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This is to certify that the
thesis entitled
The Mechanical Behavior of

CVD Diamond Thin Film Diaphragms

presented by

William Harrison Glime III‘

has been accepted towards fulfillment ~
of the requirements for

Master's degree in Materials Science

 

 

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THE MECHANICAL BEHAVIOR OF
CVD DIAMOND THIN FILM DIAPHRAGMS

By

William Harrison Glime III

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

1993

ABSTRACT

THE MECHANICAL BEHAVIOR OF
CVD DIAMOND THIN FILM DIAPHRAGMS

By

William Harrison Glime III

The behavior of centrally loaded CVD polycrystalline circular
diaphragms grown on single crystal <lOO> silicon substrates was
investigated. Circular diamond diaphragms were prepared by
mechanically grinding and chemically etching the silicon substrate.
The diamond diaphragms buckled due to a compressive residual
stress in the diamond film. The morphology of the buckled diamond
diaphragms was analyzed using laser scanning confocal microscopy
(LSCM). A nanoindenter was used to apply a central point load to
the diamond diaphragms and measure the resulting displacement.
The load deflection behavior of the diaphragms was compared to

established theoretical nonlinear plate solutions.

ACKNOWLEDGMENTS

I would like to thank my family for their support and encouragement as
well as Dr. Eldon Case, whose performance as an advisor was exemplary.

This work was funded by the State of Michigan Research Excellence Fund.

iii

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
I. INTRODUCTION

1.0 Potential of diamond films - applications

1.1 History of diamond synthesis

1.2 Development of the modern CVD method

1.3 Modern CVD methods

1.4 CVD diamond growth A

1.4a The role of hydrogen

1.4b Effect of oxygen and other gasses

1.4c Diamond nucleation on non-diamond substrates
1.4d CVD diamond growth on non-diamond substrates
1.4e Diamond film adhesion

1.5 Defects and impurities: effect on film properties
1.6 Summary of the CVD diamond growth process
2.0 Residual stress in CVD diamond films

2.1 Stress due to thermal expansion mismatch

2.2 Intrinsic stress in polycrystalline diamond films

3.0 Measurment of thin film mechanical properties

iv

.......

.......

.......

.......

.......

II.

3.1 The biaxial bulge method ....... 36

3.2 The vibrating membrane method (mechanical resonance) ....... 40
3.3 Microbeam deflection ....... 41
3.4 Ultralow-load indentation (nanoindentation) ....... 42
3.5 Point load deflection of circular diaphragms ....... 46
4.0 Deflection theory for point loaded clamped circular plates ....... 48
EXPERIMENTAL PROCEDURE ....... 52
5.0 Diamond growth parameters ....... 52
5.1 Specimen preparation ....... 52
5.2 Pre-dimple specimen mounting ....... 52
5.3 Polishing ....... 54
5.4 Dimpling ‘ ....... 54
5.5 Pre—etch mounting ....... 57
5.5a Mounting specimens A—F ....... 58
5.5b Mounting specimens 6-21 ....... 59
5.6 Etching ....... 59
5.6a Etching specimens A-F ....... 59
5.6b Etching specimens 6-21 ....... 61
6.0 Diaphragm morphology analysis ....... 64
6.1 Laser scanning confocal microscope (LSCM) setup ....... 64
6.2 LSCM line scan analysis ....... 64
6.3 LSCM data analysis ....... 69
7.0 Nanoindentation of diaphragms ....... 71
7.1 Mounting for nanoindentation ....... 71

7.2 Diameter measurement and center point location ....... 71

7.3 Deflection of the diamond diaphragms ....... 75
7.4 Nanoindenter / specimen compliance ....... 79
8.0 Off-center diaphragm loading ....... 81
9.0 SEM, TEM, and X-ray analysis of diamond film ....... V 83
10.0 Point load deflection of circular glass discs ....... 87
III. RESULTS & DISCUSSION ....... 89
11.0 Visual, SEM, TEM, and X-ray diffraction observations ....... 89
12.0 Diaphragm morphology - buckling relief of stress ....... 100
13.0 Deflection behavior of point loaded circular glass discs ....... 106
14.0 Deflection behavior of point loaded diamond diaphragms ....... 113
14.1 Repeated loading of diamond diaphragms ....... 138
14.2 Off-center diaphragm loading ....... 139
15.0 Analysis of load at failure for the diamond diaphragms ....... 141
16.0 Parameters influencing diaphragm deflection behavior ....... 144
IV. CONCLUSIONS ‘ ....... 145
V. FUTURE STUDIES ' ....... 147
VI. CLOSING REMARKS ....... 149
APPENDICIES ....... 150
A. Equipment parameters ....... 150
B. Nanoindenter calibration ....... 151
C. Seeding of substrate ....... 155
D. Grain boundary relaxation calculations. ....... 156
LIST OF REFERENCES ........ 157

LIST OF TABLES

Table 1. Material properties of diamond.
Table 2. Summary of common diamond deposition processes [27].

Table 3. Reported elastic modulus values for CVD polycrystalline
diamond films.

Table 4. “Values for constants A and B used in approximate solutions to the
point load deflection of circular plates (Equation 4.2).

Table 5. Parameters for MPCVD diamond depositon on wafer#2 [126].
Table 6. Results of LSCM line scan analysis of diaphragm specimen A.

Table 7: Radius, thickness, and load at fracture for point loaded circular
diamond diaphragm specimens.

Table 8: Specimen parameters and constant values for fitting of load-
deflection data to Equation 14.2*.

LIST of FIGURES

Figure 1. Crystal structure of diamond [1].
Figure 2. Carbon phase diagram [1].

Figure 3. Schematic of a hot filament assisted chemical vapor deposition
(HFACVD) apparatus [7].

Figure 4. Schematic of a bell jar microwave plasma assisted chemical
vapor deposition system [37].

Figure 5. Schematic of a DC plasma jet CVD apparatus [44].
Figure 6. Schematic of a combustion flame CVD apparatus [46].

Figure 7. Simplified schematic of possible nucleation and growth kinetics
for diamond CVD on a non-reacting surface [60].

Figure 8. Diagram of columnar grain growth in CVD diamond films [60].

Figure 9. Room temperature thermal strain of various materials as a
function of initial temperature [4].

Figure 10. Strain in diamond film due to thermal expansion mismatch
with the silicon substrate as a fimction of deposition temperature [4]. Due
to the relative change in coefficients of thermal expansion for diamond and
silicon, the thermally induced strain for diamond grown on silicon
substrates peaks at deposition temperatures of approximately 700°C.

Figure 11. Diagram of biaxial bulge apparatus used by Cardinale et al.

Figure 12. Schematic diagram of vibrating membrane apparatus used in
the study by Berry et al. [95,106].

Figure 13. Schematic diagram illustrating the deflection of the free
standing polycrystalline diamond cantilever beam by Davidson et al. [99].

Figure 14. Loading/unloading curve obtained from ultralow-load
indentation on diamond film DT—26 (Table 3), redrawn from [6].

viii

Figure 15 . Relative position of specimens 6 - 21 with respect to half-
wafer#2. Portions of the half-wafer which were not used in the deflection
study consists of specimens which were destroyed during processing or
fragments unsuitable for producing diaphragm specimens.

Figure 16. Mounting of diamond/silicon specimen on dimpler base using
therm0p1astic wax.

Figure 17. Schematic of dimpling process.

Figure 18. Diagram of dimpled region in the silicon substrate for
specimens A - F. Specimens obtained from wafer#2 (6-21) have a 540 mm
substrate and are dimpled to a depth of 490 mm in a similar fashion.
Figure 19. Diagram of pre-etch mounting procedure for specimens A - F.
Figure 20. Diagram of pre-etch mounting procedure for specimens 6 -21.
Figure 21. Optical micrographs of diaphragm specimens. (A) Specimen A
from wafer#1, indented into the substrate side of the diamond. (B)
Specimen 16 indented into the faceted (top) diamond surface (fractured by

indentation).

Figure 22. Micrograph of diamond diaphragm specimen mounted on glass
base and support.

Figure 23. LSCM line scan profile of diaphragm specimen A. The bi-
model morphology is attributed to circumferential buckling.

Figure 24. Position of line scans across diamond diaphragm specimen A
taken during LSCM analysis of the diaphragm morphology [122].

Figure 25. Schematic of line scan profile depicting buckled length
measurement technique.

Figure 26. Diagram of specimen situated in stage of nanoindenter. _
Figure 27. Schematic of diaphragm center location procedure and
diaphragm radius measurement. Diaphragm is purposely drawn "non-
circular” in order to illustrate the procedure.

Figure 28. Schematic of diaphragm deflection (specimens A - F). For
specimens 6 - 21 the substrate support was below the diamond diaphragm
and the indenter tip was in contact with the faceted diamond surface.

Figure 29. Schematic of off-center loading of diaphragm specimen 9.

Figure 30. Diagram of “tweezer method” for the mounting of diamond film
fragments for SEM examination.

Figure 31. Diagram of the “hammer method” for the mounting of diamond
film diaphragm fragments for SEM examination.

Figure 32. Diagram of glass diaphragm fabrication process. Specimens
were prepared with and without glue around the rim.

Figure 33. (A) Fragment of diamond film obtained from wafer#1 and
corresponding SEM surface micrograph. (B) Fragment from wafer#2 and
SEM surface micrograph. (C) Fragment of diamond film obtained from a
wafer used in LSCM buckling analysis [122] but not in this deflection
study. Included to illustrate differences in diamond film transparency and
surface morphology.

Figure 34. SEM surface micrograph of diamond specimen taken from
wafer#1.

Figure 35. SEM surface micrograph of diamond specimen taken from
wafer#2.

Figure 36. SEM micrograph of specimen obtained from wafer#2 showing
particles adhering to the surface of the diamond film.

Figure 37. SEM micrograph of particulate. The diamond coating indicates
the particles are introduced before or during the deposition process.

Figure 38. SEM micrograph of back (substrate) surface of a diamond film
specimen obtained from wafer#2.

Figure 39. SEM micrograph of cleaved diamond film/ Si substrate
obtained from specimen 13.

Figure 40. SEM micrograph of fracture surface of diaphragm 16.

Figure 41. SEM micrograph of silicon rim supporting diamond diaphragm
A showing the tapering of the silicon substrate to the edge of the diamond
diaphragm.

Figure 42. TEM selected area diffraction pattern taken from a single
diamond grain from a thin film specimen obtained from wafer#1. The
pattern agrees with that of the theoretical <110> zone for a diamond
crystal. Streaking and spot splitting indicate the presence of twins and
stacking faults in the diamond grain. Spots resulting from double
diffraction are also present.

Figure 43. X-ray 29 scan of diamond film on silicon substrate obtained
from wafer#1.

Figure 44. Load-deflection behavior of Simply-supported circular glass
coverslip prepared by placing the coverslip (no glue) over a circular hole in
a glass plate. The compliance curve obtained from indentation into the
back of the glass plate(s) was subtracted from the data obtained for the
clamped and simply supported plates.

Figure 45. Load-deflection plots obtained from point loading of circular
glass coverslips clamped by applying superglue around the rim.

Figure 46. (A) Load-deflection plot for simply supported glass beam used
in the nanoindenter calibration..( B) Schematic of glass beam setup.

Figure 47. Load-deflection plots for clamped glass coverslips with load
normalized for radius and thickness.

Figure 48. Plot of combined compliance curves taken from various
diamond specimens and specially prepared compliance specimens. The
compliance behavior was described by Equation 14.1 which was used to
subtract the compliance contribution from the diaphragm deflection data.
Figure 49. Load-deflection plot for diamond diaphragm specimen A.
Figure 50. Load-deflection plot for diamond diaphragm specimen B.
Figure 51. Load-deflection plot for diamond diaphragm specimen C.
Figure 52. Load-deflection plot for diamond diaphragm specimen D.
Figure 53. Load-deflection plot for diamond diaphragm specimen E.
Figure 54. Load-deflection plot for diamond diaphragm specimen F.

Figure 55. Load-deflection plot for diamond diaphragm specimen 6.
Deflection to 9pm repeated three times.

Figure 56. Load-deflection plot for diamond diaphragm specimen 8.
Deflection to 9pm repeated three times.

Figure 57. Load-deflection plot for diamond diaphragm specimen 9.
Deflection to 9pm repeated two times.

Figure 58. Load-deflection plot for diamond diaphragm specimen 11.
Deflection to 9pm repeated three times.

Figure 59. Load-deflection plot for diamond diaphragm specimen 12.
Deflection to 911m repeated three times.

Figure 60. Load-deflection plot for diamond diaphragm specimen 13.
Deflection to 9pm repeated three times.

Figure 61. Load-deflection plot for diamond diaphragm specimen 14.
Deflection to 9pm repeated three times.

Figure 62. Load-deflection plot for diamond diaphragm specimen 16.
Deflection to 9pm repeated four times.

Figure 63. Load-deflection plot for diamond diaphragm specimen 17.
Deflection to 9pm repeated three times.

Figure 64. Load-deflection plot for diamond diaphragm specimen 19.
Deflection to 9um repeated three times.

Figure 65. Load-deflection plot for diamond diaphragm specimen 21.
Deflection to 9um repeated two times.

Figure 66. Plot of C1 (Equation 14.3) versus t‘t/r2 for all specimens.
Dashed line represents forced fit through zero, solid line represents
floatiing intercept.

Figure 67. Load-deflection plots for off-center point loading of diamond
diaphragm specimen 9.

Figure 68. Plot of load at diaphragm failure versus t2.

I. INTRODUCTION
1.0 Potential of diamond films - applications.

The material properties of diamond (Table 1) are very impressive
but the lack of an abundant natural supply and the inability of
diamond to be effectively manufactured have limited its commercial
use to date. Industry has utilized the hardness of diamond as
abrasives and tool coatings, but diamond’s many other properties
have yet to be exploited to the same degree in practical applications.
The extreme hardness, low coefficient of friction, and corrosion
resistance of diamond make it desirable as a protective coating.
Diamond’s unmatched thermal conductivity makes it the optimal
material for heat transfer. Diamond’s wide band optical
transparency makes it useful in window applications. The effective
production of semi-conducting diamond would allow for active
diamond electronic devices which are faster, more durable, and
capable of handling more power than those using current
semiconducting materials [7 -9].

