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MEASUREMENT OF RESIDUAL STRESS IN THIN
DIAMOND FILMS BY RAMAN SPECTROSCOPY AND
THE BEAM DEFLECTION EQUATION
BY

Naoufel Turki

A THESIS

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Materials Science and Mechanics

1996

ABSTRACT

MEASUREMENT OF RESIDUAL STRESS IN THIN DIAMOND
FILMS BY RAMAN SPECTROSCOPY AND THE BEAM
DEFLECTION EQUATION
By

Naoufel Turki

The properties of natural diamond and the effect of
deposition parameters on the deposited synthetic diamond films
were reviewed. A new model for calculating thermal expansion
mismatch stress between the film and the substrate is proposed.
Residual stress in a diamond film deposited by MPCVD on a
silicon substrate was measured from the change in substrate
curvature according to Stoney’s equation and from the shift in the
Raman peak position at 1332.5 cm". Both methods were found to
measure the average stress in the diamond film. Assumptions
made to derive stress equations for both methods were not truly
satisfied. Polycrystalline diamond film presents a problem for the
Raman Shift method and the non uniformity in the diamond film
thickness coupled with the anisotropy of the single crystal
substrate and possible texture in the diamond film create
obstacles to directly applying Stoney’s stress equation. The
magnitude of the stress measured from Stoney’s equation and

Raman shift are comparable to reported values in the literature.

TABLE OF CONTENT

LIST OF TABLES ................................................................................................ vi
LISTS OF FIGURES .......................................................................................... vii
LIST OF SYMBOLS USED ................................................................................ xii
1. INTRODUCTION ........................................................................................... 1
1.1. Overview ............................................................................................. 1
1 .2. Background ......................................................................................... 2
2. PROPERTIES AND DEPOSITION OF DIAMOND FILMS ............................. 6
2.1. Properties of natural diamond ............................................................. 6
2.2. Properties of synthetic diamond .......................................................... 9
2.3. Diamond deposition techniques ........................................................ 12
2.4. Mechanical properties of diamond thin films ..................................... 13
2.5. Effect of deposition parameters ........................................................ 19
2.6. Effect of deposition pressure ............................................................ 20
2.7. Effect of deposition temperature and substrate temperature ............ 22
2.8. Effect of methane and hydrogen gas on film properties .................... 28
3. PARAMETERS AFFECTING RESIDUAL STRESS ..................................... 37
3.1. Effect of film thickness on residual stress ......................................... 37
3.2. Effect of ion beam energy on stress .................................................. 40
3.3. Effect of deposition rate on residual stress ....................................... 42
3.4. Effect of deposition pressure on residual stress ............................... 45
3.5. Effect of deposition incidence angle on residual stress .................... 46
3.6. Effect of crystallite size on stress ...................................................... 48

iii

4. STRESS MEASUREMENT METHODS 50

4.1. X-ray stress measurement ........................................................... ‘ ..... 50
4.2. Stress measurement with the energy gap method ............................ 51
4.3. Stress calculation from the curvature change of the substrate ......... 53
4.3.1. Importance of the film thickness ............................................. 60

4.3.2. Errors and resolutions ............................................................ 63

4.3.3. Advantages of the curvature method ...................................... 68

4.4. Stress measurement from the Raman peak shift .............................. 70
4.4.1. Nature of the dependence of stress on the frequency Shift 79

4.4.2. What cauSes Raman shifts ..................................................... 84

4.4.3. Advantages and weaknesses ................................................. 90

4.4.4. Limitations and sensitivity ...................................................... 93

5. DEPOSITION THERMAL STRESS .............................................................. 96
5.1. Effect of deposition temperature, thermal stress ............................... 96
5.2. Thermal stress modeling ................................................................... 97
5.3. Variation of stress with deposition temperature ................................ 98
6. EXPERIMENTAL PROCEDURE ................................................................ 113
6.1. Materials .......................................................................................... 113
6.2. Diamond deposition ......................................................................... 113
6.3. Curvature measurement .................................................................. 114
6.4. Annealing heat treatment ................................................................ 116
6.5. Raman Spectroscopy ...................................................................... 118
6.5.1. Calibration of Raman spectroscopy ...................................... 119

6.6. Film thickness and grain size measurement ................................... 120

iv

7. EXPERIMENTAL RESULTS ...................................................................... 122

7.1. Curvature measurement .................................................................. 122
7.2. Raman spectra and peak positions ................................................. 132
7.3. Film thickness ................................................................................. 133
7.4. Grain size ........................................................................................ 134
8. CALCULATION AND DISCUSSION .......................................................... 166
8.1. Stress measurement from Stoney‘s equation .................................. 166
8.2. Stress measurement from the Raman peak position shift ............... 173
9. CONCLUSIONS AND RECOMMENDATIONS .......................................... 188
REFERENCES ................................................................................................ 192

Table 1.
Table 2.

Table 3.

Table 4.
Table 5.
Table 6.
Table 7.
Table 8.

Table 9.
Table 10.

LIST OF TABLES

Physical properties of bulk diamond. page 10
Properties of various types of diamonds [ after table 23, page 295 in
[18] and [25] p. E-11]. page 11
Elastic constants and deformation potentials of silicon and diamond.
page 77
Reported diamond shifts under stress. page 78
Curvature measurement results. page 124
Toluene calibration peak positions and errors. page135
Raman peak positions of samples used. page 136
Stresses calculated from Raman peak shifts for silicon and diamond.
page 179
Summary of stress measurement results. page 180
Reported residual stress values in diamond and carbon films. page 187

vi

LIST OF FIGURES

Figure 1. Average grain size in diamond films versus methane fraction in
hydrogen. After Windischmann [21]. page 16

Figure 2. Raman spectra of diamond films prepared at a) 0.3percent CH4,
b) 2.5 percent CH4 and c) 7.5 percent CH4. After Windischmann[10].
page 17

Figure 3. Deposition rate of diamond films versus substrate
temperature. After Liou [33]. page 24

Figure 4. Raman spectra of deposited diamond films at a) 825°C

and b) 550°C. After Windischmann [21]. page 26

Figure 5. sp2 carbon fraction in diamond versus methane fraction in hydrogen.
After Windischmann [10]. page 30

Figure 6. Hydrogen content in daimond films versus methane fraction. After
Windischmann [10]. page 35

Figure 7. Average stress versus film thickness. After Blackburn [45]. page 38

Figure 8. Dependence of growth stress on diamond film thickness. After [46].
page 41

Figure 9. Residual stress versus ion bombardment energy. After Argon [3].
page 43

Figure 10. Average film stress versus deposition rate. After Blackburn [45].
page 44

Figure11. Three dimensional two layer system. page 47

vii

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18a.

FIQUI'B 18b.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Average stress in LiF films vrsus crystallite size. After Blackburn [45].

page 49
Substrate and film bowing to radius of curvature p. Ds is the substrate

diameter. t1 and t8 are respectively the thickness of the film and the

substrate. page 56 ,

Graphical reperentation of thermal stress in diamond films on a
silicon substrate. page 99

Temperature depndence of the thermal expansion coeffecients of
silicon and diamond [81]. page 103

Difference of thermal expansion coefficient od diamond and silicon
asfunction of temperature. Ra0.997. page 104

Residuals as a function of temperature for the cubic fit for the thermal
expansion difference in figure 16. page 105

Variation of YoUng's modulus with temperature accoeding to
Wachtman's equation 47. page 110

Temperature depence of Young's modulus fitted to a cubic function
in the CVD temperature deposition range with R310. page 111

Temperature dendence of thermal stress calculated from equation 51.
page 112

Surface profile of uncoated silicon 1 wafer taken with a dektak
II on the polished side. page 125

Surface profile of uncoated silicon 2 wafer taken with a dektakll on
the polished side. page 126

Surface profile of uncoated silicon 3 wafer taken with a dektak II on
the polished side. page 127

Surface profile of annealed and uncoated silicon 2 wafer taken with
a dektak II on the polished side. page 128

viii

Figure 24.

figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 29a.

Figure 30.

Figure 30 a.

Figure 31.

Surface profile of annealed and uncoated silicon 3 wafer taken with
a dektak II on the polished side. page 129
Surface profile of the diamond on silicon water in theas deposited
state taken with a dektak II on thesilicon ( unpolished ) side. page 130
Surface profile of the diamond on silicon wafer in theannealed state
taken with a dektak II on the silicon (unpolished )side. page 131
Raman spectrum of toluene used as calibration for silicon Raman
spectra and taken with a 488 nm argon laser at 1800 g/mm
and 100 microns slit width. page 137

Raman spectrum of toluene used as calibration for diamond Raman
spectra and taken with a 488 nm argon laser at 1800 g/mm
and 100 microns slit width. page 138

Raman spectrum of Uncoated silicon 2 water on the rough side taken
with a 488 nm argon laser at 1800 g/mm and 100 nms slit
width. page 139

Expanded silicon peak from the Raman spectrum of
uncoated silicon 2 wafer on the rough side. Figure 29. page 140

Raman spectrum of uncoated silicon 2 wafer on the polished side
taken with a 488 nm argon laser at 1800 g/mm and 100 nms
slit width. page 141

Expanded silicon peak from the Raman spectmm of uncoated Silicon
2 wafer on the polished side. figure 30. page 142

Raman spectrum of annealed & uncoated silicon 2 wafer on the
rough side and taken with a 488 nm argon laser at 1800 91mm

an 100 nms slit width. page 143

ix

figure 31a. Expanded silicon peak from the Raman spectmm of annealed 8:

Figure 32.

Figure 323.

Figure 3.

figure 3a.

figure 34.

Figure 34a.

Figure 35.

uncoated silicon 2 wafer taken on the rough side. figure 31.
page 144

Raman spectrum of annealed 8: uncoated silicon 2 wafer on the
polished and taken side with a 488 nm argonlaser at 1800 glmm
and 100 microns Slit width. page 145

Expanded silicon peak from the Raman spectrum of annealed &
uncoated silicon 2 wafer taken on the polished side. figure 32.
page 146

Raman spectrum of the coated silicon substrate on the back side
(rough) of the silicon diamond sample and taken with a 488 nm
argon laser at 1800 glmm and 100 microns slit width. page 147

Expanded silicon peak from the Raman spectrum of the
coated silicon substrate on the back side (rough) of the
silicon diamond sample. Figure 33. page 148

Raman spectmm of the silicon substrate on the back side (rough)
of the annealed & coated silicon diamond sample and taken with
a 488 nm argon laser at 1800 glmm and 100 microns slit width.
page 149

Expanded silicon peak from the Raman spectrum of the coated silicon
substrate on the back side (rough) of the annealed silicon
diamond sample. figure 34. page 150

Raman spectrum of the silicon substrate at the interface side of the
coated silicon diamond sample and taken with a 488 nm argon
laser at 1800 glmm and 100 microns slit width. page 151

Figure 35a. Expanded silicon peak from the Raman spectrum of the coated
silicon substrate at the interface of the siliconodiamond sample.

figure 35.page 152
figure 36. Raman spectrum of the annealed & coated siIicon substrate at the
interface side at the silicon diamond sample and taken with a 488
nm argon laser at 1800 glmm and 100 microns int width. page 153
Figure 36a. Expanded silicon peak from the Raman spectmm of the annealed
& coated silicon substrate at the interface of the silicon-diamond
sample. figure 36. page 154
Figure 37. Raman spectrum of the diamond film in the as deposited state in the
silicon-diamond sample and taken with a 488 nm argon laser
at 1800 glmm and 100 microns slit width. page 155
Figure 37a. Expanded diamond peak from the Raman spectrum of the diamond
film in theas deposited State in the silicon-diamond sample.
Figure 37. page 156
Figure 38. Raman spectrum of the diamond film in the annealed state in the
silicon-diamond sample and taken with a 488 nm argon laser
at 1800 glmm and 100 micronsslit width. page 157
Figure 38a. Expanded diamond peak from the Raman spectrum of the diamond
filmin the annealed state in the silicon-diamond sample. figure 38.
page 158
Figure 39. SEM micrograph of a cross section of the silicon-diamond sample
at the interface showing the diamondfilm at 780 times magnification.

page 159

xi

figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.

SEM micrograph of a cross section of the silicon-diamond sample

at the interface showing the diamond film at 1800 times

magnification. The location on the interface if different from that in

figure 39. page 160

SEM micrograph of a cross section of the silicOn-diamond sample

at the interface showing the diamond film at 1800 times

magnification. The location on the interface is different from that in
figure 40. page 161

SEM micrograph of a cross section of the silicon-diamond sample
at the interface showing the diamond film at 780 times
magnification. The location on the interface if different from that in
figure 41. page 162

SEM micrograph of a cross section of the coated silicon wafer at the
interface showing the full width silicon substrate at 160 times
magnification. page 163 .

SEM micrograph of the diamond film showing the microstructure
consisting of (111) oriented grains at 6.600 times magnification.
page 164

SEM micrograph of the diamond film showing the microstructure
consisting of (111) oriented grains at 6.600 times magnification.
The micrograph was taken at a different location from than in

figure 44. page 165

xii

LIST OF SYMBOLS USED

em: Thermally induced strain
om: Thermally induced stress.

a: Total residual strain in the thin film.
on: Total residual stress in the thin film.

T: Temperature.

Ts: Substrate temperature.

Es: Young’s modulus of the substrate material.

: Young's modulus of the film material.

Q

as: Thermal expansion coeficient of the substrate.

: Thermal expansion coeficient of the film.
t : Substrate thickness.

t,: film thickness.

vs: Poisson ratio of the substrate material.

Vt: Poisson ratio of the film material.

p: Radius of curvature of the films-subtrate composite.

xiii

1- INTRODUCTION

1. 1 Overview

Due to its excellent properties, synthetic diamond films are being
increasingly used and studied.

In this work, a detailed review of the properties of natural diamond is
presented in section 2.1 to serve as a basis for comparison with the
properties of deposited synthetic diamonds. Depositions techniques
and the effects of deposition parameters on the properties of synthetic
diamonds are discussed in the remainder of chapter 2.

Residual stress measurement in thin diamond films is the main topic
in this thesis. A review of the effect of film properties ( film thickness
and grain size ) as well as the effect of deposition parameters on the
magnitude and sign of residual stress in thin films is discussed in
chapter 3.

In chapter 4, x-ray and energy gap stress measurement techniques
are briefly discussed while a detailed discussion of stress measurement
from the curvature change in a coated substrate and the Raman peak
position shift are presented in section 4.3 and 4.4. Stress calculation
formulas are derived and the two methods are analyses in terms of the
assumptions made and the applicability of those assumptions to the

specific silicon-diamond system used in the experimental procedure.

In chapter 5, a new model is presented for calculating the thermal
stress that develops in diamond films upon cooling to room temperature
from the deposition temperature. The temperature dependence of the
thermal expansion mismatch between the diamond film and the silicon
substrate and the Young's modulus temperature dependence are
considered in the proposed model.

The experimental procedure is presented in chapter 6, while the
experimental results are given in chapter 7. Calculation of the stress by
the two methods and discussed of the results is presented in chapter 8.

Conclusion and recommendations are given in chapter 9.

1.2 Background

In 1909, Stoney [1] discovered large internal stresses in
electroplated films. Since then, many researchers have studied the
nature and effects of internal residual stress on thin films.

Residual stress in thin films can cause undesirable properties.
Internal stresses induced by the deposition process induce buckling of
the beam-substrate composite [2], and can promote interface cracking,
by providing additional driving force for crack propagation. Argon and
Gupta [3] found that SiC films deposited on single crystal silicon water
by plasma assisted chemical vapor deposition ( PACVD) process,

delaminated spontaneously under residual stress, when the thickness of

the film is above a critical value of about 1 pm [3]. Cracking was also

observed at the interface of semiconductor films (GaP. GaAs, lnP)

grown on silicon substrates. due to residual stress [4]. Strains Up to

2x10'3 were measured in the semiconductor films.

In silicon coating on Pitch-55 carbon fibers, the coating trapped a
large concentration of hydrogen. The trapped hydrogen in the film
resulted in large compressive residual stresses in the silicon film. Upon
embedding the coated fibers in the metal matrix, hydrogen diffused to
the metal matrix leaving voids behind which resulted in severe
debonding of the fibers from the metal matrix [3]. Blunberg [5] reported
that super conducting critical temperature in thin films increased with
decreasing film thickness. An Increase in film thickness also resulted in
an increase in the residual stress. Freedman [6] reported that thermal
stress at 275°C due to thermal expansion mismatch was sufficient to
induce a phase change to a tetragonal structure in nickel films on NaCl
substrate. The stress was compressive and measured ~1.0 GPa.

It is evident that the existence of residual stress in thin films affects
their properties. Therefore, it is critical to understand the behavior and
dependences of film stress so that the film-substrate composites behave
as they are designed.

There is an exhaustive amount of literature on the mechanisms and
measurement of residual stress in thin metal films. A lesser amount
however does exist for dielectric thin films. At a given temperature,
internal stress has two components: intrinsic and extrinsic. Extrinsic

stresses result from thermal expansion coefficient mismatch between the

substrate and the film which in turn depends on the difference between
film growth temperature. during deposition and stress measurement
temperature.

Intrinsic stresses are growth stresses arising from such effects as
incomplete structural ordering processes, which could result in lattice
misfit strains. Intrinsic stresses can also arise from contamination of the
film. Internal stresses are therefore a strong function of the deposition
process and parameters such as deposition temperature, pressure. rate,
film thickness. sputtering ion beam energy as well as other parameters
[7.8]. Choice of film and substrate materials can reduce residual
stresses arising from thermal expansion mismatch and lattice mismatch.
However, residual stress elimination or reduction can bestbe pursued
by changing the deposition parameters. Controlling all these material
and deposition parameters can affect both the magnitude and the sign of
internal stresses.

Measured stresses in carbon films are usually compressive [7.9].
The magnitude of the stress for CVD diamond is about 1 GPa [9]. The
magnitude of the compressive stresses in DLC films deposited by ion
beam sputtering methods are higher than in CVD films. Tensile stresses
in CVD films have also been observed [10]. While compressive stresses
are understood, tensile stresses in CVD diamond films are not so easily
explained. The grain boundary relaxation model ( GBRM ) has been
proposed to explain the origin of the tensile intrinsic stresses in CVD

diamond [10]. Compressive-stresses are thought to be due to ion

bombardment in sputtered films and to impurities in CVD films

[ 9.11.12 ]. When diamond is deposited on silicon the lattice mismatch
strain is tensile in the diamond films. However. thermal expansion
mismatch stress between silicon and diamond is expected to be
compressive in the deposition temperature range of CVD diamond ( less
than 1200°C). and can become tensile at temperatures greater than
1220°C [10] which is outside the temperature range for CVD diamond
deposition. Thermal compressive stresses in diamond films on silicon

substrates are smaller in magnitude compared to intrinsic stresses ( less

than 0.3 GPa at 1000°C depOSition temperature ) [10]. The sign and
magnitude of the total residual stress in diamond films is therefore
determined by the intrinsic stress. Tensile stresses in films are
undesirable because crack propagation is promoted under a tensile
stress state. Conversely, compressive stresses are desirable because
they strengthen the films by hindering the propagation of cracks [13].
High compressive stress can however cause buckling in the film and
induces wrinkles [12.14].

The sign and magnitude of total film stresses can be controlled via
variation of the parameters affecting the intrinsic stress namely the

deposition parameters.

2- PROPERTIES AND DEPOSITION OF DIAMOND FILMS

2.1 Properties of natural diamond

Natural Diamond has a unique combination of physical, optical and
electrical properties that may perhaps be exploited in application of
diamonds as a thin films [15.16]. Table 1 lists the properties of bulk
diamond.

Carbon can be amorphous or crystalline. When carbon crystallizes
in the cubic A4 structure ( named after diamond [17 ] ), diamond is
formed [18 ]. The structure of diamond belongs to the space group

Fd3 m-Oh7. Diamond has a lattice constant a - 3.567 Angstroms at room
temperature. The diamond structure has eight atoms per unit cell with

each atom covalently bonded to another carbon atom ( sp3 tetrahedral
bonds) [19]. The atomic distance (distance of closest approach) in
diamond is 1.544 Angstroms [17 ]. Diamond usually crystallizes in
octahedra crystallites whose faces are {111} planes. Less commonly,
diamond might crystallize in dodecahedra crystallites in thin plates,

with the crystals having {110} planes as their faces [18 ]. Compared to

other hard materials. diamond has a low density. (3.52 g cm“) due to
the small size of carbon atoms whose atomic radius is equal to 0.77

Angstroms. ( Carbon has an atomic number of six and an electronic

configuration of { 1s2 2sp3} [17] ).

When carbon crystallizes in the hexagonal structure, graphite is

formed. The lattice parameters are a - 2.461 Angstroms, and c - 6.708
Angstroms. Graphite has a lower density than diamond, ( 2.3 gcm'3

[18 ] ). Graphite is formed in layers with strong trigonal bonds ( sp2 ),
and an interatomic distance equal to 1.415 Angstroms in the basal plane
of the hexagonal lattice. The fourth electron in the outer shell forms a
weak bond of the Van Der Waals type. between the layers of trigonal
carbon. This weak electrostatic Van Der Waals force is responsible for
the low interplaner strength of graphite [19].

