of reviewing these earlier
methods, we will discuss a new calibration method, the intensity calibration, which was
first introduced by An (An, 1992), and in this thesis the error correction for the residual
source polarization is included in the intensity calibration for the first time.
In this new calibration method, the dc component of the radiant flux on the
detector, I0) is used. We measure I0 near the 0° and 90° azimuths of the analyzer. From I0
measured at a number of analyzer positions (from -6° to 6°) near 0°, we determine As. The
phase angle 0=^tan~ 2(P la) at these analyzer positions is calculated in order to find Ps. As
explained in Section 2.2, the effect of residual source polarization can be simulated by an
19
extension of the theoretical Jones formalism of the source-polarizer-sample-analyzer system
as shown in Fig. 2.1. For reference I0 is given here again as:
I 0 = [ (1 + e tyI r s 12(tan2Tcos2 A'+sin2A')]
4
i (1-e 2 ) taif^co^A'-sn^A' „„
x [ 1+4 ,: V —x
=
o—cos2S
2 (l + e 2) t a n ^ c o ^ A ' W A '
i (1-e 2 ) tan^cosAsin2A' . nen
+4V V — x
s—sin2Sl.
2
J
2 (1+e ) t a i r ^ c o s U ' W A '
r1
,„ 11 .
(2.11a)
This equation can be written as follows:
I 0 = ^ E21 rs 12[( 1+e^tan2 ^ cos2 A'+ sin2 A')
+^( l-e^Ctari2 ¥ cos2 A' - sin2 A') cos2S
+^(1- e2)(tan¥ cosA sin2A') sin2S].
(2.19)
Finally, Eq. (2.19) can be simplified to
I 0 = | E21 r s 12( 1+tan2 ¥)|±( 1+ e2)( 1- cos2¥ cos2A')
+\{ 1- £2)(cos2A' - cos2¥) cos2S
+1(1- e2)sin2T cosA sin2A' sin2S].
(2.20)
In order to deduce As from data collected near A' - 0 ° , we first expand Eq. (2.20) about
A' = 0. In this case, cos2A' and sin2A' are approximated as (1 - 2A' 2 ) and 2A',
respectively. Therefore, Eq. (2.20) becomes
I 0 =[|E 2 |r s | 2 (l+tan 2 ^)(l+e 2 )]
x [(1+ ^Yc)(l-cos24/)+(yssin2»FcosA)A,+2(cos2^-^Yc)A'2]I
(2.21)
20
which is quadratically dependent on A'= A - As. yc and ys are defined as in Eq. (2.12c) and
(2.12d), respectively. Equation (2.21) is differentiated with respect to A and the result to
set equal to zero. Defining A = A m j n as the experimentally determined scale reading for
which the minimum occurs in I0(A') near A'=0, then Eq. (2.21) leads to the following
result:
A s « Amin + -x tan2*F cosA.
(2.22)
Eq. (2.22) permits As to be deduced from the experiment if Ys is known.
The expression corresponding to relation (2.21) when A'= 90°, i.e., A ~ As + 7t/2,
is deduced according to the following. From Eq. (2.20), one can write
Io = [|E2|r s | 2 (l+tan 2 Y)(l+e 2 )]
x [(1- cos2*F cos2A')+^Yc(cos2A' - cos2*F)+±ys sin2*F cosA sin2A'].
(2.23)
Now A' is replaced with A'+90° where A' is small. In this case, cos2 A' in Eq. (2.23) is
replaced with -1+2A'2 and sin2A' is replaced with -2A'. Therefore, I 0 can be simplified
to
I 0 =[|E2|r s | 2 (l+tan 2 ^)(l+e 2 )]
x [(1- ^y0)( l+cos2vF)-(Y!sin2¥ cosA)A' -(2:os2*F -y^)A/2].
(2.24)
Substituting A - As for A', differentiating with respect to A, and setting the result equal to
zero yields A = Amax> for which a maximum occurs in I0 near A - As = 7t/2:
21
(As + J ) - (Amax + f ) + ^ tan2*F cosA.
(2.25)
Now we need to determine the phase angle P s which is related to the first order error and
the sample parameters (*F, A). The phase function is defined by (Aspnes, 1974a; Nguyen
et al., 1991):
0(A) = [tan-UP'/a')]^
= Ps + [tan-l(p/a)]/2.
(2.26)
(2.27)
The 2co Fourier coefficients, a and p in Eq (2.1 lb) and (2.1 lc) can be expressed to first
order in the small quantities, ys and yc. The following simple form is now obtained:
a = a 0 + Yctl - (a5/2)] - (ys a 0 Po/2),
(2.28a)
P = Po - (Yc «o Po/2) + Ys[l - (P20/2)].
(2.28b)
Substituting Eqs. (2.12a) and (2.12b) for cc0 and p o into these expressions, then
substituting the results into Eq. (2.27), and keeping terms to first order in Yi and (A-As),
one obtains:
0(A)« Ps + (A - As)cot^ cosA - Yc(A - As)cotxI/ cosA + YS/2.
(2.29a)
Thus, this expression holds for A » As. The expression corresponding to relation (2.29a)
valid to first order in Yi and [A - (As + %/2)] is
0(A) » Ps + [A - (Ag + 7t/2)]tan¥ cosA + YC[A - (As + 7t/2)]tan¥ cosA.
(2.29b)
22
This expression holds for A = As + rc/2.
We define Pi and P2 as the experimentally determined phase functions
evaluated at A = Amin and A = A max +rc/2,respectively. Substituting Amin and A max + 7C/2
from Eq. (2.22) and (2.25) into Eq. (2.29a) and (2.29b), one finds the following
expressions for Ps, including the first order corrections due to residual source polarization:
P» = P l - J Y , d - C 0 ' ^ A ) .
(2.30a)
and
2
2
Sin*Pcos
A1
Ps = P2 4Y s (lH-sin
J s2 C gfA<
).
(2.30b)
The procedure for obtaining As and Ps involves (1) measuring Amin or A max and Pi or P2,
(2) determining zero-order values of *F and A for the surface by using standard techniques
in which all errors are neglected, and (3) performing the required calculations according to
the relevant Eqs. (2.22), (2.25), (2.30a), and (2.30b). As an example of step (1), Fig. 2.3
shows Amin and Pi at pixel group number 64 measured for analyzer angle values from -6°
to 6°. In order to complete step (3), however, the value of Ys is required. Ys can be obtained
from Eqs. (2.30a) and(2.30b) using
^co^A-l
With the error parameter Ys known, it is possible to correct the calibration data to obtain
accurate values of the polarizer and analyzer calibration angles. Although Yc is not needed to
correct the calibration data, it is needed in the calculation of ¥ and A [see Eqs. (2.13a) and
(2.13b)]. Yc can be obtained from the dc component minimum and maximum values.
23
130
A ^ 0.905°
J12Q
P, =91.31°
110
100
= "90
80
70
60
-
6
-
4
-
2
0
2
4
6
ANALYZER ANGLE (degree)
Fig. 2.3 A plot showing the determination of Amjn and Pi for pixel group number 64 using
the dc component I0 and phase function 0 measured as a function of analyzer angle from
-6° to 6°.
24
Solving Eq. (2.21) at A' =0° and Eq. (2.23) at A' =90°, and combining the resulting two
equations yield,
yc=
2( X cos2y-l)
X -cos2Y
(232)
There is a second way to obtain the error parameters, yc and ys. In Eqs. (2.1 Id) and
(2.1 le), yc and Ys are related to {X4 and P4. The following two equations are obtained by
solving Eqs. (2.1 Id) and (21 le) for Yc and Ys:
«o«4-PoP4
Ys = -j
,
? [ o j + pj-2o0p0a4-(oj-pj)p4]
«oP4 + PQa4
Yc = -j
.
-[aJ + P^-2a 0 P 0 a 4 -(aJ-p^)P 4 ]
^
(2.34)
n
-,,
(2.35)
n
Now, from the measurement of Sj (j = 1~5), we can calculate (X4 and P4 using Eqs.
(2.18c) and (2.18d). Additionally, we need to obtain a 0 and p o . These two parameters are
determined from zero-order values of *F and A, which are calculated from Sj, by using the
standard techniques in which all errors are neglected.
25
2.3. Alignment, Detector Error Correction, Data Acquisition,
and Analysis
SYSTEM ALIGNMENT
Optical system and sample alignments are critical in performing accurate and
reproducible measurements. The system alignment described here has been done before the
ellipsometer was mounted to the vacuum chamber. The following steps were developed in
order to align the optical system used in this study:
(1) The goniometer was set in the straight-through position (i.e. the angle of incidence is
set at 90°) without any optical elements.
(2) A He-Ne laser is mounted at the position for the Xe lamp and two alignment targets
are placed on the goniometer rails. The alignment target is a simple device which has
a concentric circular pattern on its face and can slide along the rails.
(3) The laser is adjusted so that the beam always hits the center of the target pattern while
it slides along the rail. In this step wefixthe optical path.
(4) The optical fiber coupler is placed at the detector side. The optical fiber is in turn
coupled to the spectrograph with the detector removed.
(5) Each optical element can be positioned with respect to thefixedoptical path, including
the rotating polarizer and stepping motor-controlled analyzer. Before positioning the
polarizer and analyzer assemblies on the rail, one must check that the polarizer and
analyzer prisms are aligned properly within their holders such that the wobbling
during rotation is minimized. A laser beam reflected from the prism surface can be
visualized on a distant surface (e.g., white paper taped to the laboratory wall), and the
prism position is adjusted so that the beam spot on this surface remains stationary
26
when the polarizer motor drive is turned on. Alignment with respect to the optical
path involves ensuring that the laser beam is perpendicular to the faces of prism and
coincides with the axis of rotation. When the laser beam is perpendicular to the prism
faces, the laser beam is reflected back to the laser source point through the center of
the alignment target placed between the source and prism.
(6) The laser is replaced by the Xe lamp. With the collimation optics, the lamp and
collimator are aligned to yield the same optical path followed by the laser beam. At
this point we should be able to see the Xe spectrum on the horizontal axis at the
detector side of the spectrograph.
(7) The detector is attached to the spectrograph and aligned to match the linear focal plane
with detector array.
With the well-aligned ellipsometer, the system is mounted around the vacuum
chamber on a separate table from the chamber. The strain-free windows are attached to
optical ports on the chamber. The windows are on the bellows and can be adjusted to
ensure that the light beam passes through the windows perpendicularly. The sample is
placed on the center of the sample holder where the light impinges on it, and the system is
aligned by comparison of the spectra from two optical cycles while watching the computer
monitor. The spectra from two optical cycles in a well-aligned system can be overlapped
exactly by adjusting the four alignment screws, two of which are located on the front
ellipsometer legs and the other two located at the back side as shown in Fig. 2.4.
Accurate determination of the angle of incidence is a another important step required
to ensure that the overall measurement is reliable. The optical ports on the vacuum chamber
used in this study are oriented for an angle of incidence of 45°, not 70° which is required
for the usual ellipsometry measurement. Therefore, bellows mounted between the UHV
windows and the optical ports are used to tilt the windows with respect to the ports in order
Spectrograpl i
Microwave
Power
Microwave Guide
" "
I I Antenna
Multichannel
Detector
Input
Fiber
Output
Fiber
crr^
window
with bellow
Rotating Polarizer
Shutter
Sere vs for alignment
Collimator
Motor Drive
Source
Fig. 2.4 Schematic of RTSE and MPECVD systems: top view (left) and side view (right).
to
28
to achieve 70°. Overall, the determination of the accurate angle of incidence affects the
reliability of this study. The angle of incidence can be determined by measuring standard
samples such as crystalline Si (c-Si). The expected (*P, A) spectra for c-Si is simulated
with the well known reference dielectric function of the material assuming different angles
of incidence. A comparison of the simulation with the experimental data for Si wafer
substrate gives the angle of incidence. In particular, *F is a sensitive function of the angle of
incidence. Therefore, by adjusting the angle of incidence in the simulation, one can achieve
a good match between the simulation for *P and the data. When the Si native oxide
thickness is changed in the simulation with fixed angle of incidence, *F is not changed and
only A changes. Thus, angle of incidence determination from a Si surface are not strongly
affected by uncertainties in the native oxide thickness. A precision of ±0.02° is obtained for
repetitive measurements of different wafers as long as position of the sample holder is not
changed. The controller that moves the sample holder vertically is designed with a display
to show the position of sample holder in units of mm from the reference point, which is the
waveguide to plasma window placed between the chamber and plasma coupler. As a result,
the sample holder can be reproducibly positioned with an accuracy of ±0.1 mm. This leads
to a reproducibility of ±0.02° in angle of incidence in situations in which the sample holder
is moved between successive measurements.
Another important step is to track the calibration parameters, As and Ps, from run to
run to ensure that the same values are obtained within the acceptable tolerances of 0.03° and
0.05"/pixel group, respectively. If these careful experimental steps are followed, a
consistent value of 69.54±0.02° is obtained for the angle of incidence. Under these
conditions, the scale on the goniometer reads 69.60° for the source side and 70.10° for the
detector side.
29
DETECTION SYSTEM ERRORS AND CORRECTIONS
A characterization of the multichannel detection system is presented next which
provides the means to correct the measured Sj (j=l, 2, 3, 4, and 5) values for detector
nonlinearity and image persistence.
Nonlinearity
The procedure and basic principle applied to correct the raw spectra Sj (j=l, 2, 3,4,
and 5) for detector nonlinearity and image persistence have been described in detail in
earlier papers (An et al., 1991; Nguyen et al., 1991; An, 1992). To characterize
nonlinearity, a constant irradiance source is focused onto the entrance slit of the
spectrometer. Spectra in counts vs. pixel group are collected as a function of exposure time
(set by the accurate internal clock of the detector controller). All such spectra were
subjected to background subtraction using data obtained with a shutter blocking the incident
beam. In the presence of the most general nonlinearity behavior, the experimentally
observed counts can be obtained as an empirical function of the exposure time and pixel
group. Earlier work for the same type of detection system found that the nonlinearity
correction factor (CNL) is a linear function of the logarithm of the observed photon counts
N near N=104 of counts. The linear function is given by
CNL=(2£-l)+0.5(K)logN,
(2.36)
where £ is a value that is selected such that the function R(a, (3)=l-(a2+P2) is closest to 0
in the straight-through configuration. R should vanish for an error-free system in the
30
0.04
o
0.03 ff
D
A
V
0.02 If
«
£=1.100
£=1.075
£ = 1.050
£=1.025
£=1.000
0.01
-0.04
1.5
2.0
2.5
3.0
3.5
PHOTON ENERGY (eV)
Fig. 2.5 l-(a2+P2) vs. wavelength for different nonlinearity correction factors £. The best
one was assumed to yield the minimum ll-(a2+P2)l.
31
straight-through configuration in which linearly polarized light impinges on the detector.
When nonlinearity is present, this quantity can be considered as the deviation of the
effective ac:dc gain ratio from unity (Aspnes, 1974a). Fig. 2.5 shows a graph of R=l(a2+P2) vs. wavelength for different £ values. The correct value was assumed to be the
one that minimizes IRI=ll-(oc2+|J2)l. Fig. 2.5 shows that £=1.025 was best for the given slit
width of 0.25mm. Thus all readouts denoted by the spectra Sj (j=l~5) are corrected using
the relation Sjk,c=Sjk,r/CNL(Sjk,r)> where CNL is given in Eq. (2.36) with £=1.025, the
subscripts c and r denote corrected and raw values, respectively, and k denotes the pixel
group number.
Image persistence
In order to study image persistence, a constant irradiance source was focused onto the
entrance slit of the spectrograph in the straight-through configuration. A shutter with a full
on-off time less than the exposure time was used to block the slit while the detector was
successively scanned. This ensured that, for some pixels, two successive exposures occur
such that the first reads a high count level and the second should read zero counts (An et
al., 1991; An, 1992). In practice, the second readout gives a weak count level even after
background correction. Figure 2.6 shows the photon counts normalized to the first readout
as a function of pixel group number derived from three successive exposures. The fullopen-to-full closed shutter operation was observed to occur during the reading of pixel
groups 70-80 of the second readout. The linearly decreasing normalized count level with
pixel group at the end of the second readout and the beginning of the third readout indicates
that the shutter was closed for a linearly increasing fraction of the exposure time for
successive pixel groups. The shutter was closed during the third exposure, and zero photon
counts should be read during the plateau region at the end of the third readout. It was found
32
0.25
i
i i i I i i—i i |
i i i i I i i i i
1.00
ggggnggrgggnm
0.95
CO
C/3
O
0.90
i
to
O
0.85
0.00
20
40
60
80
100
0.80
120
PIXEL NUMBER
Fig. 2.6 Normalized photon counts as a function of pixel group number derived from three
successive exposures for the situation in which a shutter is closed during the second
exposure. The count levels for the second and third readouts are shown after normalization
by the count level from the corresponding pixel groups of the first readout. The constant
values vs. pixel group occur when the shutter is fully closed or fully open throughout the
associated exposure time. The residual counts near zero at the end of the third readout
originate from image persistence.
33
that the persistence level depends only on the total counts for the previous readout and not
on the count rate. Final results are shown in Fig. 2.7, where the image persistence level is
plotted versus the counts obtained in the previous readout. Linear behavior is observed,
revealing an effect of 0.62%. As a result, the raw data are corrected using the following
expression:
Sjk.c = Sjk.r + Cip(Sjk,r) " Qp(S(j-l)k,r)-
(2.37)
Here Qp(x) is the image persistence correction function shown in Fig. 2.7 and given by
Qp(x)=0.0062x+32.50. The second term on the right in Eq. (2.37) represents the counts
which are unread and remain to affect S(j+i)k,r: the third term represents the counts which
remain unread from S(j.i)k,r.