The potential of diamond as an engineering material is
remarkable but limited by the current methods of diamond synthesis
[7,8]. The rapid advancement of synthetic diamond production over
the past decade makes the future of diamond as a commercially
competitive material look very promising. Diamond films are
already being used commercially as speaker diaphragms in high

performance audio tweeters and as windows for X-ray lithography

2

Table 1. Material properties of diamond#

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Property Reported value ref.
Density 3.515 g/cm3 [1]
Hardness* (knoop) 75 - 113 GPa [2]
Elastic modulus (aggregate)* 1050 GPa [2]
Poissons ratio (aggregate) 0.07 [2]
Melting point (carbon triple point) ~ 4200 K [1]
Thermal conductivity* 20 W/cm K [2]
Electrical resistivity 1016 Q-cm [1]
Band gap 5.48 eV [2]
Breakdown voltage >107 V/cm [1]
Dielectric constant 5.5 [1]
Coefficient of friction (in air) ‘ 0.05 [1]
Fracture toughness (Kc - CVD Polycrystal) 4.3 MPaVfii [3]
Coefficient of thermal expansion 1 x 10'6 K‘1 [4]
Electron velocity 2.7 x 107 cm/sec [1]
Spectral transmission range* .225 - 25pm [1]
High resistance to chemical attack (moderate temperatures) [1]
High resistance to radiation damage [5]
Resistant to thermal shock [6]

 

 

l' 'Iype IIa natural diamond single crystal at room temperature unless noted otherwise
* Designates highest of known solids

Diamond crystal “types” [1,7]:

Type Ia - nitrogen impurity (~0.1%) in aggregate or platelet form.
Type Ib - nitrogen impurity in substitutional form.

Type IIa - no (trace) impurities.

Type IIb - boron impurity

3

[7,8,10,11]. Doped semiconducting diamond has been produced using
Chemical Vapor Deposition (CVD) processes [7,8,12-14] and
functional diamond p-n diodes have also been fabricated [12,14]. In
fact, researchers have predicted that the market for synthetic
diamond films will be in excess of a billion dollars by the year 2000
[7,10,11] and even that may be an underestimate given the rapid
development and improvement 'of diamond synthesis techniques.
The advancement of diamond technology in areas of industrial
tooling would also make the manufacture of other ceramics and '
composite materials more cost effective, which is one of the major

factors keeping advanced materials out of many modern markets

[15].
1.1 History of diamond synthesis

In 1797 Smithson Tennant discovered diamond is a form of carbon
[16,17]. Since that time scientists have been striving to produce
synthetic diamonds. The history of synthetic diamond production is
somewhat comical, full of fraudulent claims, misguided theories, and
extravagant techniques and equipment [16,17]. The majority of
early synthetic diamond research was based on the transformation of
graphite into diamond under thermodynamically stable conditions,
i.e. very high pressure [16]. In 1954, after more than a century of
failed attempts, it was announced that synthetic diamonds had been
produced from graphite by researchers at General Electric [17].

A lesser known, but perhaps more significant, approach to the

 

synthesis of diamond was the growth of diamond under “metastable
conditions” at subatmospheric pressures [18-21]. In 1953, W. G.
Eversole succeeded in producing new diamond on diamond seed
crystals at subatmospheric pressure using a CVD method [22 as cited
in 18,23]. Successful low pressure synthesis of diamond preceded the
high pressure approach but was virtually ignored at the time due to
extremely slow growth rates, the eventual nucleation of graphite,
and the need for a diamond substrate [18,19,21,23-25]. Since the
success of Eversole, a'variety of CVD methods for the low pressure

production of diamond films have emerged.
1.2 Development of the modern CVD method

Graphite, not diamond, is the thermodynamically stable (Figures
1 & 2) and kinetically dominant phase of carbon at other than ultra
high pressures and temperatures [7,18,19,21,23]. From the
thermodynamic standpoint, the growth of graphite is favored over
diamond growth under CVD conditions. The information available to
early researchers of diamond growth included [18,24]
1. The spontaneous transformation of diamond into graphite is
not significant at temperatures below 1300°C.
2. Carbon atoms have a high mobility on diamond surfaces at
temperatures around 1000°C.
3. Homogenous nucleation of graphite from gas-phase
hydrocarbons is unlikely.

Early researchers of low pressure diamond synthesis predicted that

 

 

 

 

carbon

 

 

 

 

 

 

Figure 1. Crystal structure of diamond [1].

 

Pressure (GPa)

 

30

25

M
O

H
01

H
O

01

 

_ DIAMOND

  
 
 
  
 
 
 
  

High-pressure /
high temperature
diamond synthesis

Catalytic
high-pressure /
high—temperature
diamond synthesis

 

833°” GRAPHITE

 

2000 3000
Temperature (Kelvin)

 

Figure 2. Carbon phase diagram [1].

 

 

6

at temperatures of approximately 1000°C, surface carbon atoms
would be more likely to migrate to and attach themselves to a
diamond site rather than form a graphitic nucleus [24]. Early
experiments however, produced only minute amounts of new
diamond on diamond seed crystals before the nucleation and growth
of graphite overwhelmed the diamond growth process [18,19].

In 1967, researchers at Case Western Reserve University, led by
John Angus, showed that hydrogen effectively etches the graphitic
carbon that eventually formed during the deposition process. The
removal of graphite occurs without removing significant amounts of
diamond [24]. Subsequent deposition and etch cycles produced
substantial amounts of new diamond on the diamond crystals but the
procedure was far to slow and inefficient to be of practical use. In
1977, Russian scientists Derjaguin and Fedoseev published a
previously unimaginable diamond growth rate of lum per hour [26].
The Russian method combined the diamond growth and hydrogen
etching processes by supplying additional energy to the gas phase via
hot filaments or electric discharge, which created a greater
dissociation of the CVD gasses (CH4/HZ) into radical species, thus
producing enough atomic hydrogen to actively etch the graphitic
carbon [8,18-20,23,26,28,29]. The process developed by Derjaguin
and Fedoseev forms the basis of the diamond CVD techniques used

today.

 

 

1.3 Modern CVD methods

One of the most widely used low pressure diamond growth
techniques is the hot filament assisted chemical vapor deposition
(HFACVD) process [7,18,19,21,29-30]. The HFACVD process (Figure
3) uses a tungsten or other filament heated to approximately 2000°C
to dissociate the introductory CVD gasses [7,18,19,21,29,30]. The
desired substrate is placed less than 1cm from the hot filaments and
substrate temperature is generally maintained between 800 and
1000 0C [7,18-20,29,31]. Uneven heating of the substrate surface by
the hot filaments is a major problem for the HFACVD technique.
Moving the substrate away from the filaments and giving it a
positive bias with respect to the filaments provides an electron
current to the substrate [18,19,21,29]. Electron bombardment
enhances the removal of graphite and assists in the breaking up of
gaseous-carbon species near the substrate surface [18,19,21].
Moving the substrate further from the hot filaments reduces the
problem of nonuniform substrate surface heating [18,19]. Chamber
pressures of 10 to 100 Torr, hydrogen concentrations of
approximately 99%, and diamond growth rates of 1 to 10um per hour
are typical for the diamond HFACVD process [18-20,29,31]. One
drawback to the process is the introduction of impurities into the
diamond film due to the decomposition of the filaments [29,32,33].

Another approach to diamond growth is plasma assisted chemical
vapor deposition (PACVD). Microwave, arc and glow discharge, as

well as radio frequency (RF) power are among the methods used to

 

 

‘

 

dissociated gas

substrate

  

hot filament

-\\
.\
\

“n“?
.W‘

\\

 

...............................................................................................
...........................................................................................
..................................................................................................

 

 

electrical connection

 

 

 

Figure 3. Schematic of a hot filament assisted chemical vapor deposition
(HFACVD) apparatus [7].

 

antenna

    
  
 

waveguide

fused silica bell jar ..... p ; ‘ plasma ball

microwave cavity

  

substrate copger substrate
ho

er and succeptor
graphite with cooling system
substrat-

holder 5:215:31 .: . :3 '-".‘
: 2| g; g . thermocouple

.5.
FEW-2° 'Cvm‘. \f A‘IL ‘

gas mixture gas mixture

'3? -—> vacuum pump

"'S'X-I'K'iill-24'3“???

302+. .

water

U

... temperature
-"°’°”’°- -" 4"" control meter

water

 

 

 

Figure 4. Schematic of a bell jar microwave plasma assisted chemical vapor
deposition system [37].

 

generate plasmas for diamond growth but the use of 2.45 GHz
microwaves is by far the most common (Figure 4) [18,19,34-37]. The
microwave plasma assisted (MPCVD) reaction chamber is typically a
fusedosilica tube inside which the plasma of hydrogen and
hydrocarbon (or other carbon containing gaseous species) is
maintained [18,19,35,38]. The substrate is generally placed inside
the plasma although diamond growth on substrates placed outside
the plasma has been reported [18,19,27]. Substrate temperature is
controlled by the relative position inside the plasma and the
microwave (or RF) power output [18,19,27]. Gas composition,
chamber pressures and growth rates are similar to those of the
HFACVD method [18,19,27].

Magnetic fields have been used to enhance the (MPACVD) process
by creating a condition of electron cyclotron resonance (ECR) [39-41].
The ECR condition provides higher plasma densities and electron
energies than ordinary microwave plasmas creating a larger and
more uniform plasma which can deposit diamond over a greater area
[41].

Arc discharge plasma jet CVD (ADPJCVD) processes have been
used to grow polycrystalline films at rates in excess of 900nm per
hour [27]. The ADPJCVD process (Figure 5) involves the dissociation
of introductory gasses using an arc discharge [18,42-44]. The are
discharge plasma has an approximate temperature of 5000°C which
readily dissociates the CVD gasses [43]. The process is limited to a
relatively small deposition area (~10mm) and film non-uniformity as

well as poor temperature control due to the high gas temperatures

 

 

 

 

w.

10

pose significant problems for this process [18,27].

High quality diamond has been synthesized on various substrates
using a combustion flame method (Figure 6) [27 ,45,46]. Using an
oxy-acetylene torch with a reducing (excess hydrocarbon) flame
provides an atmosphere containing atomic H as well as hydrocarbon
and radical species that is similar to environments in other CVD
methods [21,45,46]. A water cooled substrate holder controls the
temperature of the substrate which is heated by the flame. Diamond
growth using this method has been reported with substrate
temperatures as low as 370°C [45]. Typical growth rates in excess of
30pm per hour and the relative simplicity of the technique make the
combustion method very appealing [45,46]. Like the arc discharge
plasma jet method, the combustion flame process is plagued by poor
substrate temperature control and non-uniform film thickness [18].
A high degree of non-diamond carbon is generally present in diamond
films grown using combustion flames [45].

A variety of CVD methods have successfully synthesized diamond
from the vapor phase. Table 2 summarizes growth parameters for
various diamond CVD processes. The continuing improvement of
these methods will undoubtedly increase the marketing potential of

synthetic diamond films.
1.4 CVD diamond growth

Modern diamond CVD techniques use mixtures of carbon

containing Species (typically CH4 but gasses such as acetylene and

11

 

H2 + CH4

  
 
  

DC power supply

cathode

/

anode

4-—— plasma jet

substrate \ “/9 §\\\

[ ill

cooling water

substrate holder

 

 

 

Figure 5. Schematic of a DC plasma jet CVD apparatus [44].

 

Oxygen —‘> .
acetylene —> -; ijf-i‘y‘

inner core

    

outer flame

/

  
 

 

acetylene feather

substrate \ acetylene feather

    

;. .-.-.-.'.-.-.-.-.'. """"""" .'.-.~‘.'r7:".-7H.'5?."..-.'.-‘.-T’.".'T".‘7".‘7'7-.‘T’I‘TV.‘".CCI ..... '. . . .-.'.- ...... -.'.-.'.'.‘.‘ -.'.;.

 
   

water if: i; 1:: water cooled substrate holder "

'n'.

3‘3

outer flame

 

 

 

Figure 6. Schematic of a combustion flame CVD apparatus [46].

 

 

12

Table 2. Summary of common diamond deposition processes [27].

 

 

 

 

 

 

 

 

 

 

 

Results growth deposition
rate area advantages drawbacks

Method (um/hour) (cm2)*

heated 0 3 2 100 Simple contaminations
filament ' ' large area stability, no 02
microwave 1 - 3o 40 quality, Stablhty rate, area

(reasonable rate & area)
1 . highest rate, area, stability

DC p asma Jet 930 < 2 quality homogeneity
combustion . , ,
flame 30 - 100 < 1* ample area, stability
low pressure simple .

DC discharge < 0-1 70 large area qualltyi rate

 

arcs,

* Larger deposition areas are possible if substrate is scanned or mulitple
flames, etc. are used.

 

 

 

 

 

‘ __._ .- ._ ...._ ___...__._..._.4~.... . - . _. .—

13

COx are also used) and H2 as the introductory gas [27 ,38,43]. Upon
entering the deposition chamber, the introductory gas undergoes
significant dissociation into atomic hydrogen, acetylene (CH2),
methyl radicals (CH3), and a variety of other hydrocarbons and
radical species [47]. There has been considerable debate over which
carbon species is (are) responsible for CVD diamond growth
[31,38,48-56]. The various low pressure CVD techniques (i.e. hot
filament, plasma assisted, flame combustion, etc.) produce similar
polycrystalline diamond deposits, indicating a single growth
mechanism which is independent of the method used [21,27,53].
Acetylene, the methyl radical, methane, ethane, and other carbon
species have been proposed as the depositing hydrocarbon
[47,50,52,54,57]. Research has indicated, however, that acetylene
and the methyl radical are the most likely diamond forming species
[31,56,57]. Researchers at Case Western Reserve University use
carbon-13 isotopic labeling to discern the growth species in a typical
hot-filament CVD process [50]. The CWRU study used an HFCVD
process in which hydrogen gas wasintroduced into the reaction
chamber above the filaments. 13CH4 and 12C2H2 were introduced
from a tube directly above the substrate in order to reduce the
amount of dissociation and mixing of the isotopically labeled species.
The amount of C13 in the deposited film and in the gases (CH4, CH3,
and C2H2) directly above the substrate was measured. (111), (100),
and (110) single crystal diamond as well as polycrystalline diamond
were used as substrates. The C13 content of the deposited film

grown on every substrate agreed with the measured C13 content in

 

 

 

._.-——___——_n—

14
the CH3 directly above the substrates. The amount of C13 measured
for the acetylene above the substrate was significantly lower than
that of the deposited diamond on each substrate. This study
provided experimental evidence that the methyl radical is the
primary growth species during diamond CVD on the three {(111),
(100), and (110)} primary diamond faces. Several other studies have
also supported the methyl radical (CH3) as the primary diamond
forming species [49,55,56,58].