Amorphous carbon can be characterized as imperfect graphite

structure; the sp2 bonded carbon clusters have crystallographic layer
planes which are not oriented with respect to a common axis. The
orientation of the planes is random and the layers overlap on one
another [19].

Diamond has some excellent mechanical properties. Diamond's
hardness is the highest known ( up to 100 GPa ) [19]. due specifically to
its strong covalent bonds (high atomic bond energy ) and carbon's small
atomic radius. Diamond's high atom number density coupled with strong
covalent bonds result in a very high elastic modulus ( 1160 GPa for
single crystal diamond. Silicon, which has the same crystal structure
as diamond's, has a elastic modulus of only 180 GPa [20] ).

While diamond's room temperature thermal conductivity of 1100
W/mK is five times that of copper, diamond is a strong dielectric material

(dielectric constant equal to 5.7 ) with electrical resistivity higher than

1016 ohm-cm. Diamond’s thermal conductivity is much higher at room
temperature than other hard materials [18]. The thermal conductivity of
diamond at room temperature is one order of magnitude higher than that
of silicon. which has the same crystal structure as diamond [18].

The optical properties of diamond are equally impressive with the rest
of its properties, justifying diamond's use as optical windows for x-ray
lithography due to a unique combination of high stiffness and high x-ray
transmission [21]. Diamond has a high refractive index (2.47 at 5890
Angstroms electromagnetic wavelength [18,10] ), resulting in a low
angle of total internal reflection [18]. The optical band gap is 5.4 eV
making diamond electrically insulating at room temperature. Diamond’s
absorption spectrum is quite complex, and resulted in classifying
diamonds as type I or type II. depending on each type’s absorption in
the infrared, visible and ultra violet spectrum [18]. Type II diamonds
transmit well in the ultra violet range down to an absorption edge at
2200 Angstroms. Type I diamond however shows absorption starting at
3300 Angstroms and increases rather steeply at shorter wavelengths
[18].

Some type II diamonds are semiconductors. Therefore, type II
diamonds were further classified as type 11a and type IIb. where type
IIa are not semiconductors and type IIb are semiconductors. The type
IIb semiconductor diamonds are usually blue p-type (boron doped)

semiconductors [18]. The resistivity of type II diamonds ranges from 5 x

10” Ohm cm to a low value of 100 Ohm cm for some type IIb

semiconductors at room temperature [18]. Table 2 compares some

optical and thermal properties of type I versus type II diamonds.

2.2 Properties of synthetic diamond

lntereSt in depositing thin diamond films is motivated by diamond's
unique combination of properties. extreme hardness, chemical
inertness, high electrical resistivity, high dielectric strength, optical
transparency. and high thermal conductivity.

In the time interval following the development of techniques for
depositing diamond films at reasonable rates by various subatmospheric
pressure plasma techniques, diamond synthesis has become a rapidly
developing area. The properties of synthetic diamond are usually
different from those of natural diamond [22]. Synthetic diamond’s
properties vary with the deposition method and depend heavily on the
deposition parameters. The variation in film properties arises from
defects in the diamond lattice or from non diamond carbon phases like
graphite [22]. Chemical-vapor-deposited-crystalline diamond films
have high density, high abrasion, wear resistance, and corrosion
resistance [23] making CVD diamonds useful for applications such as
seating of twist drills and wire dies. The adhesion of diamond films to
their substrates and the internal stresses arising from the deposition

process are among the limiting factors for diamond’s extensive use.

10

Table 1. Physical properties of bulk diamond

 

 

 

PROPERTY VALUE / RANGE “if
StnIcture Cubic (diamond structure) 17
Stuckurberich ’symbol A4 17
Fd3 m-O 7
Space group '1 24
Lattice constant 3.5597 Angstroms 17
( at 25°C)
Melting point 4300°C 13
Energy gap (25°C) 5-4 9V 25
Thermal conductivity k 90-26 25
(Wcm" K")
Density 3.51 gcm'3 20
Refractive index
at 656.3 pm 2.41
18
at 226.5 pm 2-72
“82's 9332:]; 2) IR, visible. UV 18
RBSISIIVIIy > 1016 OI'II‘I‘I°CI1'I 18
Dielectric constant 5-7 19
Dielectric strength > 102-107 V/cm
Hardness ( Vickers ) 70-100 GPa 19
Youn ’s modulus 18
(sgngle crystal) "50 GPa
161 cal/mole 25

Heat of formation

 

 

 

 

11

Table 2 Properties of various types of diamonds [ after table 23.

page 295 in [18 ] and [25] p. E-11].

 

 

 

(W/cm K)

 

 

 

 

Property Type I Type He J Type IIb
IR - ' .
Absorption absorption at 6 13pm no absorption at 6 13 um
UV stro absteriptionflat strong absorption at wavelength less than
Abso on wave an 938 an 2250 An stroms
rptl SoogtAngstroms g
coefficient
of
Thermal
conduc-
tIV'IY 9.90 23.2 13.6
at 298 K

 

 

12

Diamond is also becoming a popular choice for applications such as
semiconductors. infrared-transmitting membranes, and X-ray

transparent films for x-ray lithography [21.26].
2.3 Diamond deposition techniques

Several techniques have been developed to deposit carbon thin film.
These techniques include mlcrowave-plasma-assisted-chemica-vapor-
depositlon (MPCVD) [10.21.27.28]. hot filament assisted CVD [22,29].
ion beam sputtering [1.1], and low pressure CVD [16] as well as other
methods. Diamond deposition methods can classified in one of three
categories. The first category is ion beam deposition techniques which
might use a single ion beam or dual ion beams. Ion beam techniques
are used to deposit primarily diamond like carbon (DLC). The second
category is the chemical vapor deposition techniques (CVD). Finally,
the third group which has more use than the other two groups is the
plasma assisted chemical vapor deposition (PACVD). Many deposition
setups now use microwave plasma assisted chemical vapor deposition
(MPCVD). The major advantage of the MPCVD is that transparent films
are obtained with the appropriate deposition parameters.

Diamond must be formed under extreme conditions of pressure and
temperature. Temperature and pressure spikes on the deposition
surface at the moment of ion bombardment have been proposed [19].

Temperature spikes estimated to at least 3823 degree K and pressure

13

spikes to 1.3 x 10'° Pa ( 1.2 x 105 atm ) resulted from bombardment of
the substrate by ions with 100 eV energy. The thermal agitation and the
shock wave resulting from the impacts are enough to form a diamond
nucleus 1 nm wide [19].

The proposed model [19] asserts that at room temperature. the
diamond formed is thermodynamically unstable. Diamond is however.
preserved at room temperature by the very high quenching rates
following the collapse of the temperature spikes. thus preventing the
transformation of the newly formed unstable diamond into more stable
graphitic phases [19]. However atomic hydrogen or argon [19]. present
in the deposition atmosphere, used to bombard the substrate cause
etching. which is the preferential removal of the weakly bonded sp2
carbon atoms and other non carbon ions resulting in much purer .
diamonds [19]. Only diamond with strong C-C or C-H tetrahedral bonds

is allowed to grow.

2.4 Mechanical properties of diamond thin films

The high abrasion, high hardness, wear resistance and corrosion
resistance of polycrystalline CVD diamond justify CVD diamond's use
for coatings of twist drills, machine tools. wire dies and nozzles.
Several attempts have been made to deposit diamonds with hardness
close to that of natural diamond ( 70 to 100 GPa [19] ).

In a review on diamond properties. Tsai and Boggy [19] reported that

14

for DLC films deposited by ion beam with various carbon sources
(carbon in rf plasma. carbon in arc. carbon in plasma ), hardness up to
18 GPa were obtained, when the ion beam energy is in the range of 40
to 100 eV. Higher hardness up to 24 GPa were obtained with sputter
orientation). A third material with <100> texture can be grown [31].
Clausing [31] has shown. through transmission electron microscopy and
x-ray texture analysis, that stacking faults and twinning are necessary

deposition technique by dc Magneton sputtering of a graphite target

[19]. As the sputtering power density increased from 0.25 to 25 W cm’z,
the hardness value decreased from 24 to 7.4 GPa [19].

The hardness value was also dependent on other parameters. For
instance, the hardness value of i-C diamond films increased with
substrate potential up to 700 V [19]. Films deposited in an atmosphere
containing hydrocarbons have higher hardness than films deposited in
atmospheres not containing hydrogen. While diamond deposited by
methods not including hydrogen had hardness values up to 24 GPa, the
hardness values of diamonds deposited by the decomposition of
hydrocarbons were as high as 100 GPa [19]. Diamond films deposited
by electron assisted CVD with a mixture of methane and oxygen
(2 percent by volume methane ) with no hydrogen have hardness
values approaching that of natural diamond [19]. ‘

Surface roughness of deposited diamond films vary with methane
fraction in thedeposition chamber. Diamond films deposited by MPCVD

with methane fraction in hydrogen as 0.2 to 3.0 percent, had peak to

15

peak roughness of 10 to 15 nm [10]. The surface roughness was
measured with a Dektak ll stylus type profilometer with a submicron tip
radius and by a an atomic force microscope [10]. The 10 to 15 nm
roughness value seems low for polycrystalline diamond. However.
Windischmann found the roughness to decrease with increasing
methane fraction which was as high as 3 percent. possibly explaining
the low roughness values. In films deposited by MPCVD at 0.7 percent
methane in hydrogen. the surface roughness was measured as 35 nm.
with a submicrometer stylus type profilometer [21]. Windischmann and
Epps observed that surface roughness of deposited diamond films by
MPCVD decreased with increasing methane fraction. They observed
that as the methane fraction increased, the surface of the films became
smoother. due to finer microstructure [21].

Windischmann and Epps Showed that the grain size in the diamond
films is also a function of the methane fraction in the deposition
atmosphere [10.21.31]. Figure 1 shows an obvious decrease in the
grain size with methane fraction. The data in figure 1 were fitted by non
linear regression analysis ( Marquardt approximation ) to the function
y: 112.25 exp ( 1.631 x ) + 14.115. with a correlation factor R-0.983.
Impurities can in general inhibit grain growth. The non-diamond
components in the films are thought to be the grain growth inhibitors in
diamond [10.21]. Raman studies of diamond films have shown that the
non-diamond phase fraction increases with increasing methane

concentration [10,21] (figure 2 ). Grain sizes were measured by

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INTENSITY
Arbitralunits)

 

0.3 % OH4

 

 

 

 

1.111.011,

 

 

 

 

2.5 % CH4

 

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WAVENUMBER cm'1

Figure 2. Raman spectra of diamond films prepared at a) 0.3

percent CH4. b) 2.5 percent CH4 and c) 7.5 percent

CH4. After Windischmann [10].

18

x-ray diffraction. The grain size was calculated from the FWHM of the
reflection peak corresponding to diamond. The specimens used were
deposited by MPCVD at 790°C with methane fraction ranging from 0.2 to
3.0 percent in hydrogen. The grain size decreased from 110 nm. at 0.2
percent methane to 15 nm at 3.0 percent methane [21].

The elastic properties of diamond films were not investigated as much
as other properties. In most of the studies on diamonds. the value of the
Young's modulus used was that of single crystal diamond. 1345 GPa
[18 ]. The Young’s modulus of diamond films was measured by
Davidson et al. [16]. Davidson et al. used a cantilever beam of free
standing diamond. deposited by microwave plasma assisted CVD, to

measure the deflection 5 of the beam. as a function of a static. manually

applied load P. The deflection 5 is relate to the load P by [16].

5-PL313 El (1)

where L is the beam length. and I is the moment of inertia of the beam.

A plot of 5 versus P was made and the slope was measured. The value
of the Young’s modulus was determined from the slope. Several trials
were carried. the value of Young’s modulus was in the range of 1170
GPa to 1225 GPa. which is very close to the value of Young's modulus
for single crystal of diamond. 1130 GPa [16]. A vibrating membrane

method [20] was used to measure the Young’s modulus of diamond

19

membranes. The biaxlal elastic modulus was found to range from 730 to
850 GPa. which is only 0.61 to 0.71 of that of natural diamond [20].

The properties of deposited diamond films depends strongly on the
deposition parameters. Deposition pressure. temperature and
atmosphere affect the final properties of diamond films. While almost
every deposition parameter affect some film property. the effect of
deposition temperature. pressure and methane fraction in the deposition
atmosphere can affect the properties more than any other. These

effects will be discussed in the following sections.

2.5 Effect of deposition parameters

During deposition. carbon atoms can combine in one of many ways

to form graphite plates. crystalline diamond or amorphous carbon.
Hexagonal graphite is formed with planar sp2 bonds. while tetrahedral

sp3 bonding results in cubic diamond.

Chemical vapor deposited polycrystalline diamond has two common
morphologies, the {111} material and the microcrystalline material [31].
Both of these morphologies lead to <110> texture ( preferred
to the formation of the (111) and microcrystalline diamonds [31]. The
third type exhibiting {100) facets are grown free of stacking faults and
twinning if no oxygen or boron is present in the deposition atmosphere
[31]. The author did not mention the minimum value of oxygen of boron’s

partial pressure to obtain a {111) material. Windischmann and Glen [10]

20

reported that the texture in MPCVD diamond deposited on (100) silicon
depends on the deposition temperature and methane fraction in the
deposition atmosphere [10]. At lower temperature and methane fraction.
the texture was [11]. however as the temperature and methane fraction

‘ increased. the texture changed quite frequently. then became

predominately a <220> texture [10].
2.6 Effect of deposifi'on pressure

At low temperature and pressure. the growth of diamond is not
thermodynamically favored. a high density of defects exist in the
diamond component of a CVD carbon films deposited under such
conditions [22]. During film growth. there is a competition between
diamond and graphite formation. Diamond growth dominates if hydrogen

.is used in the deposition atmosphere. The etching rate of graphite by
atomic hydrogen is much higher than the rate for diamond since the sp3

bond in diamond are stronger than the sp2 bonds in graphite and
amorphous carbon. Buckley et al. used Raman spectroscopy to
investigate the characteristics of filament assisted CVD (FACVD)
diamond [22]. The principal conclusion of Buckley's investigation was
that in FACVD carbon films. the carbon type in the film ( diamond.
graphite or amorphous carbon ) strongly depends on the total gas
pressure in the deposition chamber. AS the total gas pressure is

lowered. more disordered carbon type is formed [22]. Buckley et al.

21

used constant methane concentration at 0.2 percent and deposition
temperature of 950°C. Diamond films were deposited by FACVD on
molybdenum substrates. The only parameter that was varied was the
total gas pressure which ranged from 5 to 100 torr. Raman spectra were
taken of all specimens. The results obtained are listed as follows:

1) at low total gas pressure, (about 5 torr). the diamond peak at 1330

cm'1 was obscure, indicating a very small fraction of diamond in the
film. The film deposited at 5 torr was found to be predominately
amorphous carbon. and displays a ball-like morphology which is not
typical of diamond.

2) at total gas pressures between 5 and 30 torr. Raman spectra

displayed two broad peaks centered around 1550 cm" and 1360 cm'1
indicating the presence on both graphite and amorphous carbon
component in the film.

3) at total gas pressures higher than 30 torr. the broad peak around

1550 cm‘1 sharpened and shifted to 1578 cm". corresponding to
crystalline graphite.

In all specimens. except for the specimen deposited at 5 torr. the

position of the diamond peak at 1332 cm'1 was independent of the
applied total gas pressure [22]. There is evidence that the diamond line
does shift with externally applied pressure [32] ( section 4.4 ). The
spectroscopic resolution for the infrared devices used in this study
possibly may not allow detection of the usually small shift in the

diamond line with pressure. The line width, however. for both diamond

22

and graphite components vary with deposition pressure. The diamond
line broadening with decreasing total gas pressure indicates an
increasing defect density in the diamond component. The broadening in
the graphite line with decreasing total gas pressure indicates that the
amount of crystalline graphite is reduced. and eventually becomes
amorphous carbon at low pressures [22]. Decreasing total gas
pressure increases the disorder in both the diamond and graphite
components. Increasing the total gas pressure tends to favor the
formation of more defect free diamond component. Liou et al. found no
significant changes in the growth rate of MPCVD diamond films with

increasing total gas pressure from 6 to 50 torr [33].

2. 7 Effect of deposifi'on temperature & substrate temperature

Film growth rate depends on the deposition temperature. Grill at al.
[34] found that in presence of a substrate voltage bias of 80 volts. the
growth rate decreased with substrate temperature. The growth rate was
105 Almin at 100°C and 65 A/min at 250°C [34]. The films studied by
Grill at al. [34] were diamond like carbon films deposited on silicon
substrates by rf plasma decomposition of acetylene. The range of
substrate temperature studied was 100 to 250°C. In agreement with Grill
et al. [34]. Liou et al. found that the deposition rate of diamond. at
constant methane and total gas pressure. decreased rapidly as the

substrate temperature increased ( figure 3 ).

 

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23

The data in figure 3 were fitted ( this thesis ) by linear regression to the
function y - 1.212 - 74710" x + 0.15 10'5 x2. with a correlation factor
R20.995.

Liou [33]. Windischmann [21] and Harshavarhan [35] all agreed that
there is a temperature interval in which optimum deposition conditions
are obtained and crystalline diamond is formed. The limits of the
temperature interval. where conditions are optimum. varied between the
three authors mentioned above [21.33.35]. In Harshavarhan's study. the
temperature Interval for optimum deposition was 900 to 950°C. In
Windischmann's study. this interval reported was not clearly stated. but
the study implies that this interval is roughly 500 to 850°C. Liou found
the interval of optimum conditions to be 500 to 1000°C. The differences
in the intervals might arise from the difference in deposition methods
and parameters. The deposition method used by Liou [33] is MPCVD
with a methane fractions ranging from 0.5 to 5 percent in hydrogen gas.
Harshavarhan [35] used an oxyacetylene welding torch to deposit
diamond on silicon. Finally, Windischmann deposited diamond films by
MPCVD also with varying methane concentrations. For instance. films
deposited at 550°C had three times as much methane as films deposited
at 825°C [21]. The role of methane in the deposition process will be
discussed in section 2.8. One should note at this stage that the amount
of methane significantly affects the amount and crystallinity of diamond.
graphite and amorphous carbon.

In spite of the slightdifferences among the reported temperature

24

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25

intervals at which optimum diamond deposition occurs. the general
observations in the three studies [21.33.35] are similar. All three
authors [21.33.35] used Raman spectroscopy of the deposited films as
an investigative tool of the carbon components and their crystalline
quality. All Raman spectra of diamond films were taken at room
temperature in the three studies [21.33.35]. The following observations
were common to the three studies:

1) At temperatures outside the interval of optimum conditions

described earlier. Raman spectra show two broad peaks centered
around 1560 to 1580 cm" and 1350 to 1355 cm“. respectively

( figure 4 ). The broad peak around 1350 to 1355 cm" is believed to
arise from small graphitic crystallites less than 20 nm in size, and I or

disorder in tetrahedrally coordinated carbon network [21]. The peak
centered around 1350 to 1380 cm‘1 arises from crystalline graphite, the
line width is proportional to the crystallinity of the graphite. For
example. at temperatures less than 900°C or above 950°C [35]. the
Raman spectra shows two broad peaks; the amorphous carbon peak
centered about 1350 cm'1 and the graphite peak centered around 1580
cm“1 [35]. In the same temperature range ( below 900°C or above
950°C ). the crystalline diamond peak centered around 1332 cm'1 is
practically absent. indicating a dominance of the amorphous carbon

and graphite to a lesser extent [35]. At temperatures in the 300 to 400°C

range. the deposited films are mostly amorphous carbon.

26

INTENSITY
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b) 1 1331.2 cm’1

 

 

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WAVE NUMBER cm"

Figure 4. Raman spectra of deposited diamond films at a) 825°C

and b) 550°C. After Windischmann [21].

 

27

On the other side of the temperature interval. at 980°C. the deposited
films are mainly graphitic [35].
2) At temperatures within the interval of optimum conditions. there is a

sharp peak around 1330 to 1332 cm" in the Raman spectra of the films.

The peak centered about 1332 cm'1 is due to crystalline diamond

[10,21]. In the same temperature range. the peaks centered around

1355 and 1550 cm‘1 almost disappeared indicating a much smaller

presence of non diamond carbon. For example. at 550°C. the non

diamond components are virtually non existent as can be deduced from

the lens and sharp peak around 1332 cm" in figue 4 [21]. Figures 2 and
4 are manually reproduced in this thesis from original curves; the
precision of the data is therefore lost.

At temperatures in the range of 800 to 1000°C. diamond grains are
several micrometers wide and well faceted [21]. Outside the
temperature range of 800 to 1000°C. the grains are finer and unfaceted
[36]. At lower temperatures. films have coarser microstructures in the
range of 2 to 5 microns. Larger grains have lower grain boundary area.
And since non diamond carbon and graphite tend to precipitate at the
grain boundaries. they inhibit grain growth. Finer grains contain larger
non diamond component at 825°C than grains deposited at 550°C [21].
One should note that the grain size is also a function of the nucleation

condition through abration and seeding of the substrate surface.