DATA ACQUISITION
The encoder attached to the rotating polarizer motor shaft has two outputs. The first
generates 2n encoder pulses in one optical cycle, and the other generates one reference (Z0)
pulse per rotation. Here n=5 is the number of time slices integrated during one optical
period, which is equal to one-half mechanical period of polarizer. The phase difference
between the reference pulse and any encoder pulse is constant during the experiment. The
Z 0 pulse enables the OMA so that the controller will read out the accumulated counts
whenever one of the 2n encoder pulses arrives. With this ellipsometer, a single pair of
spectra consisting of (*F, A) can be deduced from 5 raw waveform spectra collected in 32
ms, i.e., over a single, half-rotation of the polarizer. In monitoring the film depositions in
this thesis research, the waveform spectra from 40 mechanical cycles were averaged,
leading to an acquisition time of 2.6 s for a single pair of (*P, A) spectra. With this
34
120
I ' ' ' • I ' ' ' ' IT — i — i — r
100
80
CO
60
J
40
2000
ii
ii i I i i i i I i i i iL
L_J
4000
6000
8000
10000
N obs (SCAN2)
Fig. 2.7 Detection system image persistence correction, CIP, arising from the observed
photon count level along the abscissa.
35
acquisition time, we achieve monolayer resolution at diamond growth rates of -30 A/min.
A similar 2.6 s data cycle with a shutter blocking the incident beam is used to correct for the
background light emitted by the plasma and high temperature substrate. This extends a full
data cycle to -5.2 s. Real time display of the (*P, A) spectra, along with data storage and an
intentional time delay, extends the overall repetition time for the (*P, A) spectra. Repetition
times from 10 s, without the intentional time delay, to 70 s, with a 60 s delay, have been
used in this study, depending on the deposition conditions.
Experiments to assess the precision of the ellipsometer system were performed by
repetitive measurements with selected acquisition and repetition modes. Fig. 2.8 shows
(*¥, A) near 2.5 eV measured continuously on a static, opaque Cr surface with (64 ms)/(5
s) and (2.56 s)/(10 s) acquisition/repetition time modes, respectively. The continuous
spectra consisting of -110 Q¥, A) pairs from 1.5 to 4.5 eV were acquired from an average
of 2 optical cycles in the fast mode (64 ms) and 80 optical cycles in the slow mode (2.56
s). The standard deviations in (*F, A) for the fast and slow modes are (0.025°, 0.048°) and
(0.003°, 0.008°), respectively. Thus, under optimum conditions, the precision of
multichannel instrument with parallel acquisition is comparable to that of a single-channel
photomultiplier-tube detector-based instrument, (0.009°, 0.02°). The latter precision
measurement was determined using an average of -200 independent data points at 3.5 eV
collected on a gold sample using an ellipsometer in the rotating-analyzer configuration.
These latter data points were selected from full Q¥, A) spectra collected over the range of
1.5 - 5.0 eV in 0.002 eV steps in -15 minutes. In this measurement the angle of incidence
was 70°, and 50 points per optical cycle were averaged over 164 optical cycles (Heyd,
1993).
36
133.68
1
T—r
133.66
CD
•
33.53
T—i—r
I
33.52
% . •
•
#•
133.64
*
S.D.=0.003294
& 133.62 h
133.60 {oo,
*
O
° %
°o°
C
O Q Oo O
° ° vb. ° J ^ o < ° ° ° ° „ cPno cr
o n °o °
O
133.58 |a ° cT
0o
o
O
±
200
0
Q^°
o<->
w
O
Q0
O -I
o
I
133.56
33.51
^
&
33.50
S.D =0.007932
T3
<
'
-1
I
l_
400
I
I
«
33.49 D"1
33.48
33.47
800
600
(a) TIME (second)
133.8
133.6
33.6
ri—i—i—I—i—r
~i—i—r
. sT . • • •••*•
•
<D
• •% •
*.
33.5
S.D.=0.025472-
<D
&
& 133.4
T3
•S.D.=0.048515
o
33.4
_<«">.,*
o .
133.2 (D& ^o°°J #° ° \°o o_ cb
° °coiP
Oo
. <b°
o°bo <>p
tf
o
0(?
o
«"«
o
o°%°%
o
o
133.0
JJL
_i i_
0
100
200
I
300
«
I
I
I
I
33.3
33.2
400
(b) TIME (second)
Fig. 2.8 Repetitive measurements of the eUipsometric angles at 2.5 eV for a stable, opaque
Cr film, selected from the full spectroscopic data sets. For (a), the multichannel
elhpsometer was used in the slow (2.56 s)/(10 s) acquisition/repetition mode and for (b), in
the fast (64 ms)/(5 s) acquisition/repetition mode. S.D. denotes the standard deviation for
the measurements.
37
DATA SIMULATION AND ANALYSIS
The simplest system that can be studied by ellipsometry is a single ideal interface
between two media (ambient/substrate). In the ideal case of an atomically smooth and clean
specularly reflecting substrate, the complex dielectric function of the substrate can be
deduced from the ellipsometry angles Q¥, A) if the dielectric function of the ambient
medium (ea) and the angle of incidence (9) are known. The following equation is applied in
the ideal two-medium situation:
e = ei + ie2 = ea sin28 [1 + tan20 {(1 - p)/(l + p)}2],
(2.38)
where 0 is measured with respect to the normal to the surface. The right-hand side of this
equation is often applied to experimental data even if it is not clear that the sample is a two
medium system. The left-hand side is then called the pseudo-dielectric function (Burge and
Bennett, 1964), and is written as <e> = <ei> + i<62>. This data representation is even
used for samples known to consist of multiple interfaces. In this case, no physical
information is conveyed directly by <£>.
In the case of a stratified structure which consists of a stack of n parallel layers (see
Fig. 2.9), the reflected beam contains information from each layer within the penetration
depth including the layer thickness and dielectric function. From the dielectric function of
the layer, information on its microstructure and composition can be extracted. An elegant
expression is described in the literature that uses a scattering matrix to analyze multilayered
structures (Azzam and Bashara, 1977) and is given by:
E+
S
=
11 S 12
S
21 S 22
E
n+1
0
38
Medium
Number
Thickness;
Dielectric Function
(0)
0
d ^
3
4
. %/ . '\* % ' \ ' \ > N \ \ \ \ \ \ \ \ \ \ S \ \ N \ N N \
> \ \ \ \ N \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
Ys
2
1
' - ^ * l£
(2)
.(2)
d 2 ; «P>
e \ + ie 2
d3; P
z\
.0)
(3)
+ ie 2
. (4)
(4)
d 4 ;^ 4)
e\ + ie2
dj ; .P
£j
3
(j)
+ I6 2
e<n) + ie< n)
n
n+1
(1)
^ D
=
^ U
+ te
0»i>
Fig. 2.9 General n-medium structure used in the analysis of ellipsometric data on
multilayered samples. The index j ranges from 0 to n+1 for the media (including the
ambient medium and substrate), and from 1 to n for the layers. The complex dielectric
function and thickness for the jth layer are designated as e(i) (0<j<n+l) and dj (l<j<n),
respectively.
39
where the "+" and "-" signs represent forward and backward traveling waves. The
scattering matrix S for an n-layer stack on a semi-infinite substrate is expressed as a
succession of products of matrices I and L which describe the characteristics of the
interfaces and layers, respectively:
S = IoiLiIi2L2#"Ij j+iLj+i"»In-l n Lnln „+!•
(2.40)
Here Lj is the matrix for the jth layer and Ij j+i is the matrix for the interface between the
jth and (j+l)st layers. These matrices are given by
I
1
jj+i =
l
1
r
JJ+l
(2.41)
r
jj+l jj+l *
and
Lj
=
e1(Pi 0
0 e4(pJ
(2.42)
where n : + i and t; j + j are the Fresnel coefficients for reflection and transmission, and (p: is
the phase shift incurred by the beam in traveling through the jth layer (Azzam and Bashara,
1977). These quantities are expressed by:
r
N j+jcos9 j-N jCos9 L,. j
j J+1P Nj^cosSj 4-NjCosej^.!'
=
(2.43a)
NjCos9: -Nu jcos9 ^ j
r
=
JJ+U NjCos8j+Nj+1cos9j+1'
(2.43b)
40
2NjCos8j
J
*..
J
(2 43c)
l
JJ+lp N^cosej+Njcosej^'
t .. + l s
JJ
2NiCos6:
J
J
NjCOsej+Nj+jcose^j'
(2 43d)
and
2jtdjN:COs9j
<Pj = — J - i
1.
(2.44)
In Eqs. (2.43) and (2.44), d; and Nj=,Vij" are the thickness and complex refractive index
of the jth layer, and 9; is the incidence angle at the (j, j+1) interface, and A is the
wavelength. The incidence angle 6; can be obtained from successive application of Snell's
law:
NQ sin 9Q = Nj sin9i = ^2 sin 92 = ••• = N n + 1 sin9 n+1 .
(2.45)
as long as the incidence angle in the ambient (0th medium) and the complex refractive
index, Nj (j=0~n+l), of each medium are known.
A calculation of the matrix product in Eq. (2.40) for s and p polarizations leads to
the scattering matrix elements for s and p polarizations. From these latter elements, we
obtain the two ellipsometric angles OF, A) according to:
p = tan*F • eiA = * 5 £ J***n-P,
r
0n,s S 21,s»ll,s
(2.46)
41
E
where r0 .=—- (j=P> s )- Here El and EQ are the forward and backward moving waves
in the ambient medium, respectively.
BRUGGEMAN EFFECTIVE MEDIUM APPROXIMATION (EMA)
The diamond films grown by CVD in this thesis study have nondiamond
components, typically voids and sp2-bonded carbon inclusions. In order to model the
dielectric function of a composite film consisting of two or more different components, the
well-known Bruggeman effective medium approximation (EMA) is used extensively in
ellipsometry data analysis (Aspnes et al., 1979; Aspnes, 1981; Niklasson et al., 1981;
Aspnes, 1982)
The effective complex dielectric function, eeff, of a composite layer consisting of a
random mixture of components (i.e., an aggregate microstructure) can be calculated by the
EMA from the complex dielectric functions, £i, and volume fractions, fj, of the
components. The Bruggeman EMA for an M-component composite can be expressed as:
M
£
£.
^ 7 ^ = ° '
e
i=1
eff
+2£
(2.47)
i
M
where 2fj=l.
i=l
Therefore, the effective complex dielectric functions of a composite layer consisting of two,
randomly-mixed component materials, whose dielectric functions are e a and eb can be
calculated from Eq. (2.47) according to:
42
£eff =
4+ Ns /^ 2 +8 £a e b
—^
,
(2.48a)
where
1 ^ (3fa - l)ea + (3fb - l)£b.
(2.48b)
In these equations, fa and fb are volume fractions of materials in the composite layer having
dielectric functions ea and eb, respectively, and fa+fb=l. Figure 2.10 shows the effective
complex dielectric function of a composite material consisting of diamond (completely sp3bonded crystalline carbon) and glassy carbon (completely sp2-bonded disordered carbon)
which is calculated from Eq. (2.48a). With increased glassy carbon volume fraction, the
effective complex dielectric function is changed in accordance with Eq. (2.48).
For the case of a composite layer consisting of three randomly-mixed component
materials (for example, diamond, glassy carbon, and void), eeff(fa, fb» fc. £a> £b> £c) is
more complicated. Here fa, fb, and fc are the volume fractions of materials in the composite
layer having dielectric functions £a, £b, and ec, respectively, and fa+fb+fc=l. When Eq.
(2.47) is solved for 3-component composite layer, Eeff will be:
X Y X . y3 X
eff = y ~ 2 ~ J + ! 4 Y '
e
._ .n .
(2-49a)
where
2
X=-£- +^,
(2.49b)
43
8.0
I • I ' I ' I • I • I • I • I
7.0 -
CO
. 20%
5.0 -
• • I • I I I - 1 I I ' I I I - I ••
1.5
1.0 -
^.-
20%
CO
-
0.5
„ — ~ — • 10%
5%
0%
0.0
•
I
i
. I . I . I . I . I . I
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
PHOTON ENERGY (eV)
Fig. 2.10 Real (top) and imaginary (bottom) parts of the effective complex dielectric
function of a composite material consisting of the randomly-mixed diamond and glassy
carbon.
44
% = 2(ea + e b + ec) - 3(fa£a + fbeb + fcec),
(2.49c)
v = - 2(eaeb + e b e c + eaec) + 6(faebec + fbeaec + f c e a £ b ),
(2.49d)
and
Y = 2e a e b e c +
X3 + ( 2 e a e b £ c - | 7 + ^ )
- ^ + XV
27 6
(2.49e)
In using the Bruggeman EMA, it is generally assumed that the microstructural
size of each component is large enough to exhibit bulk-like dielectric properties, but not too
large as to approach the wavelength of the probing beam and cause light scattering
(Aspnes, 1981). Within these limits, the EMA is used not only for bulk composite layers,
but also for surface and interfacial roughness layers. In this latter application, the
roughness layers are simulated by a -0.50/0.50 volume fraction mixture of the overlying
and underlying media. Such an approach must be justified based on correlations between
roughness layer thicknesses obtained by ellipsometry and by another more direct technique
such as atomic force microscopy (AFM).
The rough surface of diamond can be modeled as single layer (with sharp
interfaces on both sides) having an effective complex dielectric function calculated from the
Bruggeman EMA as a mixture of the overlying material (void) and the underlying material
(diamond, glassy or sp2 C, and void). In the analysis of the real time measurements
obtained during diamond film growth, the diamond and glassy carbon dielectric functions
characteristic of the sample temperature must be used. In this study, however it is possible
to neglect the small sp2 C component in the roughness layer and simply use a fixed
45
0.50/0.50 volume fraction mixture of diamond and void in order to simulate the optical
properties of the roughness layer. With this model, resonable agreement between AFM and
spectroscopic ellipsometry deduced roughness thicknesses are obtained as indicated in
Table 2.1. In this table, AFM-deduced root-mean-square (rms) roughness calculated from
the full 10x10 |im images are provided along with roughness layer thicknesses and 95%
confidence limits deduced using spectroscopic ellipsometry. The second column shows the
results obtained from real time data collected at a substrate temperature of 785 °C, and the
third column shows the results on the same samples obtained from ex situ measurement
after deposition using a rotating analyzer ellipsometer.
One might also consider the need to incorporate into the optical model the
roughness at the (diamond film)/(substrate) interface. In fact, AFM measurements suggest
that between larger scratches (typically 2000 A wide and 20 A deep), the seeded substrates
are relatively smooth. The rms roughness value between larger scratches is found to be -12
A. It is expected that these larger scratches do not contribute since they scatter light out of
the specular beam. Our measurements are not sensitive to the resulting irradiance loss as
long as it is not polarization-dependent. Thus, for the substrate seeded with diamond
powder, the pseudo-dielectric function at the deposition temperature is used. This can be
obtained from the real time (*¥, A) spectra and calculated using Eq. (2.38). In doing this,
we are essentially neglecting the roughness at the interface at the film/substrate interface.
Thus, the optical model for the final diamond film is shown in Fig. 2.11 along with a
schematic of the physical structure.
LEAST-SQUARES REGRESSION ANALYSIS
Ellipsometry is not a direct technique and the optical properties and/or
structural parameters of the sample under study cannot be determined from the (*F, A)
46
Table 2.1
Root-mean-square (rms) roughness determined from 10x10 (Xm atomic force microscopy
(AFM) images along with the roughness layer thicknesses and 95% confidence limits
deduced using spectroscopic ellipsometry (SE). This comparison shows that independent
measurements of roughness using different ellipsometric techniques are in good agreement
and provide values for the roughness layer thicknesses on diamond thin films that are close
to the rms values. The quantities XQE, XH/Z, and Xo/z in the first column characterize the
gas mixtures used in the deposition and are calculated from the atomic gas flows as
[C]/{[C]+[0]}, [H]/{[H]+[C]}, and [0]/{[0]+[H]}, respectively. Other deposition
parameters include a substrate temperature of 785 °C, a plasma power of 500 W, and a total
pressure of 7 Torr. The film thicknesses shown in the first column are the results from the
ex situ SE measurements.
Preparation and
ex situ
realtime
ex situ
film thickness (A)
AFM (rms) (A)
SE(A)
SE(A)
124
124±18
121+10
107
128±13
93±13
116
117+17
119+11
(Xc/s, XH/Z, XO/S)=
(1, 0.995, 0)
2154+33
(Xc/2, XH/S, XO/Z)=
(1, 0.995, 0)
810+20
(Xc/2, XH/2, XO/Z)=
(0.2, 0.97, 0.1)
2130±36
47
(a)
Cf
df
Ef
df
(b)
Fig. 2.11 (a) The assumed physical structure and (b) the corresponding optical model for a
sample consisting of a surface roughness layer and bulk layer. In this application the
pseudo-dielectric function is used for the substrate, i.e., esub=<£Sub>> a n d the surface
roughness is simulated by a mixture of diamond/void with 0.50/0.50 volume fraction, dj
(j=s, f) and 6j (j=a, s, f, sub) denote the thicknesses and the dielectric functions of each
layer, respectively.
48
spectra without some form of mathematical analysis. The one exception is in the case of a
sample consisting of a bulk single material with atomically smooth, abrupt interface to the
ambient. In this ideal case the optical properties of the bulk material can be determined
directly from {*F(hv), A(hv)} [see Eq.(2.38)]. For multilayer systems, however, {¥(hv),
A(hv)} depends not only on a number of photon energy-independent parameters, including
the thickness of each constituent layer and the volume fractions for any of the media that
can be modeled as a composite of two or more materials, but also on the energy-dependent
optical properties.