1.43 The role of hydrogen

Before the incorporation of hydrogen into the process, the growth
of useful diamond films by CVD was unattainable. Three major
mechanisms have been proposed describing the role of atomic
hydrogen in diamond CVD processes.

First is the “enhanced” etching of graphite relative to diamond by
atomic hydrogen [23,29,47,59]. The early work by Angus showed the
etching rate of graphite to be up to 500 times higher than that of
diamond in an atmosphere of atomic hydrogen [24]. Even though
graphite can readily form during diamond CVD, graphite can be even
more readily etched by atomic hydrogen, leaving diamond to grow
virtually undisturbed.

A second way in which hydrogen promotes the growth of diamond
over that of graphite is by maintaining the dangling bonds on the
diamond surface [23,29,47]. Without hydrogenated bonds, the high

energy of the diamond surface would promote reconstruction into a

 

 

 

 

‘

 

15

graphitic carbon layer [23,29,47]. Surface stabilization reduces the
critical size of diamond nuclei by reducing surface energy [60].

Atomic H also breaks up the larger gas phase hydrocarbons (i.e.
aromatic rings) which are believed to be the “precursors of
carbonaceous solid phases” [47]. The dissociation of these
hydrocarbons into smaller, diamond forming species promotes
diamond growth while inhibiting the formation of graphite or other
non-diamond carbon phases.

Dissociation of H2 into atomic H is a major function of the hot
filaments, microwave plasmas, DC arcs, etc. found in modern
diamond CVD processes. Increased amounts of atomic H produced in
the hot filament or plasma region create a “supersaturation” of H
above the substrate [53]. The increased population of atomic H
allows for the aforementioned roles of hydrogen in the CVD process.
The amount of atomic H produced by the different systems can vary,
but its presence in adequate quantities is one of the most critical

factors in successful diamond production [18,23,47,53,60,61].

1.4b Effect of oxygen and other gasses

The addition of oxygen in small quantities (< 5%) to the diamond
CVD introductory gas has been shown to improve growth rates,
extend the temperature region of diamond formation, and produce
diamond films of higher quality than those grown without the
presence of 02 [37-39,48,58,59,62,63]. A recent study [49] has

provided experimental evidence that oxygen enhances the diamond

 

 

16

growth process by producing an increased amount of atomic
hydrogen and CH3 in the CVD gas. Assuming CH3 is the diamond
forming species, a greater concentration would increase the diamond
growth rate. An increase in the concentration of atomic H promotes
the removal of non-diamond carbon species. Oxygen has also been
shown to provide selective etching of non-diamond carbon phases
[36].

A study by Kowato and Kondo [58] indicated that oxygen
suppresses the formation of acetylene, which their experimental
evidence suggests is a precursor to graphitic or amorphous carbon.
The increase in growth rate and improved quality of the films in the
study was attributed to the reduced formation of non-diamond
carbons (not just the enhanced preferential etching) as well as an
increase in the population of CH3.

The addition of water vapor (H20) has been shown to improve the
diamond growth rate [64]. The enhanced growth rate is attributed to
the same mechanisms as the addition of oxygen due to the
dissociation of the water vapor into H and OH radicals.

Doping with boron has also been shown to increase the crystalline
quality of CVD diamond films [9]. “Enhanced surface diffusion of
carbon atoms” on B doped diamond has been suggested as the
mechanism creating an improvement in the quality of the CVD
diamond by the addition of boron [9].

Significant quantities of nitrogen can be incorporated into the
diamond lattice but due to its negative effect on the thermal, optical,

and electrical properties of diamond, nitrogen is generally an

 

17

undesirable impurity [1]. Recent experimental evidence has
suggested that nitrogen can promote carbon sp3 (diamond) bonding,
which could aid in the preferential growth of diamond verses other
forms of carbon [66].

The addition of any element that can increase the amount of
atomic hydrogen, selectively etch non-diamond carbon deposits,
improve surface mobility, or increase the population of the diamond

forming carbon species could improve the diamond CVD process.

1.4c Diamond nucleation on non-diamond substrates

CVD diamond has been successfully grown on a wide variety of
substrates including metals, ceramics, glass, even graphite and
“buckyballs” [20,23,27,67]. An issue that is still being widely
investigated is the mechanism of diamond nucleation on non-
diamond substrates. Several mechanisms of diamond nucleation on
non-diamond surfaces have been proposed and experimentally
observed but the nucleation and interfacial mechanisms of diamond
growth are not well understood [18,19,23,60].

Abrading the surface of the substrate before diamond deposition
has been shown to increase the diamond nucleation density by
several orders of magnitude, which is attributed to an increase in the
area number density of surface defects on the substrate [26,33,53,68-
71]. Abrasion with diamond powders is presumed to leave behind
tiny diamond crystallites imbedded in the surface of the substrate

[20,62,69,70]. Nanometer scale diamond crystallites or “seeds” have

 

 

..——__-—_—_._.__ ._—__ _.....

18

been observed on the substrate surface by Iijima et al. using
transmission electron microscopy (TEM) and an extraction replica
method [70]. TEM observation of these particles before and after a
Short (5 min.) CVD diamond deposition show an increase in particle
size and a transition from irregular to polygonized shapes, evidence
that the diamond “seeds” provide homogenous nucleation sites for
CVD diamond crystals [70].

Abrading the substrate surface using non-diamond grit has been
shown to produce a high diamond nucleation density and “seeding”
with diamond particles without abrasion has also produced high
nucleation densities indicating both mechanisms of diamond
nucleation are effective [69]. Detailed patterning of diamond growth
on silicon has been achieved using photolithography and an argon
ion beam to “roughen” the Si surface in a desired pattern [71].
Diamond readily nucleated on the surface treated with the ion beam
while untreated surfaces remained virtually diamond free during
HFCVD diamond growth [71]. Patterning of CVD diamond growth
has also been accomplished by controlled “seeding” of the substrate
with diamond particulates [127]. Abrasion and seeding processes
consistently produce the highest diamond nucleation densities and
are used in most diamond CVD processes.

When carbide forming materials (i.e. Si, Ti, W, Mo, etc.) are used
as substrates, the formation of a carbide interlayer appears to be a
necessary step in the nucleation of diamond [18,26,69]. Nucleation
densities on carbide forming substrates have been observed to be one

or two orders of magnitude higher [26] than on substrates where

19

carbides do not form (i.e. Cu, Ni).

Homogeneous nucleation of diamond powder in the gas phase has
also been observed in diamond CVD atmospheres [61,72]. Gas phase
nucleation can “seed” the substrate surface providing sites for
diamond crystal growth.

Researchers at Ford Motor Company [73] have proposed the
existence of a new form of “metallic carbon”, which is harder but less
dense than diamond, that acts as an intermediate stage in CVD
diamond growth. The proposed material, named H-6 carbon,
consists of threefold coordinated carbon which is topologically
related to diamond and can continuously transform into diamond
without breaking or crossing any bonds. The existence of H-6 carbon
is supported by experimentally observed conducting surface layers on
CVD deposited homoepitaxial diamond. The predicted mechanism of
diamond growth through an H-6 intermediate is consistent with
observed growth rates and morphologies on various diamond surfaces
and may provide “a missing link” in the understanding of diamond
CVD [73].

Short range heterogenous nucleation of CVD diamond on silicon
[18,74-76] and B-SiC [74,7 7] has been shown to exist making the
eventual heteroepitaxial growth of diamond on non-diamond
substrates look promising. In a study by J eng et al. [7 6] local
heteroepitaxial diamond growth on silicon substrates was achieved
using an in situ surface pretreatment within the MPACVD chamber
prior to diamond deposition. The surface pretreatment produced

randomly distributed etch pits on the surface of a (100) silicon

 

 

20

substrate. Diamond was then grown on the pretreated surface using
a conventional MPCVD process. The resulting diamond deposit
showed areas of randomly oriented diamond crystals and in many
locations, large (100nm) pyramid shaped cubic crystals oriented in
the [110] substrate direction were observed. Local heteroepitaxy and
the high quality of these large crystals was verified by X-ray
diffraction, SEM and micro-Raman spectroscopy. The surface
pretreatment is believed to produce oriented diamond nucleation,
providing favorable conditions for heteroeptiaxial diamond growth on
the silicon substrate.

Adhesion, residual stress, crystal defects, and grain size are
related to nucleation. A better understanding of diamond nucleation
mechanisms is necessary if CVD diamond films are to reach their full

potential [24,74,78,79].
1.4d CVD diamond growth on non-diamond substrates

Figure 7 illustrates a likely process for CVD diamond nucleation
and growth. Once diamond nuclei have formed, surface diffusion of
carbon on the substrate and gas phase addition of carbon on the
diamond surface affect the growth of the diamond crystallite
[18,23,60]. The individual crystallites or “islands” grow together
covering the substrate surface and forming a continuous
polycrystalline diamond film [60,80]. Further growth of the
crystallites by the gas phase addition of carbon increases the

thickness of the diamond film and results in a columnar grain

 

 

DIFFUSION

i CH3
CH4 removal
H0
, m metas
o /

° 44444

me 99999

cluster 99999

° 4+ " 4+ 4+ IN.”
A AAAAA

U
0000 A .00 e... .00 .0

Figure 7. Simplified schematic 0 possible nucleation and growth kinetics for
diamond CVD on a non-reacting surface [60].

 

  
 
 

 

      

 

 

 

O
D
O
D
‘0

 

 

 

. I o

 

 

         

 

diamondfilm

ontm

fie u

-' :. x i :A . '.

8. Diagram of columnar grain growth in CVD diamond films [60].

 

22

structure (Figure 8) [60,80,81]. CVD diamond growth has been
shown to be most stable on (111) and (100) faces depending upon
deposition conditions [18,23,74,20,81]. Diamond growth; on
crystallites with preferred orientations (larger respective stable
growth surface)’will be faster than on crystals with exposed surfaces
less favorable for diamond growth. The enhanced growth of
“preferred” crystals and the extinction of crystals whose surface or
orientation is unfavorable results in an increase in the effective
“grain size” as the thickness of the film increases (Figure 8). The
columnar morphology and increasing grain size with thickness is

commonly observed in CVD diamond films grown by the various

techniques [80-82].
1.4e Diamond film adhesion

The use of diamond films as protective and wear resistant _
coatings is critically dependant on the ability of the films to adhere
to the desired substrate. Reports on the adhesion of CVD diamond
are somewhat limited and very little quantitative data on diamond
film adhesion has been provided [79]. Substrate surface preparation
(i.e. abrasion) appears to be a critical factor in improving the
adherence of CVD diamond films as measured by scratch tests or
similar methods [15,72,7 8,7 9]. Carbide forming materials, when
used as substrates, generally provide better adhesion than non-
carbide forming substrates which may be attributed to improved

chemical bonding [78,7 9].

23

Metal and diamond composite films have been produced using
CVD methods [42,83]. One method combined a plasma jet CVD
process to grow diamond crystals combined with an intermittent
plasma Spray of metal (W, Mo, Cu, Ni, etc.) by introducing metallic
powders to the plasma jet [42]. By continually decreasing the
amount of powder introduced, films consisting of a diamond-metal
mixture near the substrate and strictly diamond near the film
surface were deposited [421]. Diamond-metal composite films were
successfully produced using diamond deposition through RF plasma
CVD followed by metallic electroplating to fill the space between
diamond crystallites and further deposition of diamond by RFPCVD
to produce a continuous diamond film [83]. The adhesion of the
diamond-metal composite films to their respective substrates is
improved through the reduction of thermal expansion mismatch
between the diamond-metal composite layer and the metallic
substrate as well as bonding between the deposited metal and the
substrate [42,83]. The adhesion of the diamond crystallites produced
with these methods to the substrate was in some cases improved to
the point where the diamond crystals “will break rather than
separate from the surface” [83].

The effect of surface abrasion, nucleation density, residual stress,
chemical bonding betWeen the diamond and substrate, epitaxial
matchup, and other parameters on the adhesion of the films must be
studied further if diamond films are to be extensively utilized in

tribological and other applications where adhesion is critical.

24

1.5 Defects and impurities: effect on film properties

Defects are common in diamond films grown by the various CVD
methods [84,33]. Crystal defects (i.e. twinning and dislocations),
voids, microcracks, inclusions, and various impurities are commonly
observed in CVD diamond films [33,72,74,75,7782,84-86,this study].

Twinning, dislocations, stacking faults, and other lattice disorder
observed in CVD diamond crystals form to release stresses
accumulated during growth [7 2,86]. Nucleation twins are also
commonly observed in CVD diamond films [26,72,75]. Defect
formation has been associated with the growing together of many
“subgrains” which have different directions of crystal growth. As
these diamond subgrains cross or combine, disordered regions are
formed. The intrinsic stress in the diamond crystals has been
partially attributed to the accommodation of misfit between these
subgrains (i.e. twin boundaries) [50,75,86]. Lattice defects have
been observed to increase with increasing gas phase carbon
concentration [75,86]. Substrate temperature has been observed to
affect defect concentrations by altering the surface mobility of carbon
[18,74,86] and gas flow rate has also been shown to influence defect
density which is attributed to the change in residence time of the
diamond forming species [35]. A strong relationship between
diamond film surface morphology and crystal defects has also been
observed [18,50,67,74,85,86]. Crystal defects, mainly twinning, are
predominant on {111} diamond surfaces whereas {100} surfaces are

relatively defect free [18,46,50,72,75,82,86]. Growth rates on {111}

25

diamond surfaces, however, are generally observed to be higher than
that of {100}, which has been attributed to the high defect density of
the {111} surface promoting diamond nucleation and growth
[18,50,82,87].

Impurities, either incorporated into the diamond lattice or
occurring as inclusions or Second phases, have been observed in CVD
diamond films [9,18,32,74,77]. Substitutional impurities distort the
diamond lattice, creating residual stresses in the diamond crystal.
Nitrogen and boron are the only foreign atomic species that are
known with certainty to be incorporated with a significant degree
into the diamond lattice [1], but hydrogen [7 7] may also be a
substitutional impurity in diamond. The development of p-type
semiconducting CVD diamond by doping with phosphorous [14]
indicates that other atomic species may also form substitutional solid
solutions with carbon in the diamond lattice.