28

2.8 Effect of methane and hydrogen gas on film properties

When methane is used in the gas mixture in the deposition chamber.
the deposited diamond film properties depend on the fraction of methane
in the deposition gas. Mechanical properties[27]. optical properties
[10.21.27.371 and the morphology [9.10.26.29.31] of the film vary with
methane fraction.

The most important effect of methane fraction on diamond films is on
the type and amount of the carbon component in the film that forms
during deposition. Many researchers using various deposition method
have concluded that the amount of non diamond phases in deposited
diamond film is a function of the methane fraction in the deposition
atmosphere [9.10.21.29.31]. Raman spectroscopy and x-ray diffraction
are commonly used tools for investigating the carbon type (amorphous
carbon, graphite or crystalline diamond ) in carbon films. Raman

spectroscopy is especially powerful in detecting the non diamond

content in the films. The sensitivity of Raman signal from the sp2 bond

( unsaturated C-C ) in graphite is about two orders of magnitude higher

than the Raman signal from the sp3 bond ( saturated C-C ) in the
tetrahedrally coordinated diamond [29].
Raman spectra of diamonds from various studies have some common

features. At low methane concentrations. there is a sharp narrow peak

around 1332 cm". indicating the presence of a large fraction of

crystalline diamond [10.21.26.38]. At low methane fractions. the

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29

relative peak intensity at 1560 cm‘1 due to absorption from graphite
( relative to the diamond peak at 1332 cm'1 ) is weak. The sharp peak at

1332 cm’1 combined with the relatively low peak at 1560 cm'1
demonstrate that at low methane fractions. the films obtained are mostly
crystalline diamond. provided that other parameters such as optimum
temperature and pressure are chosen. A small fraction of small non
diamond carbon ( graphite and/or amorphous carbon) inevitably exists
in the film. even at low methane fractions [10,38]. As the methane
fraction in the deposition atmosphere is increased. the non diamond

carbon content increases as can be deduced from the increase in the
relative intensity of the 1560 cm'1 peak at higher methane fractions
[10.21].

Spectrosc0pic ellipsometry was used to measure the number of sp2

bonds ( proportional to the non diamond fraction in the film ). The

number of unsaturated sp2 bond in the film increased with methane
fraction ( figure 5). The data in figure 5 were fitted ( this thesis ) by
linear regression to the function y a 1.76 + 2.53 x. with a correlation
factor R=0.95. The same conclusion could be drawn from figure 2

which represents the change in Raman spectra of diamond films at

various methane fractions; the relative intensity of the 1560 cm’1
graphite line increases with increasing methane fraction [10]. Films
deposited by hot filament CVD [38]. using hydrogen and methane gas

mixture. showed differences based on the methane fraction used.

30

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With all other conditions kept constant. two methane fractions were
used in deposition; 0.5 percent and 1.0 percent methane fraction [38].

Under both conditions ( 0.5 and 1.0 percent methane ). Raman spectra

had a sharp peak around 1332 cm". indicating the presence of
crystalline diamond. However. in the Raman spectrum of the specimen

deposited with the lower methane fraction (0.5 percent). a relative

increase occurred in the peak around 1500 cm‘1 representing
absorption from amorphous carbon [38]. Consequently. just like
graphite. amorphous carbon production is favored in films deposited at
higher fraction of methane.

Films deposited by MPECVD (microwave plasma enhanced CVD )
[62]. with methane fractions at 0.5 percent and at 4.0 percent. showed
similar results to those in reference [38]. Indeed. specimens prepared
at 0.5 percent methane fraction contained less non diamond carbon

than specimen prepared at 4.0 percent methane. The Raman intensity of

the 1550 cm" line was lower in the film deposited at the lower methane
fraction. In another study. the Raman spectrum of a film deposited at 2
percent methane fraction was dominated by the graphite peak [26]. As
the methane fraction was reduced. the diamond line gradually come to
dominate the Raman Spectrum [26].

When ethanol was used in the gas mixture along with hydrogen. the
Raman intensity of the broad peak assigned to graphite increased with
ethanol fraction. The specimens were deposited by HFCVD at two

different ethanol fractions [9]. Both films contained line defects

 

32

consisting of twins. stacking fault. and dislocations. as well as highly
disordered regions at the crossing points of twin boundaries [38]. The
specimen deposited at the higher methane fraction contained more of
these defects [38]. The above observations may indicate that stresses
formed during film growth are partially relaxed by the formations of these
defects. The defect density increased with methane fraction [38]. thus
increasing the methane fraction may allow stresses in the film to relax
by the formation of defects. However. the trade off to stress relaxation
is the loss in diamond purity. since non diamond content increases with
increasing methane fraction.

In another study. three samples were deposited by HFCVD in a
hydrogen and methane mixture. with three different methane fractions
[29]. Films labeled A. B and C were respectively deposited at 1.0. 4.0
and 7.0 percent methane. Films A and B were identified as diamond by
X-ray diffraction. The x-ray diffraction of sample C showed a sharp line

only for the silicon substrate. Raman spectra of specimens A and B

revealed sharp lines at 1333 cm'1 attributed to Sp3 bonds. thus

supporting finding x-ray diffraction findings. The Raman spectra of films

1

C however showed a broad peak around 1330 cm' . All three samples

showed a peak around 1550 cm“ that increased with methane fraction
[29].

The growth rate of diamond films grown in an atmosphere containing
methane increases with methane fraction [21,29]. As the methane

fraction increases. the diamond film growth rate increases. then

33

decreases [29]. The diamond cluster size simultaneously becomes
smaller with methane fraction [29]. TEM observations showed that at a
1.0 percent methane fraction, the diamond crystals are clearly defined
and triangular [29]. At 4.0 percent methane. diamond grains are
smaller. At 7.0 percent methane. the particles' morphology is ball-like
without habit planes [29]. A different study [38] revealed that diamond
films deposited at 0.5% methane were crystalline consisting of (111)
planes forming triangle shapes. At 1.0 percent methane. the diamond
consists of particlesiwith a mixture of (111) and'(110) planes [38].

To explain the decrease in grain size with simultaneous increase in
the growth rate. a model was proposed [29] in which hydrogen is the
determining factor. The model assumes that the diamond cluster size
depends on the hydrogen to methane fraction ( or on the number of
A available atomic hydrogen per carbon atom) [29]. At a low methane
fraction. all the carbon atoms supplied by the decomposition of methane
builds up on the rapidly growing film. There is enough atomic hydrogen
around the substrate to ensure high etching rates of the non diamOnd
phases. At this stage. the growth rate increases with increasing
methane fraction. At higher methane fraction. too many carbon atoms
are supplied. Only small clusters of low molecular weight are formed.
most of which cannot survive at the high substrate temperature. The
decomposition of the low molecular weight clusters may be one reason
behind the slowing down of the growth rate [29]. Atomic hydrogen also

brakes up the network of weakly bonded amorphous carbon between

 

diamond clusters. allowing diamond clusters to grow. At high methane
fraction ( assuming the gas is a mixture of hydrogen and methane). less
atomic hydrogen is available to etch away the amorphous carbon
network that forms between diamond clusters. The reduced etching
power of atomic hydrogen at higher methane fractions might be a
second reason why the growth rate of diamond slows down. The
reduced etching power of hydrogen could also explain the increase in
the non diamond content of films deposited at higher methane fractions.
The hydrogen content in diamond films increases linearly with
methane fraction ( figure 6 ). The data in figure 6 were fitted ( this
thesis ) by linear regression to the function y- -0.623 + 2.66 x with a
correlation factor R=0.975. The amount of hydrogen in the films is to be

differentiated from the hydrogen fraction in the deposition atmosphere.

The hydrogen concentration was measured by 15N nuclear reaction (NR)
analysis and by elastic recoil detection (ERD) spectroscopy. A
hydrogen content of 7 to 8 percent [21] and up to 50 percent [39] was
found in many films. The presence of hydrogen in the film is necessary
to obtain good mechanical properties and infrared transparency [39].
Hydrogen stabilizes the diamond phase, films produced by
decomposition of hydrocarbons are more stable and have better
mechanical properties [22.39]. X-ray absorption fine structure (EXAFS)

measurement showed that two thirds of the carbon in diamond films have

sp3 coordination. Most carbons attached to hydrogen atoms also have

tetrahedral diamond like bonding [39].

 

 

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One third of the carbon atoms in the studied specimens have spa

trigonal bonds [39]. Hydrogen initially attached to carbon in sp3 bonds
may later detach at high temperature thus altering both mechanical and
optical properties of diamond films. If hydrogen is lost upon annealing,
film decomposition could result [39]. Loss of hydrogen and eventual
decomposition or transformation to graphite occurred upon annealing at
temperatures greater that 400°C [39]. A 100 percent transformation to
graphite resulted from a 1000°C anneal [39]. While increasing the
methane fraction in the deposition gas results in film defects which relax
the stress. the hydrogen content also rises with the methane
fraction[10]. An increase in hydrogen concentration in turn causes a
greater degree of atomic misfit in the lattice. The misfit strain induces
higher residual stress. giving rise even to spontaneous delamination
[27]. Films deposited with a methane fraction greater that 15 percent

delaminated spontaneously from silicon substrates. when film thickness

was greater than 3000 A [27].

3- PARAMETERS AFFECTING RESIDUAL STRESS

Several parameters affect the Sign and magnitude of residual stress.-

Some of these parameters are discussed next.

3.1 Effect of film thickness on residual stress

Hoffman [8] reported that in metallic thin films the average intrinsic
stress decreased with increasing film thickness. However. the average
intrinsic stress is independent of thickness for thick films. For example.
at film thicknesses greater than 2000 A. silver [40] and gold [41] films
showed practically no increase in stress. while no stress existed in
copper and silver films until a threshold thickness of 200 to 300
Angstroms is reached [40.42]. Similar results were obtained for
antimony [43] and gold film grown on quartz substrate [44] where the
Stress was zero until a threshold film thickness of few hundred
angstroms. followed by a rapid rise in stress in a narrow thickness
region of about 1000 Angstroms. A constant stress value is then
reached for thicknesses greater than 1000 angstroms [44].

The trends for residual stress as a function of film thickness in
dielectric films are not as clear as those for metal films [8]. ZnS films

evaporated at the rate of 20 A/sec have compressive residual stresses

that decrease with increasing film thickness. up to about 2 pm [45]

(figure 7 ).

37

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39

However. film stresses in carbon films on glass substrates increased up
to a carbon film thickness of 1000 A, then become independent of film
thickness at higher thicknesses [46]. The data in figure 7 were fitted
( this thesis ) by non linear regression ( Marquardt approximation ) to
the function y a: 1.237 exp( -0.506 x ) with a correlation factor R=0.99.
The sign of residual stress can also be thickness dependent. Strains
parallel to the interface in GaP. GaAs and lnP semiconductors grown on
silicon substrates changed from compressive to tensile at film thickness
greater than about 1.5 pm [4]. The tensile strains measured from the
change in the radius of curvature were however thickness independent
in the range of 1.5 to 5 pm film thickness in the semiconductor-silicon
systems mentioned [4]. Stress in SiC films grown on silicon substrates
was found to be large ( 2 GPa ). compressive and thickness
independent [3]. However. stresses in the SIC film became tensile after
an anneal at 600°C. for 30 minutes [3]. Stresses were measured from
the change in radius of curvature due to stress induced bending
(equation 25) [3].

Just like in other dielectric films. internal stresses in thin diamond
films quickly rises with film thickness. then decreases and reaches a
plateau at higher film thicknesses [46.47]. For instance. in DLC films
deposited at 300°C by electron bombardment of a carbon red. the
magnitude of the compressive stress measured during deposition from

the beam deflection increased from 0 to -2.5 GPa when a film thickness

of 500 A was reached. then the stress deceased and remained constant

40

at film thicknesses up to 2000 A [46] (figure a ).

Stress contributions in diamond films on silicon substrates include
, lattice mismatch stress and thermal expansion difference stress. At very
low film thickness of few'angstroms. the tensile lattice mismatch stress
in the film balanced by the compressive thermal expansion stress such
that the over all stress in the film ls low and compressive. As the
diamond film thickness'increases up to about 1000 A. the magnitude of
the tensile lattice mismatch stress decreases away from the interface.
Consequently. the compressive thermal expansion stress becomes more
dominant and the stress in the film becomes increasingly compressive
up to about 1000 A. The grains of diamonds start touching at about
1000 A causing a tensile stresses to increase again ( see discussion on
grain boundary relaxation model section 8.2 ). As the tensile stress
increases opposite to the compressive thermal expansion stress. the
magnitude of the total compressive stress decreases and reaches a

plateau when diamond grain growth in stopped.

3.2 Effect of ion beam energy on stress

Plasma-assisted-chemical-vapor-deposited silicon carbide films on
silicon substrates have biaxial compressive stresses that increase with
increasing ion beam energy; stress in the silicon carbide film increased
from -0.5 to ~2.0 GPa as the ion beam energy increased from 100 to 140

eV [3].

 

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Compressive stress is partially due to the presence of hydrogen in the
film [3]. Removal of the hydrogen by a degassing treatment

which consisted of an anneal at 600°C for 30 minutes. resulted in
transition of stress from compressive to tensile ( figure 9 ). The
magnitude of the tensile stress in the film was as high as 2 GPa at an

ion beam energy of 140 eV [3].
3.3 Effect of deposition rate on residual stress

Intrinsic stresses depend on deposition rate. Hoffman [8] reported
that for the dielectric films he surveyed. internal stresses could either
increase or decrease with increasing deposition rate. Compressive
stresses in ZnS films increased linearly from -0.04 GPa at a deposition
rate of 9 Alsec. to a value of -0.06 GPa at a deposition rate of 22
Alsec [45]. Compressive stresses in SiO decreased non linearly with
deposition rate from -0.15 GPa at a deposition rate of 9 Alsec. to a

value of -0.06 GPa at a deposition rate of 40 Alsec [45] ( figure 10 ).
The data for ZnS in figureto were fitted ( this thesis ) by linear
regression to the function y c 0.231 + 0.174 x with a correlation factor

Iii-0.995, while the data for SiO were fitted by non linear regression

analysis (Marquardt approximation ) to the function y - 0.056 + x“-33 +
0.0456. with a correlation factor R=0.951. Magneton iOn beam
sputtered chromium films on Corning cover-glass substrates had high

compressive stresses that decreased linearly with deposition rate [48].

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Indeed. the integrated stresses ( integrated over the thickness) in the
chromium films decreased linearly from ~350 N/m at a deposition rate
of 0.13 nm/sec. to a value of -200 Mm at a deposition rate of 1 nm/sec

[4a].

3.4 Effects of deposition pressure on residual stress

Magneton ion beam sputtered chromium films deposited at the rate of
1.0 nm/sec. in an argon gas atmosphere. had stresses that varied
dramatically with deposition pressure [48]. Indeed. for a film thickness
of 0.25 microns. a compressive stress measuring -1.5 GPa. at 0.05 Pa
argon pressure. decreased to -1.0 GPa at 0.1 Pa. then increased and
switched to a tensile stress 0.8 GPa at 1.5 Pa then again decreased to
zero at 7 Pa. Stresses were measured from the observed center
deflection of the substrate bowing under stress. (Equation 25). No
considerable change in the magnitude or sign of the stresses. as a
function of the deposition pressure was realized when argon was
replaced with krypton [48]. Blachman [49] argued that compressive
stress in copper films on molybdenum substrates are due to atomic
argon entrapped in the film. Hoffman however argued that the change in
stress from tension to compression with increasing deposition pressure
cannot be correlated to entrapped argon, sinceno appreciable

quantities of argon was found in the copper films.

3.5 Effects of deposition incidence angle on residual stress

When dielectric films are evaporated at an incidence angle other
than normal incidence. the films mechanical properties may become
unstable when exposed to air after deposition [8]. Priest et al. [50]
found that the stress in SiO films changed from 0.1 GPa tension to
-0.1 GPa compression. and the films partially delaminated from the
substrate after only three minutes expoSure to air. The author attributed
the change in the stress sign and the delamination of the film with
exposure time to the partial pressure of water vapor, since no stress
sign change or delamination were observed when samples were
exposed to dry nitrogen at atmospheric pressure [50].

Evaporation at higher angles can also result in anisotopic stresses
[8]. For iron films deposited at 36.5 degree incidence. the difference in
the magnitude of the stresses in the X and Y directions ( figure 11),

increased with increasing film thickness. At a 0.1 microns thickness.
the ratio of the stresses in the X and Y directions °x’°v was
approximately 4/3 indicating a larger stress in the X direction [50].

However, while for iron [50]. ox/oY increased from 1 to 1.2 as the

incidence angle increased from 0 to 40 degrees. “x’av for SiO [51]

deceased to 0.7 at 20 degrees then rapidly increased to 5.5 at 60
degrees. Stress anisotropy can be estimated by the interference fringes

method ( section 4.3 ). Interference fringes are formed when the film is

47

 

 

 

 

Figure 11. Three dimensional two layer system

48

illuminated with a monochromatic light. The Fringes are circular if the
stresses in the X and Y directions ( figure 11 ) are equal. Otherwise.

the stress anisotropy causes the fringes to become elliptical. The ratio

of the two ellipse radii is proportional to “x "’v [8].

3.6 Effect of crystallite size on stress

Blackburn [52] has shown that in very thin LiF films ( less than 100
A), deposited at 12 Alsec on carbon coated glass substrates. stress is
dependent on the crystallite size. Measured stress on the LiF films

were tensile and increased in a parabolic way from 0 to 0.9 GPa as the
crystallite size (average cross sectional area) increased from 0 to 10‘

A’- [52] (figure 12). The data for LiF film in figure 12 were fitted by
non linear regression analysis ( Marquardt approximation ) to the
function y - 0.0403 exp ( 0.467 x ). with a correlation factor R=0.95.
Both Halliday [53] and Blackburn [52] measured a stress value of 5 GPa
for a LiF film thickness of 100A. Stress was not dependent on
crystallite size for film thicknesses greater than 250 A [52.53].
Blackburn’s and Halliday's findings agree with the results obtained by
Fleet [54] who found that the average crystallite size in nickel films
increased with films thickness only up to a thickness of 250 A and was
constant thereafter. This would explain the stress dependence on
crystallite size which is in turn is dependent on film thickness when the

film thickness is less than 250 A.

49

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4- STRESS MEASUREMENT METHODS

4.1 X-ray stress measurement

The change in the crystal lattice parameter due to residual strain is a
measure of stress in thin films [4.8]. X-ray diffraction can be used to
measure changes in the lattice parameter. Haraki and Mitsuru [4] have
measured the lattice constant in various Isotropic materials in a
direction perpendicular to the interface. The strain in the z direction

(perpendicular to the interface is given by [4]
62- (a-ao) / a0 (2)

where

ao- known lattice parameter. and

a a the measured lattice parameter of the strained film.

The stress resulting from the strain described by equation 2 is [8]
02" (E,/ 2v.) [(a - a0) / a0] (3)

The biaxial elastic strain parallel to the interface ( in the XY plane) is

obtained by using the elastic stiffness constants C5101 the films. to

50

51

obtain the following relationship [4]:

€x'£y=(2012/C11) 5: (4)
where 82 is given by equation 2 and 1 and 2 subscripts denote the X

and Y direction. The biaxial stress in the X and Y directions is then

on - (E,/2v,)(C12/C,,) [(a-ao) / a0] (5)

4.2 Stress measurement with the energy gap method

Using a deformation potential model [4]. the strain in the film is
estimated from the photoluminescence peak shift. in the
photoluminescence spectra performed at some temperature T. T is a
temperature where the photoluminescence intensity is high. The

calculated energy gap change due to straining in the film is then [4]
Asm.[21.1(c,,-C,2)/C,, + 12(C,,+ 2C,2)/C,,1 em (24)

where

AE(T) a the change in the energy gap of the film at temperature T

and due the stress in the film.

52

8(T) - the biaxial strain measured at a temperature T.

A1 - the hydrostatic deformation potential.

71.2 . the shear deformation potential, and

The strain 80(To) at the measurement temperature To. is obtained from

the temperature dependence of the strain given by

SOON-6(1) '1' AMT.) (T-To) (7)

where AOI('I') is the difference in thermal expansion coefficient between

the substrate and the film. The biaxial stress in the film ( parallel to the
interface). at the measurement temperature T . can be obtained by

combining equations 6 and 7 to yield

ca: [Es/(l-vs)]/[ mam/(21.,((3,,--C,2)/C11 +
A22(0111' 2C12) [011” (3)

53

4.3 Stress caiculab'on from the curvature change of me substrate

When dissimilar isotropic materials are joined together. stresses
arise at the interface as well as within the layers. These stresses can
arise from holding one member under stress at the time of joining. by an
expansion in one member after joining, or by joining materials with
different expansion coefficients as is the case for diamond-silicon
composite system.

To measure the total internal stress (thermal and intrinsic) in thin
films. many authors have used a stress calculation method based on
measuring the change in curvature of the substrate before and after the
deposition of the film. Windischmann [10.55]. Gehan [27]. Rossingnon
and Evans [56]. and Nir [8] used Stoney’s equation ( equation 9 ) to

measure stresses in thin films

ca-E.t.°/i6li-v.)t.pi <9)

where the terms are defined after equation 23.