The ultimate goal of the least-squares regression analysis (LRA) is to minimize the
unbiased estimator of the mean square deviation a by adjusting the structural parameters, c
is defined as
'/2
N
a=
^N-p-1
X
tan ^ca,(hVi) - tan ¥exp(hVj)
cosAca,(hVi)-cosAexp(hVi)
i= l
(2.50)
where N is the number of data points over the spectral range and p is the number of
unknown independent parameters. Superscripts 'cal' and 'exp' represent the calculated and
experimental Q¥, A) spectra.
In performing least-squares regression analysis, the dielectric functions of all
components of the sample structure are assumed to be known. LRA is initiated by
assuming with a physically acceptable model that matches our expectations considering the
sample history. The sample structure to be assumed could include the material components,
the number of media, and the number of components for each medium. Then, initial
guesses are made for all photon energy-independent free parameters. The complex
dielectric functions of any bulk composite layers, interfacial roughness layers, and/or
surface roughness layers are determined via the Bruggeman EMA from the known
49
dielectric functions of each component and the guessed volume fractions. From the
complex dielectric functions of the layers, their thicknesses, and the angle of incidence, the
{*Pcal(hVi), Acal(hvi), i=l,...,N} spectra can be calculated for comparison with the
corresponding experimental spectra. In fact, rather than randomly guessing the photon
energy-independent parameters, we apply a grid search in p-dimensional space in an
attempt to confine the initial guesses within a smaller region of parameter space near the
global minimum in a. Adjustments are made to the initial guesses using the least-squares
regression analysis approach in an attempt to obtain an overall global minimum in a for the
chosen physically-acceptable model. This minimum in a is used to quantify the quality of
the final fit of the calculated spectra to the experimental results according to Eq. (2.50), and
its value becomes a criterion to assess the validity of the initial physically-acceptable model
chosen. The most appropriate model exhibits the lowest a.
For real time data analysis, we apply LRA successively to each pair of SE spectra
collected as a function of time. We generally assume that the thicknesses of each layer and
the volume fractions of each component are time dependent. In addition, it is possible that
the structural model required to fit the data changes over time as the film grows. For
example, the single layer that forms during thin film nucleation may develop into a twolayered structure after coalescence. The latter structure consists of a surface roughness layer
on top of the bulk film as in Fig. 2.11. In our modeling, it is assumed that the intrinsic
dielectric function of each component is not changed with time, for example due to particle
size effects.
50
CHAPTER 3
CHARACTERIZATION OF SUBSTRATE TEMPERATURE IN
DIAMOND GROWTH PLASMAS
3.1. Introduction
As the applications of diamond thin films prepared by plasma chemical vapor
deposition (CVD) techniques become more demanding, improved fine-tuning and control
of the process are required. The important parameters in diamond film deposition include
the substrate temperature, CH4/H2 gas flow ratio, total gas pressure, and gas excitation
power. Among these parameters, the temperature is the most difficult to determine and
control over the required range (typically 400-1000 °C). The origin of this problem is the
extreme environment associated with diamond film deposition. This includes not only the
high substrate temperature, but also the high power flux at the substrate surface due to the
impinging particles and the radiation used for gas excitation.
Because of the difficulty of establishing suitable contact between a thermocouple
and the substrate in the diamond growth environment, the substrate temperature is
sometimes inferred from the temperature of a nearby fixture in the reactor, such as the
substrate holder. The problems with such a method are clear when excitation source heating
and/or radiative cooling are substantial. Because of such problems, infrared pyrometry is
used more widely for substrate temperature determination in diamond growth
environments. However, most pyrometers obtain the temperature from an absolute
irradiance measurement. Thus, complications can arise due to the optical losses that may
51
occur upon transmission through the reactor window (e.g., from absorption by graphitic
carbon deposits), or due to errors in the assumed emissivity of the surface. In general, in
order to achieve accuracy, frequent calibration of the pyrometer may be necessary. Here,
spectroscopic ellipsometry is used to determine the true substrate temperature under
diamond growth conditions through the temperature dependence of the optical properties of
the substrate. Thus, it is shown that spectroscopic ellipsometry can determine not only
material parameters of interest, such as the thickness and composition of films on the
substrate, but also the substrate temperature.
In this thesis research, extensive capabilities have beer* developed which were
specifically designed for monitoring the diamond growth process. In this and the following
chapters of the thesis, we will describe the unique capabilities of multichannel real time
spectroscopic ellipsometry (SE) for providing materials parameters of general interest in
microwave plasma CVD diamond deposition. In the present chapter, we will provide a
detailed discussion of the substrate temperature measurement capability in view of its
importance in diamond deposition. In Chapter 4, the parameters of interest to be discussed
include the evolution of the bulk and surface roughness layer thicknesses, void and sp2 C
volume fractions, and diamond mass thickness, as well as an approximate nucleation
density. Although microwave plasma-enhanced CVD (MPECVD) methods are utilized
here, the experimental approach discussed in detail is also applicable to the other deposition
methods such as filament-assisted CVD.
In the studies in this and the following chapters, the ellipsometer is mounted around
the microwave plasma-enhanced CVD reactor used for diamond film growth. For this
ellipsometer, optical fibers are incorporated into the input and output optical system. The
input fiber is believed to reduce the small source polarization effect which would otherwise
lead to optical errors. In Chapter 2 it was shown that any residual source polarization can
52
also be corrected in the rotating-polarizer multichannel ellipsometer calibration and datareduction procedures.
3.2. Experimental Apparatus and Procedure
In this research, an ASTeX (Applied Science and Technology, Inc., Woburn, MA
01801) 2.45 GHz microwave plasma-enhanced CVD reactor system was employed, having
a vessel constructed from stainless steel. With such a deposition system, highly-uniform,
fine-grained, nanocrystalline films can be prepared as described in the literature
(Windischmann et al., 1991; Hong et al., 1994). A simplified schematic of the reactor
system and associated real time spectroscopic ellipsometer is shown in Fig. 3.1. Ports on
the reactor vessel are oriented to permit SE measurements. Stress-free windows are
employed for optical access, and the windows are mounted on bellows, allowing them to
be aligned so that the incident and reflected beams are transmitted normal to the window
surface. The reactor system has double walls and is water cooled. The chamber is
evacuated by a mechanical pump [Alcatel: 16 cubic feet per minute (cfm); motor: 3/4HP,
Franklin Electric]. A throttle valve (Model No. 253, MKS) is used in conjunction with an
exhaust valve controller (Model No. 252, MKS) to maintain a constant pressure in the
vacuum chamber. The pressure is measured using a high accuracy pressure transducer
(Model No. 390, MKS). A schematic diagram of the plasma-enhanced CVD system is
shown in Fig. 3.2. The plasma is generated by a 1 KW power supply (S-1500i Microwave
Power Generator, ASTeX) which drives a 2.45 GHz magnetron, coupled via a circulator
(Model CS2, ASTeX) to a rectangular waveguide. The microwave energy is confined in
the waveguide and propagates along its length. The reflected power is reduced by
controlling the tuners (B in Fig. 3.1) which move the antennas in or out in order to match
the generator and load impedance to the characteristic impedance of the waveguide so that
53
B
MICROWAVE
POWER
"
GAS in
V>»»}i»»»}}»}}mW}>})>}}))))))»»jp,
^•.i".-»
mm .
lllllllllllllll
To PUMP
T
Z TRANSLATION
DETECTOR
CONTROLLER
a
b
c
d
e
f
g
h
i .
Xe source
input fiber optic system
shutter
rotating polarizer
strain-free windows
stepping motor-controlled analyzer
outputfiberoptic system
grating spectrograph
multichannel detector
A: waveguide
B : tuner and antenna
C: plasma
D: substrate
E: graphite sample stage
F : r.f. substrate heater
Fig. 3.1 Deposition system and multichannel spectroscopic ellipsometer employed to
monitor microwave plasma-enhanced CVD of nanocrystalline diamond thin films in real
time.
heater control (ASTeX)
tuner/antenna
microwave power head
microwave guide
Model No. 270B
signal
conditioner
(MKS)
plasma coupler
Model No. 274
3-ch selector
(MKS)
Model No. 252A
exhaust valve
controller
(MKS)
microwave
power supply
RF heater
power supply
motor drive for changing substrate position
mechanical pump
| Q massflowcontroller (MKS)
BARATRON (Model No. 390, MKS)
tX
diaphram valve (DL series, Nupro)
Fig. 3.2 ASTeX microwave plasma-enhanced chemical vapor deposition system. The exhaust valve
controller controls a throttle valve to maintain a constant pressure in the vacuum chamber. A 3-ch
selector is used to select one of 3 pressure transducer channels for display. The selection can be done
manually with a front panel switch or remotely. The signal conditioner has a display to provide for a
front panel display in various pressure units.
55
the maximum power is delivered to the plasma.
In-vacuum sample alignment capability in the z-direction in Fig. 3.1 is provided by
substrate platform translation. Angle of incidence is controlled using a wing-base
goniometer that supports both optical rails. The angle of incidence calibration is performed
by measuring the standard samples as described in the previous chapter. Tilt alignment is
controlled by adjusting the ellipsometer position. This adjustment is assisted by four
screws, two located at each leg of ellipsometer and two located at the rear of the
ellipsometer on each side of the central axis. These alignment screws were custom-made in
order to achieve a more precise alignment capability (See Fig. 2.3).
Untreated Si wafer substrates are used for substrate temperature calibration.
Substrates are mounted onto the graphite substrate platform which is rf heated to a
temperature that can be controlled independently of the microwave power over a relatively
wide range (IPX series induction-heating power supply, Advanced Energy). With the
system well-aligned and calibrated as explained in the last chapter, several ellipsometry
spectra are measured. After pumping the chamber to a base pressure of 1.1 Torr, the
alignment is rechecked and additional spectra are measured. Then the desired pressure and
heater temperature are set on the respective controllers, and no further action is undertaken
until the desired conditions stabilize. After a series of spectra are measured in this stable
state, the substrate and its platform are raised ~2 cm above the optical plane and the plasma
is ignited with pure H2 in order to achieve a stable plasma configuration. This plasma
ignition approach is employed for both temperature calibration and diamond growth, the
latter described in Chapter 4. Because of the present limitations in viewing angle, H2
plasma ignition can not be observed directly by real time SE. After plasma ignition, the
substrate platform is lowered to the optical plane while the plasma is stabilized by tuning
the microwave power. Next, the optical alignment is rechecked. Finally, SE data
acquisition is initiated. For Si substrate temperature determination, as well as for diamond
56
growth, the waveform spectra from 80 optical cycles were averaged, leading to an
acquisition time of 2.56 s for a single pair of (*P, A) spectra. A similar 2.56 s data cycle
with a shutter blocking the incident beam was employed to correct for the thermal and
plasma radiation background. The repetition time between spectra was 10 s.
3.3. Experimental Methods and Data Interpretation
The well defined features in the c-Si substrate optical functions near 3.38 eV at 25
°C have been utilized to calibrate the substrate temperature under pure H2 gas plasma
conditions. The only difference in the calibration plasma conditionsfromthose of diamond
growth is the absence of the low CH4 flow (typically - 1 % of the H2 flow). In this
calibration, two distinct facts are relevant. (1) The sharp features in the c-Si optical
functions are present only in the optical response of unseeded c-Si and (2) diamond does
not grow on unseeded c-Si in the calibration plasma environment. When seeded according
to the procedure described in Chapter 4, the sharp features are completely broadened out
but are only partially regained upon annealing above 500 °C. The dielectric functions of
unseeded and seeded c-Si processed and measured at 25 °C are shown in Fig. 3.3. Also
shown for reference in Fig. 3.3 is the 25 °C dielectric function of c-Si which was first
seeded and then annealed to the diamond deposition temperature of 785 °C.
The 3.38 eV features in the dielectric function of the c-Si substrate arise
predominantly from the Ei transitions along the A directions in the Si band structure
(Aspnes and Studna, 1983; Lautenschlager et al., 1986). The energy position Ec for these
transitions has been found to decrease linearly with temperature for 80<T<550 °C
according to the equation (Lautenschlager et al., 1986)
Ec (eV) = 3.375 - 4.07 x 10"4T(oC).
(3.1)
57
T—«—i—'—i—«—r
CO
V
—o—
c-Si(s,,8 2 )
—°— seeded c-Si
-20 - —*— seeded and annealed c-Si
• 1 • I I I I I ' I I I '
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
PHOTON ENERGY (eV)
Fig. 3.3 Real (<ei>) and imaginary (<62>) parts of the room temperature pseudo-dielectric
functions measured by ex situ spectroscopic ellipsometry for three separate c-Si substrates,
which were (1) unseeded, (2) seeded, and (3) seeded and annealed at the diamond
deposition temperature of 785 °C.
58
This behavior is shown qualitatively in the temperature calibration experiment of Fig. 3.4.
Using this equation, the true substrate temperature (Teujps) can be found once Ec is
determined. Here, we assume that this linear behavior extends to higher temperatures as
well. Such behavior would be in accordance with the Bose-Einstein statistical factor, which
describes the change in energy gap with T. A best fit to this factor for the Ei transitions
below 350 K yields an average phonon frequency corresponding to 245 K (Lautenschlager
et al., 1987).
From the dielectric function near the Ei feature at the true temperature of 900°C, an
absorption coefficient of 4.5xl05 cm-1 is obtained. Thus, the penetration depth of the light
is 220 A, and this is the region of the substrate from which the temperature is obtained. As
a result, the temperature obtained by SE is a true characteristic of the surface.
To perform the calibration, the unseeded c-Si is placed on the substrate holder and
the H2 plasma conditions are set as described above. Then, the temperature is increased to
the maximum accessible nominal value as indicated by a thermocouple embedded in the
substrate holder and the Si wafer is allowed to equilibrate for SE measurement. After
measurement, the thermocouple temperature is reduced to another value and the
measurement is repeated. In all, spectra are collected at six to eight nominal substrate
temperatures.
After terminating the plasma and cooling the sample to 25°C, a final measurement is
made. Because the dielectric function of c-Si is well-known at 25°C (Aspnes and Studna,
1983), least-squares regression analysis of the data from the final measurement allows us
to assess the possible existence of a transparent layer on the c-Si after the heating cycle. If
the dielectric function of the transparent layer was assumed to be that of Si02 and
temperature independent, then thicknesses of ~20-30 A were deduced in a number of
different heating cycles. We have found that to a good approximation (±4 A), this layer
exists at the highest temperature and is stable for successive measurements. For this
59
2
20 -
1.5
2.0
2.5
3.0
3.5
4.0
PHOTON ENERGY (eV)
Fig. 3.4 Real (ei) and imaginary (£2) parts of the dielectric functions of c-Si measured at
different temperatures by real time spectroscopic ellipsometry.
60
reason, the measurements for calibration are performed from high to low temperature.
Measurements from low to high temperature would lead to a change in the thickness of the
transparent layer with successive measurements.
Previous studies of the microwave plasma CVD process have suggested that the
layer that forms at high temperature under H2 plasma exposure is not SiC>2, but rather a
low-density form of SiC (Collins et al., 1989). This layer can form on the substrate, even
in the absence of CH4, due to chemical vapor transport of C from the graphite substrate
platform to the Si surface. Thus, it was proposed that the graphite substrate holder was
etched by the H2 plasma generating hydrocarbon species such as C2H2 and CH3 which can
be reincorporated at the substrate surface. However, the microwave plasma CVD system
used in the previous experiments was of the bell jar type (ASTeX). In this type of system,
the substrate and its holder are immersed within the plasma so that extensive etching of the
graphite holder occurs, making possible the transport of C from the graphite holder. The
deposition system used in the present study is not of the bell jar type but rather is
constructed from a vertically-erected stainless steel can as shown in Fig. 3.1. In this latter
configuration, the plasma does not make contact to the sample surface, and is thus a
'remote plasma'.
In this remote plasma case, we sought to determine the nature of the 20-30 A
overlying layer that forms in the pure H2 plasma. For this experiment, we used an ex-situ
ellipsometer in the rotating analyzer configuration. First an unseeded c-Si wafer was
measured with the ex-situ ellipsometer. Then the c-Si was placed in the deposition system
in order to expose it to the H2 plasma for 30 mins. The substrate was heated at 785 °C, the
plasma power was 500 W, and the hydrogen flow rate was 99 seem. After the exposure,
the sample was cooled to room temperature and immediately measured with the ex-situ
ellipsometer again without changing the alignment or the calibration parameters. This
second measurement revealed a 29 A thick overlying layer on the sample surface (assuming
61
optical properties identical to SiC>2). In fact, however, three possibilities for this layer: (1)
diamond, (2) SiC<2, or (3) SiC. The first case is highly unlikely because the sample was not
seeded and experience has shown that diamond will not grow on such a surface even in a
CH4+H2 plasma environment. In order to check the remaining possibilities of Si02 or SiC,
the sample was etched with HF (HF: deionized water=l:3) for 2 mins. If the overlying
layer is SiC, it will not be etched in the HF solution, but if it is SiC«2, the layer will be
etched away. After the etching process, the sample was remeasured with the ellipsometer,
and it was observed that the overlying layer was removed. This experiment shows that the
overlying layer was a SiC<2 (~29 A), and the validity of the previous application of the SiC>2
dielectric function in simulating the transparent layer on c-Si in the calibration experiment
was verified.
With estimates of the transparent layer thickness for all measurements, the true
dielectric function of the underlying c-Si can be extracted by a mathematical inversion
routine utilizing Newton's method (Oldham, 1969). In order to extract the temperature
from the resulting dielectric function, a critical point analysis of the Ei transitions is
performed. This involves taking the second derivatives of the dielectric function with
respect to photon energy and fitting the results for the real and imaginary parts assuming an
excitonic lineshape (Lautenschlager et al., 1987), i.e.,
^ = 2Ae i *[(E-E c+ iiy 3 ].
dE 2
(3.2)
where A, Ec, T and <E> are the amplitude, transition energy, broadening parameter and phase
factor, respectively.