The presence and nature of hydrogen impurities in diamond is
difficult to identify using current technology, but its effect on crystal
and film quality is believed to be significant [32,88]. Hydrogen plays
an integral part in the CVD growth of diamond and its effects as an
impurity in diamond films needs to be studied further.

Impurities of amorphous carbon, graphite and various carbides,
for example, have been observed in CVD diamond films as inclusions.
Amorphous and graphitic carbon are continually deposited during .
the diamond CVD process [18,19,23,24]. Atomic hydrogen etches
graphite up to 500 times more efficiently than it removes diamond

[24]. Depending on deposition conditions, however, measurable

26

quantities of non-diamond carbon phases often exist in CVD diamond
films. Raman spectroscopy is approximately 50 times more sensitive
to sp2 (graphitic) type carbon and is often employed in analyzing the
non-diamond carbon content in CVD diamond films [34,89].

Etching of the substrate and chamber material in the diamond
CVD environment has been observed [18,80]. Substrate, or other
foreign material entering the CVD gas can also introduce impurity
phases (i.e. carbides) in the depositing diamond film [18].

The nature of the diamond crystal growth (i.e. “islands” to
continuous film to columnar structure) leads to the formation of
voids in the polycrystalline films [60,this study], and residual
stresses in the diamond films may lead to the formation of
microcracks [50,85]. '

Texturing of the crystals in CVD diamond films has been observed
by many researchers [35,7 5,81,82,84,85]. Crystal orientation with
<110> directions normal to the surface of the substrate is most
common to polycrystalline diamond films grown by the various CVD
methods [35,75,81], but <100> and higher order texturing, as well as
random orientation has also been observed [85]. Texturing in CVD
diamond is a function of nucleation and the preferred diamond
growth planes. The mechanical properties (i.e. elastic modulus and
especially hardness) are orientation dependant [1,2,85]. Strong
texturing will therefore influence the mechanical behavior of CVD
diamond films.

It is also interesting to note that natural diamond is composed of

approximately 99% C12 and 1% C13 [1]. Diamonds synthesized from

27

a highly pure (99.9%) C12 source have shown a 50% increase in
thermal conductivity, and calculations indicate that ~100% C12
diamond would have a thermal conductivity near 50 W/cm K, which
is over twice that of “normal diamond” [1,90]. Optical and electrical
properties of diamond are also expected to improve as the C13
content is reduced [1,130]. Increasing the C13 content is expected to
increase the already unparalleled hardness of diamond [11]. CVD
diamond films have been grown with high C13 content (20 to 99%)
[50,91] but a study of the mechanical properties on 13C diamond
films has not been presented.

The presence of lattice defects, impurities, voids, microcracks, and
texturing will most certainly effect the electrical, thermal and
mechanical behavior of CVD diamond films. An intricate
relationship between deposition parameters, residual stresses,
growth planes and morphologies, texturing, and the presence and
population of defects exists. Understanding this relationship is

critical to the development of diamond CVD processes.
1.6 Summary of the CVD diamond growth process

Spear and Frenklach summarize diamond CVD experimental

observations as follows [20]:

i. Gas activation is absolutely required.

ii. The chemical nature of the gaseous carbon precursor does not
appear to be critical to CVD diamond growth.

28

iii. The various methods used produce similar diamond deposits.

iv. The presence of hydrogen is required for efficient diamond
growth.

v. The addition of oxygen can improve diamond growth.

vi. Acetylene and primarily the methyl radical (CH3) have been
indicated as the predominant growth species.

vii. Co-deposition and formation of graphite accompanies
diamond growth.

viii. The temperature dependance of diamond growth rate
initially increases with temperature and then decreases. This
behavior is a result of the competition between diamond and
graphitic growth.

ix. Diamond nucleation rate is strongly affected by substrate
preparation method.

x. {111} and {100} faces dominate the surface morphology of the
films and twinning often occurs on {111} surfaces.

29

2.0 Residual stress in CVD diamond films

Residual stresses have been shown to affect the physical
properties of materials [92,93]. Residual stress in diamond films
results from the combined contribution of intrinsic or deposition
induced stresses and extrinsic or stresses due to thermal expansion
mismatch with the substrate [94,95]. Both compressive and tensile
room temperature net residual stresses have been reported for
polycrystalline diamond films [89,94,95] but the majority of the
diamond films reported in the literature had a residual compressive

stress at room temperature.

2.1 Stress due to thermal expansion mismatch

The relatively low thermal expansion of diamond [4] dictates a
compressive thermally induced stress at room temperature for films
grown on practical substrates under current CVD conditions. Figure
9 gives the relative thermal expansion of diamond compared to other
common materials. Silicon is the most, common substrate used in the
growth of CVD diamond films and was the substrate used for films in
this study.

To compute the thermally induced residual strain at room
temperature for diamond grown on silicon, the thermal expansion
polynomials [4] for diamond and silicon were compared (Figure 10).
Using typical substrate temperatures for diamond CVD growth (600-

1000°C) the predicted strain induced by thermal expansion mismatch

30

 

°°9 _THERMAL STRAIN

0.8 -
r

0'7 "’ Alumina

smcon
0.4 -—

0-3 '- Diamond

R. T. thermal strain (96)

0.2-

0.1 -

 

 

0.0 . .1 i 1 l Ml 1 l 1 l 1 l 1 l 1 l 1 l 1 l 1
300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

initial temperature (K)

Figure 9. Room temperature thermal strain of various materials as a
function of initial temperature [4].

R. T. thermal strain (96)

31

 

  

 

 

 

 

 

 

 

0.06
DIAMOND FILM
THERMAL STRAIN
0.04 -
Thermal expansion polynomials [4]
Diamond:
0.02 " AL ..
— = -o.010 - 5.911x10'°T + 3.320x10‘7T2 - 5.544x10'11T3
L Silicon:
TA.L— = -o.071 + 1.887x10'4T + 1.394x10'7 T2 - 4.544x10'11T3
0.00 J 1 l l l l l l I l l L 1 J l L 1 1 1 l l 1 J l
250 500 750 , 1000 1250 1500

Deposition temperature (K)

Figure 10. Strain in diamond film due to thermal expansion mismatch
with the silicon substrate as a function of deposition temperature [4]. Due
to the relative change in coefficients of thermal expansion for diamond and
silicon, the thermally induced strain for diamond grown on silicon sub-
strates peaks at deposition temperatures of approximately 700°C.

32

between silicon and diamond is roughly 5 x 10“. Assuming the
silicon substrate has a thickness several times that of the diamond
film, which is generally the case, then the majority of the expansion
mismatch will be accommodated by the diamond film [96,97]. The
thermally induced residual stress at room temperature can be
calculated by multiplying the value for the residual strain by the
biaxial elastic modulus for diamond (~1150 GPa) [94].

Due to the relative change in the thermal expansion coefficients
between diamond and silicon with increasing temperature the
thermal expansion mismatch at room temperature between diamond
and silicon reaches a maximum at a deposition temperature of
approximately 700°C (Figure 10). Increasing the substrate
temperature during deposition above 7 00°C will result in a decrease
in the room temperature thermally induced stress in the diamond
film. In fact, based on the thermal expansion of diamond and silicon
[4], growing diamond films on a silicon substrate at approximately
1350°C would result in a net thermally induced room temperature
residual stress of zero. Unfortunately, a 1350 °C substrate
temperature is well beyond the range of diamond CVD growth
parameters [10-20,23,27,74].

2.2 Intrinsic stress in polycrystalline diamond films
Intrinsic or “deposition stress” in polycrystalline films can be the

result of epitaxial mismatch, impurity, surface energy, interface

energy, grain boundary energy, defect density, and growth mode

33

effects [92]. For relatively fine grained polycrystalline thin films,
grain boundary density may play the major role in the development
of growth stress [92,94,98].

The grain boundary relaxation model, developed by Finegan and
Hoffman is commonly used to describe the intrinsic stress in
polycrystalline films [92,94,98]. The grain boundary relaxation
model is based on the following physical argument described by
Windischman [94,98]. As the film grows from isolated nuclei, to
crystallite “islands”, to a continuous film, interatomic attractive
forces across the gaps and pores between contiguous grains cause
elastic deformation (relaxation) of the grain walls. This relaxation is
balanced by intragrain tensile forces imposed by adhesion to the
substrate. By relating the intragrain strain energy to the difference
in the surface energy of the adjacent crystallites and the energy of
the resulting grain boundary the following approximation for the

intrinsic stress was derived:

r0 = distance of closest approach between atoms

r0 E d = grain size
0 " [3“: (1-v)’] E = elastic modulus (2'1)
v = Poissons ratio

In a study by Windischman et al. [94] on the intrinsic stress in

‘ CVD diamond films, the grain boundary relaxation model accurately
estimated the intrinsic stress in polycrystalline diamond films grown
on silicon substrates which was experimentally determined from the
radius of curvature of the silicon substrate after diamond deposition

[94]. Windischmanns calculation of the stress due to thermal

34

expansion mismatch between the diamond film and silicon substrate
does not agree with the thermally induced strain predicted from
thermal expansion polynomials for diamond and Silicon obtained
from Touloukian et al. [4]. An error in the Windischmann et al. [94]
calculation of thermally induced stress at room temperature is also
evident by the lack of a peak in thermal strain (Figure 10) at a
deposition temperature of approximately 7 00°C. The cause of the
discrepancy is not obvious from the information presented by
Windischmann et al. but the error resulted in an underestimation of
the thermally induced residual compressive stress in the diamond
films of approximately 40% at room temperature. In this study,
thermal expansion polynomials for diamond and silicon obtained
from Touloukian et al. [4] were substituted into the analysis used by
Windischmann et al. (Appendix D). The substitution produced
results in agreement with the grain boundary relaxation predictions.
Comparing the values obtained for the intrinsic stress in diamond
films used in a study by Berry et al. [95] to the intrinsic stress
predicted from the grain boundary relaxation model (Equation 2.1)
presented by Windischmann et al. resulted in agreement. The grain
size in the films used in the studies by Berry and Windischmann
were very fine (~ 0.05 - 0.7 pm) and thus one would expect a larger
contribution from grain boundary effects due to the relatively high
grain boundary density. As the grain size increases, the grain
boundary density rapidly decreases and grain boundary
contributions to the intrinsic stress in polycrystalline films will

therefore be diminished allowing contributions from defects and

35

other factors to become dominant.

The residual stress state for typical CVD polycrystalline diamond
films is very complex. The nature of low pressure diamond
nucleation and growth results in nonuniform crystal structures
during the early growth stages. The potential for defect formation
and the presence of second phases as the film thickness increases is
also presents a problem in understanding the nature of the residual
stress state in polycrystalline diamond films. Net residual stress can
be effectively measured but a complex stress state through the
thickness of CVD diamond films is evident by the “curling and
warping” of the films upon release from the substrate [99,93,this
study]. Residual stress is a major problem facing the researchers of
diamond films. Understanding and controlling the nature of residual
stress is essential if diamond films are to be utilized in the variety of

applications for which they show potential.

36

3. Measurement of thin film mechanical properties.

Biaxial bulge [100,101], ultra-low load indentation [6,102-105],
mechanical resonance [95,106], Brillouin scattering [107,108], beam
bending [99,109,110], plate deflection [97], and many other methods
have been used to experimentally determine the mechanical
properties of thin films. -

Jaing et al. [107 ,108] used Brillouin light scattering to measure
sound velocity in thick (~400um) polycrystalline CVD diamond films
with large (~40um) grains. The measurements provided a value of
1037 GPa for the elastic modulus of the CVD diamond crystallites
([110] oriented) which is in excellent agreement with the modulus for
natural diamond. The Brillouin scattering technique is unable to
effectively measure the macroscopic (many grain) properties of CVD
diamond thin films.

For polycrystalline CVD diamond thin films, measurement of the
macroscopic mechanical properties has been attempted using the
biaxial bulge [100], mechanical resonance [95], beam deflection [99],
and ultralow-load indentation [6,105] methods with results
presented in Table 3. These methods will be discussed along with a
method using the point load deflection of circular diaphragms to

measure residual stress an elastic properties of SiNx thin films [97].
3.1 The biaxial bulge method

The biaxial bulge method [100,101,111] uses uniform pressure to
deflect a circular diaphragm of the film under study, providing

37

pressure versus deflection information. The pressure versus
deflection information combined with a mathematical model for the
mechanical behavior of the diaphragm provides a value for the
biaxial modulus of the diamond film.

Residual stress, diaphragm morphology (wrinkling or initial
deflection) and the apparent stiffness of the material can greatly
affect the results of a biaxial bulge experiment [111]. Cardinale et al
used the biaxial bulge method to measure the mechanical properties
of polycrystalline diamond films prepared by microwave plasma
assisted CVD [100]. A schematic of the apparatus used in the study
is depicted in Figure 11. The films were grown on Silicon substrates
and had a thickness of approximately 10 um. By etching a circular
hole with a radius of approximately 1 cm in the silicon substrate, a
polycrystalline diamond diaphragm, held around its periphery by the
silicon substrate, was created. A roughing pump was used to apply a
vacuum to one side of the diaphragm while the diaphragm deflection
was measured using an optical method [100].

Cardinale et al. measured diaphragm deflections of up to 100 um.
The diaphragm was modeled as a spherical cap with a correction for

non-spherical deformation (equations 3.1,3.2).

o = biaxial stress
7%: (3.1)

e = biaxial strain
P = pressure
r = diaphragm radius
th h = diaphragm central deflection
3 = t = film thickness (3 2)
:2 B = correction factor (2/3 for spherical displacements) '

38

Non-spherical deformation of the diaphragm was observed in the
study but the details of the deformation were not presented. The
correction for the non-spherical deformation was determined using a
diaphragm of silicon and of glass with thicknesses in excess of 100
um and a diaphragm radius of approximately 1 cm. Using the known
values of elastic modulus for silicon and glass they experimentally
determined a value of 2.46 for [3 (Equation 3.2), the correction factor-
for non-spherical deformations. Biaxial modulus values for two
diamond films were reported and presented in Table 3.

The study by Cardinale et al. [100] resulted in reasonable values
for the biaxial modulus of the polycrystalline CVD diamond films but
their method is highly questionable. The use of the silicon and glass
diaphragms, which had a plate rigidity (Equation 3.3) [113]

D = plate rigidity
E t3 E = elastic modulus of film (33)

D = 12(1_V2) t = film thickness
v = Poissons ratio

 

approximately two orders of magnitude greater than that of the
diamond film, to estimate the behavior of thin diamond diaphragms
with a similar radius seems unreliable.