Gel and Frechette [57] derived equation 9 through a minimization of
elastic strain energy in the composite system. A similar derivation was
used by Argon and Gupta [3] to obtain a stress curvature for a circular
substrate-film composite.

Consider a two layer system as shown in figure 11. Under

equilibrium. the stresses in the system can be resolved in an X,Y and Z

coordinate system as shown in figure 11. The strains within a layer in

the XY plane are given in terms of the stresses by Hook’s law for elastic

deformation by [57]

ex = [(3x - voy- vol]! E (10)

o:y =. [0’ - vox- vozll E. (11)

E is the Young's modulus of the layer and v is the Poisson's ratio of the

layer. 8,. and 8’ are the strain in the X and Y directions. cry and (I" are

stresses in the X and Y directions. v is the layer’s Poisson’s ratio. The

magnitude of a biaxial stress (3‘ within the ith layer is then given by [57]
01=E151’(1"V1)- (12)

£1. 0’' and vI are respectively the strain. the stress and the Poisson’s

ratio in the ith layer. Equilibrium requires that the sum of all forces in

the multi-layer body be equal to zero or [57]

2 0i d1 = 0. (13)

where d1 is the thickness of the ith layer ( figure 5 ). If we use equation

(6) for the stress, then equation13 becomes

55

2 as, I(1—v.) =0. (14)

At the interface. the strain differential a”. between the two layers is

given by

Generally. the interface between two stressed layers is spherically

curved ( figure 13 ). If the radius of curvature p is not small. the strain

within a layer perpendicular to the interface is linearly proportional to
the distance t)i separating the neutral axis of the ith layer from the

interface. If a point is at a distance 2 from the interface. then the strain

in the ith layer at that point is given by [57]
£I=(nI -Z)/p. (16)

Equation 15 for the strain differential a1.2 can now be rewritten with the

help of equation 16 as follows:

31.2 = (“1'"2) I P (17)

At any point X, Y, Z in the system. the energy density is given by

film

Substrate

 

 

 

Figure 13. Substrate and film bowing to radius of curvature p, Us is
the substrate diameter. t,and ts are respectively the

thickness of the film and the substrate.

57

Io ds = (1/2) oxsx+(1/2)oys = as. (18)

The strain energy per unit area II) for the entire system is [57]

¢ = (E,/1-v,) I812d2+ (E2 Il-vz) Iszzdz. (19)

Using equation 16 for s and (11) for 112. the strain energy is then

1b = (E1 l1-v1).Il(n1"Z)2/p2 dz 4'

(132II-v2)_I‘('rI1-a1,2p-Z)"’/p2 dz. (20)

The requirement for minimal strain energy is satified by setting the

partial derivative of the strain energy with respect to 11 and p

respectively to zero. This leads to an expression for the neutral axis

distance and another one for the radius of-curvature. given by [57]

p .. [5,2d,2 + Syd.2 + 4 S1 S._d,2 + 4 s1 Szdzz +

4 S,Szd12 +6 S182d1d2]/ [ 6 a,,ZS,S2 (d,+d2) ]. (21)

58

Where d1and dzare layer thicknesses as shown in figure 7. and

S1. E,d,/(1-v,)
$2. E202/(1-v2) (22)

are the stiffness of both layers. A similar equation to equation 21 was

given [4] in term of the strains 8 parallel to the interface:

Up = [s E,E2d,d2 (d,+d2) s ] / [ E,d1 + Ezdz ) ( E,d,3 + Ezdz" ) +

SE,Ezd,d2(d,+d2)2]. (23)

If for the two layer system. shown in figure 7. we treat layer number
one as the thin film and the second layer as the thicker substrate, then
we can do the following substitutions

d1 .- tt . film thickness
d2 - t. - Substrate thickness
_E1 = E, a Young’s modulus of film material

E2 . E. . Young’s modulus of substrate material

v1 = v. a Poisson's ratio of film material

v2 = v. = Poisson’s ratio of substrate material.

59

With the help of equation 12. Rossignon and Evans derived the

relationship of the stress to the radius of curvature from equation15

oar-[Es ‘32 /6(1-vs)t,p] [(I+t,/ts) (1 -4t,/ U] (24)

This equaion can be further simplified if 1' << ts. yielding to what is

known as the Stoney equation [8]
on =[ E,3 182 /6 (1-vs)t,p 1. (9)

Equation 9 is therefore applicable only for film thickness much smaller
than substrate thicknessand for the central deflection of the wafer much
smaller than its diameter.

Rubin et al. [58] calculated the residual stress based on the center

deflection 5 of a beam of length L. The expression Rubin used is

on.4Est525 / 3(1—vs)t,L2 (25)

Stress measurement according to Stoney’s equation is more straight
forward than Raman spectroscopy use for stress measurement. The
parameters needed for the a measurement are the wafer properties.
which in case of the silicon wafer. are well known. the film thickness

and the curvature. The major assumptions made are the isotropy of the

 

60

film and substrate [57jand that no stress develop in the substrate [4]; the
substrate behaves rigidly since it is much thicker than the film. elastic
changes occur only in the film [20]. The stress measured must be the
elastic range. It is also assumed that the interface bonding is strong
enough not to allow slippage or spelling and that the substrate is

initially flat. otherwise. the difference in deflection before and after the

film is deposited must be used instead.
4.3.1 Importance of the film thickness

What the radius of curvature method measures is the force per unit
thickness rather than a stress value. If the film thickness is uniform. the
uniform stress ( equal to the average stress ) is simply obtained by
dividing the force per unit thickness by the thickness value. However
the above scenario represent the best possible conditions which are:
the film thickness is uniform and the force per unit width has a constant
value ( a direct result of the assumption of film thickness uniformity ).
Unfortunately. neither assumption holds. In the case of MPCVD
diamond films the film thickness is not uniformly distributed [10.21]. The
force per unit with is not constant; Hoffman [48] carried an in situ
measurement of the force per unit width in Cr films by interferometric
observation ( section 4.3.2 ) of the resulting deflection during film

deposition. The force per unit width was calculated from the quantity

[ Es 182/ (1 "V112” ( lg, + v I») where kx and I3, are experimentally measured

61

constants. Hoffmann found the force per unit width to decrease linearly
with film thickness [48]. Consequently. even the value of the force per
unit width measured by the radius of curvature change reflects the
average force per unit width in the film. The obtained stress value in
Stoney’s equation is therefore the average force per unit width divided
by the average film thickness. A more accurate stress measurement
with Stoney's equation'would involve the following steps; first an in situ
method ( Hoffman’s methods described above or in section 4.3.2 for
instance ) has to be used to map the curvature change during
deposition as a function of theinstantaneous film thickness. The value
of the force per unit thickness as function of the film thickness is then
obtained as did Hoffmann with Cr films [48]. Second. the film thickness
distribution along the radial direction of the film must be mapped. At a

given point of the film surface where the thickness is some value to, the

instantaneous stress is given by the ratio of the force per unit thickness

evaluated at to, divided by the thickness layer dt at the height to. The

total stress is thus the sum of the contributions of all dt layers from zero
to the maximum height. One can conclude from the above discussion
that the value of the stress as given by Stoney's equation reflects a
stress value that averages both the force per unit width and the film
thickness over the entire film thickness range which differs from Raman
stress measurement giving the stress value within the skin depth. An
interesting case occurs when the film thickness is less than the skin

depth as is the case for a diamond film few microns thick. In this case,

62

the laser beam samples the entire thickness, thus both the interfacial
stress and bulk stress are measured. and possibly the an average stress
is obtained.

The most important consequence of stress measurement by
measuring the curvature of the film is that the measured stress is the
average stress in the film; including the interfacial. bulk and surface
stresses. The stress obtained in a film from the change in the radius of
curvature measurement gives an average stress while the Raman and x-
ray stress measurement gives the near surface or interfacial stress [59].
Stress values can be very different at the interface from average
values. since the thickness dependence of stress is a well established
fact [8]. According to the derivation of Stoney's equation. the average
stress obtained assumes a uniform film thickness distribution over the
measured area. In MPCVD deposition, the film thickness does vary from
the center towards the edges of a circular film. Windischmann
deposited films by MPCVD where the film thickness was 3.0 microns at
the wafer center and drOpped to 50 percent of the center value at a
radial distance of 25 mm, and 1.25 microns at 37 mm, the average
thickness was 2 microns [10.21]. The area of measurement had to be
reduced to decrease the effect of the thickness gradient [10.21]. Since
the stress is assumed to be inversely proportional to the film thickness.
even small variation in the film thickness result in resolved stress
variation over the area of measurement. For instance. in ZnO films the

stress was 0.73 GPa at 5 microns film thickness and 0.58 GPa at 10

63

microns [56]. Thus. a 50 percent decrease in film thickness resulted in
26 percent increase in stress. Measurement of an average value of the
film thickness becomes-critical to accurate average stress measurement
in the film.

Given a film with a non uniform film thickness distribution. the
measured stress value from the change in curvature does not give a
reliable representation of the film stress since only an average value is

obtained. the upper and lower limits of stress values are thus

 

“unknown. :

4. 3.2 Errors and resolution

Film thickness measurement with 2.5 to 10 nm accuracy is routinely
obtainable with a profilometer stylus [3]. The process involves
thickness measured by masking the substrate during deposition and
creating a step at various edges of the film. The steps are measured
with a profilometer and an average value of the thickness is taken
[3.12]. Other thickness measurement methods are SEM and light
interference methods which offer a similar error range to the profilometer
step measurement. All of the thickness measurement techniques should
take into account the film thickness variation; the spatial distribution
and number of measurements on the film thickness affect the measured
average value of the thickness. Perhaps the best method for measuring

the average film thickness is the differential weight analysis; the film

and substrate are precision weighted. the substrate is then chemically
etched out and the film is weighted again. Alternatively. the substrate
is weighted first. then weighted again after the film is deposited.
Assuming a diamond density of 3.515 g/cm3 , the volume of the film is
estimated and divided by the base area of the film resulting in an
average value of the film thickness. 3 preferred value for Stoney’s
method [60].

The measurement of the film thickness from a created step is not
convenient for a real application because it must have an area where
no film is deposited. SEM observation involves destroying part of the
samples and differential weight analysis results in complete removal of
the film from the dissolved substrate. Film thickness measurement with a
light interference method is a nondestructive method that can be used to
measure the film thickness.

Many authors have reported the use of a profilometer to measure the
radius of curvature of the substrate bowing under stress [3.27]. A
commercially available Dektak II was often used [3]. However the
method for radius of curvature measurement most frequently used is the
light interference fringes method. Interference fringes are formed by
placing the film-substrate composite against an optical flat which is a
specially ground surface that is often glass. Then the specimen is
illuminated with a monochromatic light through the glass. Bending of
the sample causes the formation of set of closely spaced interference

fringes [8.56]. The radius of curvature is then given by [56]

65

p = x"2 / R71. (26)

where 2xn is the diameter of the nth dark fringe. and A. is the

 

us.
wavelength of the illuminating monochromatic light. For a circular film- I‘

substratesystem ( figure 13 ). if the fringes are circular then the

stresses in the X and Y directions have the same magnitude. However i}

if the fringes are elliptical. then stresses in the two directions are L

unequal [56]. Some authors measured the stress from the curvature of
the stressed film compared to a perfectly flat surface [4]. however the
net curvature change [55] before and after the film deposition results
from the film stress. For instance. the curvature is measured before and
after a silicon film is chemically etched out. the net change in the
curvature is then attributed to film stress [59]. For the measurement of
the beam deflection with a stylus, the deflection of the stylus under a 25
mg load is assumed negligible [3]. The error in measuring the deflection
with Stoney’s equation was found to be less than 20 percent compared
to measured deflections on a simply supported circular plate under

load. The relative error in repeated measurements is less than 10
percent [3]. The deflection of a beam measured with Optical microscope

with a point-to-point focus technique has an accuracy of 0.1 microns

[16]. Many authors approximated the radius of curvature by 22/ (8 w).

where z is the measured bow height and w is the distance over which

the bow is measured given that z/w << 1 [59]. Given the accuracy of
the film thickness and curvature measurement stated above. the stress
is measured from radius of curvature to an accuracy within 0.09 GPa
[56].~and 0.05 GPa [34]. The reported stress resolutions for the stress
measurement from the radius of curvature is 0.01 GPa [10].

Hoffman reported on the minimum detectable force per unit width for
a variety of deflection measurement techniques [8]. To convert the
force per unit width to a stress resolution. the force per unit width are

divided by a typical 1 micron film thickness. the obtained resolution
ranges from 10'5 GPa for mechanical and interferometric techniques to

about 10'3 GPa for optical and x-ray techniques. Thus very high stress
resolution can be obtained with the curvature measurement methods.
The stress resolution can be improved by using thinner substrates.

The measurement of the beam or wafer deflection as an in situ.
method during the deposition is at a disadvantage compared to Raman
spectroscopy because there is a difficulty in isolating the stress
transducer from the energetic deposition environment. it can be can be
costly and difficult to use [15]. Raman spectroscopy would only require
a window for the laser beam to pass through the deposition chamber
wall. The advantage of in situ measurement over conventional methods
is that one can measure curvature of films as thin as 30nm and directly
measure the intrinsic growths stress [15]. since thermal stresses do not
develop until the film and substrate are actually cooled to room

temperature. Hoffman [15] measured the insitu stress in molybdenum

67

film by the incremental voltage change of the capacitive film with
incremental deposited film.

The maximum difference in the elastic modulus of (100)silicon is 16
percent. but no important variation in curvature were observed for any
orientation of the stylus with respect to the water when the film is
uniform [3]. The Young's modulus in Stoney's equation representing the
substrate should be average in-plane modulus [3]. Using a single
crystal for the substrate thus introduced an error in the stress value as
calculated from Stoney’s equation, since the elastic constant are not
isotropic; they depend on the crystallographic orientation. The
assumption of isotropic-materials. for Stoney’s equation to be

applicable, should hold; the condition for isotropy is [60]

the ratio is equal to 1.21 for diamond and 1.56 for silicon. The
applicability of Stoney’s equation can be argued in the case of diamond
and silicon since they are essentially isotropic but not truly isotropic.
One should note however that the elastic constants ratio as a condition
for isotropy is dependent on the reported value of elastic constants and
thus can get closer or farther from 1 depending on the scatter in the
values of the elastic constants. It would be also a problem to interpret
stress reSults if the magnitude of the stress is beyond the elastic

deformation of diamond. Clausing measured stresses in diamond films

68

that approach the stress at fracture. the magnitude of the stress was as
high as 6.1 GPa. while the stress at fracture is about 11 to 20 GPa the
measurement method was x-ray diffraction [31]. Clearly. such
measurement would not be reliable by radius of curvature method
because the stress value is in the plastic deformation range. Further
errors in the measured stress according to Stoney’s equation would
arise if the films are delaminated. bowing of the substrate due to film
stress can no longer be measured by Stoney’s equation [27], the
interface is assumed to be strong enough to avoid debonding.

If a reliable nondestructive technique can be used for film thickness
measurement. the radius of curvature method becomes a nondestructive
method for stress measurement. Measurement of the curvature with a
stylus can be destructive though; the surface can be scratched with the

stylus [59].

4.3.3 Advantages of the curvature methods

Some of the advantages of stress measurement from the change in
the radius of curvature over the Raman shift and X-ray measurement
have already been discussed earlier. Other advantages include stress
measurement in films of any morphology ( amorphous or crystalline )
while Raman method measures stress only in single or polycrystalline
materials. the same is true for x-ray stress measurement [59]. The

radius of curvature is a direct and easy mechanical measurement of

69

stress [59], while Raman and x-ray techniques involve various
assumptions and are rather lengthy. Raman spectroscopy requires a
lengthy set up time and careful calibration. and thus is a lot costlier
than curvature measurements.

The only systematic stress measurement study that used x-ray.
Raman and curvature methods was done by Trimble et al. [59].
Polycrystalline silicon films with an oxide layer were used. X-ray (400)
peak shift from the change in the inter planar spacing in the 50 microns
thick polycrystalline silicon films through the oxide layer yielded a
stress of 0.037 GPa within 0.01 GPa. the skin depth is 5 microns at the

at 40 Kev x-ray line. Raman measurement yielded no shift with a 0.2

cm" resolution corresponding to stress resolution of 0.05 GPa. The
conclusion was that the stress was less than 0.05 GPa which is higher
than the stress value measured by X-ray. the sampling depth in the
silicon was 3 microns at 647 nm Ar laser line. These measurements
represent stress only within 3 to 5 microns from the interface. Using the
radius of curvature method. the stress was found to be about an order of
magnitude smaller; about 0.004 to 0.006 GPa depending on the
orientation of the measurement direction across the water. stress
anisotropy is thus observed with this method [59]. From the fact that the
stress measured by the change in the radius of curvature is much
smaller than the stress measured by the x-ray technique. one can
conclude that Stoney’s equation provides an average value of the

stress over the entire thickness x-ray diffraction samples stress only at

70

the interface where the’stress is expected to be higher than in the bulk

of the film.
4.4 Stress measurement from the Raman peak shift

In materials with the diamond crystal structure. the triply degenerate
zone-center phonon mode is known to split and shift under stress [61].
The degeneracy of phonon mode is lifted by lowering the crystal
symmetry due to an applied or residual strain [62]. The shift of the zone
center mode with stress can therefore be used a measure of stress in
diamond film as well as-a pressure sensor as a diamond anvil cell DAC
[63]. In the following paragraphs. a derivation of the phonon frequency
shift due to stress is reported for single crystals with application to
diamond under a biaxial stress state in the XY plane.

In presence of strain. two atoms in a unit cell are assumed to behave
according to the dynamical equations describing the zone-center

phonon modes and have the form [61]

m 'azui/ at2 s - 2 Kii uj

= - ( 1<°ii uI + 2( akii / ask, ) ck, ui) (28)

where ui is the ith component of the relative displacement of the two

atoms in the unit cell. m is the reduced mass of the two atoms in the unit

71

cell and K” are atomic force constants. K01] = m v02 is the effective

spring constant of the F29 triply degenerate diamond mode in the
absence of strain. ( 8K” lat-zkl ) era = Kim is the change in the spring

constant due to the strain 810- i. j, k and I are crystallographic axis [61].

Since diamond has a cubic symmetry. there exist only three

independent K’ components. namely

K’liii '3 m p
K’II“ m q

p, q and r are independent deformation potentials ( strain derivatives )
[61]. With the assumption of harmonic motion, the phonon frequencies

for the strained lattice can be deduced from equation 28 which results

in a 3 X 3 secular determinant with eigenvalues it [64]. The

eigenvalues are given by [64]

).-.=vs.2-v2 (29)

where v is the line frequency of the stressed film and Va is the

SI

frequency of the unstressed film. Equation 29 can be approximately

72

rewritten as

v ~Vo+Al2VO (30)

SI

The solution to the 3 X 3 secular equation is a cubic in A therefore.
it has three solutions. Depending on the stress state. the three
eigenvalues can be all equal under a hydrostatic stress to completely
independent under a uniaxial stress parallel to onethe <110> directions
of the sample [61.65].

Equation 28 can be solved for the strains in the film as a function of
the frequency change. In the case of a non hydrostatic stress state. two
eigenvalues are equal and thus only two eigenvalues are independent.
The corresponding phonon frequencies according to equation 30 are

the doublet and the singlet which are respectively given by [61.64.66]

Vs: Vo-I- 2Vh- 2Vu/3 (31)

where vh and vu are respectively the shifts due to hydrostatic and shear

component of the strain [67]. The hydrostatic component of the stress
does not cause Splitting of the zone center phonon [62]. but contributes
to the total observed frequency shift [62].

The stresses in the film can be determined from the strains using the

73

following equation [9]

81) " Sijkl 6k (32)

Considering that the Z axis is perpendicular to the surface of the film.

that X = [100]. Y = [010] and Z = [001] and that the stress at the surface

is zero. the biaxial stress Oxx = <3W a o in the film is non zero and [64]

8x=8

x y=(811+812)6

Y

szz = 2 S12 0

e. = 0 for i s j. (33)

For a biaxial stress state vh and vu are given by [66]

vh so (p+2q)(S11+S12)/6v0

\ru=o(p-q)S12/2v0 (35)

From the above equations. the shift of both the singlet and the

doublet due to a biaxial stress state is determined to be

Avs=vs -V0=O’/2Vo[2p S12+2q(s11 +512”

Avd = vd - v0 = CI 2110 [ p (S11 + S12) + q( 811 +3 812) (36)

74

Equations 36 are identical to those used for the singlet and doublet
shift due to a biaxial stress in thin films given by Engler [68] and
Nishioka [64] and differ‘from the equations given by Ceideira et al. [61]
for a uniaxially applied stress.