Typical experimental data for a critical point analysis are shown in Fig. 3.5, along
with the best fit parameters. In this case, the nominal substrate temperature readings of the
62
200
Experiment
Best Fit
100
CN
0
co
CO
CN
CO
-100
-200
+
200
A =4.23 eV
0=-63.13°
E =3.002 eV
r =0.396 eV
100 -
CN
-. • • _
CN
0 -
CO
CN
CO
^o
-100 -
-200
2.5
3.0
3.5
4.0
PHOTON ENERGY (eV)
Fig. 3.5 Critical point analysis used to determine the amplitude, transition energy, phase
factor, and broadening parameter from the Ei transitions in single crystal Si substrate.
63
thermocouple and pyrometer were 900 and 930 °C, respectively, and the plasma power
was set at 1000 W, using a 100 standard cm3/min (seem) flow of pure H2 at a pressure of
20 Torr. From the best-fit value of Ec=3.002 eV, a true surface temperature of 916 °C is
calculated. Figure 3.6 shows a compilation of results, in which the temperature error, i.e.,
the difference between the true temperature determined by SE (TeiiipS) and the indicator
temperature (Tjndic) is plotted vs. the true temperature under four sets of conditions ranging
from no plasma to a 1000 W plasma. In all cases, a 100 seem flow of pure H2 is used. For
the open points, the indicator temperature is from the thermocouple embedded in the
substrate platform. For the solid points at the highest temperatures, corresponding to 1000
W, the indicator temperature is from pyrometry which has a limited range of operation.
The results in Fig. 3.6 show clear trends with an average precision of ~±4 °C. In
the absence of a plasma at 1 Torr pressure, the thermocouple reads too high by values
ranging from 30 °C to 140 °C for 200 °C<Teiiips<750 °C. These errors are due to poor
thermal contact, since the substrate is simply resting on the platform, and also to radiative
losses. For a plasma power of 1000 W, the thermocouple reads too low by values ranging
from 100 °C to 15 °C for 350 °C<Teiiips<900 °C. These errors are attributed to the power
input to the surface from the plasma. Additional results in Fig. 3.6 indicate the important
effect of gas pressure on the temperature. That is, a higher pressure plasma (20 Torr) at
400 W is more effective at coupling energy into the substrate surface than a lower pressure
plasma (7 Torr) at 500 W. The solid points in Fig. 3.6 indicate that pyrometry
overestimates the true temperature by 15 - 30 °C.
The results of Fig. 3.6 show the possible influence that parameters such as power
and pressure may exert on the ultimate properties of diamond, not only directly, through
changes in plasma conditions, but also indirectly, through changes in surface temperature
and possibly through electron bombardment. From the limited data available in Fig. 3.6,
one can conclude that a pyrometer is effective in tracking such changes, at least within
64
120
80
U
o
40
a
0
CO
13
•0---.Q
.o
-40
-80 -
•120 -
Pyrometer
Indicator
20 Torr
1000 W
Thermocouple
Indicator
— e — 20 Torr
- -*— 7 Torr
- - 0 - - l Tonx
200
X
400
600
ellips
800
1000
(°C)
Fig. 3.6 The difference between the true temperature obtained by ellipsometry, TeiiipS, and
that obtained by other methods, Tjndic, including a thermocouple embedded within the
substrate holder (lines and open points) and a pyrometer (filled points).
65
errors of 15-30 °C. However, pyrometers have a limited range of operation, and plasma
heating effects are of great interest in any attempts to deposit diamond on low temperature
substrates.
Further information can be extracted from Fig. 3.7 which shows the broadening
parameter T obtained from a critical point analysis of the c-Si substrate as a function of the
true surface temperature. Results under four different conditions of Fig. 3.6 are combined
in a single plot. This parameter is a sensitive function of defects that may be present within
the penetration depth of the light, 220 A. The fact that the variation in the broadening
parameter for the 1000 W plasma exposure is identical to that obtained in the absence of the
plasma, indicates negligible plasma-generated damage (at least within our sensitivity limits)
within the c-Si substrate at equilibrium. Thus, if incident plasma species do interact more
than 30 A below surface (i.e. beneath the overlayer on the surface), then the resulting
defects anneal at a faster rate than they are created. The broadening parameters vs.
temperature for all conditions are fitted to the following parabolic equation.
T(T) = a + bT + cT2
(3.3)
Here a = 0.1443 eV, b = 1.553xl(H eV/"C, and c = 1.262x10-? eV/CC)2. The
temperature T has units of [°C] and the broadening parameter T has units of [eV]. These
fitting parameters can be compared to those in the literature obtained for 77<T<547 °C in
which a = 0.1030 eV, b = -1.830x 10"9 eV/°C, and c = 3.352x 10"12 eV/(°C)2
(Lautenschlager et al., 1987). The origin of the difference between our results and those in
the literature are unclear at present.
66
i
•
i
i
i
1000W, 20 Torr
500W, 7 Torr
400W, 20 Torr
OW, ITorr
•
i
1
0.4 -
i -
• < • o
'
1
i
0.5
>
1
i
0.3 -
•
i
0.2
•
I
0.1
200
400
.
I
.
600
ellips
800
1000
(°c)
Fig. 3.7 The broadening parameter T, associated with Ei transitions in Si as a function of
the true surface temperature of the substrate as determined from analyses similar to that of
Fig. 3.5. A result (dashed line) from the literature is included for comparison with that of
the present work (solid line).
67
3.4. Application to Diamond Film Growth
As an application of accurate substrate surface temperature calibration, the growth
rate of diamond has been determined as a function of temperature under a set of standard
deposition conditions. For this experiment, the substrates were seeded with diamond
powder, and the total gas pressure, microwave power, and [CH4]:{[CH4]+[H2]} gas flow
ratio were 7 Torr, 500 W, and 1:100 (in seem), respectively. The calibration run used for
the determination of the surface temperature from the thermocouple reading for this
experiment appears in Fig. 3.6 as the long-dashed line.
Figure 3.8 shows the microstructural evolution during MPECVD diamond film
growth from an analysis of real time SE data collected during the growth process as the
temperature was decreased in a stepwise fashion. The models and results of the real time
SE data analysis will be discussed in detail in Chapter 4. Here the results are used to
determine the diamond volume fraction in each of the two layers of the structure
(roughness/bulk). From the diamond volume fractions and the two layer thicknesses, the
diamond mass thickness at each different temperature can be calculated. This approach
excludes the non-diamond carbon and void components of the film.
In the experiment, five sequential depositions were performed on the same substrate
at nominal temperatures as read by the thermocouple, ranging from 500 °C to 900 °C. The
deposition at 900 °C was performed first and was allowed to nucleate and coalesce,
reaching a total physical thickness (bulk plus surface roughness) of ~ 1100 A before
determining the growth rate from an additional ~200 A of bulk layer deposition. Then, the
substrate temperature was lowered to the next nominal value of 800 °C, and the diamond
film was grown at this temperature using the previously deposited film as the substrate.
This sequence was continued until a deposition at 500 °C was completed.
The change in diamond mass thickness versus time and the deposition rate versus
68
1.0
O
o
o
o
o
0.8
oo
0.6
f =0.50
v,s "•-'"
<*-r
0.4
0.2
^.b
ooooocoocooocjaBiii] iiimiiiliajtoajjjjj)!,
ccccDccmrcooo
0.0
I
• 1 '
f—r-
'
I
•
0.4
0.3
, &
0.2
sp2,b
0.1
''"""'IDlfflTt'|occcccccarccco
0.0
'
i — ' — i — •
I
'
2000
1600
°<
^
1200
800 400 0
0
20
40
60
80
100
120
TIME (min)
Fig. 3.8 The microstructural evolution, deduced by real time spectroscopic ellipsometry
and plotted vs. time, for a sequence of five depositions performed on the same Si substrate
at different temperatures. The temperature values indicated here are characteristic of the film
surface and have been determined by the calibration of Fig. 3.6. dj are the bulk (j=b) and
surface roughness (j=s)2 layer thicknesses. In addition, fsp2,b, fsp2,s. fv.b. and fv>s are the
volume fractions of sp C (sp2) and void (v) in the bulk (b) and surface roughness (s)
layers.
69
the reciprocal of the true substrate temperature from the calibration run are presented in
Figs. 3.9 and 3.10, respectively. The growth rates in Fig. 3.10 were calculated as the
slopes of the observed linear variations in the diamond mass thickness, dmass, shown in
Fig. 3.9. The diamond mass thickness dmaSs is defined as the volume of diamond per unit
area, and is determined in the two-layer [(surface roughness)/bulk] least-squares regression
analysis of the real time SE data shown in Fig. 3.8. dmass is given by
dmass = fd.bdb + fd,sds,
(3.4)
where db and ds are the bulk (b) and the surface (s) roughness layer thicknesses, and
fd,b=l-fsp2,b-fv,b and fd,s=l-fsp2,s-fv,s are the volume fractions of diamond in the two
layers of bulk (b) and surface (s) roughness.
The growth rate in Fig. 3.9 exhibits a maximum near about TeiiipS=785 °C, a
qualitative feature that has been observed by other researchers (Spitsyn and Bouilov, 1988;
Zhu et al., 1989a; Kondoh et al., 1991; Kweon et al., 1991; Gicquel et al., 1993). This
behavior has been attributed to a competition between growth and etching (Spitsyn and
Bouilov, 1988) or to a competition between adsorption and desorption of the precursors
(Zhu et al., 1989a), such that diamond phase etching (relative to graphite) or precursor
desorption is enhanced at higher temperatures. The maximum possible activation energy for
diamond growth over the temperature range from TeiiipS=534 to 695 °C in Fig. 3.10,
obtained from the slope at the lower temperatures, is ~9 kcal/mole. This is a factor of 2-4
smaller than the values reported by other workers for diamond growth on non-diamond
substrates by various methods (Kondoh et al., 1991). The latter values range from 20 to 30
kcal/mol. Our results, however, fall between the activation energies for homoepitaxial
growth of diamond by filament-enhanced CVD on (100) [8±3 kcal/mol] and (111) [12+4
kcal/mol] diamond surfaces measured over the range from 735 °C to 970 °C
70
400
°<
240 -
45
60
75
90
TIME (min)
Fig. 3.9 Increase in diamond mass thickness, deduced by real-time spectroscopic
ellipsometry and plotted vs. time, for a sequence of five depositions performed on the same
Si substrate at different temperatures as determined by the calibration of Fig. 3.6.
71
102
—1
1
1 1 1 1
•
•
1 1 1
i
i
.
i
|
i
.
i
i
|
i
i
Data
i
•
•
•
-
^ ^
10 1
E =9kcal/mol
-_
10°
0.8
• '
.
.
1 .
0.9
.
.
.
i
1.0
1.1
1.2
1.3
k3 /ryi
/ T ^ - l1"
107T.„.„
(K"
)
ellips
Fig. 3.10 Mass deposition rate of diamond as a function of true temperature obtained from
the sequence of five nanocrystalline diamond film depositions shown in Fig. 3.8.
72
(Chu et al., 1992).
The results obtained here are reliable for three reasons. First, an accurate calibration
of the substrate temperature has been undertaken that avoids some of the errors associated
with pyrometry as described above. It is well known that even small errors in temperature
measurement can generate large errors in the slopes of the Arrhenius plots. Second, the real
time ellipsometric method for determining the diamond deposition rate is not only more
accurate, but it excludes the nondiamond carbon and void components of the film from the
deposition rate. Third, because the results of Fig 3.9 represent the growth of the diamond
phase on a diamond film substrate at each temperature, the results of Fig. 3.10 are not
distorted by the temperature-dependent induction time often observed for diamond
nucleation on treated Si substrates. The latter consideration may be the most important in
accounting for the smaller activation energy obtained here in comparison to previous
studies of diamond growth on nondiamond substrates.
73
CHAPTER 4
REAL-TIME SPECTROSCOPIC ELLIPSOMETRY STUDIES OF
DIAMOND FILM GROWTH BY MICROWAVE PLASMAENHANCED CHEMICAL VAPOR DEPOSITION (MPECVD)
4.1. Introduction
Diamond is well known as a valuable and strategic material because of its high
hardness, chemical resistance, low coefficient of friction, high thermal conductivity, high
hole mobility, wide band gap, and high breakdown voltage (Yarbrough, 1992). As the
applications of diamond thin films become more demanding, real-time monitoring of the
deposition process becomes increasingly important in order to ensure that desired bulk
material and interface characteristics are met.
Optical probes are advantageous because they are passive and can be performed in
situ without making direct physical contact to the film surface. In addition, optical
experiments require no equipment internal to the reactor. Because of its ability to provide
both amplitude and phase information in a reflection geometry, ellipsometry is among the
most powerful optical probes available for this purpose (Collins and Kim, 1990; An et al.,
1992). As mentioned in the previous chapter on substrate temperature calibration, real time
spectroscopic ellipsometry (RTSE) measurements can provide the time evolution of the
bulk and surface roughness layer thicknesses, as well as the time evolution of the volume
fractions of the different components in the bulk layer. Such results are obtained from an
analysis of data collected during film growth. The first results of this part provide important
74
insights into the development of threefold-coordinated nondiamond (or sp2 C) defects in
films prepared under different conditions, as well as the relative distribution of the defects
between diamond grains and grain boundary regions. Such studies are leading to methods
for reducing the grain boundary contributions that form preferentially during the
coalescence process.
4.2. Experimental Details
The deposition system and RTSE instrumentation used to investigate the diamond
growth process are the same as those used in the temperature calibration experiments.
However, in this case, dry substrate seeding is used. In this seeding procedure, the
crystalline Si (c-Si) wafer substrate is hand-polished with <0.25 u,m diamond powder
(Warren Diamond Powder Co., Inc.). A cotton swab is used to abrade the substrate in a
circular pattern, and then the residual powder on the surface is removed with a clean cotton
swab. The polishing procedure was found to be critical in obtaining (i) a high nucleation
density in the early stages of growth, (ii) a smooth specular surface in the later stages, and
(iii) a macroscopically uniform thick film, as noted from the purity of the interference
colors.
Figure 4.1 shows an image of a diamond-seeded substrate obtained by atomic force
microscopy (AFM). This AFM image shows that between larger scratches (2000 A wide
and 20 A deep), the seeded substrate is relatively smooth. The rms roughness value
between larger scratches is found to be -12 A. The diamond seeded substrates were also
studied by ex situ SE. The experimental pseudo-dielectric functions obtained in this study
at room temperature are shown in Figs. 4.2(a) and 4.2(b) along with the best fit optical
models. The modeling for the ex situ SE data collected on the as-seeded substrate given in
Fig. 4.2(a) showed that the surface was amorphized by abrading with diamond powder.
75
X 0.200 UM/aiu
2 25.000 r W a i v
Fig. 4.1 Atomic force microscopy (AFM) image of a diamond-seeded Si substrate. The
bright spot on the upper boundary of the image appear to be a diamond particle remaining
from the seeding procedure.
76
— ex situ measurement
— Best Fit
A
CO
V
-3
15
12
A
o
CO
V
a-Si/void(fv)
6
a-Si
3
1.5
0
2.0
2.5
J
i
3.0
3.5
4.0
PHOTON ENERGY (eV)
Fig. 4.2(a) Ex situ SE data (<ei>, <£2>) for the diamond seeded substrate at room
temperature along with the best fit calculated result employing the one-layer optical model
shown in the inset. This model stimulates a structure that is completely disordered
throughout the penetration depth of the light, with a roughness layer on the surface. LRA
shows that the layer thickness d is 152 A and the void volume fraction fv is 0.66.
77
12
-j
1
1
1
f
6
A
to"
V
3
0
ex situ measurement
Best Fit
-3
+
15
12
A
CO
V
9
6
a-Si/c-Si/void
3 h
0
1.5
<*2
c-Si/void(fvsub)
J
L
2.0
J
2.5
L
3.0
_i
3.5
L
4.0
PHOTON ENERGY (eV)
Fig. 4.2(b) Ex situ SE data (<ei>, <E2>) for a diamond-seeded substrate measured at room
temperature after annealing to the deposition temperature of 785°C. Also shown is the best
fit to the data using the two-layer optical model given in the inset. This model stimulates a
recrystallized bulk region with a roughness layer on the surface. The amorphous
component in the surface layer accounts for a reduced Si grain size near the surface. LRA
indicates that dj is 66 A, d2 is 118 A, the void volume fraction in the substrate fv,Sub is
0.06, and the void and c-Si volume fractions in the surface roughness layer fv s and fc s are
0.44 and 0.41, respectively.
78
Damage due to the abrasion nearly eliminates the Ei feature in the c-Si optical functions,
indicating a highly defective structure. After annealing to the typical deposition temperature
(~800 °C), however, the Ei critical point reappears as shown in Fig. 4.2(b), and modeling
suggests that the surface has recrystallized.
With the exception of the polishing procedure, the detailed methods for this
experiment follow those of the temperature calibration experiment described in the previous
chapter. After ignition of a pure H2 plasma with the substrate platform raised above the
optical plane, the platform is lowered while the plasma is tuned to ensure that the reflected
power remains low (about 0-1 W). Although it was found that no carbide formed on the
unseeded Si wafer substrate in the initial H2 plasma exposure (see Sec. 3.3), the same
conclusion cannot be drawn here owing to the seeding procedure which damages the Si
surface. In any case, it appears that diamond nucleation is controlled by the seeding, not by
any carbide formation. This conclusion is based on the fact noted below that the nucleation
density is nearly independent of the [CH4]/{[CH4]+[H2]} gas flow ratio used during
diamond growth. After the platform is lowered the optical alignment is rechecked. Finally,
data acquisition is initiated, and CH4 is introduced, defining t = 0 in the RTSE monitoring
process. After the diamond film is grown to the desired thickness, the plasma is
extinguished. Next, data acquisition is stopped and at about the same time, the CH4 flow is
terminated and the heater is turned off. After the film/substrate reaches room temperature,
another pair of spectra is measured. Finally, the system is pumped out and a final pair of
spectra is measured.