A recent study examining the reliability of the bulge test
indicated that current biaxial bulge test models are invalid for thin
films in compression due to diaphragm buckling effects [111]. The
diaphragms in the study by Cardinale et al. were in residual
compression and the effect of residual film compression on

diaphragm deflection behavior was not addressed.

39

 

optical probe

    

diamond diaphragm
4— to transducer to vacuum ——>

 

 

 

 

Figure 11. Diagram of biaxial bulge apparatus used by Cardinale et al. [100].

 

driver diamond membrane

 

 
   

\

/A Si wafer detector

 

first vibrational mode

E........mnnmlIIIlIIIllIllll||l||||l||llllllllllllllllmm“1......

   

 

 

 

Figure 12. Schematic diagram of vibrating membrane apparatus used in the
study by Berry et al. [95,106].

40

3.2 The vibrating membrane method (mechanical resonance)

Berry et al. used a mechanical resonance technique to measure
the mechanical properties of circular polycrystalline CVD diamond
diaphragms [95,106]. Polycrystalline diamond films in residual
tension at room temperature were grown on silicon substrates. By
etching away a circular region of the substrate taut diamond
membranes were created. The fundamental flexural frequency of the
diamond diaphragms were determined using an electrostatic
excitation apparatus (Figure 12). The tensile stress in the
diaphragm was determined from its relationship to the radius,
density, and resonance frequency for an ideal circular diaphragm.
Measurement of the residual stress was performed at several
temperatures between 100 and 700 K to determine the temperature
dependence on the stress in the diaphragms. The temperature
dependence of the strain in the diaphragm is due to thermal
expansion mismatch between the Silicon and diamond and was
calculated from the known thermal expansion for silicon and
diamond (Section 1.6). Comparison of the measured temperature
dependence of stress with the predicted thermal strain over the given
temperature range yields a value for the biaxial modulus of the
polycrystalline CVD diamond films (Table 3).

Residual stresses which are nonuniform through the thickness of
the diaphragm, indicated by the curling of the films upon release
from the substrate [92] have been observed in CVD diamond films

[99,this study]. Porosity in the polycrystalline diamond films

41

resulting in a lower density than the value for natural diamond used
in the study, the “un-rigid behavior” of the silicon substrate, and
diaphragm rigidity (assumed zero) are a few of the parameters which
may have resulted in significant error in the measured modulus for
the CVD diamond films. Also, the vibrating membrane method can

not be used to study diaphragms in compression, which is common

for CVD diamond films.

3.3 Microbeam deflection

The deflection of cantilever microbeams has been used to measure
the elastic modulus of polycrystalline CVD diamond films [99].
Davidson et al. [99] produced polycrystalline diamond cantilever
beams using a novel process involving photolithography, patterning,
and plasma/ chemical etching. A fabricated diamond cantilever beam
3168um x 639nm x 13pm was mounted under an optical microscope
and manually loaded using a hook and weight (Figure 13). The
deflection of the beam was measured with a “point to point focus
technique” using the calibrated stage of the optical microscope
accurate to approximately ilum. Three loads (0.2, 0.5, and 1g) were
attached to the end of the beam with a hook and the corresponding
deflection was measured. A deflection in excess of 300 microns was
obtained for the maximum (1g) load. From the load versus deflection
data and an expression for the deflection of a cantilever beam the
elastic modulus of the polycrystalline diamond film was estimated. A

second technique using a single load and three diamond cantilever

42

beams of various lengths was also used to estimate the elastic
modulus of the films. Both methods gave values for the elastic
modulus of the polycrystalline CVD diamond of 1170 GPa and 1220
GPa respectively) Which are somewhat higher than the reported
modulus of single crystal natural diamond (1050 GPa).

In Davidson’s study, the cantilever beams would “curl up slightly”
when freed from the substrate, which may indicate non-uniform
residual stress in the diamond films [93]. Warping of the
diaphragms across the width of the cantilever beam would
significantly increase the beam’s bending stiffness, resulting in
inflated measured modulus values. How the observed curling and
warping in the diamond cantilever beams affected the deflection
behavior was not addressed in the Davidson et al. study.

Weihs et al, used a similar method of beam deflection to measure
the properties of thin film microbeams of silicon, gold, SiOZ, and
other materials (diamond films were not included) [109,110]. The
study utilized a nanoindenter to provide the load-deflection

information. The use of a nanoindenter could greatly improve the

results of the Davidson et al. or similar studies.
3.4 Ultralow-load indentation (nanoindentation)

Ultralow-load indentation is often used to measure the hardness
and modulus of thin films [6,102-105]. Beetz et al. [6], used a
nanoindenter to measure the modulus of diamond thin films grown

by hot filament CVD on silicon substrates. Several indentations

43

 

vvvvvvvuvvvvvvvvvvvvvuu-vvvvvuvvuuouvv-uo vvvvvvvvvvvvvvvvvvv

o v 4 v v u v vvvvvvvvvvvvvvvvvvvvar-vervevavvvvvvv'vv vvvvvvvvvvv

Silicon substrate

  
  

   

 

 

 

 

 

Figure 13. Schematic diagram illustrating the deflection of the free standing
polycrystalline diamond cantilever beam by Davidson et al. [99].

 

61

LOAD (mN)
co

   

unloading

 

 

 

10 2'0 3'0 310 5'0 60 7'0 00 9'0
DISPLACEMENT (nm)

Figure 14. Loading/unloading curve obtained from ultralow-load indentation
on diamond film DT-26 (Table 3), redrawn from [6].

,.. 44

were made across two diamond coated silicon wafers. The elastic
modulus of the film was estimated using the unloading portion of the
force displacement curve obtained for each indentation [Figure 14].
Averaging the elastic modulus values obtained from the individual
indents produced values of 874 GPa (film with 0.5um grains, poor
faceting, and a small degree of non-diamond carbon) and 536 GPa
(film with ~ 611m grain size, typical diamond (111) faceting, and
virtually no non-diamond carbon).

Accurate calculations of modulus from ultralow- load indentation
data requires “that the test surface be smooth to dimensions much
smaller than the indent depth” [103], The tremendous scatter (over
an order of magnitude) in the modulus values obtained from the
individual indents in the Beetz study indicates the difficulty in
obtaining accurate measurements on faceted diamond films using the
ultralow-load indentation method.

O’Hern and McHargue [105] used ultralow-load indentation to
measure the hardness and modulus of CVD diamond films with
surfaces smoothed uSing mechanical methods. The roughness of the
diamond surface after “smoothing”, however, was not presented.
The indentation response of the diamond films was compared to the
indentation response of a type IIa natural diamond crystal with [100]
orientation used as a reference. The measured elastic modulus for
the diamond films was slightly higher (~10%) than that of the single
crystal reference but a high degree of scatter in the modulus
measurements from the individual indents was also observed in the

O’Hern et al. study.

45

Table 3. Reported elastic modulus values for CVD polycrystalline diamond films.

 

 

 

 

 

 

Study and Method ThiCkneSS Residual stress Reported elastic
specimen designation" of growth of film (pm) at 298K (MPa) modulus (GPa)
Biaxial Bulge [100] 864+ 38
- 9.5 -
RUB-164 MPACVD 9'6 (V:.I)
RDD-l97 ' 1&0 - 6.8 1059': 90
Vib. membrane [95]
1D .. 2 139 765
2D MPACVD .. 2 58 657 (V=.1)
3D ~ 2 9.4 711
Beam deflection [99]
C7 13 1176
MPACVD -
var. lengths 13 unavailable 1225
Nanoindentation [6]
DT-26 HFACVD 1.5 - 7 . 536
unavailable
DT—23 unavailable 874

 

 

 

*The individual specimen labels assigned by the original researchers are listed to allow the
reader to directly identify each specimen in the study cited.

46

The size of the indenter tip used in ultralow-load indentation
determines the volume of material that contributes to the
experiment. The tip size and shape were not reported in the
aforementioned diamond film indentation studies, but typical
indenter tips will result in a contact area of only a few square
microns. Determining the macroscopic behavior of a material, which
may depend on defects and other parameters, using information

gained from such a small area is questionable.
3.5 Point load deflection of circular diaphragms

In a study by Hong et al. [97] the mechanical deflection of circular
diaphragms of silicon nitride was used to measure the residual stress
and elastic modulus of the SiNx thin films. The thickness of the
diaphragms ranged from 0.09 to 0.27 pm and diameters of 1100 to
4100 um. The circular SiNx diaphragms were prepared using a
photolithography and etching technique. A nanoindenter was used
to deflect the circular diaphragms with a point load at their center.
From the load-deflection behavior of the diaphragms in residual
tension a value for the elastic modulus and the residual stress in the
films was obtained using classical plate deflection theory (Section 4)
with modifications for residual tension.

The study by Hong et al. was limited to films in tension due to the
buckling of the diaphragm for films in compressive residual stress.
The technique provided reasonable values for the residual stress and

elastic modulus for the SiNx thin films but the deflection behavior of

47

the diaphragm is much more sensitive to the residual tensile stress
in the film than to the elastic modulus. Therefore, the use of the
Hong et al. technique for the measurement of the elastic modulus of
thin film diaphragms in tension is “not very accurate” [97]. The use
of classical plate theory to describe the behavior of plates undergoing
large deflections is also questionable as will be discussed in the

following section.

48

4.0 Deflection theory for point loaded clamped circular plates

Classical plate theory describes the deflection behavior of a flat,
fully clamped circular plate loaded at its center with the following

expression [1 13,1 14]:

 

r = radius of plate
w = Prz D = plate rigidity (Equation 3.3) ( 4 1)
161tD W = central deflection .

P = point load

Classical plate deflection expressions, based on Kirchhoff theory,
assume the stretching and the transverse shearing of the plate is
negligible [115]. These assumptions hold as long as the magnitude of
the central plate deflection is a fraction of the plate thickness
[113,115,116]. For larger deflections, generally greater than one-half
the plate thickness, deformations in the middle surface of the plate
(i.e. stretching) must be considered for accurate results
[113,115,116].

Plates undergoing large (greater than one-half the thickness)
deflections exhibit “geometrically nonlinear behavior” which can only
be accurately described using nonlinear solutions [115].
“Geometrically nonlinear” refers to a change in the load-bearing
behavior of the plate due to changes in configuration during loading
and does not imply material nonlinearity.

Governing equations for the point load deflection of a fully
clamped circular plate were developed by Von Karman in the early
1900’s and require coupled nonlinear differential equations

[117,118]. Equations of this type are generally very difficult to solve

49

and an “exact” point load plate deflection solution has “defied all
efforts” [118]. Several approximate solutions to the large deflection
of centrally loaded circular clamped plates have, however, been
presented [113,115,117-119]. .

Using a strain energy method (Ritz-Galerkin method) Timoshenko
and Woinowsky-Krieger developed the following expression
describing the central deflection of a circular plate with a central

point load [113]:

.r = radius of plate
' E = {lilate lillasktlilc modulus
t = p ate t 'c ess
(N + A N3 ) = B [El-i] P = point load (4.2)
Et N = normalized deflection (w/t)
A,B = constants (Table 4)

Banerjee and Datta [117,120,121] used a modified energy
expression to de-couple the governing equations and develop an
approximate solution to the point load deflection behavior of a
circular plate. The Banerjee et al. solution is virtually identical to
the solution obtained by Timoshenko and Woinowsky-Kreiger
(Equation 4.2) with only a slight difference in the constants A and B
for the various plate boundary conditions [Table 4].

Schmidt [118] used a perturbation method to derive approximate
solutions to the large deflection problem which are in excellent
agreement with the approximate solutions of Timoshenko and
Bannerjee [115].

Bert and Martindale used a numerical analysis based on the
energy method to study the point load deflection behavior of fully
clamped circular plates [115]. The numerical results were consistent

with the approximate solutions presented in the literature.

50

Table 4. Values for constants A and B used in approximate solutions
to the point load deflection of circular plates (Equation 4.2).

 

Bannerjee [117] Timoshenko [113]

 

 

 

 

 

Boundary conditions* A B A B
Edge
Clamped immovable .43 .2 17 .443 .217
fifig‘zable .11 .217 .200 .217
Edge
Simply- immovable 1.26 .551 1.43 .552
su orted
pp fififizable .16 .551 .272 .552

 

 

 

 

 

 

 

 

* Boundary conditions are described as follows:

I“

immovable moveable

Clamped

 

edge immovable - No rotation or in-plane movement at boundary.
edge moveable - No rotation at boundary, unconstrained in-plane movement

Simply-supported.

   

immovable moveable

edge immovable - Free to rotate, no in-plane movement at boundary.
edge moveable - Free to rotate, unconstrained in—plane movement.

51

Experimental data for the very large (>1.5 t) deflection of
centrally point loaded fully clamped isotropic circular plates is
unavailable in the literature so the approximate solutions to this
problem have not been compared to experimental results [115].

Experimentally observed deflections tend to be larger than those
predicted by the theoretical approximations (i.e. equation 4.2),
especially for clamped plates, which is attributed to the difficulty in
obtaining “theoretical” boundary conditions (i.e. absolutely no
bending, rotation, or slipping at the boundary of a fully clamped
plate) [115,117].

52
II. EXPERIMENTAL PROCEDURE

5.0 Diamond growth parameters

Diamond films for this study were grown using a microwave
plasma assisted chemical vapor deposition MPACVD process.
Growth parameters for the diamond film from which specimens A - F
were obtained (wafer 1) are unfortunately unknown. Deposition
parameters for the diamond film grown on wafer 2 (specimens 6 - 21)

are presented in Table 5.
5.1 Specimen preparation

The diamond coated silicon wafers were cleaved into 1cm squares
using a razor blade. The cleaving process involved the placement of
the wafer on a paper towel with the diamond side up. A crack was
initiated on an edge of the wafer using a razor blade and then
propagated by applying pressure with the razor blade. The position
of the 1cm square Specimens with respect to the wafer was recorded
for specimens 6 - 21 as well as the position of any large fragments

that were produced (Figure 15).
5.2 Pre-dimple specimen mounting

The 1cm square specimens were secured using a thermoplastic

wax to the stainless steel cylindrical base of a dimpling instrument

53
Table 5. Parameters for MPCVD diamond depositon on wafer #2 [126].

 

 

 

 

 

 

 

 

 

Single crystal (100) p-type silicon wafer r = 5 cm, seeded
substrate with diamond using a photolithographic process [127].
microwave power 1820 watts at 2.45 GHz
chamber pressure 40 Torr
substrate temperature 840°C
H2 flow rate 400 sccm
CO flow rate 3 sccm
CH4 flow rate 5.5 sccm
deposition time 8 hours
weight gain 91 mg

 

 

 

 

 

diamond side up

  

 

 

 

Figure 15 . Relative position of specimens 6 - 21 with respect to half-wafer
#2. Portions of the half-wafer which were not used in the deflection study con-
sists of specimens which were destroyed during processing or fragments
unsuitable for producing diaphragm specimens.