Usually. the Raman spectra are given in terms of the scattered

intensity as a function of the wave number w (cm") rather than the

frequency. The relationship between the wave number w. the frequency

v and the speed of light c is given by
v=2ncw Q“
where c = 3 x 1010 cm/sec. Equation 36 can be rewritten as
V=61t101°w(cm'1) V (37)
Given the above relationship then

V0 (1/sec) = 6 1:1010 wo(Cm'1)

Av (1/sec) = 6 1: 101° Aw (cm") (38)

The values of S". p. q are reported for diamond and silicon are given

in table 3. Using these'values. the relationship between the biaxial

75

stress in the diamond film and the diamond line shift of both the singlet

and the doublet are calculated in this work to be

08 (GPa) = -8.11672 10'4 wo Aw (cm'z)

od(GPa) .. 46.3014 10" w0 Aw (cm'z) (39)

taking wo = 1332.5 cm-1 [69]. then

 

68 (GPa) = -1.08 Aws (Cm'z)

od(GPa) . -2.17 Awd (cm-2) (40)

From the above linear relationship of the stress with line shift, the
diamond pressure coefficient for a single crystal under a biaxial stress
are 0.93 cm'1/GPa for the singlet line shift and 0.46cm'1/GPa for the
doublet line shift. Equation 40 are derived for diamond single crystals
with an homogenous biaxial stress parallel to the surface of the diamond

film.

It is interesting to note that the coefficient 1.08 GPa/cm" calculated
here for a biaxial stress. in the XY plane is.equal to the coefficient given
by Yoshikawa [9] for a tensile uniaxial stress along [001]. The above
similarity is to be expected since in the configuration used in this

thesis, the compressive stress in the XY plane of the film is going to

76

induce a tensile stress in the 2 direction which corresponds to the
[001] direction of applied stress in Yoshikawa’s calculation [9]. From
the above observation one is allowed to'compare the calculated
coefficient in equation 40 for a biaxial compressive stress state with
experimentally measured values of the same coefficient for tensile r
stress in the <100> direction given that there are no published results

to the author’s knowledge) for frequency shift under a biaxial stress for

 

diamond. The survey of the reported values for the diamond frequency
shifts under various stress distributions is summarized in table 4. l:

According to table 4. the experimentally determined shift coefficient for
uniaxial stress along the <100> is 1.37 GPa/cm'1 [70] which is close to

the 1.08 GPa/cm'1 calculated here. Gezan et al. [62] reported that the
estimated calculated stress value to cause a 1 cm-1 shift is 1.081GPa
which is in very close agreement with the value calculated here (1.08
GPa). One should note that even though the calculation issimple. no
calculated shift coefficient under biaxial stress was reported in the
literature for either single crystals or polycrystalline diamond. One

would conclude here that the calculated value of shift coefficient 1.08

GPa/cm‘1 is a reasonable value to use for further stress calculation

assuming a (100) orientation.

77

Table 3. Elastic constants and deformation potentials
of silicon and diamond.

Property Diamond silicon
su (sped) 9.5240 10‘ 76.8 10‘
5.2 (spat) -0.9913 10‘ -21.4 10‘
p (seca) -1.0710 10” -1.43 10”
q (coca) -5.2620 10" -1.39 10”

 

Ta

Re

78

Table 4. Reported diamond shifts under stress.

Measured
pressure
coeft.
cmd/GPa

calculated Pressure
range
(GPa)

Pressure
coett.
cud/GPa

Diamond
sample

63
72

73
71
70

70
70

69

74
65

75

hydrostatic

isotropic

// [10°]

hydrostatic

II [110]
II [001]
// [111]

Hydrostatic

Hydrostatic

Hydrostatic
Hydrostatic

hydrostatic

2.90

N/A

N/A
0.66
N/A
N/A
N/A

N/A

0-25
0-18

N/A

0-30

12.1

15-40

0-30

O-2.3

DAC'
(100) plate

single
crystal

(100) plate
(110) disk
(100) plate
(111) plate
(100) plates

Natural
diamond

(100) POD“
DAC’

single

° Diamond anvil cell

” Polycrystalline diamond

79

4.4.1 Nature of the dependence of stress on the frequency shift

The phonon frequency shift with stress depends on many factor. The
crystallographic orientation of the single crystal. the orientation with
respect to the single crystal of the incident laser beam as well as that of T
the scattered beam, the polarization of the laser beam. and the stress

distribution are the key elements in correctly measuring the stress in a

 

single crystal from the measured frequency shift. -
The stress in single crystals was found theoretically [61] and I

experimentally [64.71] to vary linearly with frequency shift. The stress

varied linearly with shift for Ge. GaSb. GaAs [61] and diamond under a

variety of stress distributions [9.65.69.70.71.72.74]. Furthermore, the

linear dependence of the stress on frequency shift holds for both the

singlet and doublet splits as well as in the no-split case [32.61.65].

However. the dependence of the stress on the frequency shift is linear

only to about 40 to 70 GPa [74]. The stress range of interest in this work

is less than 10 GPa. therefore the assumption of linearity is solid for the

purpose of measuring stress in thin films.
For diamond and silicon, the stress measurement is made easier due

to their cubic diamond structure which reduces the number of

parameters necessary for stress calculation. namely the elastic

constants Sii (Cii ) and deformation potentials p. q. r. The elastic

constants for diamond are available in the literature [9]. however. there

is a considerable scatter in the reported values due to various

80

measurement methods. For instance. the value of C11 was found to be'

151 GPa by Brillouin scattering measurement and 390 GPa by the
ultrasonic wedge method [76]. which is more than twice the value of 151
GPa. The same kind of scatter exists for the deformation potential
constants. Furthermore. the deformation potentials are derived for
uniaxial and hydrostatic stress conditions and not a biaxial stress state.
Therefore, until precise deformation potentials are measured under a
biaxial stress state. it remains unknown how much of an error is being
made by using already published deformation potential constants.
Accurate values of the deformation potential constants are critical to
the precise measurement of the strains from which the stresses are
calculated. To avoid errors due to scattering in the elastic constants.
one might look at the strain values instead of the stresses for various

stress measurement techniques.

Unlike other phonon frequencies. the F29 frequency ( at 1332.5cm‘1

for diamond [69] and 520.7 cm'1 for silicon [59]) shift primarily under
stress ( from its unstressed position) and does not shift from other
effects. For instance. the characteristic line of graphite is known to
shift with incident laser frequency [77].

The F29 band in diamond crystals is known to shift with stress. but

more critical to stress measurement is the splitting of the band under

stress. Under a hydrostatic stress state, the F29 band does shift but

does not split [70]. However, Under a non-hydrostatic stress state, the

81

triply degenerate phonon line of the diamond structure splits into non
degenerate (singlet) and doubly degenerate phonons (doublet) or into
three singlets [61]. For instance. in Ge film under biaxial stress parallel
to the film surface, the triply degenerate line split into a singlet and a .
doublet under a uniaxial stress parallel to either a <100> or <111>
crystallographic directions. the triply degenerate line in diamond single
crystals splits into a singlet arising from bonds parallel to the stress
direction and a doublet perpendicular to the stress direction. but split
into three singlets under a uniaxial stress parallel to the <110>

crystallographic directions [61.62.65]. Under a biaxial stress, the F29

line also splits into a singlet and a doublet [68]. The magnitude of the
frequency shift differs with the stress state; the shift from the singlet in a
uniaxial stress state is different from the magnitude of the shift of the

singlet in a biaxial stress state. For instance. the estimated stress to

cause 1 cm'1 shift under hydrostatic stress is1.081 GPa for diamond and
0.609 GPa for silicon which is lower than under uniaxial stress. namely
1.9435 GPa for diamond and 0.825 for silicon [62]. Furthermore, the
magnitudes of the shift of the split bands also differ, in all cases the
highest frequency is that of the singlet [63]. The ratio of the intensities
of the singlet to the doublet is 4 to 1 for Ge single crystal under uniaxial
stress [61]. Since the singlet has the highest frequency [63] and
corresponds to bond deformation in a direction parallel to the stress
direction[61]. one can conclude that the highest frequency shifts occurs

from deformation in the plane or direction of stress.

 

82

The magnitude of the shift also depends on the polarization of the
laser beam. If the laser beam is polarized such that the electric field is.
directed parallel to the stress direction [32]. the shift of the line is about
3.5 times as compared to the case where the electric field is
perpendicular to the stress direction [32]. If the laser light is polarized
such that the electric field forms an angle with the stress direction, the
shift is a linear combination of the two shifts parallel and perpendicular
to the stress [32]. For a completely random polarization. the observed
shift is half the sum ofthe two shifts. and the line width reflect the
contribution of both shifts [32].

The magnitude of the shift is also dependent on the assumed value of

the diamond phonon frequency in the unstrained state. Most authors
assume the value of 1332.5 cm“1 [59.73], but other values have been
used, 1333 cm" for instance [72]. In the case of small stresses. a 0.5

cm“1 error in the above assumption will result in a stress error of the
order of 0.1 GPa. which is a considerable error.

Once it is known whether or not the F29 band split and what it splits

into. according to the stress distribution and sample-laser orientation. it
becomes important to identify the band or bands being observed in the
Raman spectra. The scattering geometry is the determining factor. In
back scattering geometry, only the singlet is observed [9.74]. the
doublet may exist but is not observed. For example, in back scattering
geometry with Z=[001] along the laser beam direction. only the singlet

is observed the doublet is preserved but not observed [68].

83

As can be seen from table 4. the highest frequency is observed
under a hydrostatic stress state. In the case of a planar homogenous
stress applied to a flat sample. there is an extra uniaxial compressive
stress that will drive the shift coefficient towards a truly hydrostatic
condition [74]. For diamond. if the shift coefficient under the biaxial
compressive stress is used as in equation 40, a possible systematic
error is the contribution of the uniaxial tensile stress parallel to the
surface of the film [74]. For instance. an homogenous stress applied by
a flat solid included a uniaxial compressive stress along [001]

perpendicular to the surface. the shift coefficient was experimentally

found to be 2.90 cm“1 / GPa. Furthermore, the samples used were
polycrystalline [74]. The condition used in reference 74 are very close
to those used in the present work. Knight [26] interpreted shift in PCD
films as due to stress and calculated the stress from the pressure

dependence of the shift in diamond of Sharma [63], the shift coefficient

Knight used was 2.33 cm'1 IGPa or 0.42 GPa/cm". From the above
discussion. its seems that the shift coefficient that fits the stress
measurement in films under biaxial (homogenous) stress ( and a stress

perpendicular to the film surface), is 0.35 to 0.45 rather than 1.08

GPa/cm‘1 calculated from the secular equation. The rationing behind
the above choice is that the calculated value from the secular equation
considers only the contribution to the shift from the biaxial stress and
not the stress in the z axis of the film. Furthermore. the model is for a

single crystal and thus cannot be used for a polycrystalline material.

 

4.4.2 What causes Raman shifts

In order to interpret shifts as stress. it critical that there are no other

effects causing shift'that can be mistaken for stress.

The F2" phonon frequency of diamond at 1332.5 cm'1 was found to I

down shift with the fraction of ‘30 isotope of carbon [24]. The normal

isotopic 130 concentration is 1.1 percent. Increasing the amount of ‘30

 

up to 91 percent. resulted in negative band shifts down to 1288.7 cm'1 I
[24]. Diamond band position is independent of excitation wavelength [9]

and also independent of the laser excitation source type (i.e. argon.

krypton. The electric field effect on the diamond frequency position

was, investigated [62]; the electric field necessary to cause a

1 cm-1 shift is high about 106 V/Cm. dielectric breakdown is expected
to occur at such applied field. Thus no contribution to the frequency
shift from the electric field is expected [62]. The next source of
frequency shift that must be considered is the temperature rise due to

laser heating. The diamond was found to change very weakly with

temperature. a net shift of about 2 cm'1 resulted from about 400 °C
temperature increase [69]. Thus. the effect of laser beam heating on the
shift can be ignored, especially that diamond has a very high heat
conductivity ( 5 time that of copper at room temperature); the heat will
dissipate quickly into the diamond bulk.

The only considerable frequency shifts of the diamond band reported

85

in the literature are due to deposition parameter. lattice mismatches and
thermal stress ( thermal expansion mismatch stress ). A rather
inconsistent shift with deposition pressure is reported throughout the

literature [22,60]. There is a systematic shift of the diamond peak with

methane fraction in MPCVD depositions. Positive shifts of about 1 cm'1

occurred for methane fraction up to 4.0 percent [26.29]. Larger shifts to

3 cm'1 are observed at 7.5 percent methane fraction [29]. Similar shift

with methane fraction were observed with ethanol in the deposition gas.

Unusually high shift of 13 cm“ were observed at methane fraction less
than 1 percent [26]. Lattice mismatches between the film and substrate

are also a source of frequency shift. In diamond films deposited on hard

substrates such as alumina and silicon carbide. shift of -5 to +13 cm‘1
are observed [26]. The dependence of the shift on the deposition
temperature is such that at the temperature range where crystalline
diamond is formed the shifts are small . For deposition temperature such

that non diamond phases are formed the shift are in the order of 1 to 3

cm". At 1200°C. the diamond line completely disappeared [26]
The deposition parameters including gas pressure. temperature,
methane fraction and hydrogen fraction ( proportional to the methane

fraction ), were shown in previous sections to affect the degree of

ordering by changing the sp3 to Sp2 bond ratio and result in growth
stresses. In graphite polycrystalline films. the stress was found to be

dependent on the grain size. There is no evidence to support the same

 

argument for diamond; the grainsize is linearly proportional to the
methane fraction [10,21]. It is therefore difficult to separate the effects
of grain size and methane fraction on the stress in the film and thus on
the frequency shift. Deposition temperature variation also affect the
degree of ordering as well as varying the degree of thermal expansion
mismatch between the film and substrate and consequently affecting the
magnitude of thermal stress during the cooling down from deposition.
Lattice mismatch between the film and substrate induce interfacial
stresses. The only parameter that is shown to significantly induce

diamond band shifting that is not stress induced is the amount of

isotopic 13C in the film. There is no reason to believe that the 130

fraction in deposited film is greater that the normal isotopic fraction. it

is therefore evident that the shifts of the diamond band at 1332.5 cm" is
stress induced. Indeed it is rather evident that the F29 mode of diamond
shift with stress. There is long list of studies done on the pressure
dependence of the diamond line [32.69.70.74]. In most cases however.
the Studies used single crystals and externally applied hydrostatic
pressure with a gas medium or a uniaxial stress along a known
crystallographic orientation. To the author's knowledge. no systematic
study has been carried on the diamond line dependence on residual
growth stress with polycrystalline samples. From the available data on
the pressure coefficient of diamond under various stress distribution. on
can only speculate on the magnitude of the shift coefficient with stress

for polycrystalline films under biaxial stress in a plane parallel to the

87

interface.

Given the above arguments, one can cautiously assume that in the
case of polycrystalline diamond films. the shift of the diamond peak is
stress induced.

The laser skin depth of most ceramics is few microns. For graphite.
the skin depth is 0.6 microns at 488 nm wavelength [32]. For silicon,
the skin depth is about 3 microns at 644 nm [59]. The very small skin
depth of the laser beam probing the sample implies that the observed
shift are due to surface effects and may or may not reflect the stress
state in the bulk of the sample. In the case of diamond the depth of
focus is plus or minus 50 microns about the focal plane [72]. Given that
the diamond film thickness hardly exceeds 10 microns. the diamond film
is entirely on focus and thus the shift observed from stress do reflect the
stress distribution over the entire film thickness in the volume being
probed by the laser beam. The volume in consideration is a cylinder
with the height being the film thickness and the base equal to the laser
beam spot diameter ( assuming a Circular laser beam cross section ).
The residual stress distribution in the film is such that at the first few
hundred Angstroms from the interface. the stress is high due the
contribution of the lattice mismatch and thermal expansion mismatch.
The stress than levels off towards the free surface of the film. Therefore
it seems that the measured shifts reflect the contributions of both
interfacial and bulk stress within the film thickness. Within the probed

volume, the C-C bond distortion is going to decrease away from the

88

interface. there is going to be a spectrum of phonon frequencies
corresponding to the various bond distortions from the interface to the
free surface of the film. The spectrum of frequencies is reflected in the
Raman spectra by a widening of the diamond line. The highest shift is
going to be due to the greatest distortion which occurs at the interface.

Broad diamond peak might indicate stress inhomogeneity within the

scattering volume; a sharp line about 2 cm" wide results from
homogenous stress [73]. Thus line width is an indication of stress
homogeneity [73] but is not the only contributing factor line
broadening.

Since the beam spot size is about 2 microns. the probed area is very
small compared to the sample dimensions. The measured shift from the
probed area would thus reflect the stress state from only the scattering
volume in that area; the stress measures this way is then a local stress
and does not reflect the macroscopic stress state of the film. If the
stress is known to be homogenous over the volume of the film. than the
local stress measurement would be a good representation of the stress
in the film. However, if the macroscopic stress distribution is not
uniform. the locally measured stress within the beam spot diameter
cannot be taken as a representative of the stress in the film. The
advantage to measuring stress in a micro-volume is the ability to
actually map the stress distribution by taking point to point measurement
across the surface of the film. The above method would be an excellent

way to map stress anisotropy in a film. The derivation of the shifts due

89

to stress is based on a single crystal with known orientation with
respect to the laser beam. In the case of a polycrystalline film as is the
case in most diamond films investigated. the derived stress calculation
equations Cannot be directly used. However. the average grain size in
diamond films deposited by MPCVD is about 1 micron. Given that the
beam size at the sample surface usually about 1 to 5 microns which is
about the same as grain size and given that the film thickness usually
about a micron. smaller than the average grain size. it is likely that the
laser beam is focused on a single crystal or the boundary between two
grains. Because of the possible scattering from only one or two grains.
the theory may be applied. The questions becomes whether the stress
state within a single crystal represent the isotopic stress distribution in
the diamond film.

It is usually assumed that growth stresses in diamond films are
isotopic and thus uniform across the film in a plane parallel to the
interface. Furthermore, the stress is a function of the film thickness. If
the film thickness is not uniform. then the stress in the film cannot be
homogenous in directions parallel to the interface. Windischmann
reported that the thickness of MPCVD films decreased to 50 % of its
value at the center of film at a radial distance of 25 mm [21]. The
variation was attributed to the non uniformity of the plasma electric field
[21]. The thickness variation across a film can be easily monitored by
Raman spectroscopy since the intensity of the Raman line increases

linearly with film thickness [26] because of increased scattering volume

 

90

with increasing film thickness. The ratio of the scattered intensities at
two different point in the film is probably equal to the ratio of the film
thicknesses at the same points. given that the exact same conditions

are used for the measurement.
4.4.3 Advantages and weaknesses

The reported stress magnitudes in thin diamond films ranges from
zero to about 2 GPa. The stresses measured are therefore small; the
resolution of the frequency shift measurement and the errors due to
experimental setup must be small enough so that small stress
magnitudes can be detected trough small frequency shifts.

In Raman spectroscopy. the resolution is a function of the slit width.
the number of slits per millimeter of the natural line width of the laser
used. How precisely the stress is measured depends on how accurately
one can define the position of the diamond band and determine its
center. The center of the band is taken as the position of the band
rather than the maxima of the band peak. If the diamond band is
symmetric, then the maxima is obviously at the center of the peak which
can be then easily measured. if the band is not symmetric, the center of
the peak has to be determined by either a graphical method or a
computational method where the peak is fitted with a function and the
center is mathematically computed. The resolution is therefore

dependent on natural and artificial line broadening. The line width

91

(usually taken as the full width at half maximum ) is the sum of the

contribution of instrumental line broadening ranging from 2.5 to 4.0 cm’1
and which depends directly on the slit width of the spectrometer. on the

intrinsic broadening and non homogeneous stress effects. The natural

line width of the diamond band is 1.65 cm‘1 [74]. As explained earlier.
there can be a broadening of the band due to non homogeneous stress
distribution in the scattering volume. resulting in more then one

displaced diamond phonon frequency. A small increase ( less than 1

cm’1 ) in line width over the natural line width indicates both
homogenous stress distribution [74] and limited instrumental
broadening. High resolution is obtained with a slit width of 75 microns
when the line width represents true width without instrument broadening

[26]. Slit widths of 150 to 400 microns will result in medium to low
resolutions. At low resolution of 8 cm“. the line suffers from instrument

broadening [9.22]. A 3 cm'1 resolution is considered high

resolution[9]. A spectrometer slit width of 100 microns resulting in a

spectral resolution of 1 cm'1 [75]. The lateral spatial resolution Raman
spectroscopy was reported to be 2 microns within the optical skin depth
[32], ( more conventional characterization techniques have a spatial
resolution about 1 mm ) [32]. 1 micron lateral resolution and 6 microns
depth resolution have also been reported for Raman spectroscopy [63].
Whalley [75] measured the diamond band center graphically by

determining the mean frequency of the band as a function of intensity.

92

A best line fit is then drawn through the obtained points. The line is
extrapolated to the band. The intersection with the band is taken as the
band center and peak position [75].

Measuring the peak position by the line extrapolation method is

accurate to within 0.1 cm". the error was taken as the standard

deviation for many repeated measurement [75]. The error in shift
measurement taken as the standard deviation from repeated
measurements was 1.3 cm‘1 [74]. 1.2 cm’1 [65]. The errors of 1.2 and 1.3
cm'1 in references [74] and [65] are higher than in reference 75 for the
same measurement method. Errors as high as 1.3cm'1 are too high for
stress measurement in diamond films. since the shifts observed are of
the order of 1 to 3 cm“. A computer generated position measurement
would reduce these errors. A computer software can be used to isolate
and expand the peak of interest from the rest of the Raman spectrum.
Errors in the order of 0.1 cm'1 can be achieved ( See section on
experimental procedure ).