Data analysis employs the Bruggeman effective medium approximation (EMA),
multilayer optical computation and least-squares regression analysis (LRA) to extract
photon energy-independent free parameters of thickness and material volume fraction
(Aspnes, 1981). These analysis procedures were explained in Chapt. 1 in detail. The EMA
is used to determine the dielectric function of composite materials [e.g. (diamond) + (sp2
79
C) + (void)] from the dielectric function of the components and their volume fractions, as
explained in Chapt. 1. In the analysis, a reference dielectric function for diamond from the
literature was used (Edwards, 1985); however, this dielectric function was modified in
accordance with earlier studies (Ramachandran, 1947) to account for the elevated substrate
temperature. Figure 4.3 shows results at selected temperatures. The dielectric function for
sp 2 C was obtained from measurements of optically polished glassy carbon. These
measurements were performed at different substrate temperatures using the same
ellipsometer and deposition system as for diamond growth. Due to possible polishing
damage, which may lead to a lower density structure on the glassy carbon surface, the
absolute sp2 C volume fractions are more uncertain than relative values. The dielectric
functions for glassy carbon at different temperatures are shown in Fig. 4.4.
4.3. Results and Discussion
This section presents results obtained in least-squares regression analyses of the
OF, A) spectra collected using SE in real time during nanocrystalline diamond thin film
growth. Typical real time data acquired during film growth to a thickness of 2140 A are
shown in Fig. 4.5. The reactant gas flow was 1 seem of CH4 and 99 seem of H2, yielding
a flow ratio [CH4]/{[CH4]+[H2]} of 0.01; the thermocouple reading was 800 °C
(corresponding to a true substrate surface temperature of 785 °C); the total pressure was
maintained at 7 Torr; and the plasma power was 500W. The spectra in Fig. 4.5 are shown
in the form of the pseudo-dielectric function, calculated from the ellipsometry data (*F, A)
using
<e> = e a sin26 [1 + tan28 {(1 - p)/(l + p)}2]
(2.38)
80
7.25
7.00
6.75
Of
6.50
6.25
6.00
5.75
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
PHOTON ENERGY (eV)
Fig. 4.3 Real part (ei) of the dielectric function of diamond at different temperatures. The
imaginary part £2 is zero over the photon energy range from 1.5 eV to 5.0 eV.
81
CO
CO
1.5
2.0
2.5
3.0
3.5
4.0
PHOTON ENERGY (eV)
Fig. 4.4 Real (ei) and imaginary (£2) parts of the dielectric functions of optically polished
glassy carbon measured with RTSE at different temperatures along with a data at room
temperature from the literature (Williams and Arakawa, 1972).
82
Fig. 4.5 Typical RTSE data collected during diamond film growth, shown in the form of
the pseudo-dielectric function: real part, <ei> (top) and imaginary part, I<e2>l.
83
as explained in detail in Section 2.3. Here ea is the dielectric function of the ambient, 6 is
the angle of incidence, and p = tan*F exp(iA). The real time data set of Fig. 4.5 is
composed of 127 pairs of spectra collected vs. time and 111 spectral points collected vs.
photon energy, corresponding to a total of 2.8xl04 data values.
Fig 4.6 provides an overview of the fixed and variable parameters in the LRA that
characterize the microstructural evolution of the diamond film. As shown in the schematic
of Fig, 4.7, in the initial stage of growth, the film is expected to exhibit isolated diamond
nuclei that increase in size with time. In this stage, an optical model for the discontinuous
diamond film is developed that consists of a single layer containing a mixture of diamond,
sp2 C, and void. Here, the sp2 C and void contents simulate the defects within the isolated
diamond nuclei and the free space between nuclei, respectively. With continued growth, the
diamond particles make contact and interlock to form a continuous film. However, it is
unlikely that the microstructure present during nucleation will be completely healed during
the coalescence process. Thus, a two-layer optical model for the film is developed to
describe coalescence and growth, with each layer presumably being composed of diamond,
sp2 C, and void. The surface layer simulates roughness, and its sp2 C and void contents
simulate the defects in the protruding grains and the free space component between the
protrusions, respectively. The underlying layer simulates the interlocking grains of the bulk
layer, and the sp2 C content simulates the graphitic defects in the grains and at grain
boundaries. The void content simulates trapped space resulting from incomplete
interlocking of nuclei (see Fig. 4.7).
The one-layer model has three free parameters and the two-layer model can have as
many as six. In all analyses, the two-layer model is simplified by neglecting the sp 2 C
content in the surface layer, and by assuming that the surface layer void volume fraction is
0.50. Previous analysis suggests that any underestimation of the surface layer sp2 C
content leads to a corresponding overestimation of the bulk layer sp2 C content by the
84
1.0
TWO-LAYER
MODEL
SURFACE/BULK
ONE-LAYER
0.8 -MODEL.
NUCLEI
0.6
0.6?
0.4
0.2
0.U5
h(a)
*
0.0
0.4
H
fV)b
MiiiiiiiiiiiimwuiiiiniiiiiUiii
uw wwwwwg
I
'
1
I
wwuutmuauf
I
1
0.3
a, 0.2
0.1
0.0
2000
ex situ
^1500
^ 3 1000
500
Til' 1111II | ix Luul m ||»IIIIII|||||M|UI||IH||||IIII»>IIIIHIIIIIIIIHIII»|»
0
0
10
20
30
40
50
60
70
80
TIME (min)
Fig. 4.6 Evolution of microstructure during MPECVD diamondfilmgrowth, deduced from
an analysis of RTSE data. This film was grown to a bulk thickness of 2140A. The
substrate surface temperature, plasma power, pressure, and CH4/(CH4+H2) gas flow ratio
were 785 °C, 500 W, 7 Torr, and 1%, respectively. d(b, s) are the bulk (b) and surface (s)
roughness layer thicknesses. fv,b and fv2,s are the void volume fractions in the bulk and
surface layer; fsp2,b and fSp2,s are the sp C volume fractions in the bulk and surface layer,
respectively.
85
(a) 3 parameters (d, fsp2, fv)
diamond/sp C /void
V
(b) 4 parameters (ds,db, fsp2,b, fv,b)
diamond/void (0.5/0.5)
diamond/sp2 C /void
Fig. 4.7 (a) One-layer and (b) two-layer optical models used to simulate diamond film
growth in the nucleation and coalescence/bulk growth regimes, respectively. The
compositional
parameters (fsp2, fv) and (fsp2,b» fv.b) are the independent volume fractions
of sp2 C and void in the nucleating layer of the one-layer model and the bulk layer of the
two-layer model, respectively.
86
equivalent mass thickness (i.e., thickness times volume fraction) (Cong et al., 1991b). As
a result, the modeling provides the total sp2 C content in the film, irrespective of its location
within the cross-section.
The transition separating the one- and two-layer model regimes in Fig. 4.6 is
identified by three simultaneous events that occur in the modeling.
1. The void volume fraction in the nucleating layer drops below -0.5 as the
transition is crossed from below, i.e., from shorter to longer times. (Note that 0.48 is the
void volume fraction for contacting hemispheres on a square grid.)
2. The unbiased estimator of the mean square deviation, a measure of the quality of
the best fit, increases abruptly for the one-layer model as the transition is crossed from
below. This can be seen in Fig. 4.8 for the data analysis of Fig. 4.6.
3. The bulk layer thickness in the two-layer model approaches zero when the
transition is approached from above, i.e., from longer to shorter times.
Thus, a one-layer model is used for t<15 min in Figs. 4.6 and 4.8 and a two-layer model is
usedfort>15min.
When the nucleating and bulk layers are very thin, it is difficult to extract their
compositions. An assessment of this problem provides a measure of the present sensitivity
of RTSE. Future gains may be possible through an improved reference dielectric function
for sp2 C. It is likely, however, that the appropriate sp2 C dielectric function depends
sensitively on the size of the sp2 C clusters, and thus depends on the evolutionary stage and
growth conditions of the diamond film. In any event, in both one- and two-layer models,
the relative sp2 C content can be determined quite accurately in films as thin as 60 A. In
one- and two-layer models, the void content can be determined for films as thin as 50 A
and -500 A, respectively. These sensitivities explain the dashed lines in Fig. 4.6, which
correspond to fixed compositional parameter values, in contrast to the points which denote
free parameter values. In the one-layer regime, for t<8 min, where the nuclei thickness is
87
0.14
5
10
15
20
25
30
TIME (min)
Fig. 4.8 Unbiased estimator of the mean square deviation a obtained in a least-squares
regression analysis of RTSE data collected during the deposition of Fig. 4.6. Here a onelayer model is assumed, and the abrupt increase in o indicates nuclei are beginning to make
contact to form a bulk layer. Thus, for t>15 min a two-layer model must be used (see Fig.
4.6).
88
less than 50 A, the sp2 C (center) and void (top) volume fractions are fixed at 0.025 and
0.62, values that yield continuity with the results for 8<t<15 min. In the two-layer regime
for t<27 min, the void fraction in the bulk layer isfixedat 0.15, again assuming continuity
with the results for t>27 min.
Now we are in a position to assign a physical interpretation to these data, starting
with the one-layer regime. It is found that although the growth rate is very slow in the first
8 min (an average of 4.9 A/min, in terms of physical thickness), there is no induction time
during which growth is completely absent. After another 7 min, the physical thickness
growth rate increases to 27 A/min as the total thickness increases to 240 A. During this
time, the sp2 C volume fraction, remains relatively constant at 0.03 in the one-layer regime.
This component is attributed to defects within the isolated diamond grains. On the other
hand, the void fraction gradually decreases from 0.62 to 0.5, indicating that the particles
are increasing in size and starting to make contact as the two-layer regime is approached.
These features are emphasized in Fig. 4.9 which shows the physical thickness for 8<t<15
min and the diamond mass thickness for 0<t<15 min as a function of time during the
diamond deposition of Figs. 4.5 and 4.6. If the particles can be approximated as
hemispheres on a square grid at the time of contact, then an average spacing and nucleation
density of 480 A and 4 x 1010 cm-2 are estimated, respectively.
Further information on particle shape in the nucleation regime can be obtained by
modeling the data for the void fraction vs. thickness as shown in Fig. 4.10. Here
theoretical calculations for the decrease in void fraction [fv(d)] with increasing film
thickness in the nucleation stage are compared with the results from an analysis of the
RTSE data for a diamond film prepared at a temperature of 785 °C (open circles). The
gradual increase in void fraction with decreasing thickness and the apparent trend toward
-0.6 as d approaches zero is inconsistent with three-dimensional growth from point source
(e.g., spherical nuclei). In this latter case, the void fraction must vanish as d approaches
89
JUU
250
•
i
•
1
i
1
i
1
i
1
i
1
i
1 i
-
• ~
•
•
200
•
<
•
150
•
•
•
100
•
•
•
50
••
i1
0
1 i
1
i 1 i 1 i 1 i 1 i 1
i_
1' 1 ' 1 ' 1 ' 1 ' 1 ' 1 •.
•
100
•
80
•
-
<
60
•
-
•
•
•
40
•
•
•
20
0
0
2
4
6
8
10
12
14
16
TIME (min)
Fig. 4.9 The physical thickness for 8<t<15 min and the diamond mass thickness for
0<t<15 min as a function of time during diamond deposition. This film is the same as that
enlarged in Fig. 4.6.
0.70
1
,
j
,
J
i
I
i
^
,
r
i
I
0.65
0.60
0.55
0.50
0.45
0
50
100
I
150
200
i
L
250
FILM THICKNESS (A)
Fig. 4.10 The void volume fraction (fv) vs. thickness in the nucleation regime for a
diamond film prepared with a substrate temperature of 785 °C and a [CH4]/{[CH4]+[H2]}
flow ratio of 0.01. These results were obtained using a one-layer model of the nucleating
film, consisting of diamond, sp2 C, and void. The solid line is the best fit result based on a
model of hemispheroidal nuclei as shown in the inset.
91
zero. The results suggest that, at least in the first 50 A, the nuclei have grown much faster
in the plane of the substrate than out of the plane. This leads to disc-shaped nuclei in the
early stages of nucleation that may gradually evolve into hemispheroidal structures prior to
nuclei contact. Such shapes are consistent with the AFM images of the 350 A diamond film
in Fig. 4.11. The solid line in Fig. 4.10 is a fit to the following expression:
fv=l-(2rc/3)(r/s)2,
(4.1)
which is deduced by considering hemispheroidal diamond particles located on a square
grid. In this expression, it is assumed that the in-plane radius of the hemispheroids r is a
linear function of the out-of-plane radius or thickness d, i.e.,
r = ro + ad,
(4.2)
where ro is the initial size in the monolayer limit and a is the ratio of the growth rate in the
plane of the substrate relative to that out of the plane. In addition, we assume that the
spacing between nuclei, s, is given by s=2.5dC) where dc is the thickness at which nuclei
make contact. This latter expression derives from AFM measurements of s. The best fit in
Fig. 4.10 yields the two variable parameters ro=249 A and a=0.116. This result is
consistent with HR-XTEM measurements which reveal the lattice planes of diamond nuclei
250 A in extent at the interface to the Si substrates.
After the particles make contact, the two thicknesses exhibit clear trends. First, the
surface layer thickness decreases due to the coalescence process, which leads to a filling of
the gaps between particles. Consequently, a surface smoothing process is observed as the
roughness layer drops from 270 A at the beginning of bulk layer growth to its stable value
of 125 A. Initially, the bulk layer thickness increases abruptly in the early stages of
92
Fig. 4.11 AFM image of the 350 A thick microwave plasma CVD diamond film deposited
with a 1% [CH4]/{[CH4]+[H2]} gasflowratio, a surface temperature of 785 °C, a plasma
power of 500 W, and a total pressure of 7 Torr.
93
coalescence, but then increases nearly linearly with time at a rate of 31 A/min.
In the one layer regime, the sp2 C volume fraction remains relatively low and
constant as mentioned earlier. In the coalescence regime, however, a rapid increase in the
sp2 C fraction is observed in the first ~300 A of bulk layer formation. Such an effect is
ascribed to the formation of defects in the boundary regions between grains that make
contact during coalescence. A subsequent decay in fsp2,b is observed, and this decay is due
to a reduction in the average sp2 C content in the accumulating bulk layer. Thus, the decay
of the sp2 C volume fraction implies a gradient or thickness dependence of the sp2 C
content in the film. For example, the dashed line decay in Fig. 4.6(b) is calculated
assuming that all sp2 C in the bulk layer resides within -300 A of the substrate interface.
The reasonable match to the data suggests that the contribution to the sp2 C from each
successive atomic layer deposited after -300 A is not significant. Thus, we conclude that
for this gas flow ratio, a relatively small sp2 C fraction exists within the isolated nuclei and
coalesced grains. A large fraction exists in the grain boundary regions, but only within the
coalescence thickness (-300 A in this case) near the substrate. In the early stages of
coalescence, the internal surfaces of neighboring grains are shadowed from the plasma.
This may reduce the flux of atomic H from the plasma which promotes defect formation.
After the film coalesces and its surface smoothens, direct plasma exposure exerts a
beneficial effect on any remaining grain boundary regions, leading to material with a lower
sp2 C fraction atop the fully coalesced film. Further decay in the sp2 C fraction may also be
related to an increase in grain size with thickness which reduces the volume of the grain
boundary regions.
Figure 4.6(a) shows that the void fractions averaged through the bulk layer at
thicknesses of 500 and 2000 A are 0.15 and 0.08, which implies gradual densification of
the film. The relatively large density deficit in the final film is consistent with atomic force
94
microscopy (AFM) images, which reveal ~800 A voids between nanocrystals in isolated
regions of the surface (see Fig. 4.12).
The solid points at the end of the deposition in Fig. 4.6 have been obtained in an
analysis of ex situ SE data collected on a second instrument, with the sample at 25 °C. The
ellipsometer for ex situ measurements is in the rotating analyzer configuration. Good
agreement with the results of the real-time SE analysis is obtained for the compositions and
roughness layer thickness. The difference in bulk layer thickness between the final in situ
result at 785 °C (1980 A) and the ex situ result at 25 °C (2240 A) can be attributed to the
fact that the film exhibits a thickness gradient over the surface and the two measurements
probed different spots. Figure 4.12 shows an AFM image of the diamond film of Fig. 4.6
obtained in an ex situ study. An analysis of the AFM image yields a root-mean-square
(rms) roughness thickness of 120A, indicating that for diamond film surfaces the RTSE
analysis provides a roughness value (125 A) close to rms.
The final film was also measured with micro Raman spectroscopy (ISA U-1000,
Jobin Yvon) to confirm the existence of the diamond component. Figure 4.13 shows
Raman spectra of the diamond film plotted as a function of wavenumber. A sharp peak is
observed at 1333 cm-1 for the diamond phase and the strongest broad peak at -1500 cm-1 is
attributed to disordered sp2 C. Upon inspection, it would appear that the film mainly
consists of sp2 C. However, Raman spectroscopy is known to be extremely sensitive to
graphitic defects. Specifically, the Raman efficiency of graphite has been reported to be -50
times larger than that of diamond (Wada and Solin, 1981). An additional feature is
observed at 1140 cm-1. It has been proposed that this feature is due to disordered sp3bonded carbon which may be a precursor to the formation of diamond (Nemanich et al.,
1988; Shroder et al., 1990). Another feature observed in Fig. 4.13 is the peak at -1355
cm-1 which is at a frequency higher than that of the diamond phase. This peak is attributed
95
Fig. 4.12 Atomic force microscopy (AFM) image of the 2150 A thick microwave plasma
CVD diamond film of Fig. 4.6 deposited with a 1% [CH4]/{[CH4]+[H2]} gasflowratio, a
surface temperature of 785 °C, a plasma power of 500W, and a total pressure of 7 Torr.