54

(South Bay Technologies, Temple City, CA) used for TEM sample
thinning (Figure 16). The base was heated on a hotplate set at 75°C.
A small amount of thermoplastic wax (~0.1g) was placed in the
center of the base and allowed to melt, forming a bead. The base was
removed from the hotplate and placed in a shallow dish of water to
cool. The 1cm square Specimen was pressed into the wax and
centered on the base using fingers before the wax had a chance to
harden. Moderate pressure (~5 N) was maintained on the specimen
using fingers until the wax completely hardened. The sample was
visually checked for level with respect to the base. If the specimen
appeared to be out of level, the base was reheated and the specimen

was again pressed into the softened wax. -
5.3 Polishing

While attached to the dimpler base, the silicon surface of the
specimen was polished using polishing wheels and 511m, 0.3um and
0.05pm alumina grit respectively. Polishing of the Si surface results
in a more uniform etch with less pitting or other etching related
defects as compared to unpolished specimens but is not critical to the

specimen preparation process.
5.4 Dimpling

After polishing, the base was secured to the dimpling instrument.

The dimpling of the specimens was performed using a 0.5N load,

 

diamond/
Sl waferfl. melted
wax

dimpler

base \ _>

   

 

 

 

Figure 16. Mounting of diamond/silicon specimen on dimpler base using
thermoplastic wax. '

 

    
 
 
 
   

alumina slu
rry , ~ wood applicator

dimpling wheel
\_>
\ H

specimen

 

dimpler base
(20 rpm)

 

 

 

Figure 17. Schematic of dimpling process.

 

dimple d region silicon substrate

 

 

 

 

fi
diamond film

 

 

 

Figure 18. Diagram of dimpled region in the silicon substrate for specimens
A - F. Specimens obtained from wafer #2 (6-21) have a 540 um substrate and
are dimpled to a depth of 490 pm in a similar fashion.

56

20rpm base rotation, 90rpm wheel speed and a slurry of glycerol and
600 grit aluminum oxide mixed 5 to 1 respectively by weight (Figure
17-18). Specimens A - F were dimpled using a brass wheel 10mm in
diameter and 0.8mm in thickness. Specimens 6 - 21 were dimpled
using a brass wheel 15mm in diameter and 1.3mm in thickness. The
wheel was secured to the dimpling axle and the base was carefully
centered beneath the wheel using the stage positioning knob. The
counterbalance on the dimpling arm was adjusted to provide a 0.5N
load. Base and wheel rotation was initiated and the arm lowered
until the wheel made contact with the specimen.

The slurry was applied to thewheel using a wooden rod until the
Wheel was completely coated in slurry (~0.5cc). The depth sensor on
the dimpling instrument was adjusted to correspond with the top
surface of the sample and the attached digital micrometer reset to
zero. The depth sensor, which consisted of an electrical contact
between the dimpling arm and a peg on the micrometer was adjusted
to a distance of .25mm for specimens A - F with substrate thickness
of .275mm and .49mm for specimens 6 - 21 with substrate thickness
of .54mm. The dimpling process was automatically terminated when
contact between the sensor and dimpling arm was made.

The dimpling process required approximately 20 minutes for
specimens A - F and 100 minutes for specimens 6 -21. The slurry was '
removed with a water rinse followed by immersion in acetone and air
drying. In order to reduce the risk of damage to the diamond film
during dimpling and handling, dimple depths were maintained such

that roughly 50pm of silicon substrate remained between the bottom

57

of the dimple and the diamond film. The dimpling process produced
a “pseudo-hemispherical” dimple with a flat circular bottom (Figure
18). The radius of the pseudo-hemispherical dimple corresponds to
the diameter of the respective dimpling wheel while the diameter of
the flat dimple bottom corresponded with the dimpling wheel width
(0.8mm for specimens A - F and 1.3mm for specimens 6 - 21) and any
error (assumed to be less than ~.5mm) in the centering of the
specimen. Repeated dimpling of the specimens using the same brass
wheel produced a measured decrease in the wheel diameter. The ‘
final diameter of the 15mm brass wheel after dimpling over 15
specimens was measured to be 12.8mm. The reduction of the
dimpling wheel is attributed to mechanical grinding and the rate of
reduction is assumed to be linearly related to the circumference of
the dimpling wheel. The resulting radius of the pseudo;
hemispherical dimple is also expected to decrease with successive
specimens corresponding to the reduction in dimpling wheel

diameter. Samples 6 - 21 were dimpled in numerical order.
5.5 Pre-etch mounting

The specimen was removed from the dimpler base by reheating on
the hotplate and sliding off the sample when the wax became
sufficiently soft. The specimen was soaked in acetone for 30 minutes,
gently rubbed with fingers, then rinsed with acetone to remove any
wax which may have adhered to the diamond surface. Following the

acetone rinse, the specimen was immersed in methyl alcohol and

58

allowed to air dry.
5.5a Mounting specimens A - F (Figure 19).

A 3mm section was cut from a glass tube with a 7mm inner
diameter and 1mm wall thickness using a low-speed diamond saw
(Isomet, Buehler, Lakebluff, IL). The ends of the glass tube were
ground smooth using 600 grit silicon carbide paper. A 1cm square
glass plate 1.2mm in thickness, cut from a microscope slide, was
glued to one end of the 3mm tube using Torr Seal (Varian Vacuume
Products, Lexington, MA) epoxy. A wooden rod was used to apply a
thin continuous bead of the Torr Seal to the end of the glass tube.
The tube was then pressed onto the glass plate. A 50g weight was
placed on the tube to maintain pressure between the tube and base
while the Torr Seal was allowed to harden for 1 hour at room
temperature. A thin continuous head of Torr Seal was applied to the
other end of the glass tube which was then lightly pressed onto the
diamond side of the specimen and centered above the dimple. A 50g
weight was placed on the base and the Torr Seal was allowed to
harden for 1 hour. Torr Seal was then applied around the edges of
the sample and to all exposed diamond surfaces using a wooden
applicator. An additional head of Torr Seal was applied around the
joints between the tube,'base and sample, to ensure the etchant could
not leak into the tube. N 0 Torr Seal was applied to the silicon (top)
surface of the specimen and any overflow of Torr Seal from the edges
was removed from the top surface with a razor blade. The Torr Sea]

was allowed to cure for 24 hours at room temperature.

59

5.5b Mounting specimens 6 - 21

A long (~8cm) glass tube (7mm inner diameter, 1mm wall
thickness) was attached to the silicon substrate centered above the
dimple (Figure 20) using a head of Torr Seal epoxy applied in a
manner similar to that for specimens A-F. The Torr Seal was

allowed to cure for 24 hours at room temperature

5.6 Etching

An etching solution of 10 molar KOH was prepared by placing 11g
anhydrous KOH pellets in a 50ml Pyrex beaker and adding 14ml

deionized water.
5.6a Etching specimens A - F

The 50ml beaker was placed in the bottom of a 2000ml jacketed
beaker containing 200ml distilled water. A constant temperature
circulator (Fischer Scientific model 800, , which pumped distilled
water through the walls of the jacketed beaker was started and set to
60°C. A watchglass was placed over the 50ml beaker to prevent
water droplets. which condensed on the lid of the jacketed beaker
from falling into the etchant.

The temperature of the water bath inside the jacketed beaker was
monitored by a mercury in glass thermometer placed through a

stopper in the lid of the jacketed beaker. After the temperature of

60

 

dimpled specimen

diamond surface

 

  
 

glass tube
bead of Torr sea]

glass base

 

 

r ,,,,,,,,,,,,,,,,,,,,,,, ’1; ,,,,,,,,,,,,,,,,,,,,,,,,,,, a .......... dlfill

Slde VleW Si substrate

 

Torr Seal

   
  

      

diamond film

\ glass tub/

 

 

 

Figure 19. Diagram of pre-etch mounting procedure for specimens A - F.

 

bead of
Torr Seal
glass tube diamond side

 

—+

 

 

dimple

 

 

 

Figure 20. Diagram of pre-etch mounting procedure for specimens 6 -21.

61

the bath had stabilized the circulator was adjusted to bring the bath
temperature to 60°C as read by the thermometer in the bath. The
sample was then placed in the beaker containing the KOH etchant.
The sample was etched until a diamond diaphragm of the desired
size (1mm to 2mm in diameter) was exposed. The etching process
was visually monitored. Etching times ranged from 4 to 8 hours,
depending upon the depth of the dimple and the final size of the
exposed diamond diaphragm. After removal from the etchant the
sample was placed in a 100ml beaker containing deionized water at a
temperature of 60°C. The beaker containing the water and sample
was removed from the jacketed beaker and allowed to cool to room
temperature. After soaking for at least 1 hour, the sample was

immersed in acetone and allowed to air dry.
5.6b Etching specimens 6 - 21

The ~8cm glass tube with attached specimen was hung from the
side of a 250m] beaker partially filled with deionized water (~200 ml)
such that the open end of the glass tube was above the water line and
the specimen was immersed in water. The beaker was then placed
in the 60° C bath (see previous section) and the water temperature
inside the beaker was allowed to stabilize. KOH etchant (~ 2ml), as
prepared for specimens A-F, was placed in the glass tube attached to
the specimen using a pipette. The beaker was replaced into the 60° C
water bath inside the jacketed beaker. Etching times ranged from 4

to 6 hours. Several of the specimens became “unglued” from the

62

tubes during the etching process. When this occurred the specimen
was re-attached to the tube and the etching process repeated.

After the desired dimple diameter was attained, the beaker
containing the tubes and specimens was removed from the bath. The
KOH was poured from the tubes which were then flushed with
deionized water. After thoroughly flushing, the tubes were filled
with deionized water and the specimen was allowed to soak 1 hour.

After the etching process, the specimens were twisted off the glass
tube using fingers. If the bond between the glass tube and specimen
could not be broken with a moderate amount of force (less than
approximately .5 ft-lb) then the glass tube was cut ~3mm above the
sample using a low-speed diamond saw. After cutting the specimen
was rinsed in warm soapy water to remove any cutting oil, followed
by a rinse and soak in methyl alcohol. After removal from the alcohol
the specimen was allowed to air dry. After drying, the open end of
the attached glass tube was glued to a 1cm square glass plate
following the method described for specimens A - F.

Specimens which were removed from the glass tube by twisting
were re-mounted on a 3mm glass tube following the procedure
described for specimens A - F.

After the mounting procedure was complete, specimens A-F and 6
- 21 were virtually identical with the exception of substrate thickness
(257 and 540 um respectively) and the exposed surface of the
diaphragm. Specimens A - F were prepared such that the substrate
side of the diamond film was exposed while the faceted surface of the

diamond film was exposed for specimens 6 - 21 (Figure 21).

63

 

150nm

 

 

 

 

 

Figure 21. Optical micrographs of diaphragm specimens. (A) Specimen A
from wafer#1, indented into the substrate side of the diamond. (B) Specimen
16 indented into the faceted (top) diamond surface (fractured by indentation)

64

6.0 Diaphragm morphology analysis

Visual inspection of the diamond diaphragm specimens A - F
indicated the existence of a “wrinkling” and “blistering” effect. Using
a fiber-optic lamp to apply light at various angles while viewing the
sample under an optical microscope provided further evidence of a
buckled diaphragm morphology. A Laser scanning confocal
microscope (LSCM, Appendix A) was used to nondestructively
investigate the morphology of several diamond diaphragms. The
Diaphragm morphology was attributed to the release of compressive

residual. stress in the films by the buckling of the diaphragm.
6.1 Laser scanning confocal microscope (LSCM) setup

The diamond diaphragm sample (Figure 22) was placed on the
stage of the LSCM and the surface was brought into focus using an
eyepiece and 10x objective. A single line argon ion laser was used as
the source of illumination with the LSCM set in reflecting mode.
Using a 10x objective and 20x electronic enhancement the surface of
the diaphragm was viewed on an attached color monitor. The
dimensions of the circular diaphragm were recorded using on-screen

cursors and length readout provided by the LSCM software.
6.2 LSCM line scan analysis

After the diaphragm dimensions had been recorded, the
approximate center of the diaphragm was determined by the

intersection of perpendicular diameters. Using the package software

 

Q)

6i

 

65

provided with the LSCM a line scan was taken across the center of
the diaphragm.

To perform a line scan, the laser on the LSCM rasters across a
single line defined by the user with an on-screen cursor. As the laser
rasters the specimen the motorized stage of the LSCM drops down
bringing the specimen out of the focal plane of the optical objective.
The motorized stage is then stepped up in 0.1um increments taking
the sample through the focal plane of the optical objective. The
reflected intensity of points along the scanned line is electronically
recorded in conjunction with the vertical position of the motorized
stage.

After the line scan has been completed, a plot of the points of
highest reflected intensity and their relative vertical position is
presented on the monitor (Figure 23). The points of highest reflected
intensity occur when the corresponding point on the diaphragm is “in
focus”. The plot of the points of highest intensity provides a cross-
sectional or “in plane” view of the diamond diaphragm along the
scanned line. The accuracy of the method is believed to be within i
1pm based on the thickness of the diamond film and the ~5um focal
length of the 10x objective lens used. The use of an objective lens
with a shorter focal length (typical for larger magnifications) would
reduce this error but allow only portions of the diamond diaphragm
cross-section to be viewed on the monitor. Line scan information
would then have to be “pasted together” in order to analyze the
diaphragm morphology making the use of a larger objective

impractical (i.e. using a 50x objective would require 5 line scans to

66

 

 

2mm

 

 

 

Figure 22. Micrograph of diamond diaphragm specimen mounted on glass
base and support.

 

 

 

 

 

Figure 23. LSCM line scan profiles of diamond diaphragm specimen A.
The bi-model morphology is attributed to circumferential buckling.

67‘
span the diameter of the diaphragm).