A critical element to precise measurement of the peak position is the

calibration process with a Raman spectra having well known peak

positions. Calibration can be accomplished with peak p0sition

accuracy to within 0.05 cm'1 [66].

93

4.4.4 limitations and sensitivity

Stress measurement by Raman spectroscopy is a powerful tool for
surface Stress measurement. for diamond. the laser focal depth is 20 to
30 microns [65.74]. The skin depth is usually in the order of 2 microns
for non transparent material. Thus the main limitation of the Raman
stress measurement method is that only surface stress measurement can
be achieved. However. for thin films of thickness equal or less than the
skin depth at the laser wavelength used. all of the film is in focus. and
thus stress over the entire film is averaged. Another limitation of the
method is that the stress measured represent the area within the laser
diameter and the skin depth. Thus. unless the stress is known to be
uniform, the measurement is not only at the surface but also local.
Measurement at various location of the surface is necessary to map the
stress distribution. As explained earlier. the local stress measurement .
can be used as a means to measuring stress anisotropy. If the film
thickness profile is known. the laser spot can be applied at point where
the thickness is known; the dependence of stress on film thickness can
for instance be evaluated. Conversely. the measured magnitudes of
stress over a given area could be used to map the film thickness

variation over the given area.

The Raman signal is not sensitive to cluster sizes about 50 A in

diameter. Raman spectrum of diamond film consisting mainly of diamond

clusters 40 A in diameter did not show a diamond line, so local Stress

at these clusters cannot be measured from Raman shifts. For the same
40 Angstrom diamond clusters, X-ray absorption near edge structure
(XANES) spectroscopy showed the same spectrum as for diamond with
fully developed grains [29]. thus proving to have a higher sensitivity to
very small particles. Small amounts of diamond in graphite cannot be
detected since scattering cross section of graphite is 50 times that of
diamond [78]. . The sensitivity of the Raman signal can be enhanced with
surface enhanced Raman spectroscopy (SERS). With SERS. it is
possible to analyze layers 20 nm in mean thickness by coating the
diamond surface with a mono layer of silver [78]. SERS is thus an
excellent way to measure stress in very thin films that are 20 to 50 nm
thick and can be used as an in situ method for stress monitoring during
film growth. In situ measurement allow to measure the intrinsic growth
stresses separately since thermal mismatch stresses develop only upon
cooling to room temperature from the deposition temperature. I

Another limitation of Raman spectroscopy is that thermal
decomposition of films can occur at high laser power. if the laser power
is reduced to avoid thermal decomposition of the film. the Signal can be
weakened. in diamond films. thermal decomposition did not occur at low
laser power of 60 mW [37].

The advantage of Raman spectroscopy over conventional methods is
its sensitivity to very small perturbation to the crystal phonon
frequencies. For instance X ray diffraction measurement of lattice

constant ranging of 0.3562 nm to 0.3566 nm did not yield any

95

recognizable differences while well resolved shift up to 2.7 cm-t from
the same diamond samples with a 3 cm'1 resolution [9]. It is however
difficult to resolve shifts less than 0.2 cm“. For a diamond film a 0.2

cm'1 correspond to a stress of 0.08 GPa which is less than the average
error reported in the calculation of the stress in diamond films with the
Raman shift.

Another advantage of Raman spectroscopy arises when there is
more that one film layer on substrate. Peaks from the various layers can
be obtained and the stress in every layer can be calculated. The
absorption of the various film layer becomes critical since the laser light
can be fully absorbed before it reaches a given layer. To measure
stress by other methods. the layer are etched out one by one and net
changes are attributed to the specific layer removed.

Stress measurement by Raman spectroscopy is a non destructive
techniques [32]. Since, a simple optical microscope is used to focus
the laser beam on the sample. the sample dimensions are often not a
problem. An optical microscope can be designed to accommodate any

specimen Size.

5- DEPOSITION THERMAL STRESS

5.1 Effect of deposition temperature. thermal stress

Residual stress arising from thermal expansion mismatch between the
film and the substrate depends on temperature difference AT. between

the substrate temperature during film growth and the measurement

temperature. usually room temperature. The thermal strain 8Tb is then [8]

81-h = Aor(T) AT. (41)

Aa(T) is the difference of thermal expansion coefficients between the

film and substrate. Aa(T) is a function of temperature Since the thermal
expansion coefficients of the film and substrate are each functions of
temperature. As the deposition temperature increases. differential
expansion stresses vary according to the temperature dependence of
both the film and substrate’s thermal expansion coefficients. Intrinsic

stresses decreases with temperature [8]. The thermally induced stress.

6 in the film can be calculated from the thermally induced strain in

m.

equation 41, and is given by

°m=Er(°‘i'°‘s)(Ts'T0) <42)

96

97

Where E.=E,(T) is the Young’s modulus of the film and 01.: 09(T) is the

thermal expansion coefficient of the film, as: 018(T) is the thermal
expansion coefficient of the substrate, Ts is the substrate temperature
during deposition and T0 is the measurement temperature. From the

stress equation 42. stress dependence on the deposition temperature

is evident.

5.2 Thermal stress modeling

Thermal stresses can be easily calculated for a thin film-substrate
system. However. thermal stress in thin films is difficult to determine
experimentally because the temperature of the film is not easily .
measured. Thermal stress arising from thermal expansion coefficient
mismatch depends on the substrate temperature during deposition and
the temperature at which the measurement of the stress is taking place
and on the substrate material. If bending of the beam during heating is
ignored ( the substrate is much thicker than the film ). the biaxial thermal

stress is given by [55]

°Th=Er(°‘r'as)(Ts'T0)/(1'Vs) (43)

where 5,: E.(T) is the Young’s modulus of the film. or. =a.(T) is the

thermal expansion coefficient of the film. as=Ots(T) is the thermal
expansion coefficient of the substrate. Ts is the substrate temperature
during deposition and T0 is the measurement temperature. A positive

stress usually exists in metal films over a glass substrate. while a
compressive stress state develops in metal films deposited on alkali
halide substrates [8]. In 0.25 microns thick chromium films. deposited
on glass wafers by Magneton sputtering ( current density of 25 to 300
Am'2 ), the thermally induced tension ( stress integrated over the
thickness of the film ) was measured as -21 Nm“. The total internal
tension in the chromium film was -250 Nm'1 at the same thickness. The
magnitude of thermal stress is therefore much smaller than that of the
internal stress; less than on tenth in this case [55]. The stress was

measured from the change in the substrate curvature. ( Equation 25)
5.3 Variation of stress with deposition temperature

During the deposition period. the substrate will expand. When a film
has a [smaller thermal expansion coefficient than the substrate. the
substrate shrink more than the film during the cooling down to room
temperature. Compressive stresses develop in the film provided no
slippage in the interface occurs between the film and substrate ( figure
14 ) . A tensile'stress will develop it the film has a higher thermal

expansion coefficient than the substrate.- For instance. GaP films

99

 

Silicon substrate at room temperature

I |

Silicon substrate and diamond film
at deposition temperature

: diamond film
—.—> ‘—

| Substrate silicon

 

 

 

at room temperature if allowed to shrink separately

 

film
Substrate

 

Diamond-silicon composite

Figure 14. Graphical representation of thermal stress development

in diamond films on a silicon substrate.

100

deposited on silicon substrates developed a tensile thermal strain

equal to 0.9 x 10‘3 . thermal expansion coefficient of GaP is greater
than that of silicon [4].

Diamond films deposited on silicon substrates have differential
thermal stresses that are compressive as long as they are deposited at a
temperature less than 1220°C [10]. In most of the literature. thermal

stress is calculated from

oTh = E. (01,- as) ( Ts - To) / (1 - v.) (43)

Generally a single average value of the thermal expansion coefficient is
used for the entire temperature interval from deposition to room
temperature [4]. Furthermore. the Young’s modulus is treated as a
temperature independent constant [10 ] which of course is not the case.
For DLC films deposited at low temperature around 100°C the
assumptions may be justified since the temperature interval is not as
high as in CVD films where the temperature interval between deposition
and room temperature can be as high as 1000°C. Windischmann used a

better approach to calculate the thermal stress. Windischmann used an
average value of or,- as for every 100°C temperature interval. then

summed the individual contributions of all intervals [10].
A new model for thermal stress calculation is presented here

and believed to be an improvement over the model presented by

101

Windischmann [10]. The Young's modulus of diamond and the thermal
expansion mismatch between the film and the substrate are
temperature dependent. consequently. an integration over the
deposition to room temperature interval is used here instead of adding
up stress contributions from a number of finite temperature

intervals as proposed by Windischmann. The model is essentially

not very different from the model used by Windischmann; by

integrating over the temperature range. contribution to stress from

an infinite number of intervals are added up instead of finite 100
degrees intervals. as used by Windischmann. The temperature
dependence of the Young’s modulus of diamond is taken into account
while Windischmann treated the Young's modulus as temperature
independent. The biaxial thermal stress will be recalculated in this work
taking into account the temperature dependence of the expansion
coefficients of the film and the substrate as well as the Young's modulus
of the film .

The thermal strain in the films was given by

1:1.h = AOL(T) AT. (41)

The Aa(T) AT term should be treated as the contributions of the

thermal expansion difference Aa at a temperature interval dT summed

over the entire temperature range. Therefore equation 41 should be

102

rewritten as

err. = I a.(T) - aslT) dT (44)

from the deposition temperature to room temperature. The thermal
expansion coefficients of silicon and diamond are functions of
temperature ( figure 15 ). The thermal expansion coefficient data in

figure 15 was used to calculate the thermal expansion coefficients

difference or,— 01s at regular temperature intervals.

The data for (01,- as ) (T) as a function of temperature was fitted by

linear regression analysis. The resulting fitted function is given by
(as- 01,)(T) = +1.6410‘6- 4.01 10'°T + 3.310"12 T2 - 1.88 10'15 T3 (45)

where T is in degree Celsius The above function (equation 44 ) was
fitted with a correlation coefficients R =0.997 ( figure 16 ). The above
fit is a good as can be further seen in the plot of the residual (figure 17 ).
The Young’s modulus of diamond is expected to decrease with
temperature as is the case for many ceramics. For instance. the
Young's modulus of alumina [79] was found to decrease with
temperature according to Watchman's equation ( equation 46 ) [79].
Anderson [80] argued that Watchman's equation is valid for many

ceramic oxides as long as the Poisson’s ratio is not a strong function of

103

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temperature. Anderson [80] attempted to relate the empirical
temperature independent constants of Watchman's equation to the
Debye temperature and the Gruneisen constant [80].

Experimental data for the temperature dependence of the Young’s
modulus of diamond could not be located. Some elastic constant values
of diamond are available [9]. however, data for elastic constants from
the same author at different temperatures were not available. Due to the
scatter in the elastic constant data in the literature. Young's modulus of
diamond at various temperatures cannot be calculated from published
data either.

Alternatively. an estimate of the temperature dependence of the
Young's modulus of diamond is attempted here. As is the case for many
ceramic oxides. the temperature dependence of the Young’s modulus of
diamond is assumed to behave according to Watchman’s equation. The
latter assumption involves the assumption that the Poisson's ratio of
diamond is not a strong function of temperature. Watchman’s equation

is given by
E(T)=Eo-bexp(-To/T) (46)

where E(T) is the Young's modulus at a temperature T . E0 is the

Young’s modulus at zero degree Kelvin and b and T0 are

experimentally determined parameters. Anderson estimated To to be

107

equal to half the Debye temperature [79]. The Debye temperature of
diamond is 6:2248 degree Kelvin [81] such that To =1224 K. We

assume that there is no fall off in the magnitude of Young’s modulus from

zero degrees Kelvin to room temperature. thus Eo can be estimated

as1150 GPa which is the room temperature value of Young’s modulus of

diamond [82]. The last step would be to estimate the value of the b
constant. For many ceramics. the magnitude of the Young's modulus is
drops about 1 percent for every 100 degrees temperature increase. For

instance. the drop off in the Young's modulus of alumina [79] and M90

[80] was about 1 percent per 100°C. The Constant b is then calculated
from the drop off of the Young's modulus. A value of 0.4 was calculated

for b assuming a drop off in the Young’s modulus of about 1 percent per

100°C for diamond. Watchman’s equation for diamond's Young's

modulus with the assumptions mentioned above is then given by

E(T) = 1145 - 0.4 exp ( - 1224/T ), (47)

where E(T) is in GPa and is T in degree Kelvin. Figure 18a is a plot

of E(T) as a function of temperature according to equation 47.

The temperature range of interest for diamond deposition is 300 to

1300 K ( 0 to 1000°C ). Since (01.- Ois)(T) E(T) needs to be

integrated later a polynomial approximation of E(T) makes the

108

integration easier. The E(T) curve over the 300 to 1300 K was
therefore fitted to a cubic with a correlation coefficient equal to R=1.0.

The fit is clearly very good. The approximated function of over 0 to

1000°C ( figure 18b ) is then given by
E(T)=1147.22- 2.8110’2T - 2.5510‘4T2 +8.410’3T3 (48)

where E(T) is in GPa and is T in degree Celsius.
Now that expressions as a function of temperature exist for both the

Young’s modulus and the thermal expansion difference. the thermal
stress {(Ot,- 015)): E} (T) can thus be integrated over the deposition

temperature range. Let

em = I {(c.- as) x E} (T) dT (49)
Then the thermal stress is given by
and“) = err.) — cm.) (50)

Since the measurement temperature is usually room temperature. then

To: 25°C and <D(To) is treated as a constant. By substituting equations

47 and 48 into equation 49. and evaluating <I>(25°C). and substituting

109

the expression for <D(T=Ts) and <D(To=25°C) into equation 50. the

following expression for oTh(T) is obtained

0111(1) = 4.5810'2-18910'3 T + 232106 T2 -113 109 Ta

4 2.71043 T4 2310'16 T5 4.1271019 T6-2.310'23 T7 (51)

Figure 19 is a plot of the biaxial thermal stress as a function of the
deposition temperature according to equation 51 corrected for the
various values of Poisson's ratio of diamond reported in the literature
[83.76.82.60]. One should note here that the Poisson’s ratio value of
0.07 [82.60] has been reported in two recent studied on polycrystalline

diamond films. which is the microstructure studied here.

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6- EXPERIMENTAL PROCEDURE

6.1 Materials

The samples used are silicon wafers with the (100) crystallographic
axis perpendicular to the surface of the wafer. One surface of the
silicon wafer is polished and the backside is rough. Reference 84
provides the specification about the cutting, polishing, surface
roughness as well as other information. Measurement on the silicon
wafers were carried in the as provided state with no modification to the
wafers except for an annealing treatment.

One (100) silicon wafer with diamond films deposited on the
polished side was supplied by Jie Zhang, a Ph.D. student in the
Electrical Engineering department at Michigan State University. The
silicon wafers were two inches in diameter, including the wafer with the

deposited diamond film.

6.2 Diamond deposition

Diamond films were deposited by Jie Zhang on (100) silicon wafers
using the microwave plasma chemical vapor deposition (MPCVD) [85]
method. The MPCVD deposition was carried at 2.45 GHz. The
deposition temperature was 9800 and the deposition plasma pressure

was 70 torr, the microwave power was maintained at 750mW. The

113

114

deposition lasted less than four-hours. The deposition atmosphere was
a mixture of 1.0 percent methane in hydrogen. The deposition setup is

illustrated in figure 2 of reference [85].

6.3 Curvature measurement

The curvature in the silicon wafer with and without the deposited
diamond film was determined by measuring the center deflection ( bow )
in the silicon wafer. The bow was determined from the surface profile
obtained with a DEKTAK IIA type surface profilometer.

To carry a measurement on the DEKTAK IIA, a sample is placed on a
rotary stage ( 127 mm in diameter ) that allows to rotate the sample 360
degrees about an axis perpendicular to the stage surface. The
positioning of the sample is done with an X and Y thumb wheel that
allows to move the rotary stage ( thus the sample ) in the X and Y
horizontal directions. A rough leveling wheel allows the rotation of the
sample about an axis running parallel to the rotary stage surface ( thus
parallel to the wafer surface ); this rough leveling allows to position the
sample so that its surfaces are as parallel as possible to the horizontal
plane. The rotary stage does not move up and down. Instead, a focus
knob allows to move in the 2 direction an arm into which is connected
the stylus, a camera and an optical microscope. The focus knob is used
to put the sample surface in focus for either the optical microscope or

the camera so that details to be measured are in focus. When a camera

115

is used, a video screen shows the stylus and the area around the
contact between the sample surface and the stylus. All of the already
described functions are manually operated.

When the DEKTAK HA is turned on, the video screen shows various
options that can programmed for the measurement. The parameter to be
programmed and automatically executed later are the scan length from
50 microns to 30 millimeters. the scan speed ranging from low to high,
the scan range with automatic or manual sample leveling, the scan
profile type, a step or peak and valley type. An R cursor and M cursor
stand for reference and measurement cursors can be moved on the
video screen to obtain measurements at any point within the scan
length.

The DEKTAK ”A has a vertical resolution of 0.5 nm. The stylus tip
radius is 12.5 microns. The stylus tracking force is field adjustable from
10 to 50 mg. The maximum sample thickness allowed is 20 mm. The
Dektak profilometer is connected to a thermal printer as the output
device.

Once the parameters are programmed, a measurement can be done.
The video camera focuses from the stage to about 20 mm above the
rotary stage. The sample is positioned and put in focus with the
camera. The scan mode is turned on. An initial scan is executed
according to the stored parameters. The first profile of the surface is
usually not leveled; the profile appear on the video screen such that the

first contact point appear at Z=0 and the point at the end of the scan

116

appears at some point on either side of the 2:0 plane. The rough
leveling thumb wheel is used to rotate the sample such that both the
begin and end point of the scan are at the 220 plane. Two function are
available for automatic improved leveling and Zeroing (setting the end
point of the scans to 2:0) when the manual leveling is close to within
few thousand Angstroms from leveling at Z=0 ). The profile is finally in
its final form and a measurement can be obtained. The profile can be
manipulated by moving the borders of the plot. A copy of the final plot
is sent to the printer. A measurement of the height of a feature for
instance can be either done on the printout. since it is properly scaled,
or alternatively by moving the reference cursor which reads the
horizontal position or the measurement cursor which reads the height of
a given feature.

The above procedure was used to measure the center deflection of
the silicon wafers in the as provided state, on annealed silicon wafer
and on the silicon side of the diamond-silicon film before and after it
was annealed. No measurement was carried directly on the film surface
to avoid stylus tip scratching because of the very high hardness of

diamond. The scan length was kept constant at 30 mm in all samples

6. 4 Annealing heat treatment

Annealing of the diamond film on the silicon substrate and two

silicon wafers was carried in a non oxidizing atmosphere. The furnace

117

used was an MRL Thermtec three-zone horizontal muffle tube. The
temperature control is achieved by a Eurotherm type 812 controller
toward the middle of the tube and type810 Eurotherm controller at the
two ends of the tube. The samples are placed in an alumina inner tube,
on top of a tube dee that provides a flat surface. All the samples were
placed on silicon scrap pieces to avoid contact and contamination from
the alumina. The innertube is sealed with a stainless steel sealant a
plastic gasket. The seal allows for the constant flow of nitrogen gas
during the annealing._ The inner tube is heated inside the muffle tube.
Two inconel tubes are connected to the inner alumina tube trough the
stainless steel seal and to the nitrogen gas source. The gas flow
arrangement consist of the tubes connecting the nitrogen source, a
mechanical pump, two Nupro T valves and a flow meter.

Two silicon wafers and the silicon-diamond sample were placed

inside the alumina tube, the temperature controller was programmed
such that a temperature increase rake at 10°C per minute heats up the
inner tube and the sample to 650°C, the temperature was then
maintained at 650°C for one hour. Finally, a temperature decrease rake
of 10°C per minute cools down the set up to room temperature, the
samples were left in the furnace overnight to make sure they cool down
slowly so that no thermal stresses develop during cooling.

During the heating rake, the inner tube chamber was first vacuum
pumped to remove the air in it. The vacuum is then turned off and by

using one of the valves, the inner tube chamber was flushed with

118

nitrogen. The nitrogen flow was increased until a flow rate of 2 liter per
minute was set. The nitrogen gas was flowing during the heating,
annealing and cooling stages. The nitrogen flowing out of the inner
alumina tube through a plastic tube was released in an oil bath

preventing air from flowing in the inner tube during annealing.