96
1333 cm-1
a
I
900
1050
1200
1350
1500
1650
1800
-1>
Wavenumber (cm")
Fig. 4.13 First-order Raman spectrum of a microwave plasma CVD diamond film
deposited with a 1% [CH4]/{[CH4]+[H2]} gas flow ratio, a surface temperature of 785 °C,
a plasma power of 500W, and a total pressure of 7 Torr. The sharp feature at 1333 cm-1 is
indicative of crystalline diamond, while the feature between 1450 and 1550 cm-1 is
attributed to disordered sp2-bonded carbon. The peak centered at 1355 cm-1 is attributed to
microcrystalline graphite.
97
to microcrystalline graphite (Nemanich et al., 1988; Shroder et al., 1990; Mermoux et al.,
1992). In summary, the Raman spectrum is typical of a relatively thin nanocrystalline
diamond film, dominated by the defects that occur at the interface to the substrate and at the
boundaries between the ~200 A grains.
Figure 4.14 shows a high-resolution cross-sectional transmission electron
microscopy (HR-XTEM) image of a film deposited under the same conditions as that of
Fig. 4.6. The only difference is in the film thickness of the two samples (the former is 800
A thick and the latter is -2000 A thick). This image shows an interface layer (100-300 A
thick) between the substrate and the diamond film. This intermediate layer might be
interpreted as one of the several possibilities including (1) a disordered intermediate layer
consisting of diamondlike sp3 C and/or transparent SiC interpreted erroneously in the
optical model as crystalline diamond, or (2) disordered sp2 C or graphite microcrystallites
(Meilunas et al., 1989; Tsai et al., 1991; Shah and Waite, 1992; Waite and Shah, 1992;
Fallon and Brown, 1993; Jiang et al., 1994; Tzou et al., 1994) appearing correctly in the
optical model as the sp2 C between grains. In this case, the diamond crystallites are not
visible either because they are disordered [see, e.g. possibility (1)], or because they are not
appropriately oriented with respect to the electron beam to image the lattice planes. Further
study is needed to understand the intermediate layer observed in this image and relate it to
the optical model.
4.4. Diamond films deposited under various conditions on C-H-O
phase diagram
Because of their importance in controlling many of the diamond film properties, the
evolution of the average sp2 C and void volume fractions were studied as a function of
thickness for diamond films prepared with different gas mixtures. Fig. 4.15(a) shows the
98
lOnm
•VJf
V
Epoxy
Diamond
Interface
c-Si
Substrate
Fig. 4.14 High-resolution cross-sectional transmission electron microscopy (HR-XTEM)
image which shows the interface region between the c-Si substrate and diamond film. The
deposition condition parameters were as follows: 1% [CH4]/{ [CH4]+[H2]} gasflowratio,
500W plasma power, 785 °C surface temperature, and 7 Torr total pressure.
99
•-">
V
non-diamond carbon
growth region afl
dfa
II"
1 <J(||I"
^
no grp.wih--region
(this study)
H
X 0 / y=0/(0+H)
Fig 4.15(a) C-H-0 phase diagram for carbon film growth which is divided into the three
distinct regions of non-diamond growth, diamond growth, and no growth. Each side of the
equilateral triangle represents the atom fractions of the gas phase composition of one of the
three parts C-H, H-O, and O-C, having values ranging from 0 to 1 (0% to 100%).
100
C-H-0 diamond deposition phase diagram (Bachmann et al., 1991). It reveals that low
pressure diamond synthesis occurs only within a well-defined region of the gas phase
compositional diagram, positioned along the line obtained for different CO+H2 mixtures.
This diagram shows three different regions characterized by (1) non-diamond carbon
growth, (2) diamond growth, and (3) no growth. On the oxygen-rich side, the diamond
domain is limited by the region where no material is deposited at all, whereas on the
carbon-rich side, deposition of non-diamond carbon dominates. As a general trend, the
phase purity of the material increases from the carbon-rich to the oxygen-rich side of the
diamond domain. Here, we will study the effects of hydrogen and oxygen in the gas phase
on diamond thin film growth. We will also study diamond thin film growth using CO in
hydrogen as the source gas.
EFFECT OF HYDROGEN AND OXYGEN ON THE STRUCTURAL
EVOLUTION OF DIAMOND THIN FILM
In this section, we will consider the effect of preparation conditions on the bonding
and structural evolution of diamond films, namely the effect of increasing CH4 and O2
flows. For this study, the atomic C/H/O contents in the gas phase are quantified by the
three volumeflowratios which uniquely identify the position on the phase diagram, Xc/z
= [C]/{[C]+[0]}, XH/z = [H]/{[H]+[C]}, and X 0 /z = [0]/{[0]+[H]}. In the first
experiments described here, XQ/Z is fixed at 0 (Xc/z = 1), while XH/Z = 0.972, 0.986,
and 0.995 [which correspond to 6%, 3% and 1% CH4/(CH4+H2)], as shown in Fig.
4.15(b). Thus, Figs. 4.16 and 4.17 show the role of the CH4 content in H2 gas on the
evolution of film composition.
From the evolution of the nucleating and surface roughness layer, ds, in Fig. 4.16,
it is clear that nucleation and coalescence occur similarly under the full range of CH4/H2
101
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Xo/s=[0]/{[0]+[H]}
Fig. 4.15(b) Enlarged hydrogen-rich sector of the C-H-O phase diagram. The points on the
diagram indicate the experiments done for this thesis research. We observe diamond
growthover a much wider range of XQ/S than in previous studies.
102
T3
T3
0
10
20
30
40
50
60
TIME (min)
Fig. 4.16 Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond films prepared
with different atom-volume flow ratios XR/I = [H]/{[H]+[C]}: (a) 0.972, (b) 0.986, and
(c) 0.995 which correspond to 6%, 3%. and 1% CH4 in (H2+CH4), respectively. The
growth rates are 30.0, 43.2, and 30.7 A/min for 6%, 3%, and 1% CH4 in (H2+CH4),
respectively.
103
0.0
0.4
•
I
I I
'
I
' I
(b) -
0.3
W
0.2
0.1
1
0.0
0.4
1
.
1
h
(c) -
0.3
OH
W
0.2
0.1
0.0
400
800
1200
1600
2000
BULK THICKNESS (A)
Fig. 4.17 Volume fraction of sp2-bonded C plotted as a function of bulk thickness for
nanocrystalline diamond films prepared with different atom-volume flow ratios XH/Z =
[H]/{[H]+[C]}: (a) 0.972, (b) 0.986, and (c) 0.995 which correspond to 6%, 3%, and 1%
CH4 in (H2+CH4), respectively. The final film thickness of these films is ~2000 A in each
case.
104
conditions, however, the final film surface is smoother with the higher hydrogen atom
fractions. Figure 4.16 also shows that the growth rate during nucleation becomes slower
with increasing H atom fractions (note shift in vertical line to longer times with increasing
XH/Z) and this is observed in several literature studies (Spear, 1989; Kweon et al., 1991).
In spite of this, the bulk film growth rate after coalescence is the same for the 1% and 6%
ratios at 30 A/min and reaches a peak value of 43 A/min at the 3% ratio.
As shown in Fig. 4.17 the rapid formation of sp2 C occurs similarly under the full
range of conditions; however the decay of sp2 C content with time in the bulk layer
depends sensitively on the deposition conditions. For the 6% CH4/(CH4+H2) flow ratio,
the sp2 C volume fraction peaks at 0.35 for a bulk film thickness of 300 A and decays to
0.18 for a thickness of 2140 A, a factor of 4.5 higher than the corresponding value (0.04)
for the 1% ratio. The increased final sp2 C contents in the films with higher
CH4/(CH4+H2) flow ratio are confirmed by Raman measurements of the three samples of
Fig. 4.17. These Raman spectra are shown in Fig. 4.18 for the samples prepared with 1%,
3%, and 6% CH4/(CH4+H2) flow ratios. Note that for thefilmprepared with 3% ratio, the
1333 cnr 1 peak associated with diamond vanishes. Thus, diamond becomes undetectable
in the film when the sp2 C volume fraction increases above -0.05. This results from the
factor of -50 higher sensitivity of the Raman measurement for sp2 C in comparison with
diamond. Note also in Fig. 4.18, that the 1350 cm-1 peak attributed to microcrystalline
graphite increases in amplitude and shifts to higher wavenumber with increasing CH4 flow,
making it especially difficult to observe the diamond phase. Finally, the 1140 cm-1 peak
attributed to disordered sp3 C decreases with increasing CH4 flow.
Overall the observed behavior suggests that the evolution of the film in the
nucleation process depends in large part on the seeding process, and is only weakly
dependent on deposition conditions. However, once sp2 C forms in the coalescence
process, the ultimate properties of the film are a sensitive function of the deposition
105
a
1
1000 1100 1200 1300 1400 1500 1600 1700
Wavenumber (cm"1)
Fig. 4.18 Raman spectra measured for the samples deposited under different C atom
fractions corresponding to 1%, 3%, and 6% CH4 in (CH4+H2). Other conditions are the
same for all samples including a surface temperature of 785 °C; a plasma power of 500W;
and a total pressure of 7 Torr.
106
conditions. Although the near-optimum 1% CH4/(H2+CH4) flow ratio cannot eliminate the
sp2 C that forms in the coalescence process owing to the shadowing process noted earlier,
further growth of sp2 C after coalescence is impeded and improved properties of the film
evolve in the thick layers. We propose that the dominant sp2 C contribution in thick, fully
coalesced films prepared under these conditions may occur within the diamond grains. In
contrast, for the 6% flow ratio, the sp2 C formed during coalescence appears to serve as
nuclei that promote formation of additional nondiamond material, presumably at grain
boundaries, with subsequent growth.
Next, controlled additions of O2 to (H2 + CH4) and their effect on the evolution of
the composition of the diamond thin film will be discussed. In these experiments, XH/Z is
fixed at 0.97, while (XC/x, X 0 /z) = (1, 0), (0.50, 0.03), (0.33, 0.06), and (0.20, 0.10).
Other conditions are fixed for all samples including a surface temperature of 785 °C, a
plasma power of 500 W, and a total pressure of 7 Torr. Figure 4.19 shows that the growth
rate during nucleation increases with the initial addition of oxygen (6 seem CH4, 3 seem
O2, and 91 seem H2). However, it decreases with further increases in the O atom fraction.
The addition of oxygen increases the bulk film growth rate at the low O/C ratios as in parts
(b) and (c) of Fig. 4.19, and decreases the growth rate as the no-growth boundary is
approached. The evolution of the sp2 C with film thickness in Fig. 4.20 shows a clear
trend with increasing gas-phase O content (i.e., increasing Xo/s)- In this case, the role of
O is to compensate the otherwise detrimental effects of excess gas-phase C (Liou et al.,
1990; Wu et al., 1992; Fayette et al., 1994a). In addition, the diamond film becomes
denser with increasing atomic oxygen fraction.
The maximum ratio of X0/2 = 0.10 in the series of Fig. 4.19 was established by
RTSE so as to correspond to the maximum sustainable gas-phase O content before the nogrowth regime is entered. This indicates another advantage of real time monitoring by SE.
Namely, after film deposition was ascertained using real time monitoring under low Xo/z
107
0
10
20
30
40
50
60
70
80
TIME (min)
Fig. 4.19 Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond films prepared
with different atom-volume flow ratios (XC/z, X0/z) = ([C]/{[C]+[0]}, [0]/{[0]+[H]}):
(a) (1.00, 0.00), (b) (0.50, 0.03), (c) (0.33, 0.06), and (d) (0.20, 0.10). The growth rates
are 30, 30.3, 33.9, and 25.2 A/min, respectively. For these depositions, XH/Z =
[H]/{[H]+[C]} was fixed at 0.97 [6% CH4 in (H2+CH4)].
108
0.4 -(a)(o.i8)
0.3 -
,
en
0
450
900
1350
1800
2250
BULK LAYER THICKNESS (A)
Fig. 4.20 Volume fraction of sp2-bonded C (left scale) and void (right scale) as a function
of2bulk layer thickness, showing the effect of controlled additions of O2 in (H2+CH4). The
sp C fraction in thefilmis suppressed, so that the film quality improves with increasing O
atom fraction. For these depositions, XR/E = [H]/{[H]+[C]} was fixed at 0.97 [6% CH4 in
(H2+CH4)].
109
gas flow conditions, Xo/z was increased until the growth/no-growth boundary was
reached as indicated by the lack of changes in the real time spectrum. Then Xo/z was
decreased again until a reasonable growth rate was observed. In fact, we observed, with
our reactor system and conditions, diamond growth over a much wider range of Xo/z than
in previous studies. This is thought to be due to the lower microwave power and remote
nature of our plasma. Here the quality of thefilmobtained with Xo/z = 0.10, as gauged by
the lower sp2 C after 2000 A, is superior in comparison with diamondfilmsprepared under
the standard conditions of 1% CH4 in (H2+CH4) (without O2). This result is consistent
with previous experimental proposals, namely that the deposition of graphite or amorphous
carbon is suppressed by oxygen additions to the plasma owing to a reduction in the
acetylene concentration or to the oxidation of non-diamond carbon, so that the quality of the
deposited diamond is improved (Chang et al., 1988; Kobayashi et al., 1988; Liou et al.,
1990; Fallon and Brown, 1993).
Raman spectra for the samples deposited with different O2 flow ratios are shown in
Fig. 4.21. These spectra support the RTSE results showing the reduction in the sp2 C
Raman peaks at 1350 cm-1 and 1560 cm-1 with increasing atomic O fraction and the
appearance of the sharp peak for diamond near 1333 cm-1 at the highest O fraction. In
addition, the peak at 1140 cm-1 attributed to disordered sp3 Cfirstincreases with increasing
O2, then appears to decrease suggesting that at the highest O2flowthe crystallinity of sp3 C
component of the film has improved. HR-XTEM also verified that the highest quality of
diamond film was deposited with Xc/z = 0.2 and Xo/z = 0.1. Figs. 4.22(a) and 4.22(b)
shows the images of HR-XTEM of the near interface region between the diamondfilmand
c-Si substrate for this sample. An disordered interface layer similar to that discussed earlier
is observed, and its thickness is estimated to be ~ 150 A. A faceted grain is shown on the
lower left side in Fig. 4.22(a) and its approximate diameter is -250 A. This value is the
same as the thickness of the film at the onset of coalescence as obtained in the RTSE
110
•
1000
I
1100
•
I
1200
I
I
1300
.
I
1400
1
—
I
1500
—
I
—
I
—
1600
1
—
I
1700
Wavenumber (cm")
Fig. 4.21 Raman spectra measured for the samples deposited with (Xc/z» Xo/z) values of
(a) (1.0, 0.0); (b) (0.50, 0.03); (c) (0.33, 0.06); and (d) (0.20, 0.10). Other conditions are
the same for all samples: a surface temperature of 785 °C; a plasma power of 500W; and a
total pressure of 7 Torr. In addition, XH/Z = [H]/{[H]+[C]} was fixed at 0.97 [6% CH4 in
(H2+CH4)].
Ill
Diamond
Interface
c-Si
substrate
20 nm
Fig. 4.22(a) HR-XTEM image showing the interface between the diamond film and c-Si
substrate. A faceted grain is shown on the lower left side and its approximate diameter is
-250 A. In this case the diamond film was deposited with (XH/S, X C / I , XO/E) = (0.97,
0.2,0.1). The plasma power was 500W; the surface temperature was 785 °C; and the total
pressure was 7 Torr.
112
Diamond
Interface
c-Si
substrate
Fig. 4.22(b) HR-XTEM image showing locally-oriented growth of nanocrystalline
diamond grains on the substrate. In this case the diamond film was deposited with (XH/Z,
Xc/Z. Xo/z) = (0.97, 0.2, 0.1). The plasma power was 500W; the surface temperature
was 785 °C; and the total pressure was 7 Torr.
113
measurement. This is consistent with the grain size being limited by the nuclei spacing for
these films. Figure 4.22(b) shows the locally oriented heteroepitaxial growth of
nanocrystalline diamond grains on the seeded Si substrate. The observation of a
heteroepitaxial crystallite in this region suggests that what we have been calling the
"disordered interface layer" in the HR-XTEM images is not fully disordered, but contains
crystallites which only become visible in HR-XTEM when the electron beam probes at the
correct angle with respect to the lattice planes. This suggests that the interface layer is a
mixture of diamond crystallites and disordered sp2 C and is the same near-interface sp2 Crich material detected by RTSE in the coalescence process.
Figure 4.23 summarizes schematically an important conclusion extracted from the
experimental results of Figures 4.16-4.21, which was proposed in many earlier studies but
not clearly proven. Irrespective of the growth conditions, a region with a high volume
fraction of sp2 C is formed at the interface to the substrate when diamond particles begin to
make contact. It is believed that this phase forms owing to insufficient plasma H exposure
as a result of shadowing of the coalescing nuclei from the plasma. As a result, the sp2 C
phase is trapped between coalescing crystallites (Sato and Kamo, 1989; Fayette et al.,
1994a; Haq et al., 1994), and this prevents it from being eliminated with subsequent
growth (Zhu et al., 1989b; Haq et al., 1994). However, once the film surface becomes
sufficiently smooth after coalescence, no further shadowing occurs and sp2 C development
is impeded under the optimum growth conditions. Under excess CH4 conditions, the sp2 C
at the grain boundaries serves as nucleation sites for extensive sp2 C generation with
continued growth.