If the line scan showed the Specimen was “tilted” or out of level
with the stage of the LSCM then transparent plastic “Scotch” tape
was used to shim the Specimen into level. The process was repeated
until the specimen was as level as possible. Having the specimen
level was not imperative to produce accurate results but aided in the
manual data collection procedure and provided an improved
appearance of the line scan data during the data acquisition process
(Section 6.3).

Line scans were taken at specified intervals above and below the
center line scan. After the line scans spanned the entire diaphragm
the specimen was manually rotated 90° (using fingers) and the
process repeated (except for the tilt correction procedure). A
schematic of the line scans across the diamond diaphragm is depicted
in Figure 24. All line scan information was recorded electronically
by the LSCM.

Deflection information could be taken directly from the LSCM
monitor using the on-screen cursors. Electronic enhancement of the
line scan profiles by increasing the magnitude of the vertical
displacement by 5x aided in the acquisition of morphology and
deflection information.

Prior to the manual movement of the specimen on the LSCM stage
the position of several “landmarks” or distinct features of the
diaphragm and silicon rim were recorded. The landmarks could then
be used to reposition the diaphragm after movement or removal from

the stage.

68

 

 

1 A‘Il-L '

2 71......“

3 III-IIIIIK

4 III-II...-

5 III-III... 1295“!“

6 III-II...-

7 ‘IIIIIIII'

8 ‘IIIIIIIIV

9 ullllllu
“.." v

10 11 12 13 14 15 16 17 18

 

 

 

Figure 24. Position of line scans across diamond diaphragm specimen A
taken during LSCM analysis of the diaphragm morphology [122].

 

 

lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll

\

Pixel locations

    

 

 

 

Figure 25. Schematic of line scan profile depicting buckled length
measurement technique.

69
6.3 LSCM data analysis

All line scan information was transferred to a graphics
workstation for analysis using VoxelView (Vital Images, Fairfield,
Iowa) package software. The line scan information was
electronically reproduced on the workstation monitor and manually
analyzed by J. Mattavi [122]. Data from the line scan profiles was
acquired using pixel locations on the workstation monitor.
Approximately 30 data points were taken from each line scan profile.
The data points were manually entered into a data file to be analyzed
with a PC.

The length of the buckled line scan profile was determined by
summing the distance between consecutive data points (Figure 25).
The length of the line scan profile was compared to the “un-buckled”
cord length to provide a value for the buckling strain along that

particular cord.

_ buckled length
8 — cord length

 

(6.1)

Thorough LSCM analysis was performed on only two diamond
diaphragms, specimen A and a specimen obtained from a CVD
diamond coated Si wafer which was not used in this study. During
the early “learning” stages of LSCM morphology measurement, the
central deflection of several diamond diaphragms was investigated
but only limited information (i.e. general trends) on the diaphragm
morphology was obtained during these measurements. No

morphology measurements were performed on specimens 6 - 21.

70

Table 6. Results of LSCM line scan analysis of diaphragm specimen A [122].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

line # (figure 25) arc length (um) cord length (um) strain(x10°4) data points
1 867.68 867.09 6.90 20
2 1064.25 1063.77 4.51 20
3 1163.88 1163.50 3.22 20
4 1255.47 1254.92 4.34 24
5 1252.81 1252.15 5.31 28
6 1247.38 1246.61 6.19 32
7 1183.86 1182.79 9.01 29
8 975.50 975.04 4.68 26
9 782.15 781.14 12.9 21
10 814.59 814.38 2.52 21
11 1097.44 1096.92 4.78 25
12 1172.27 1171.71 4.87 31
13 1272.10 1271.43 5.28 35
14 1280.45 1279.74 5.54 37
15 1272.08 1271.43 5.13 35
16 1172.31 1171.71 5.14 31
17 1097 .43 1096.92 4.60 25
18 814.83 814.38 5.50 21

 

Average apparent strain induced by buckling = 5.58 x 10‘4

 

71

7.0 Nanoindentation of diaphragms

A Dow Interfacial Testing System designed for composite fiber
debond testing was used to apply a point load to the diamond
diaphragm specimens. Details of components in the system are

provided in Appendix A.
7.1 Mounting for nanoindentation

A phenolic ring (Buehler, Lakebluff, IL), 2.5cm outer diameter,
2.2cm inner diameter and 1.9cm in height, was filled to a level
approximately 4mm below the top of the ring with Epofix epoxy
(Struers, Westlake, OH). Plastic masking tape was placed across the
bottom of the ring and the Epoxy was mixed and poured into the ring.
The ring was placed on a level surface and the epoxy was allowed to
harden for 8 hours at room temperature. The hardened epoxy
produced a smooth, level surface inside the ring to which the
specimen was superglued. Superglue was applied to the corners of
the glass specimen base which was positioned inside the phenolic

ring and pressed into place using fingers.
7.2 Diameter measurement and center point location
The phenolic ring/specimen was secured in the motorized stage of

the nanoindenter using three set screws (Figure 26). The

diaphragm, which was parallel to the nanoindenter stage, was

72

 

' . . XObjective '

indenter tip

specimen

 

_ l " /—\ phenolic ring

     

set screw

.v'.MoroRlzsn:srAGE'

 

 

 

Figure 26. Diagram of specimen situated in stage of nanoindenter.

73

manually positioned beneath the optical microscope of the
nanoindenter. The vertical position of the stage was manually
adjusted to bring the diaphragm into the focus of the 50x objective
lens. The optical image was electronically magnified an additional
20x (total of 1000x) and displayed on a black and white monitor.

The motorized stage of the nanoindenter was equipped with
manual motor controls and could also be controlled using the
attached PC and keyboard. The motorized stage has an X and Y (the
plane of the diaphragm) step resolution of lum and Z (vertical) step
resolution of 0.04pm. The position of the stage was displayed by the
stage motor controls. Using a marker on the monitor, the relative
location of any point on the diaphragm could be determined from the
position of the motorized stage.

To measure the diaphragm diameter, the center line of the
diaphragm was visually approximated. The distance across the
approximate center line (diameter 1) was determined from the
position of the points on the rim of the diaphragm. The midpoint of
the approximate center line was determined and the diameter of the
diaphragm perpendicular to and passing through the midpoint of the
center line was measured (diameter 2). The midpoint of diameter 2
was determined and the diameter of the diaphragm perpendicular to
and passing through the midpoint of diameter 2 was measured
(diameter 3). This procedure was repeated until the center points of
consecutive diameter measurements were in close proximity (20pm
or less), which was usually after the second or third diameter

measurement (Figure 27). Measurement of the diaphragm diameters

74

45° from the center line and passing through the approximated
midpoint of the diaphragm was also performed. The average
diaphragm diameter was determined from the average of the four
diameter measurements. The center point of the diameter was
approximated from the centers of the four measured diameters.

A measurement of the vertical displacement of points on the
diaphragm could be made using the focal plane of the 50x objective in
combination with the motorized stage by recording the Z position of
the stage at the point where the diaphragm was in focus. The focal
length of the 50x objective is ~2um. Combining the focal length with
human error in determining when the surface is “in focus”, limits the
measurement of the initial (residual stress induced) central
diaphragm deflection on the nanoindenter to approximately 4pm (100
vertical steps). The relative central deflection of the diaphragm was
determined from the approximate vertical position of points around
the rim of the diaphragm and the approximate vertical position of
the center point. The degree of “tilt” of the specimen was also
approximated from the relative vertical position of the points around
the rim of the diaphragm.

For specimens 6 - 21, which had the faceted (top) diamond surface
exposed for indentation, the boundaries of the diaphragm could not
be distinguished by the optical microscope on the nanoindenter. By
turning off the light in the microscope as well as the roomlights and
using a penlight to “backlight” the relatively transparent diamond
diaphragm, the boundaries of the diaphragm could be distinguished
by the intensity of transmitted light (the opaque silicon substrate

75
effectively blocked the light, defining the rim of the diaphragm).

7.3 Deflection of the diamond diaphragms (Figure 28)

After the center of the diaphragm was located the stage was
moved to position the diaphragm center beneath an indenter tip
connected to the 50x objective. The position of the indenter tip with
respect to the focal point of the objective lens (marker on the monitor
screen) was determined by a prior calibration procedure.

The Interfacial Testing System (ITS3) software package, designed
for automated fiber debond testing, was used to automatically control
the motorized stage position and collect the load-deflection data. The
following parameters defined the motion of the stage during the

deflection of the diaphragm:

step size (vertical) = 0.04pm

step rate = 4 steps/sec

maximum allowable load = 2g

loading increment = 1g (defines number of loading cycles)

load drop for debond (fracture) 0.2g

During positioning, the stage of the nanoindenter was moved at a
rate of approximately 500 steps per second for all directions (X, Y,
and Z). The stage would position the indenter tip above the center of
the diaphragm and then drop down a predetermined distance

(determined by the prior calibration) before attempting data

76

Si SUBSTRATE

initial guess for Centerline

 

\ djaph ragm center

a proxrmated from
c uster of diameter
centers.

 

 

Figure 27. Schematic of diaphragm center location procedure and diaphragm
radius measurement. Diaphragm is purposely drawn “non-circular” in order
to illustrate the procedure.

 

substrate

indenter tip

  

/'

diamond diaphragm

 

fl

stage motion

faceted (top) side
of diamond film

 

 

 

Figure 28. Schematic of diaphragm deflection (specimens A - F). For
specimens 6 - 21 the substrate support was below the diamond diaphragm and
the indenter tip was in contact with the faceted diamond surface.

77

acquisition. The software was capable of handling only 300 steps
(12pm) of vertical stage travel during data acquisition. Deflections
in excess of 12pm required manual data collection or additional runs
with the diaphragm partially deflected before initiating data
acquisition. Contact with the diaphragm was defined by the first
non-zero load measured by an electronic balance attached to the
stage of the nanoindenter. During automatic measurements all load-
deflection data was recorded by the computer, printed, and stored on
a floppy disk.

The motorized stage of the nanoindenter had a maximum vertical
travel length of 40,000 steps (1.6mm). The accompanying ITS3
software allowed for only 20,000 steps (0.8mm) of vertical stage
travel during positioning and data acquisition. The allowable
working distance was defined by the maximum stage travel of
1.6mm. The allowed working distance for automatic data acquisition
(0.8mm) was defined by the ITSS software. Included in the working
distance was an “indenter clearance” providing a margin of safety
between the indenter tip and the surface of the sample during the
positioning of the stage. Collisions with the specimen during stage
positioning could damage the indenter tip and/or motorized stage
and care was taken to avoid such a collision. If sufficient clearance
between the indenter tip and specimen could not be attained using
the working distance defined by the ITS3 software then manual stage
positioning and data acquisition was required.

Manual operation of the nanoindenter during positioning and data

acquisition was performed using the motorized stage controls

78

(buttons). The diaphragm measurement and centering process is as
previously described. After locating the center of the diaphragm, the
stage was dropped to provide clearance for the indenter tip. The
stage was then moved a predetermined amount to position the
indenter tip above the center of the diaphragm. The stage was
moved vertically by an amount determined by the prior calibration
and the additional “clearance” distance, bringing the indenter tip
close to the surface of the diaphragm. The stage was then moved
vertically at approximately 4 steps per second (0.04pm each) by
manually pressing the vertical control key at the specified rate.
Contact with the diaphragm was determined from the stage position
at the first registered load. Load values were read and indicated
vocally by the operator and recorded using an audio tape. The
recording was done at twice normal tape speed. Replaying the tape
at normal speed aided in the collection of data. By counting the
number of audible “clicks” emitted by the stage control, the position
of the stage at the point where the appropriate load was vocally
recorded could be determined. Since the step rate is fairly slow and
the step size is small the error due to human response time is
negligible.

The collection of data for diaphragm deflections in excess of 12pm
was also performed by partially deflecting the diaphragm prior to
automatic data acquisition. The partial deflection of the diaphragm
was attained by increasing the vertical component of the
“calibration” relationship between the focal point and the indenter

tip which essentially “tricks” the nanoindenter into beginning data

79

collection from an already deflected diaphragm. The amount of “pre
data” deflection induced by the indenter tip was approximately 811m
(200 steps) which allowed a total diaphragm deflection of roughly
20pm. A 20pm deflection was beyond the failure point of all the
diamond diaphragms tested. The data for the pre-deflected
diaphragm was shifted to correspond with the data in which no
initial deflection was induced before data collection. The measured

' deflection values for pre-deflection data was Shifted by an amount
that brought the measured load values for the data sets in agreement

for deflection values where the data overlapped.
7.4 Nanoindenter / specimen compliance

The compliance of the nanoindenter and sample during the
diaphragm deflection measurements was estimated using two
specifically prepared specimens. The compliance specimen was
prepared with the method used in preparing the diamond diaphragm
specimens with the exception of the grinding and etching procedure.
The silicon surface was polished using polishing wheels and alumina
grit (5, 0.3, and 0.05pm respectively). The approximate center of the
specimen, as determined by the underlying circular glass tube, was
located and indented with a force-of 0.25N (approximately 10 times
the typical load for diaphragm fracture). Silicon has been shown to
exhibit anomalous behavior during indentation due to a stress
induced phase transformation [123]. The anomalous behavior during

indentation of the silicon substrate was also observed in this study.

80

The initial 0.25N indent provides a site where further indentations
at lower loads would not be expected to cause further phase
transformation. Several indents were made in the initial depression
using parameters (step rate, etc.) identical to those for diaphragm
deflection. The load versus deflection of the sample was recorded for
each indent. The entire procedure was repeated at two additional
locations in the vicinity of the sample center and on the second
compliance sample. An estimate of the elastic response of the silicon
in the vicinity of the indenter tip during indentation of the
compliance specimen was made by comparison with low-load
indentation data obtained by Pharr [123]. The elastic response of the
silicon substrate during indentation in the Pharr study was less than
0.1um for the range of loads used in this study (less that 40 mN).
Although the indenter used in the Pharr study (Berkovitch) was not
identical to the indenter tip used in this study (10pm hemi-spherical)
the elastic response of the silicon is still expected to be negligible for
indents made in the compliance specimens.

Compliance data was also collected from indents made on the
diamond surface of specimens 8, 11, 12, 14, and 21 in away from the
diamond diaphragm. Loads during the compliance test on the
faceted diamond surfaces were limited to less than 60mN in order to
reduce the possibility of indenter tip damage. 60mN is beyond the
range of maximum loads sustained by the diamond diaphragms

before failure.