6.5 Fiaman spectroscopy

Raman spectra of all the samples were taken with a laser Raman
microprobe available at the department of chemistry, and operated by
Dr. Thomas Carter, chemistry specialist, department of chemistry at
Michigan State University. The laser used is a Spectrophysics model
164 continuous argon ion laser operated through a cavity prism that
isolates the laser wavelength used from the laser plasma lines. The
laser is operated at 487.98 nm. An external prism further disperses the
exciting laser light to isolate laser plasma from the 488 nm line. The
sample is placed on the stage of the micro attachment of a Spex 1877
tipple spectrometer. The laser light is focused on the sample using a
series of mirrors and a Zeiss ( L. D-EPIPLAN ) 40 times objective lens
which is also used to collect the back scattered light from the sample.
The scattered light is received by the tipple monochrometer-detector
assembly with three dispersion stages that are essential to reducing the
amount of stray radiation reaching the detector which otherwise can

overshadow the much less intense Stokes scattered radiation. The

119

dispersion elements are ruled gratings. Raman spectra are then
acquired with scanning monochrometers that allow to detect only the
frequencies of interest. The output of the scanning is a plot of the
scattered intensity as a function of the wavenumber. The output is sent
to a minicomputer system that can record the data and plot it on a
monitor. The stored data is then used to generate a plot with any of the
conventional plotting computer software.

Throughout the various scans, the laser power was 850 mW, with
only 85 mW reaching the sample surface. A slit width of 100 microns
was used. The detector dispersion elements was set to 1800 grating per
millimeter. The laser light was in normal incidence to the surface of the
sample and was polarized such that the electric field is parallel to the

sample and stage surfaces.
6.5.1 Calibration for Raman spectroscopy

The calibration is done with a toluene sample. Toluene has several
sharp peaks the position of which are independent of the laser
wavelength. Toluene fluid is inserted in a capillary tube and placed on
the stage in contact with the laser beam. The laser light is focused on
the toluene sample and a scan is taken. When all the toluene peaks are
sharp and well resolved, the calibration is carried by first assigning the
appropriate wavenumber to each known peak according to the standard

toluene Raman spectrum. The actual positions of the toluene peaks from

120

the calibration sample are fitted with a cubic to match the assigned
values to the various peaks. The peak positions in wavenumber are
then checked. If all the peaks are at the correct wavenumber position
within an acceptable error, the calibration is done and actual
measurements on any sample can be carried. It was noticed during the
calibration that the error in the position of the peaks in not constant from
one peak to another. This is attributed to the cubic nature of the peak
position fit. To reduce the effect of the variation in errors from peak to
peak, the calibration with toluene was done differently depending on
whether the sample scanned is silicon or diamond. When the sample

scanned was diamond the calibration was done such that the center of
the spectrum is at the diamond position of 1332 cm". Similarly, the

calibration spectrum is centered at the silicon position at 521 cm'1 when
silicon samples were scanned. This procedures proved capable of

reducing the errors of both silicon and diamond spectrum measurements.
6.6 Film thickness and grain size measurement

Micrographs taken with scanning electron microscopy SEM were
used to measure the film thickness and the grain size in the diamond film
on the-silicon wafer.

Strips about 1 cm long and 3 mm wide were cut from the silicon-
diamond wafer. The strips were mounted on cylindrical stand with an

epoxy / araldite ( Ciba-Geigy ) glue that cures and hardens in a few

121

minutes after it is applied. One sample was glued flat on the stand such
that the diamond film faces up, and was used to take micrographs of the
grain size. Two other samples were mounted and glued on one edge to
allow for the measurement of the diamond film and silicon substrate
thicknesses. All three samples were then sputtered with gold with an
EMSCOPE gold sputterer. The gold sputtering was done at a 0.1 torr
vacuum at 20 mA. The sputtering rate was 7 nm per minute. After 3.5
minutes, the sputtered gold film thickness was about 24.5 nm. After the
gold sputtering, the samples were scanned with a JOELJSN-SSCF
scanning electron microscope (SEM), operating at 15 KV accelerating
voltage. The magnifications used for film thickness measurement
ranged from 160 times for the silicon tot800 times for the thinner
diamond film. The magnification used for grain size measurement on the
diamond film was 6600 times.

The film thickness for the silicon and diamond was determined by
taking several measurements on the micrographs. An average value of
the film thickness was then calculated.

The grain size of the diamond film was determined by the linear
intercept method, where the grain size G is given by L / ( n M ), where
L is the measured length on the micrograph n is the number of the line-

grain boundary intersections and M is the micrograph magnification.

7- EXPERIMENTAL RESULTS

7.1 Curvature measurement

The results of the curvature measurements are summarized in table
5. The curvatures of the as provided silicon wafers was measured on
three separate wafers respectively called silicont, silicon 2, and
silicon 3. Only silicon wafers 2 and 3 were later annealed. All three
silicon water had two curvatures in opposite directions, probably from
buckling to maintain the mechanical stability of the wafer. Figures 20,
21 and 22. The original deflection of the silicon wafers in the as

provided state, was taken as the average of the two deflection
measurements in silicon 2 and 3 and equal to do =19.15 103 :l: 500

angstroms. Silicont wafer had two defections, almost symmetric about
the center of the wafer. Thus it is not used for the reference deflection
calculation.

There was no obvious change in the curvature of the annealed
wafer silicon 2 and 3 ( figures 23 and 24 ) as compared to the same
silicon 2 and 3 wafers in the as provided state. The diamond deposition
caused the positive deflection of 19,150 A to be reversed to a
negative -76,000 A bow ( figure 25 ), resulting in a net, bow change

of -95,150 A. The annealing of the diamond film caused the center

122

123

deflection to decrease from -76,‘000 to -65,000 A ( figure 26 ). Thus a

net change of -11,000 A resulted from annealing the diamond film on
the silicon wafer. Surface profiles taken on the rough side of the
uncoated silicon wafers had high surface roughness. Therefore,
accurate deflection measurements from the rough side of uncoated

silicon wafers were not possible.

124

Table 5. Curvature measurement results.

Sample State ' Center defection Measurement
/ Error surface

(1000 Angnstroms)

 

Silicon.1 as provided . +6.2 / 0.5 polished
Silicon.2 as provided +19.8 / 0.5 polished
Silicon': as provided +18.5 / 0.5 polished
silicon 2 annealed ‘+19.8 / 0.5 polished
Silicon.3 annealed +18.5 / 0.5 polished
Diamond as deposited -76.0 / 2.5 Si/rough
Diamond annealed -65.0 / 2.5 Si/rough

. uncoated wafer

Silicon 1. 2 and 3 refers to the three uncoated silicon wafers numbered 1. 2 and 3
used in the experimental procedure.

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132

7.2 Raman spectra and peak positions

The calibration spectrum obtained with toluene is given in figures 27
and 28. The calibration in figure 27 was done such that the error in
peak position around the silicon peak is minimized. The calibration in
figure 28 used for Raman spectra of diamond was centered around 1332
tlcm to minimize the error in the diamond peak position. Table 6
provides the toluene positions [86] and the measured toluene peaks
after the calibration was done. The error in the peak position is also
given. The measured values of the toluene peaks are read on the
computer screen with the help of a cursor that can be moved to any
point of the Raman spectrum. Since the position of the cursor is

dependent the screen resolution, the variation in wavenumber

corresponding to one screen pixel was measured to be 0.1 cm". The

calibration error due to the dependence of the cursor position on the
screen pixel resolution is 0.05 cm". The average error in the measured
peak position ( table 6 ) was 0.04 cm“. The error due to the calibration

is thus taken as 0.05 cm'1 which is the larger of the two, since the two
errors mentioned above are dependent.

The Raman spectra of the silicon 2 wafer on both surfaces in the as
provided state are given in figures 29 and 30, and in figures 31 and 32
for the annealed silicon 2 wafer. Figures 33 and 34 give the Raman
spectra of the silicon substrate surface before and after annealing,

while the Raman spectra of the silicon substrate at the silicon diamond

133

interface are given in figures 35 and 36. Finally, the Raman spectra of
the diamond film before and after the annealing heat treatment are given
in figures 37 and 38 respectively. In all Raman spectra. the silicon and
diamond peaks were isolated and expanded graphically withbut loss in
resolution. A computer graphics software was used to expand the
individual peaks given in figures 29a to 38a. Table 7 summarizes the
results obtained for the peak position measurements

The method used here to determine the peak position is the same

method described by Whalley [75] with 0.1 cm'1 error taken as the
standard deviation for many repeated measurement [75]. The method

was described in section 4.4.
7.3 film thickness

Several film thickness measurements were taken on the SEM
micrographs given in figures 39 to 43. All the measurements on figures
39 to 43 are from the same film-substrate sample. The silicon substrate
thickness is uniform, since no variation greater than the measurement
error were observed across the sample cut. The thickness of the
diamond film however is not uniform. The film is thicker at the center of
the wafer and becomes much thinner at the edges of the wafer. The
diamond film thickness decreased from 1.25 microns at the center of the
wafer to 0.5 microns at a radial distance of 20 mm from the center of the

wafer. Several film thickness measurements were taken from figures 39

 

134

to 42 and resulted in an average diamond film thickness of 0.97 microns
with a 0.11 microns standard deviation taken as the error in film
thickness measurement. Along the 2 cm strip cut from the silicon-
diamond wafer, most of the film is at a roughly uniform thickness of 1.2
microns. There was however a region of the film where the thickness is
about 10 microns. The10 micron thickness region spreads only in an
area of about 15 microns diameter and is not representative of the film
thickness distribution. The average silicon wafer thickness was 0.456

mm with a 0.07 mm standard deviation (figure 43 ).
7.4 Grain size

The grain size of the diamond film was determined by the intercept
method. The diamond film grain size was calculated to be 1.97 microns.
The grain size seems to be uniformly distributed across the wafer as can
be seen in figures 44 and 45 taken at two different locations on the
diamond film. The diamond grains do not appear as sharp and as
developed as MPCVD diamond grains in published works elsewhere

[9]. The faces of the grains parallel to the silicon-diamond interface are
clearly{111} family planes so that the normal to the film surface
(necessary for the stress calculation from Raman shift ) is of the<111>

family directions.

135

Table 6. Toluene calibration peak positions and errors.

 

Toluene Toluene measured Error
peak position peak position

(cmd) (cmd) (cm‘)
521 521.0 0.0
622 622.1 0.1
786 785.9 0.1
1004 1003.9 0.1
1031 1031.0 0.0
1211 1211.0 0.0
1380 1380.0 0.0

1605 1605.1 0.1

136

Table 7. Raman peak positions of samples used.

Sample State Peak position Measurement
(cmd) surface
fi
Silicon 2 as provided 520.62 polished
0
Silicon 2 as provided 520.59 rough
3
Silicon 2 annealed 520.49 polished
i
Silicon 2 annealed 520.51 rough
es
silicon .
substrate as provided 520.12 rough
. . .0
Silicon
substrate annealed 520.13 rough
*9
Silicon
substrate as provided 521.95 interface
0 0 ”
Silicon
substrate annealed 522.22 interface
Diamond as deposited 1333.91 diamond
Diamond annealed 1333.09 diamond
* uncoated wafer n coated wafer

Silicon 2 refers to one of the hree uncoated silicon wafers numbered 1, 2 and 3 used
in the experimental procedure.

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Figure 35.

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Figure 37. Raman spectrum of the diamond film in the as deposited state in the

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at 1800 glmm and 100 microns slit width.

 

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Figure 37.

 

 

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silicon-diamond sample and taken with a 488 nm argon laser

at 1800 glmm and 100 micronsslit width.

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at the interface showing the diamondfilm at 780 times magnification

160

 

Figure 40. SEM micrograph of a cross section of the silicon-diamond sample
at the interface showing the diamond film at 1800 times
magnification. The location on the interface if different from that in

figure 39.

161

 

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figure 40.

162

 

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Figure 42. SEM micrograph of a cross section of the silicon-diamond sample
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163

 

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164

 

SEM micrograph of the diamond film showing the microstructure

Figure 44.

consisting of (111) oriented grains at 6,600 times magnification.

165

 

Figure 45. SEM micrograph of the diamond film showing the microstmcture
consisting of (111) oriented grains at 6,600 times magnification.
The micrograph was taken at a different location from than in

figure 44.

 

8- CALCULATION AND DISCUSSION

From the results obtained above, the residual stress in the diamond
film and the silicon wafer at the interface will be calculated using

Stoney's equation and the Raman shift.
8.1 Stress measurement from Stoney's equation

Stress measurement according to Stoney’s equation in the case of a thin
film deposited on a thicker substrate requires the following assumptions
( summarized from section 4.3 )

1) The wafer properties are known, the in-plane Young's modulus, the
Poisson’s ratio, and substrate thickness which must be uniform.

2) The film thickness is known and should be uniform. The value of the
film thickness in Stoney’s equation must be an average value.

3) The curvature of the substrate due to the stress in the film is known,
and is independent of the orientation of the stylus scan measurement
direction.

4) The film and substrate materials are isotropic.

5) The substrate is rigid ( it is much thicker than the film ) and thus, no
stresses are developed in the substrate.

6) the interface bonding is strong enough not to allow slippage or

spalling.

166

 

167

7) measured stresses are in the elastic range.

The applicability of Stoney's equation to measure the growth stress
in thin diamond films deposited on (100) silicon wafers is argued here
by checking the assumptions listed above against the obtained
experimental results.

The mechanical properties of (100) silicon wafers are well known.
The biaxial Young's modulus ( includes the Poisson’s ratio value ) for
(100) silicon is 180 GPa [10,59]. The substrate thickness was measured
from an SEM micrograph and was 0.456 mm (figure 43). The substrate
thickness was uniform. Thus assumption number one above checks well.

As stated above. the diamond film thickness is not uniform; the film
becomes thinner towards the edge of the circular wafer. For MPCVD
deposition of diamond films the non uniformity of the film thickness is not
random and arises from the higher plasma density at the center of the
deposition chamber as compared to the outer limits of the chamber
[10,21]. Thus unless the deposition mechanism is improved, the
variation in film thickness is a likely event in all MPCVD depositions.
The film thickness of the sample used in this study dropped to 40
percent of the value at the center of the wafer at a radial distance of 20
mm. The thickness gradient is this study is similar to the thickness
gradient reported by Windischmann [10,21]. Windischmann used
MPCVD diamond films where the film thickness dropped to 50 percent of
the center value at a radial distance of 25 mm [10,21]. The area of

measurement had to be reduced to decrease the effect of thickness

168

gradient [10,21]. In this study, the DEKTAK ll scan length was only 30
mm. Thus. the radius of curvature measurement involves a thickness
gradient over a distance of only 15 mm on either side of the wafer
center. Therefore. the thickness gradient over the 30 mm measurement
distance is less severe than in the case where the whole 54 mm wafer is
scanned.

The assumption of film uniformity is thus not well satisfied and
therefore errors in the measured stress values are expected. One
should note however that since Stoney’s equation provides an average
value of the stress in the film, the error in stress measurement due to
thickness variation would be small if the calculated average thickness
is close to the real average film thickness. It is also important to note
that the film thickness variations is not random, but decreased steadily
towards the wafer edges in a symmetric way. The average film
thickness can therefore be determined more accurately than in the case
where the film thickness variation is completely random.

The third assumption that the curvature should be spherical and
independent of the measurement direction on the silicon wafer also is
not well satisfied. The single crystal substrate wafer is highly
anisotropic. The maximum in-plane difference in the elastic modulus of
(100) silicon however is 16 percent [3], even though no important
variations in curvature were observed for any orientation of the stylus
with respect to the wafer when the film is uniform [3]. The Young's

modulus in Stoney’s equation representing the substrate should be the

 

169

average in plane modulus [3]. Using a single crystal for the substrate
thus introduced an error in the stress value as calculated from Stoney's
equation, since the elastic constant are not isotropic; they depend on
the crystallographic orientation.

The assumption of isotropy of the film and substrate materials for
Stoney's equation to be applicable should hold for the diamond film.

The'condition for isotropy is that 2 044/( 011-012) =1 (equation 27

)[60], the ratio is equal to 1.21 for diamond and 1.56 for silicon. One
should note however that the elastic constants ratio as a condition for
isotropy is dependent on the reported value of elastic constants and
thus can get closer or farther from 1 depending on the scatter in the
values of the elastic constants. As expressed above, the silicon wafer
is a single crystal and thus highly anisotropic. Cubic crystals are
anisotropic with respect to the elastic modulus. However, the diamond
film is polycrystalline with uniformly distributed grain size.
Polycrystalline diamond can be macroscopically isotropic, unless the
film has a texture ( preferred orientation ). Errors due to the anisotropy
of the silicon wafer as well as any possible texture in the diamond film
are inevitably introduced in the stress measured from the curvature.
Evidence of possible anisotropy effect can be seen on figures 25 and
26; the wafer deflection profile is slightly off symmetric and obviously
non spherical; it is rather elliptical. One can thus conclude that the
assumption of material isotropy is not fully satisfied.

The assumption that the silicon wafer is rigid; all the deflection in the

 

170

wafer in due to the stress in the film, cannot be directly verified from
Stoney’s equation. Any stress in the silicon water can however be
detected from the Raman peak position of the silicon wafer. Raman
stress measurement ( next section ) revealed stresses in the silicon
water that have opposite signs on the two sides of the wafer. The stress
thus goes through a neutral plane. The magnitude of the interfacial
strain on the silicon side of the interface was greater than the magnitude
of the strain on the diamond side of the interface. When the two
surfaces of a beam are under opposite stress signs ( compression
versus tension ), the neutral plane where the stress is zero shifts if the
beam is loaded.

The ratio of the substrate to film thickness for the sample used in this
study is about 450 to 1. Thus the assumption that the film thickness is
much smaller than the substrate thickness holds well. The error induced

by neglecting the term ( 1 - ‘1 I t, ) is about 0.002 GPa. an insignificant

error since the stress is determined only to within two significant digits.
From figures 39 to 42, one notices that while there is no spelling or
cracking in the silicon-diamond interface, there is some limited
interfacial cracking as can be seen in figure 41. It is however not
possible to determine whether the interfacial cracking is due to a weak
interfacial bond strength or to the cutting of the SEM sample from the
original silicon-diamond sample. But since most of interface is not
cracked, it is realistic to assume that the interfacial bonds are strong

enough to avoid spelling or cracking at the interfacial plane.

 

171

All of the parameters and constants for stress determination by
Stoney’s equation are known and given below. The stress before and

after annealing of the sample is thus calculated next.

t' = 0.97 microns ( diamond film thickness)

t$ = 0.456 mm ( silicon substrate thickness )

Es/1-u = 180 GPa ( biaxial Young's modulus of silicon )
L . 30 mm ( stylus scanning distance )

80 = -95.150 angstroms

8a a -84,150 angstroms

80 and Sa are the net center wafer deflection respectively before and

after annealing. The stress in the diamond film is given by

on: 4Est82A6 / 3(1— Vs) t, L2 (52)

where A8 = 5a - 80. By substituting the above parameter values into

Stoney’s equation, the average residual stress in the diamond film on

the(100) silicon substrate is given by

6R(GPa)=-. ~5.893 A8 (meters) (53)

172

Substituting the values of the center deflections of the wafer as
provided and the annealed sample. the residual growth stress in the
diamond film is -O.57 GPa. After annealing the silicon-diamond sample,
the compressive residual growth stress was reduced to - 0.49 GPa. All
of the deflection is assumed to be stress induced; the stress is
calculated from shifts where the deflection of the uncoated wafer was
subtracted. The annealing treatment thus resulted in a stress decrease
of 13 percent. .

The magnitude of the residual stress in the diamond film (-0.57 GPa )
is only 0.05 percent of the Young's modulus of diamond. Thus, the
stress magnitude measured from the radius of curvature is well within
the elastic deformation range of diamond; assumption number 7 holds
well.

The magnitude of the measured residual stress ( -0.57 GPa )
represents the macroscopic average stress in the entire diamond film.
Since the film thickness is not constant, the value -0.57 GPa represents
only an approximation to the value of the integrated force per unit with
over the total thickness range. The accuracy of the obtained value -
0.57 GPa ) depends on how closely the average diamond film thickness

( 0.97 microns ) approximates the real average film thickness.

 

 

 

173

8.2 Stress measurement from the Raman peak position shift

The stress measurement from the Raman peak shift is not as straight
forward as the measurement from the change in the curvature of the
substrate. In section 4.4, the parameters controlling the calculation of
the stress from the peak shift were discussed in detail as well as the
application to the silicon-diamond composite system.

According to the discussion in section 4.4 the 3 X 3 secular
equation results in two independent eigenvalues corresponding to the
singlet and doublet frequencies of the strained cubic crystal lattices of
both silicon and diamond. Only a singlet results under a hydrostatic
stress while three independent singles result from a stress parallel to a
<110> direction. From SEM micrographs ( figure 44 and 45 ), the
orientation of the diamond grains in the sample used in this work is
assumed to be (111) such that (111) planes are parallel to the interface
and perpendicular to the laser beam direction. The silicon single
crystal is oriented such that the [100] direction is perpendicular to the
interface and parallel to the laser beam. Both a singlet and a doublet
frequencies result from the sample-stress configuration used. for both
silicon and diamond. In section 4.4, it was also argued that under the
current back scattering geometry, only the singlet is observed for both
silicon and diamond. The equations of stress as a function of Raman
peak shift were derived for a biaxial stress parallel to <100> planes as

in the case of the silicon substrates. However, the equations derived

 

174

have to be readjusted for the <111> orientation of diamond.
For the (100) silicon single crystal, the equation for residual stress
as a function of the singlet peak frequency shift was derived in section

4.4 and is given by

on: VoAvs/[pS12+q(S11 +812 ] (54)

where Avs = vs - v0 and V0 is the frequency of unstressed silicon. Table

3 gives the elastic constants and deformation potentials for both silicon
and diamond. Using the values in table 3 for silicon, the stress-

frequency shift relationship is given by
08(GPa) = -0.25 Aws (cm-1). (55)

For <111> diamond, the stress-frequency shift relationship is given
by

05(GPa) = -0.45 Aws (cm-1). (56)

Equations 55 and 56 correspond to the sample geometry, orientation,
laser polarization and back scattering geometry used in this study. The
laser light used for the Raman scanning of the samples is polarized such
that the electric field is parallel to the sample interface. As explained in

section 4.4, the electric field parallel to the interface is also parallel to

 

175

the biaxial stress orientation and thus would result in detecting the
maximum frequency shift of the singlet in both diamond and silicon ( as
given by equation 55 and 56 ).