114
Fig. 4.23 Model for diamond growth showing the evolution of sp2 C content under (a)
optimum diamond growth conditions (for example, XH/I=0.97, XO/E=0.10) and (b)
nonoptimum conditions (for example, XH/Z=0.97, XO/Z=0.00). In (a), the sp2 C that
forms during coalescence is trapped between coalescing crystallites without further sp2 C
formation. In fact, some of the sp2 C that forms in the early stages may actually be etched
away under the optimum conditions. In (b), the trapped sp2 C serves as nucleation sites for
extensive sp2 C generation with continued growth.
115
SUBSTRATE TEMPERATURE EFFECT ON DIAMOND FILM
GROWTH
The substrate temperature as measured through RTSE calibration is another
important parameter that affects the diamond film growth process. Results from RTSE
measurements are shown in Fig. 4.24, 4.25, and 4.26. These figures depict the effects of
substrate temperature on (i) the bulk layer and the nucleating and surface roughness layer
thicknesses, (ii) the estimated nucleation density, and (iii) the evolution of sp2 carbon in the
bulk films, respectively. In this set of experiments, all other deposition parameters
including total flow rate (100 seem), pressure (7 Torr), and microwave power (500 W)
were kept constant. In addition, the methane concentration was fixed at 1% in the CH4+H2
gas mixture.
Figure 4.24 shows that the growth rate during nucleation increases with increasing
substrate temperature, and this is believed to be related to the increased nucleation density
with increasing substrate temperature shown in Figure 4.25. This latter increase appears to
occur weakly in the 530 - 630 °C temperature range and then more abruptly from 630 to
700 °C before gradually approaching a saturation value close to 5xl0 10 cm-2. The surface
temperature can influence a number of factors in the growth process, for example (i) the
degree of coverage of the substrate by film precursor species, (ii) the precursor surface
diffusion lengths, and (iii) the sticking and recombination coefficients for the radicals
involved in the nucleation process (Fayette et al., 1994b). Hayashi et al. (1992) found a
similar temperature dependence of the nucleation density over the 800 - 1000 °C range as
has been observed here, and explained the variation in terms of a change in the adsorption
state of the precursor from predominantly physical at low temperatures to predominantly
chemical at high temperatures. This change was attributed to the ability of precursors to
remove surface hydrogen at the higher temperature, as well as to a increase in the area of
116
(a) T.H.-S26 °C
T3
H
13.9 A/min
s
cgeogeaxoBgmeeneatfnnBnaeqpDDDCBBeB
°2l
(b) TeUi =695 °C .
T3
geaoaaxmoon
18.8 A/min
I
i
I
i
(c) Temps=810 °C
T3
20.2 A/min
•
T3
I
'
(d) T emp =841 °C •]
100
J
150
19.4 A/min
i
I
i
200
250
TIME (min)
Fig. 4.24 Bulk layer thickness (db) and the nucleating and surface roughness layer
thickness (ds) evolution as a function of time for nanocrystalline diamond films prepared
with different substrate temperatures. The growth rates are 13.9, 18.8, 20.2, and 19.4
A/min for TeiiiPs=626, 695, 810, and 841 °C, respectively. For these depositions, XR/Z =
[H]/{[H]+[C]} was fixed at 0.995 [1% CH4 in (H2+CH4)].
117
'a
o
o
o
5
r—i
.X.
4 -
3
2
•
-
"
.
500 550 600 650 700 750 800 850 900
T
ellips(°C)
Fig. 4.25 The effect of substrate temperature on the nucleation density. The substrate is
c-Si, the gas mixture is 1% CH4 in (H2+CH4), the total gas flow is 100 seem, the
microwave power is 500 W, and the pressure is 7 Torr.
118
capture of the precursors by diamond nuclei as a result of a increased diffusion length at
higher temperature due to a higher chemical reactivity of the surface. Fayette et al. (1994b)
proposed a second explanation based on the enhanced formation of an amorphous carbon
or a carbide phase on the substrate surface at the higher temperatures which can serve as
nucleation sites (Le Normand et al., 1993).
Figure 4.26 shows that the sp2 C evolution at the lower substrate temperature
(Tellips = 626 °C) is very different from that at the higher substrate temperature (TeiiipS =
810 °C) over the entire deposition. Namely, at the lower substrate temperature, the amounts
of sp2 C in the nuclei, in the near-interface region, and in the final bulk film are
significantly increased. In our deposition process, it is quite likely that the gas phase
concentration and chemical nature of the growth precursors close to the substrate are
different depending on the substrate temperature. Such difference during diamond chemical
vapor deposition has been reported in several papers (Weimer et al., 1991; Celii and Butler,
1992; Corat and Goodwin, 1993). However, this may not necessarily account for the
observed behavior. For example, other models based on the temperature dependence of the
surface growth mechanism (i.e., surface diffusion and/or reaction processes) may account
for the observed results (Zhu et al., 1989b). Figure 4.27 summarizes the overall results for
the sp2 C evolution for the experiments performed at different substrate temperatures. With
the increase in substrate temperature, the sp2 C volume fractions within the nucleating and
substrate interface layers decrease continuously even up to the highest temperature of 850
°C. However, with further growth of the film, it appears that optimum quality diamond
films can be achieved around TeiiipS~750 °C as shown in Fig. 4.27(c). In Fig. 4.28,
temperature dependence of the growth rate is presented for the same series of runs. This
figure shows a maximum value of growth rate around the temperature of 780 °C. Here the
trend in deposition rate is the same as that deduced for a sequentially deposited film as
presented in Chapter 3.
119
(a)Telli =626°C
+-+-•-
-i—+-H
o.o
+-H*
(b)Tellips=810°C
0.4
0.3
CL,
0.2
0.1 h
0.0
0
400
800
1200
1600
2000
BULK LAYER THICKNESS (A)
Fig. 4.26 The effect of substrate temperature on the evolution od sp2 C volume fraction in
the diamond film. The substrate is c-Si, the gas mixture is 1% CH4 in (CH4+H2), the total
gasflowis 100 seem, the microwave power is 500 W, and the pressure is 7 Torr.
120
o§
0.09
55k
0.06
i—
£Ld
0.03
>
0.00
i—'—r
T
"-
(a)
CM
0.50
00 <f
• I ' M
I ' M
(b)
0.40
0.30
^ O
>
0
£
0.20
0.06
•
I • I '
1 l
(c)
0.04 I—I
*J
o
HH
0.02 -
>
0.00
600
_L
650
700
750
Tellipsv
800
850
900
Q
Fig. 4.27 Sp2 C volume fractions vs. the substrate temperature calibrated by RTSE
measurement (a) within the nuclei, (b) within the bulk film after -300 A of growth (at the
peak in the sp2 C content), and (c) within the bulk film after 2000 A of growth. The gas
flow ratio was 1 % CH4 in (CH4+H2), the plasma power was 500 W, the total pressure
was 7 Torr, and the nominal substrate temperatures as read by thermocouple embedded in
reactor were 600, 700, 850, and 900 °C.
121
1
ZH
1
'
1
'
1
1
1
1
-
a
20
•
-
<
3
•
•
16
-
-
•
12
0
600
1
1
650
1
1
700
1
,
1
750
ellips
1
800
.
1
850
1
900
(°c)
Fig. 4.28 Bulk layer growth rate vs. substrate temperature. A maximum in the growth rate
is observed for a surface temperature between 700 °C and 800 °C.
122
DIAMOND GROWTH USING CARBON MONOXIDE (CO) AS A
CARBON SOURCE
Diamond thin films can be synthesized conventionally using various excitation
sources (e.g. microwave plasmas, heated filaments, etc.) and various gas mixtures. We
have already presented the microstructural evolution of diamond thin films grown with
CH4 in H2 and with CH4 and O2 in H2 as the gas sources. Oxygen is a good candidate to
improve the diamond film interface quality as seen in the previous discussion. Recalling
that the CO line on C-H-0 phase diagram passes through the center of the diamond growth
regime, we expect that any combination of CO and H2 would yield high quality diamond
thin films. Thus, CO is a good candidate as a source gas for scientific studies because it
allows one to systematically reduce the H-content in the plasma to zero.
Initially it was thought that CO was so stable at high temperature that it could not be
used as the carbon source for diamond synthesis in spite of an existing patent to the
contrary in 1968 (Hibshman, 1968). However, more recently many researchers succeeded
in diamond synthesis by microwave plasma CVD using a mixture of CO + H2 (Ito et al.,
1988; Suzuki et al., 1989; Hayashi et al., 1990; Muranaka et al., 1990; Cerio et al., 1992).
For the experiments using CO+H2 in this thesis study, the same reactor system as
previously described was used, and the deposition conditions included a substrate surface
temperature of 785 °C; a plasma power of 500 W; a total pressure of 10 Torr; and a gas
flow ratio, XH/E = [H]/{[H]+[C]} ranging from 0.98 to 0.00. Diamond-seeded crystalline
silicon (c-Si) was used as the substrate. Figure 4.29 shows the value of the sp2 C volume
fraction, fsp2 for various ratios of CO+H2 gas mixtures. These values are obtained just
after the peak in the sp2 C volume fraction associated with the coalescence process. At this
point the bulk layer thickness is -400 A. The initial trend in the sp2 C evolution with
increasing CO content in H2 is similar to that for O2 additions in (CH4+H2). fsp2 first
123
0.25
1
1
'
1
'
1
•
1
•
0.20
S
0.15
-
\°
OH
ir<N t0.10 -
o\
2-^o
0.05
0.00
0.0
1
0.2
.
0.4
i
0.6
i
i
0.8
i
1.0
XWZ(=[U]/{[H\+[C]})
Fig. 4.29 The sp2 C volume fraction for different XH/Z values ranging from 0.10 to 0.98
measured just after coalescence. Three sets of result are shown by circles and triangles.
Differences are due to the fact that the samples of the different sets were cut from different
Si wafer substrates.
124
decreases with increasing CO (i.e., decreasing XH/Z) until XH/Z = 0.9. With a minimum
near XH/Z = 0.9, fsp2 increases again but shows an additional weaker minimum near XH/Z
= 0.5. For XH/Z < 0.3, fsp2 increases more rapidly with decreasing XH/Z- For XH/Z = 0,
no film is obtained.
Film growth rates as a function of the CO level in H2 are shown in Fig. 4.30. A
trend is clearly distinguishable. As the hydrogen atom fraction, XH/Z. decreases from 0.98
to 0.8, the growth rate increases to a maximum, ~40 A/min, at XH/Z = 0.8. The growth
rate from CO (5 seem) and H2 (80.8 seem) at XH/Z = 0.97 was 32% less than that from O2
(10 seem), CH4 (5 seem), and H2 (79 seem) at the same XH/Z- With decreasing XH/Z from
the maximum at XH/Z =0.8, the deposition rate decreases. As XH/Z is reduced further
below 0.3, the deposition rate increases before dropping to zero at XH/Z = 0. This latter
increase is due to an increase in theflowof CO from 9.3 seem for XH/Z = 0.3 to 40 seem
for XH/Z = 0.2. This increase in flow was necessary due to H2 flow meter limitation for
low flows. Thus, depletion of precursors appears to be occurring at the low flow of CO.
It was reported that the concentration of hydrocarbons in the reactor exhaust gas
increases with increasing percentage of CO in H2 (Muranaka et al., 1991a; Cerio et al.,
1992; Johnson and Weimer, 1993). These studies were limited to the narrow region
between XH/Z = 0.99 and XH/Z = 0.88. Therefore, the results found here could not be
correlated with the ones in the earlier reports. One might expect the growth rate to increase
with decreasing XH/Z due to a increase in the relative amount of C in the gas phase.
However, the growth rate shown in Fig. 4.30 decreases over the range from XH/Z = 0.8 to
XH/Z = 0.3 so that this explanation appears to be incorrect. A more likely explanation is
given by Cerio and Muranaka, namely that oxygen activates the surface for diamond
growth presumably by producing radical sites by H atom abstraction. This accounts for the
increase in growth rate as XH/Z decreases from 0.98 to 0.8. The decrease in growth rate
with the increased CO for 0.3<XH/Z<0.8 may be due to enhanced oxidation rates of solid
125
48
:s
1
1
•
1
•
i
i
i
rfH~.
40 —
32 -
i
J6~NP
i
i
2
24 -
16
/
\^_9^
"/
\-
°
8
0
L
0.0
.
i
.
0.2
i
I
0.4
0.6
.
I
,
0.8
1.0
X
H/zK[H]/{[H]+[C]})
Fig. 4.30 The bulk layer deposition rate for gas mixtures of CO in Efe ranging from XH/Z ;
0.00 to 0.98. Three sets of result are shown as open and closed circles and triangles.
126
carbon at the surface and the depletion of gas phase carbon-containing precursors due to
increased atomic oxygen (Hayashi et al., 1990; Saito et al., 1990; Muranaka et al., 1991b;
Cerio et al., 1992).
4.5. Investigation of Ni substrates under Diamond Thin Film
Growth Conditions
The heteroepitaxial growth of diamond thin films on non-diamond substrates by
chemical vapor deposition has long been sought. Although c-Si is one of the most widelyused substrate materials, it has a large lattice constant (a=5.43 A) compared to that of
diamond (a=3.56 A). This lattice mismatch can generate considerable strain, and the
presence of such a large interfacial misfit is believed to be the primary obstacle in forming
oriented two-dimensional diamond nuclei (Yang et al., 1993; Zhu et al., 1993).
Nickel (Ni) is one of the few materials that has a lattice constant close to that of
diamond (a=3.52 A for Ni versus a=3.56 A for diamond). The high solubility of Ni for
carbon, its strong catalytic effect on hydrocarbon decomposition, along with the
subsequent graphite formation, however, have prevented low pressure CVD diamond
nucleation on the Ni surface. In fact, whenever the diamond phase forms on Ni substrates
the deposition of an intermediate graphite layer is observed (Rudder et al., 1988; Belton
and Schmieg, 1989; Eimori et al., 1993). Such an intermediate layer prohibits the oriented
growth of diamond films in registry with the Ni substrates.
In this study, we observed how a Ni substrate is affected by pure H2 and
(CH4+H2) plasmas under diamond film growth conditions This is a first step in
understanding how carbon and hydrogen interact with the Ni surface, and what C phases,
if any are present on the surface at different stages in the growth process. The Ni substrate
in this study was a thin film prepared on quartz by sputtering and its thickness was about
127
2400 A. The microwave plasma CVD reactor system was same as that used for diamond
thin film growth on c-Si substrates. First, the Ni substrate was heated from room
temperature and stabilized at 800 °C while RTSE measurements were performed. Next, the
sample was exposed to a pure H2 plasma using a flow rate of 99 seem; a microwave power
of 500 W; and a total pressure of 7 Torr for a time duration of 60 min. Finally methane gas
(1 seem) was added to the H2 plasma. The sample was exposed to both plasmas for a total
of 2 hours. The Ni sample was also measured with ex situ SE before and after the entire
experiment. Figure 4.31 shows the ellipsometry data (A, *F) at a photon energy of 3.0 eV
vs. the elapsed time during the processing steps. There is comparatively little change during
annealing at 800 °C for 10 min. This time period was chosen for the anneal because in
performing the diamond film growth experiment, it usually takes 10 min or less from the
time when the temperature setting is reached until the plasma is ignited. After ignition of the
H2 plasma and the addition of CH4, the ellipsometry data change significantly over time.
The effect of the H2 plasma on Ni was studied using the spectra collected just
before CH4 addition. The spectra were simulated using various possible structural models
including overlay er formation or substrate modification. In these simulations the last
spectra obtained during annealing at 800 °C was converted to a dielectric function assuming
a single interface model [Eq. (2.33)]. This dielectric function served to characterize the
substrate in the H2 plasma analysis. The simulations showed that using graphite as an
overlayer on Ni fitted the data best and the regression analysis gave a 5+1 A thick
overlayer. In addition, a small volume fraction of graphite (fgrap = 0.05±0.01) was
incorporated within the substrate in the best fit model. We suggest that the graphite forming
during the pure H2 plasma treatment arises from a chemical vapor transport process. In this
process the graphite substrate holder is etched by the H2 plasma, generating hydrocarbon
species which react at the Ni surface. The model for the H2-exposed Ni sample is
consistent with results reported previously for the graphitic layer formation on unseeded Ni
128
108
106
104
i
•
i • i • i • i • i
without plasma
/ @ 800 °C
• i • i
CH4 add
without plasma
@25°C
102
100
I [ I i i | I 1 I 1 I | I 1 I | 1
30
. without plasma
@25°C
29
28
'
without plasma
@800°C
CH4add
27
26
25
24 h
Hydrogen plasma
23
-40 -20 0 20 40 60 80 100 120 140
TIME (min)
Fig. 4.31 (A, *F) at 3.0 eV plotted vs. time showing the changes in the raw data for a Ni
substrate as a function of the various processing conditions: (1) heating from 25 °C to 800
°C, (2) annealing at 800 °C, (3) exposure to a H2 plasma, and (4) exposure to a plasma of
H 2 andCH 4 .
129
surfaces (Belton and Schmieg, 1992). In addition, the fact that bulk Ni modification is
required in the modeling suggests that a small amount of C is diffusing from the surface
into the bulk. However, it is likely that the picture suggested by the EMA, namely, clusters
of graphite within the Ni matrix is not correct. It is more likely that the optical effect of the
included graphite is the same as that of a reduction in the electron mean free path of the Ni
which can occur due to the diffusion of either C atoms or H atoms into the bulk Ni. More
work needs to be undertaken in an attempt to understand this effect better.
In order to analyze the data collected during exposure to the H2+CH4 plasma, the
so called '£a minimization' approach was utilized. The substrate dielectric function used in
this analysis was that of the modified Ni material obtained after H2 plasma exposure. This
was calculated from the real time data set (collected just before introducing the CH4) using
a single interface model. Because of its thickness, it is safe to neglect the presence of the 5
A graphite overlayer for the purposes of the subsequent modeling. In Sa minimization, the
final thickness of a presumed overlayer on the substrate was assigned a trial value
appropriate for the sample after H2+CH4 plasma exposure. Then the dielectric function of
the overlayer was mathematically inverted from the last (*F, A) spectra obtained during
H2+CH4 plasma exposure. (The inversion procedure is similar to that described in the
temperature calibration experiment.) With the resulting trial dielectric function of the
overlayer, the entire real time data set measured during H2+CH4 plasma exposure was
analyzed using a one-layer model as in the diamond nucleation analysis. To complete this
first step E a(tj), the sum of the unbiased estimators of the mean square deviation for the
full real time analysis was calculated as a measure of the quality of the overall fit and the
validity of the initial thickness guess. In the next step, another trial overlayer thickness was
chosen, differing from the first value by a preselected increment. Then the same analysis
procedures as in the first step were applied. After several iterations with different thickness
values covering the penetration depth of the light, the sum of unbiased estimators of the
130
mean square deviation, £ o(tj), for each step was plotted versus the trial thickness value.
In this plot a minimum value was observed and the trial dielectric function (ei)end» £2,end)
corresponding to this minimum in £ o(tj) was used for the overlayer. In the X a
minimization procedure the initial increment in the trial overlayer thickness was set at a
relatively large value in order to avoid local minima which would lead to an incorrect result.
After the global minimum in £ o(tj) is identified, the increment size can be reduced in
order to achieve a more accurate thickness. Figure 4.32 shows the result of this approach,
which revealed a minimum in £ a(tj) for an overlayer thickness of 193 A. The associated
dielectric function (£i,end» £2,end) is compared to that of the initial Ni film and the H2plasma modified Ni (all at 800 °C) in Fig. 4.33. Figure 4.34 shows the overlayer thickness
and a vs. time for the one layer model using (£i,end> £2,end) as the overlayer dielectric
function.
With this first analysis as a starting point, we can assess its validity based on the
overall quality of the fit which is characterized by the time evolution of o in Fig. 4.34. It is
clear that in the initial stages of CH4+H2 plasma exposure, the one layer model with the
dielectric function of Fig. 4 33 is not appropriate. However, for t>15 min, a is as low as
can be expected given the instrument precision. Thus, over this latter time regime the single
layer model appears to be sufficient. As a result, the graph of d vs. time in Fig. 4.34 can be
divided into two time regions t<to and t>to, where to=15 min. For t<to, the one-layer model
analysis was repeated, again using the Za minimization analysis outlined above with the
expectation that a more appropriate dielectric function characteristic of the initial material
would be deduced. With this new analysis performed at t=7 min, the thickness of the initial
layer (di) was found to be 40 A. After extracting the dielectric function (e^, e^) associated
with the 40 A film, the IXJ minimization analysis for two layer model was performed again,
focusing on the last spectrum collected at t=66 min during H2+CH4 plasma exposure. In
the initial two-layer Za minimization, the 40 A film was assumed to be left at the substrate
131
0.40
- i — i — | — i — | — i — | — i — | — i — | — i — | — i — p
0.35
Ea
0.30
-
0.25 i
150
• i i i • i i i • i • i • i •»
160 170 180 190 200 210 220 230
guess
Fig. 4.32 The result of Ea minimization for the analysis of a Ni substrate exposed to a
(CH4+H2) plasma using an optical model consisting of a single layer. A plot of IXJ vs. the
trial overlayer thickness is shown along with a second-order polynomial fit used to
establish the minimum. The minimum occurs for an overlayer thickness of ~ 193 A.
132
T
1
r
CO
V
CO
l.end' ^ . e n d '
<
•15
8,
.>, <8,
u>
l.sub '
2, sub
i I i I i I i 1 ' I i
- before H2 plasma ignition
- (Ej, S2) @ RT in literature
0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
PHOTON ENERGY (eV)
Fig. 4.33 The dielectric function (eiiend, £2,end) corresponding to the overlayer obtained by
the So minimization method in Fig. 4.32. This result is compared to the bulk dielectric
functions of Ni (i) at room temperature from the literature, (ii) at 800 °C from this study,
and (iii) at 800 °C after H2 plasma exposure also from this study.
133
200
0.003
0.002
0
10
20
30
40
50
60
70
TIME (min)
Fig. 4.34 The results of real time analysis of data collected during exposure of a Ni sample
to a H2+CH4 plasma assuming a one-layer growth model. The dielectric function and final
thickness of the layer were established using the 2a minimization method of Fig. 4.32.
Shown here are: (a) the thickness vs. time, and (b) a vs. time.
134
interface without any changes in its thickness or optical properties. With this assumption,
the second layer thickness was found to be -150 A thick. From this thickness, we could
extract the dielectric function for this second layer (e®, s®) , which is expected to be
similar to that found in the one-layer analysis.
Now the dielectric functions for all layers including the substrate are known. These
are designated (ei)Sub. e2,sub). ( s ^ 6 ^ *
and
( 8 ir E 2^ ^ or t h e
su
bstrate, first layer, and
second (top) layer, respectively and are included in Fig. 4.35 for comparison. With the
known dielectric functions, the real time analysis was performed for the entire data set
(0<t<66 min) using the one layer model for 0<t<to and two layer model t>to. The results of
the final analysis are shown in Fig. 4.36. As noted earlier, the layer established by the onelayer model for 0<t<to is assumed to remain fixed at the substrate interface for t>to. Within
this model, the interface layer in Fig. 4.36 forms first before the top bulk layer develops
and can be interpreted as the finite width of a diffusion front. In this layer, the
concentration of C and H must be lower than in the top bulk layer which serves as a
continuous source of C and H for the diffusion front. However, after considering the
results in Fig. 4.35 carefully, this interpretation is contradicted by the observation that the
dielectric function of the first (underneath) layer, (e i »82'> is more strongly modified from
that of the substrate Ni in comparison with the second (top) layer.
Because of this contradiction, a different optical model was used to perform the 2 a
minimization analysis for two layer model. In this alternative model, the initial 40 A film
was assumed to be left at the surface rather than at the interface. With this assumption, the
new interface layer thickness was found to be -255 A thick. From this thickness, a new
dielectric function for the interface layer (eipejj1') was extracted and is shown in Fig. 4.35
along with the dielectric functions extractedfromthe previous assumption that the initial 40
A film was left at the interface. The top layer is most likely a Ni-C-H alloy whose optical
properties are much different than Ni (see Fig. 4.35). In Fig. 4.36, the a values for the two
135
CO
CO
1.5
2.0
2.5
3.0
3.5
4.0
4.5
PHOTON ENERGY (eV)
Fig. 4.35 The dielectric functions (ei, sub , e2,SUb)» (*f,ef), (ef.e^), and
(ef,ef)
corresponding to the substrate, first (underneath) layer, second (top) bulk layer, and an
alternative bulk layer. (ef,e^) was obtained for t<to assuming one-layer growth model,
C2S
(Tk
and (s l , ey) was obtained for t>to assuming that a two-layer model is correct and that the
layer with ( e ^ e ^ is left at substrate interface. (ef,ef) (solid line) was obtained for t>t0
assuming that the two-layer model is correct and that the layer with (e^ej*) is left at
surface. The Zo minimization analysis was applied in both time regimes.
136
0.010 i — • — r
0.008
-,—.—|-
i—•—r
L (a)
0.006
t>
0.004
0.002
0.000
6—
I i1i1iIi I
240
200
160
^
120
0
10
20
30
40
50
60
70
TIME (min)
Fig. 4.36 Results of real time analysis of data collected during H2+CH4 plasma exposure
of a Ni sample assuming a two-layer model: (a) a vs. time and (b) thicknesses vs. time.
The dielectric functions used for the analysis are (ei)Sub» e2,sub)» (^j . e ^ , (E®,e®), and
(8j ,8^) as shown in Fig. 4.35. The solid circles are for a model using (s^ ,e^) as the
dielectric function for the underneath interface layer (thickness dj)and (e ®,e!!p as dielectric
function for the top bulk layer (thickness db). The open circles are for model using
(Ej ,e^) as dielectric function for the top surface layer (thickness ds) and (e j ,8?0 as
dielectric function for the underneath bulk layer (thickness db). The improved a values
show that the latter model (open circles) is the correct one.
137
different models are compared. The open circles are for the analysis performed using the
assumption that the initial 40 A film was left at the surface. On the other hand, the solid
circles are for the analysis performed using the assumption that the initial 40 A film was left
at the interface. It is clear that the former model is the correct one, and the two correct
dielectric functions are given in Fig. 4.35 with (e^e^O being for the top layer and
(s j , E^) being for the underlying layer. Figure 4.36 also compares the thickness evolution
for the two layers (dj and db for the interface and bulk layers when the first layer is
assumed to remain at the interface, and db and ds for the bulk and surface layers when the
first layer is assumed to remain at the surface). In this case also the model with the lowest
a(t) yields the most reasonable thickness trends.
In performing this experiment, if the Ni thin film sample is exposed to the plasma
for too long time, the sample starts becoming semitransparent due to a continuous etching
of the Ni-C-H alloy. Therefore, a thicker Ni sample should be used for a longer experiment
to prevent excessive complexity in the optical model. In addition, a ex situ chemical
analysis methods such as SIMS (secondary ion mass spectroscopy) or Auger sputter-depth
profiling needs to be undertaken in order to support the results deduced by RTSE.
138
CHAPTER 5
CONCLUSIONS AND FUTURE WORKS
Real-time spectroscopic ellipsometry (RTSE) based on the rotating polarizer
configuration and photodiode array detection system was developed and utilized for
studying diamond thin film growth by microwave plasma enhanced chemical vapor
deposition. The novel detection system was investigated in detail in order to reduce
systematic errors and improve the accuracy of the RTSE data. This included
characterization of nonlinearity and image persistence and the correction of these errors. A
new calibration method based on the dc irradiance level was reviewed, and the first order
corrections for residual source polarization were introduced. For further improvement of
RTSE in the future, a more detailed study of source polarization is required to assess the
assumptions involved in the theory first developed here. This includes the validity of the
Jones matrix approach and the overall assumption of a first order analysis. It is also
important to reduce this error at its source, rather than incorporating complex correction
procedures. Any such reduction is helpful since it may eliminate the need for higher order
correction terms. With respect to the non-linearity correction, it appears necessary to
improve this procedure to ensure that l-(a2+P2) vanishes above 3.7 eV. The fact that it
does not is most likely related to an incorrect functional form for the correction factor at low
count levels.
As an application of RTSE, a detailed study of microwave plasma enhanced CVD
diamond film growth was undertaken. First, the use of RTSE to calibrate c-Si substrate
139
temperature under the conditions of diamond film growth was described. Calibration
curves have been established that relate the nominal substrate temperature, as measured by
a thermocouple mounted in the substrate platform, to the true substrate temperature as
measured by SE over the range from 200 to 900 °C. The temperature obtained by RTSE is
characteristic of the surface because the penetration depth of the light is 220 A. This
represented a first step in the use of RTSE to achieve greater control in the subsequent
diamond deposition studies. As an application of accurate substrate surface temperature
calibration, we have determined the growth rate of diamond as a function of the true surface
temperature (500 °C<T<800 °C) under a set of standard deposition conditions. The growth
rate was found to reach a maximum near about 800 °C. The maximum possible activation
energy for diamond growth over the temperature range from 500 to 700 °C was ~9
kcal/mol.
A large part of this thesis work was devoted to the evolution of the microstructure
and sp2 C content with thickness in nanocrystalline diamond prepared using different gas
mixtures. For this experiment, c-Si was seeded by abrading the surface with diamond
powder having a particle size less than 0.25 u,m, which led to the high nucleation density
(~4xl010 /cm2). The diamond films studied here were prepared using the various feed gas
mixtures: (1) H2+CH4, (2) H2+CH4+O2, and (3) H2+CO. The microwave power was 500
W, the temperature was ranged from 500 to 900 °C, and the pressure ranged from 7 to 10
Torr. The results provided insights into the diamond deposition that are leading to
improvements in the interface quality of the materials.
We found that the RTSE data collected during diamond deposition were consistent
with a transition from a one-layer optical model, describing isolated nuclei, to a two-layer
optical model describing a coalesced structure. The isolated diamond nuclei prior to
coalescence exhibited a low volume fraction of sp2 C (typically about 0.01-0.03) over a
relatively wide range of gas compositions. When the particles make contact (after a
140
thickness of ~260 A), a large fraction of sp2 C (-0.4) often develops between nuclei. This
sp2 C is trapped between coalescing crystallites and further sp2 C does not develop with
increasing thickness under optimum conditions (e.g., 1% CH4 in H2) once the film surface
becomes smooth (~100 A roughness). At higher CH4 flows in H2, the grain boundary
defects arising in the coalescence process serve as nucleation sites for extensive sp2 C
generation in the subsequent growth process. With the addition of O2 to CH4 and H2, one
can scan out the region of the C-H-0 gas-phase diamond-growth diagram nearest the Hvertex. In fact, the growth-etch boundary which runs parallel to the line connecting the CO
point with the H-vertex can be identified using RTSE in an instantaneous feedback mode.
With O2 additions to the gas that bring the mixture just within the growth-etch
boundary (e.g., CH4=5 seem, 02=10 seem, H2=79 seem) diamond films with a very high
quality interface to the substrate can be obtained. An improved bulk structure also resulted;
for example, the sp2 C volume fraction of -2000 A thick bulk diamond films was reduced
from 0.16 for 6% CH4 in H2 with no O2 to 0.02 for 6% CH4 in H2 but with an 11%
addition of O2. Using CO+H2 as the feed gas for film growth, the diamond phase could
also be obtained. Furthermore, this study showed that there is an optimum CO/H2 flow
ratio defined by the phase diagram coordinate XH/Z=[H]/{[H]+[C]}=0.9 above and below
which the diamond interface quality degrades. This optimum appears to have been
overlooked in previous studies by other workers who have focused on the bulk properties
of films prepared by CO+H2. In the previous studies, the diamond bulk properties have
been reported to degrade with increased CO/H2 ratio without showing any maximum.
In the present study when the nucleating and bulk layers are very thin (d~50 A
when a one-layer model is applied and db~150 A when a two layer model is applied), it
was difficult to extract the layer compositions. Future gains in this area may be expected
through an improved reference dielectric function for sp2 C.
141
In this study, it was found that the diamond seeding procedure was very difficult to
control and did not always produce the same nucleation conditions (as an example see Fig.
4.27). Thus, a new method to compensate for these unexpected variations is needed. One
of the new methods to improve the nucleation density and to avoid the irreproducible
effects on nucleation is to eliminate the seeding step by using the bias-enhanced nucleation
method. In this process the wafer is pre-treated by negatively biasing it during plasma
exposure to generate diamond nuclei on the Si surface (Yugo et al., 1991; Wolter et al.,
1993). This method may eliminate the variations sometimes observed in the course of this
thesis research.
As a first step in studies of diamond thin film growth on other substrates besides
seeded Si, RTSE was applied to investigate the evolution of the properties of a thin film Ni
sample during exposure to the H2 and CH4+H2 plasmas under conditions used to obtain
diamond in the studies on Si substrates. Ni has a close lattice constant close to that of
diamond (i.e., a=3.52 A for Ni and a=3.56 A for diamond). The analysis showed that data
obtained under H2 plasma exposure were fitted best with a thin graphite layer on Ni.
Simultaneously the bulk optical properties of the Ni were modified by diffusion of H
and/or C impurities. Exposure to CH4 in H2 led to a much larger change in the optical
properties of the Ni due to the incorporation of larger amounts of C into the network. In
this case, the change is large enough so that a diffusion front can be detected passing
through the film. This modified layer is metallic in nature and presumably contains Ni, C,
and H. No additional C phases beyond the few monolayers of graphite are detected on the
Ni surface.
Future studies of diamond growth on both Ni and other metals need to be
undertaken in order to better understand the substrate modification and interface properties
of these films. For example, diamondfilmson Mo substrates have potential applications in
142
cross-field amplifiers operating in the microwave region. Such devices rely on electron
emission from the surface of the diamond film which may be a sensitive function of the
volume fraction of sp2-bonded C in the material. Thus, the ability of RTSE to provide the
information as a continuous function of film thickness may lead to improved control over
film preparation which may be needed to obtain devices with the desired characteristics.
143
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VITA
Byungyou Hong was born January 25, 1960 in Seoul, the Republic of Korea to
Myun-Hoo Hong and Dong-Ryun Park. He has a brother, Taik-Yoo Hong, and two
sisters, Ji-Min Hong and Seung-Jin Hong. Byungyou graduated from Kyunggi High
School in 1979. In 1986 he graduated from Sungkyunkwan University with a Bachelor of
Engineering degree in Electronics. He served in the Korean Army for two and half years
between 1981 and 1983.
In 1989 he graduated from the University of Florida with a Master of Engineering
in Electrical Engineering. After that he transferred to Pennsylvania State University and
continued his work in the doctoral program in the Department of Electrical Engineering.
He joined the Materials Research Laboratory in December 1991.
On August 9, 1986, Byungyou married Hyejung Kim in Seoul, the Republic of
Korea and has two daughters, Joanna Hong and Rachel Hong, and a son, Edward Hong.
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