As was the case for stress measurement from Stoney’s equation, the
major assumption made will be checked for the stress measurement from
the Raman peak frequency shift.

To correctly measure the stress from the Raman peak frequency shift,
the following assumption and conditions have to be satisfied:

1) p, q and r, the independent deformation potentials ( derived with the

assumption of harmonic motion as described is section 4.4 ) are

accurate for the stress state of the samples used.

2) the stress measured is in the elastic range.

3) a singlet and a doublet result if the stress is truly a biaxial stress.

4) The crystallographic orientation of the sample is known.

5) The sample is a single crystal.

6) The laser light polarization and back scattering geometry is
known.

7) The theoretically derived shift coefficient with stress (equations 55

and 56 ) do represent the sample-stress-laser beam orientation.

8) The relationship between stress and frequency shift is linear as

predicted by the theoretical model.

The discussion of the above conditions ( one to eight ) was
completed in section 4.4. A summary of the discussion is presented

here. Conditions 2, 6, and 8 are well satisfied. From the stress values

176

measured with the change in the radius of curvature, the stress was
indeed in the elastic range. The laser Raman set up uses a 180 degree
back scattering geometry and the polarization of the laser light is
accurately known. The relationship between stress and frequency shift
is linear to stress magnitudes greater than 40 GPa. The stresses
measured in thin diamond films hardly exceed the single digit range ( in
GPa) and thus the linearity assumption holds well.

The deformation potentials are critical to accurate stress
determination. A scatter exists in the reported values in the literature,
though the number of independently reported values is low.
Furthermore, the reported values are for hydrostatic and uniaxial stress
states. No deformation potentials have been reported ( to the author's
knowledge ) for a true biaxial stress state for either diamond or silicon.

It is not feasible in this study to determine whether the stress in the
diamond film is truly biaxial. In the case where the stress deviates from
a true biaxial state, the error introduced is unknown.

The orientation of the silicon wafer is precisely known. However,
the orientation of the diamond film can only be assumed to be <111>
from SEM micrographs ( figures 44 and 45).

The main problem with using Raman shifts to measure the stress in
diamond films is that the film is polycrystalline. The theoretical -
derivation of the shifts due to stress is based on a single crystal with
known orientation with respect to the laser beam. However, the

calculated average grain size in the diamond film is about 2 microns.

 

177

Given that the beam spot size at the sample surface was also about 2
microns and given that the film thickness less than a micron, it is likely
that the laser beam is focused on a single crystal or on the boundary
between two grains. The infrared scattering is possible from only one or
two grains, the theory may be applied. Whether the stress state within a
single crystal represent the homogenous stress distribution in the
diamond film is not known.

A compressive biaxial stress state in the diamond film parallel to the
XY plane results in a tensile uniaxial stress in the 2 direction. Thus the
shift coefficient with stress under biaxial stress derived from theory can
tentatively be compared with coefficients determined experimentally

under a uniaxial stress along a <111> direction of diamond. A

frequency shift coefficient with stress of 0.45 GPa/cm‘1 [70] was
reported for a uniaxial stress along the [111] direction; the diamond
sample was a (111) single crystal plate and the stress range used was
less than 1 GPa which makes it a very suitable case for comparison with

the similar conditions used in this study. Both the theoretical and

measured value of the shift coefficient are equal to 0.45 GPa/ cm'1
under almost identical conditions; thus the result can be used with some
degree of confidence.

Stresses were calculated from the experimentally measured shifts
using equations 55 and 56. The results are presented in table 8.
The stress measurement results from both the change of radius of

curvature and the shift in the Raman signal are summarized in table 9.

178

Several important results can be deduced from table 9.

The residual stress measured by both methods has almost the same
magnitude. A relative difference of only 3.3 percent is observed
between the stress value obtained by the two methods for the as
deposited diamond film. A relative difference of 4 percent is recorded
for the stress values measured by the two methods for the annealed
diamond film. The relative stress change in the diamond film after it was
annealed was 20 percent from the Raman shift measurement and 14
percent from the change in curvature measurement ( table 9 ).

The stresses measured by both method are very close for the as
provided and annealed sample. Furthermore, the relative change in
stress as a result of the anneal is also close for both methods. The
immediate conclusion is one of two possibilities, either the stress is
very uniform so that both methods are observing the same stress
magnitude or that the two methods are measuring the same average
stress in the diamond film. For a thick sample ( thickness much higher
than laser extinction distance ) the stress measurement from the Raman
shift would be the surface stress. In this work, the diamond film, which
is less than one micron thick, all of the film is in focus and thus the
stress measured from the peak shift is necessarily averaging both the
interfacial and bulk stresses in the film. A supporting argument to the
latter point made is that the strain measured at the interface from the
peak shift of the silicon is greater than the strain measured in the

diamond film. The interfacial strain is expected to be higher than the

179

Table 8. Stresses calculated from Raman peak shifts for
silicon and diamond.

 

Sample State Measurement. Shift Stress
surface (cm‘) (GPa)
_ ._- == _____________
Silicon 2 as provided polished -0.08 +0.02
I
Silicon 2 as provided rough -0.11 +0.03
‘ .
Silicon 2 annealed polished -0.21 +0.05
*
Silicon 2 annealed rough -0.19 +0.05
0 a
Silicon
substrate as provided rough -0.58 +0.15
Silicon.’
substrate annealed rough -0.57 +0.15
Siliconfl
substrate as provided interface +1.25 -0.31
Siliconn
substrate annealed interface +1.52 -0.38
Diamond as deposited diamond +1.31 -0.59
Diamond annealed diamond +1.04 -0.47

. uncoated wafer .. coated wafer

Silicon 2 refers to one out of three uncoated silicon wafers numbered 1, 2 and 3

in the experimental procedure.

180

Table 9. Summary “of stress measurment results.

State Stress Strain Stress Strain

(Raman) (Raman) (Stoney) (Stoney)
GPa x 10‘ GPa x 10‘

Diamond as -0.59 -5.03 -0.57 -4.86

film deposit

Diamond annealed -0.47 -4.01 -0.49 -4.18

film

Silicon ‘ as -0.31 -17.3 N/A _N/A

substrate deposit.

interface

Silicon'I annealed -0.38 -21.52 N/A N/A

substrate

interface

Silicon“ as +0.15 +8.31 N/A N/A

substrate deposit.

backside

Silicon ‘ annealed +0.15 +8.31 N/A N/A

substrate
backside

. coated wafer

181

bulk strain since the compressive thermal expansion mismatch between
the film and the substrate is greatest at the interface. Thus if the Raman
shift provides the value of the interfacial strain rather than the average
strain in the diamond film, the strain observed in the diamond film would
have been about three times higher than the measured value to satisfy
the condition that the strain is continuous at the interface. One can
draw the conclusion that the stress measured in the 0.97 microns thick
diamond film is the average stress over the film thickness in the volume
probed by the laser beam. The origins and magnitude of the stress
measured in the diamond film will be discussed later.

The immediate question that must be answered is whether the shift
measured is actually a stress related shift or some other shift effect. It
was argued in section 4.4 that for the silicon-diamond system and the
laser Raman spectroscope used, there is no reason to expect any shifts
other than stress induced shifts. The measured strain on the interface
on the silicon side is greater than the strain in the diamond film. As
expressed above, if the stress measured by the Raman shift is the
average stress in the film, the average stress would be lower than the
interfacial stress measured on the silicon side. The point to be made
here is that even though the strains on both sides of the interface are
not equal, the measured shifts are possibly stress induced, the stress
measured in the diamond is averaged over the film thickness while the
shift in the silicon wafer at the interface is sampled only 2 microns deep

out of the 456 micron thickness ( at the 488 nm wavelength [59] ). Thus

182

the measured stress in diamond is an average value while the stress
measured on the silicon side in an interfacial stress. It is therefore not
unusual for the strain on the silicon side of the interface is greater than
the strain on the diamond side.

A second indication that the measured shift is stress induced is the
fact that the shift measured on either side of the silicon wafer are of
opposite signs; the interface side of the silicon wafer is in compression
(-0.31 GPa ) and the back side is in tension ( + 0.15 GPa ). Since the
stress changes sign from one side to the other of the substrate, the
stress ( strain ) must go through a neutral plane where the stress is
zero. The stress profile across the thickness of the substrate is not
expected to be symmetric about the half-thickness plane of the silicon
substrate because the film and the substrate have different stiffness and
thickness values. According to Oel and Frechette [57], the neutral axis

position measured from the interface is given by

11548.§2+Ssstsz+3ssts§llb6ss(t.+ts)l (57)

where, s, and 89) are respectively the stiffness of the film and the
substrate. The term 3 Ss ts2 was substituted in for the term 4 S8 IS2 since

118 must approach (ts/2) when t'approaches zero.

183

Given that

ha: +0.97 microns,

t5 = -0.456 mm,

s, = 1.3 10-3 GPa/m,
and s = 82.3 10-3 GPa/m,

S
where the X=0 plane is taken at the interface. the distance 118 of the

neutral axis of the silicon substrate away from the interface is 0.38 mm.
Thus the neutral axis of the silicon substrate has moved away from the
stiffer diamond. Since the neutral axis of the substrate is moved away
from the interface, the stress on the interface side of the substrate in
expected to be higher than the stress on the back side of the silicon
substrate. Indeed, the stress on the interface side is twice as much as
the stress on the back side stress in the silicon substrate respectively

( -0.31 GPa versus 0.15 GPa (table 9) ). The stresses in the silicon
substrate after the anneal. shows the same type of stress distribution as
for the as-deposited state.

The annealing of the diamond film was carried to check if both
methods are sensitive to the change in stress magnitude due to the
anneal. As stated earlier, The relative stress relief due to annealing
measured from the Raman shift was 20 percent while the same relative
stress relief measured from the curvature change was 14 percent. An
interesting feature occurred at the silicon interface. Upon annealing,

the Raman shift of the silicon at the interface increased, indicating that

 

184

the stress state has become more compressive ( from - 0.31 to
0.38 GPa ), while the decrease in the shift of the diamond peak resulted
from a decrease in the stress in the diamond film. A possible
explanation of the stress change is the diffusion of hydrogen across the
interface from the diamond side to the silicon side. Indeed, at the
annealing temperature of 650 C for 1 hour, some limited diffusion of the
hydrogen 'in the diamond film to the silicon substrate is expected. As a
result, the stress in the silicon at the interface increased due to the
hydrogen impurity that diffused in. It is a well established fact in the
literature that hydrogen induces compressive stresses in both diamond
[47] and silicon [55]. Incidentally, the relative increase in the stress
magnitude due to annealing at the silicon ( at interface ) is 21 percent,
just about the same magnitude of the stress decrease in diamond ( 20
percent ). The annealing treatment reduced the stress only slightly.
Annealing for more than one hour and/or at higher temperatures might
be necessary to completely relief the stress in the diamond film.
Another point of concern is whether the silicon wafers have any
stress before the deposition of diamond and whether the annealing of
the silicon diamond system affects the silicon wafer separately. To
answer the question, both the silicon wafer bow and Raman shift have
been measured on separate silicon wafers before and after annealing
under the same conditions as the silicon-diamond sample. The silicon
wafers as provided by the supplier have a curvature due to the

processing method, several treatment are carried to make sure that the

185

silicon wafers do not have any residual stress [85]. The original
curvature of the wafers used is consistently the same for all the wafers
annealed or not with the exception of one sample where the bow is
much smaller than the other silicon wafers ( table 5 ). The shift in the
silicon peaks of the silicon wafers resulted in calculated stresses of
0.02 to 0.05 GPa, greater than the error in the stress measurement but
roughly about 50 times smaller than the stresses in the diamond film. If
the observed shifts in the separate silicon wafers are stress induced,
their magnitude is small compared to the film stress and thus can be
neglected. Annealing of a silicon wafer resulted in no change in the
shift, furthermore the shifts on either side of the wafer were consistently
the same for all wafer. Consequently, there is no reason to believe that
neither the bow nor the Raman shifts are stress induced. Had the bow
or shifts been stress induced, the annealing would have affected the
magnitude of the shift and the sign of the shift on either side of the water
would have been of opposite signs. The only possibility left is that the
wafers are under a uniformly compressive stress, as indicated by the
sign of the shift, rather than a bending stress.

Table 10 provides some reported stress measurements on diamond
and carbon films. The magnitude of the compressive stress in the
diamond film is lower than the calculated compressive stress that results
from the thermal expansion mismatch after cooling to room temperature.
The thermal stress that results from the thermal expansion mismatch

between the film and the substrate upon cooling down from the

186

deposition temperature was calculated as a function of the deposition

temperature. At the deposition temperature of 980°C, the compressive
thermal stress is -0.83 GPa ( figure 19 ). On top of the thermal mismatch
stress, hydrogen and graphite component in diamond contribute to the
compressive stress. Since the measured compressive stress

(-0.57 GPa ) is lower than the thermal compressive stress ( -0.83 GPa )
a tensile stress must have offset the compressive thermal mismatch
stress and resulted in a lower measured compressive stress. One
contribution of the tensile component of stress in the lattice mismatch
stress. The lattice constant of silicon is larger than the lattice constant
of diamond. As a result a compressive stress contribution develops at
the silicon side of the interface and a tensile stress contribution on the
diamond side. Windischmann [10,21] found diamond film under a tensile
stress state. The magnitude of the stress was about +0.3 GPa.
Windischmann explained the origin tensile stress with the grain
boundary relaxation model (GBRM). The GBRM claims that films
deposited under low adatom mobility and/or in the absence of energetic
particle bombardment develops a porous microstructure. Tensile
stresses develop in this type of microstructure ( called Zonel ) because
of attractive atomic forces acting across the micropores and the grain

boundafies[10L

187

Table 10. Reported residual stress values in diamond and carbon films

 

 

 

 

 

 

 

 

 

 

 

 

 

7 Stress Proposed Film
Sumatran Flin hternal mm“, m.
a“. "mu M 11150.] w 0120 811088 mm finch-1' MOM
(will (run) “5"" (.1 (u) in.)
.565
10 01m $23,, 0.7 -°2 1° -‘2 +b 1 ‘ MPCVD
+525
11 DLC Slim NM NM 2.0 2 2 1880
DLC 1 0.7 mphws -0.5
27 Won 1:: l 2.3 rf.
-0.‘l
OW $1“! 2.0 _ 0.3 10 0.7 +094 3 3
20 Mentmei ‘° MPCVD
451$
DLC M 03 -.5 1 2
12 e W b reso
12 -3.0
Diamond -
Sllbon 1 b 3 .N to .04 +00 1 2
21 time .0 move
+.15
4 4
87 Gm NM NM 3mm -0.8 NIA
26 Dianond Alumina 1° '3 2° '1“:
.55
FACVD
T 10 to 20 -1.7 4 MIA
0 MIA ?
902 10 b 20 +2.1
SiALON 10 to 20 +1.7
1‘ cm 9"“ 02 N/A {"5 NIA N/A IBSD
46 Gabon Glass 02 NM 8.0 NIA NIA lBSD

 

 

 

 

 

 

 

 

 

 

(a)

1: stress calculated from change In substratecurvature. equation 9.
2: stress calculated from change In substrate detection. equation 25.
3: vibrating menlbrane method [20]

4: cc bond length and crystallite size effect [07]

(so)

1: Grain boundary relaxation model

2: atom displacement. ion beam energy. andlor hydrogen effect
3: Differential expansion coefficient model

4: Stress calculated from shift in first order Fiaman spectrum.

(iii)

MPCVD: Microwave plasma chemical vapor deposition
tBSD : Ion beam sputter deposition
FACVD: Plasma assisted chemical vapor deposition.

 

 

9- CONCLUSIONS AND RECOMMENDATIONS

A review of the literature revealed that the properties of diamond
films deposited by MPCVD are dependent on the deposition
~ parameters. Growth stresses are also dependent on the deposition
parameters.

The thermal stress arising from the thermal expansion mismatch
between the diamond film and the silicon substrate was calculated
taking into account the temperature dependence of both the Young's
modulus of diamond and the thermal expansion mismatch between the
film and the substrate. The proposed model is believed to be an
improvement over an existing model [10]. However, the assumptions
made on the Young's modulus of diamond probably caused large errors
in the magnitude of the calculated thermal (stress. The estimated stress
would become more accurate should data on the temperature
dependence of the Young’s modulus of diamond become available.

The magnitude of the residual stress measured in the diamond film
was almost equal by the Raman shift and curvature change methods.
Annealing of the silicon-diamond sample resulted in stress relief of 14
percent as measured from the curvature change and 20 percent as
measured from the Raman peak shift. The two methods are measuring
the average stress in the diamond film since the film thickness is not

uniform and the stress is inversely proportional to the film thickness,

188

 

189

thus not uniform.

Diamond is transparent to the argon laser light used at 488 nm
wavelength, thus the Raman shift are sampled over the entire film
thickness of 0.97 micron.

The experimental results show that the observed Raman shift in this
work are stress induced. Indeed, annealing of the silicon-diamond
sample resulted in a measured stress relief equivalent to the magnitude
of the stress relief measured from the curvature change. Raman shifts
measured on opposite sides of the diamond coated silicon substrate are
of opposite signs; one surface is in compression while the other surface
is in tension. Furthermore, annealing of uncoated silicon wafers
separately did not result in measurable Raman shifts or curvature
changes, thus the measured shifts are due solely to the stress in the
diamond film. Raman shift can consequently be treated as stress-
induced and thus be used for stress measurement.

The stress relief in the diamond film as result of the annealing at 650
degree Celsius for one hour in nitrogen is interpreted from the diffusion
of hydrogen from the diamond to the silicon across the interface; the
magnitude of the Raman silicon shift ( thus the stress ) at the interface
increased upon annealing.

The measured strain at the interface was not continuous as
predicted by the theory; the Raman shift ( and thus the strain ) was
considerably higher on the silicon side of the interface. Two

explanations were offered. First, the strain ( thus stress ) measured on

 

190

the diamond film was an average value since all of the film in the laser
focus, while the shift on the silicon side of the interface results from the
interfacial strain; the laser beam is sampling within 2 microns deep out
of the 456 microns wafer thickness. The interfacial strain in the silicon
is higher than the average strain in the diamond film. Second, the
assumptions made to derive the stress-shift relationship are well
satisfied for the single crystal silicon with known orientation, while it is
not the case for the polycrystalline diamond film whose orientation was
assumed as (111); to be able to apply the equation to stress
measurement. Since the stress-shift relation was derived for a single
crystal with known orientation with respect to the stress and the laser
beam, the magnitude of the Raman shift from the polycrystalline diamond
film cannot be directly converted into stress. For silicon, the shifts can
be converted to stress more confidently. Continuity of the strain at the
interface would thus provide us with the value of the interfacial strain
and thus stress from the measured strain on the silicon side of the
interface. The average or macroscopic stress in the film cannot
however be measured reliably from the Raman shift.

For the stress measurement from the curvature change, the isotropy
assumption is not satisfied for either the silicon or the diamond.
However, since the diamond is polycrystalline, it might be
macroscopically isotropic with respect to the elastic modulus. Stress
measurement in the diamond film from the change in curvature is more

reliable than from the Raman shift.

191

The magnitude of the stress measured in the diamond film (-0.57
GPa) is lower than the calculated thermal expansion mismatch stress.
Tensile stresses must have offset the compressive stress. Lattice
mismatch stress and attractive forces across grain boundaries and
pores ( GBRM [10] ) could have contributed to the tensile stress.
However, the calculated thermal stress ( -0.83 GPa ) could have been
exaggerated due to the several critical assumptions made to derive the
stress equation.

Finally, contribution of the processing method to the curvature in the
diamond coated wafer is not known; a more meaningful study would
involve measuring a silicon wafer curvature and Raman shift, deposit
the film on the same wafer, then measure the shifts and curvatures
before and after annealing. Furthermore, experimental studies on the
stress dependence of the Raman peak position for polycrystalline
samples under a true biaxial stress are needed for comparison with
theoretical models and accurate stress determination in thin deposited
diamond films. A theoretical model for stress-Raman shifts calculation
taking into account the polycrystalline nature of a material would also
be very helpful for accurate stress measurement in polycrystalline

films.

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91 :q 9’ s»

10.
11.
12.
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