81

8.0 Off-center diaphragm loading

To study the effect of off-center point loading of the diamond
diaphragms, specimen 9 was loaded at various distances (0 to 400nm)
from the center of the diaphragm. In order to prevent diaphragm
failure before all the loadings could be performed, the maximum load
was maintained at 30mN, which produced a central deflection of
approximately 13pm. Figure 29 provides a schematic of the off-

center loading of diaphragm specimen 9.

82

 

   
 
  

diamond diaphragm

 
   

400 um

 

V r

 

L
v

V

1570um

 

 

 

Figure 29. Schematic of off-center loading of diaphragm specimen 9.

83
9.0 SEM, TEM, and X-ray analysis of diamond film

After load-deflection data was collected for the diamond
diaphragms, fragments of the diaphragms were collected for SEM'
analysis. The collection of the diaphragm fragments was performed
using two methods. One method involved the use of tweezers to
fracture the diaphragm and collect the resulting diamond film
fragments (Figure 30). The fragments were secured “on end” to a
circular aluminum SEM stub coated with a low vapor pressure
adhesive tab. The collection and handling of the diaphragm
fragments with tweezers was very tedious and the diamond film
fragments were often destroyed (broken into pieces too small to
handle) during the process.

A second, somewhat less tedious method, utilized a hammer to
obtain fragments of the diaphragm for SEM analysis (Figure 31).
The diaphragm specimen was placed on a table with the diaphragm
side up. An aluminum SEM stub was placed on the specimen and
centered over the diaphragm. A sharp hammer blow(s) to the
aluminum stub resulted in the fracture of the silicon substrate and
the debonding of the silicon substrate from the glass tube. The
specimen tended to fracture into “pie shaped” segments and large
pieces of the silicon substrate with portions of the diamond
diaphragm still attached were created. The silicon/diaphragm
fragments could be easily handled with tweezers and positioned on
an aluminum SEM stub. Conductive (colloidal graphite) cement was

used to secure the silicon/diamond fragments to the SEM stub.

84

 

Top View Of
Al SEM Stub

    
    
 

'\ adhesive

tweezers

  
   

fractured
diaphragm

diamond film
fragments

 

 

 

 

Figure 30. Diagram of “tweezer method” for the mounting of diamond film
fragments for SEM examination.

 

gianilond
lap ra
fragrnen'clzIsn

\ “ Vt /
graphite
cement

1 Si substrate /7

tweezers

Si substrate
fragments

     
  

 

 

 

Figure 31. Diagram of the “hammer method” for the mounting of diamond
film diaphragm fragments for SEM examination.

85

Although this method is much less tedious than the first and often
produced better results, it also resulted in an occasional catastrophic
failure of the entire specimen. If the specimen did not fracture as
expected, tweezers were then used to collect the diaphragm
fragments.

The aluminum SEM stubs with the diamond fragments were
placed in an Emscope sputter coater to be coated with gold. The
stubs were tilted slightly (~ 20°) in the sputter coater so as to allow
the face of the fragments to be adequately coated with a layer of gold.
After approximately 15nm (for horizontal surfaces) of gold had been
deposited the specimens were tilted slightly in the opposite direction
and another 15nm of gold was applied. The “double coating” of the
specimens was performed to ensure adequate conductivity of the
diamond fragments during SEM analysis.

After gold coating, the stubs were placed in a JOEL35 SEM.
Using the tilt and stage position controls, the diamond diaphragm
fragments were located and oriented with the fracture surface
perpendicular to the electron beam. Alignment of the diamond film
fragment with the electron beam produced significant image
distortion due to edge and other SEM specimen/beam interaction
effects. The image distortion was used to locate the stage tilt angle
at which a particular fragment was aligned with the beam; After
alignment, the stage was tilted an additional 3° to improve image
quality for film thickness measurements.

The thickness of each fragment was measured at several locations

directly from the CRT on the SEM using a plastic ruler and the

86

micron markers provided by the SEM. Several micrographs of the
fracture surface of the diaphragm fragments were also taken. The
average value of the fragment thickness measurements was used as
the diamond diaphragm thickness.

Prior to SEM analysis, a magnification calibration of the SEM
was performed using a copper calibration disc (Ted Pella Associates),
which is essentially a tiny ruler with 10pm line spacing. Any
discrepancy in the indicated magnification was noted and used
during the diaphragm thickness measurements. The working
distance was found to be important with respect to the SEM
magnification calibration. Specimen fragments to be analyzed were
positioned at or very near the recommended working distance to

' insure accurate magnification indication.

Specimens for TEM analysis were prepared from films obtained
from wafer #1. Free-standing diamond film fragments (3mm x 3mm)
were prepared by etching the substrate in 10 molar KOH at 60°C.

' The diamond fragments had a thickness of roughly 1.5mm and
required thinning prior to TEM analysis. Thinning of the fragments
was preformed using an argon ion mill.

Analysis of the diamond film in a Phillips 80 TEM consisted of
brightfield and axial darkfield imaging, as well as selected area
diffraction (SAD).

X-ray diffraction was performed on a diamond film obtained from
wafer #1. The diamond film, still on the silicon substrate, was glued

to the aluminum specimen holder of a Scintag XDSZOOO and a 20

scan of the specimen was performed.

87

10.0 Point load deflection of circular glass discs

To test the ability of the nanoindenter and the load-deflection
procedure for the measurement of elastic modulus, a glass disc
specimen was prepared and tested. The circular glass disc specimens
(Figure 32) were prepared using glass coverslips (thickness = .145-
.210mm), superglue, and two rectangular glass plates (76mm x
51mm x 1mm). Circular holes (18mm and 23mm in diameter) were
cut in the center of two glass plates using a diamond hole saw. An
additional glass plate was superglued to the annular glass plates for
added rigidity.

The deflection of the glass plate was performed using the
nanoindenter and a method similar to that used for diaphragm
deflection. The glass plates could not be loaded to fracture without
fear of damage to the nanoindenter. Maximum load for the glass
diaphragms was 2.6 N.

Two diaphragms were prepared by supergluing coverslips over the
18mm hole. Another diaphragm was prepared by placing (no glue) a
coverslip over the 23mm hole in the glass plate.

After deflecting the glass diaphragms with the nanoindenter, a
compliance test was performed on the glass plates. The glass '
diaphragm sample was placed over the stage of the nanoindenter
with the “backside” of the glass plate facing upward. Three
indentations were made in the approximate center of the glass plate.
Load-deflection data was collected by the nanoindenter and stored on

a floppy disc.

88

 

76mm

51mm 7 m

 

 

 

 

 

 

 

 

glass microscope slides

 

glass cover slip

 

surfirglue

1/ %e
I

1.0mm —[ l I g

I: 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 32. Diagram of glass diaphragm fabrication process. Specimens were
prepared with and without glue around the rim.

Bar—‘1‘:-_ "

89
III. RESULTS & DISCUSSION

11.0 Visual, SEM, TEM, and X-ray diffraction observations

Actual diamond films obtained from wafer #1, and wafer #2, are
presented in Figure 33 along with an additional diamond film which
was used in LSCM buckling measurements but not in this diaphragm
deflection study. The relative “whiteness” or clarity of the diamond
film gives a rough indication of film quality (i.e. darker films are
expected to contain a higher degree of graphitic or non-diamond
carbons). Visual observations of film appearance indicate that the
films used in this study, which are reasonably “white” were of fairly
high quality. '

An optical stereographic microscope with magnifications up to 65x
was also used to view the surfaces of the diamond films. Diaphragms
obtained from wafer #1 (A-F) appeared to be free of foreign materials
(i.e. particulates and residue picked up during processing) but a
random distribution of relatively large (up to 30mm) particles were
apparent on the faceted surface of diaphragms 6 -21 obtained from
wafer #2. The particulates observed on diaphragms 6-21 resisted all
attempts of removal, including rubbing, and when scraped with the
edge of a razorblade (while being viewed under the microscope)
considerable effort was required to dislodge them from the surface of
the film.

Figure 21 (Section 5) shows optical micrographs of typical
diamond diaphragm specimens. All diamond diaphragms exhibited a

90

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 33. (A) Fragment of diamond film obtained from wafer #1 and
corresponding SEM surface micrograph. (B) Fragment from wafer #2 and
SEM surface micrograph. (C) Fragment of diamond film obtained from a
wafer used in LSCM buckling analysis [122] but not in this deflection
study. Included to illustrate differences in diamond film transparency and
surface morphology.

91

high degree of circularity as observed visually, and based on
measurements made using the nanoindenter, the diameters in any
given direction varied by less than 5% for all diaphragms used in this
experiment. '

SEM analysis of the top surface (surface away from the substrate)
showed that the films consisted of highly faceted diamond
crystallites (Figures 34-35). Specimens from wafer #1 had a surface
dominated by (111) planes with twinned morphologies, while the
surface of specimens obtained from wafer #2 had a large percentage
of (100) as well as (111) planes. Surfaces of films obtained from both
wafers is consistent with those of films reported by a number of
researchers in the literature.

A large number of smaller crystallites which do not appear to
extend through the thickness of the film were present in specimens
obtained from both wafers used in this study. These smaller
crystallites are assumed to be the result of diamond nucleation on
the growing diamond surfaces.

The large particulates which were observed under an optical
microscope on the surface of specimens obtained from wafer #2 were
also observed in the SEM. As can be seen in Figures 36 and 37, the
particles are covered with diamond crystallites, which means they
were present before diamond deposition or were introduced during
the deposition process. The nature of the large particulates is
unknown and it is possible that they are made up entirely of diamond
crystallites, but judging by their shape and size (up to 30pm) this

seems unlikely. The presence of the particulates is not expected to

92

 

 

 

511m

 

 

 

Figure 34. SEM surface micrograph of diamond specimen taken from
wafer #1.

 

 

 

5pm

 

 

 

Figure 35. SEM surface micrograph of diamond specimen taken from
wafer #2.

93
significantly influence the deflection behavior of the diamond
diaphragms.

SEM observation of the back (substrate) side of the diamond films
showed a relatively smooth surface with a number of large (up to
~0.2p.m x 211m) voids present between adjoining grains (Figure 38).
The debris present on the substrate side of the films is assumed to be
introduced during post deposition processing but the origin of the
particles is not known. The grain size of the crystallites at the
substrate surface of the films was approximately 1.2um for
specimens obtained from wafer #1 and 111m for wafer #2.

SEM imaging of the fracture surface of the diamond film
diaphragms indicates the columnar structure typical of the CVD
diamond growth process (Figure 39 - 41). The fracture of the
diamond film appears to be inter-granular (along grain boundaries),
as evident by the rough and uneven fracture surface. Figure 41 is a
micrograph of a fractured diaphragm specimen taken in the region of
the silicon rim. The silicon rim of the diaphragms gradually “tapers”
down to the diamond film. This tapering is a result of the specimen
preparation procedure (i.e. the grinding of a hemispherical dimple)
and the effects of the tapered rim on the deflection behavior of the
diaphragm will be discussed in upcoming sections.

A diamond film specimen obtained from wafer #1 was analyzed
using transmission electron microscopy. TEM analysis was intended
to provide insight into the orientation relationship between the
individual crystallites in the diamond films by using selected area

diffraction to discern their relative orientations. Unfortunately, the

94

 

 

100nm

 

 

 

Figure 36. SEM micrograph of specimen obtained from wafer#2 showing
particles adhering to the surface of the diamond film.

 

 

 

10pm

 

 

Figure 37. SEM micrograph of particulate. The diamond coating
Indicates the particles are introduced before (or during) the deposition

95

 

 

lum

 

 

 

Figure 38. SEM micrograph of back (substrate) surface of a diamond film
specimen obtained from wafer #2.

 

 

r"t , \
/ .

V. "'1"
. .I ' ,3

'r
r

 

5pm

 

 

 

Figure 39. SEM micrograph of cleaved diamond film/ Si substrate
obtained from specimen 13.

96

 

 

211m

 

 

 

Figure 40. SEM micrograph of fracture surface of diamond diaphragm 16.

 

 

 

311m

 

 

Figure 41. SEM micrograph of silicon rim supporting diamond
diaphragm A showing the tapering of the silicon substrate to the edge of
the diamond diaphragm.

97

double tilt holder for the TEM used in the study was not operational
during the time the TEM analysis was performed, making the
orientation of the individual diamond crystals virtually impossible to
determine. Diffraction patterns were obtained for numerous
diamond crystallites obtained using the smallest (30pm) SAD
aperture on the TEM. Diffraction patterns indicative of a single
crystal low-index zone (Figure 42) could only be obtained for three of
the largest diamond crystallites (diameters ~ 3pm). Analysis of the
diffraction patterns agreed with the theoretical predictions for a
diamond <110> zone for each of the three diamond crystals from
which they were obtained. Streaking and extra spots around the
diffraction spots corresponding to the <111> direction indicates
twinning parallel to {111} planes. Spot splitting in the diffraction
patterns was also observed and is attributed to the presence of
stacking faults in the diamond crystallites. Axial dark-field images
using diffraction Spots from the diamond <110> zone patterns
provided no evidence of any orientation relationship between the
surrounding crystallites and the crystal from which the low-index
diffraction pattern was obtained. It is interesting to note that the
only low index zone pattern produced was that of the <110> zone,
which agrees with the <110> texturing commonly observed in CVD
diamond films. The TEM analysis of this study, however, is far too
limited to make any conclusions as to the nature of the texturing (if
3113') in the diamond film studied.

Figure 43 is the result of an X-ray 20 scan'of the diamond film

obtained from wafer #1. The relatively small diamond peaks, and the

98

 

 

 

 

 

Figure 42. TEM selected area diffraction pattern taken from a single
diamond grain from a thin film specimen obtained from wafer #1. The
pattern agrees with that of the theoretical <110> zone for a diamond
crystal. Streaking and spot splitting indicate the presence of twins and
stacking faults in the diamond grain. Spots resulting from double
diffraction are also present.

 

 

 

 

300 lllllllllllllllillillllIlllllllLLlLMll'lllillllill
X-RAY 26 SCAN OF DIAMOND
.FILM ON SILICON SUBSTRATE s'°°"“°°’
200— —
.‘2
C
3
O
O
100~ -
Diamond(111)
Diammdtzzof
c IITIIIIIIIIiTjTIIIIIIIl[ITIITITIIIIIIIIIIYYITIIII
30 35 4O 45 50 55 60 65 70 75 80
29

Figure 43. X-ray 20 scan of diamond film on silicon substrate obtained
from wafer #1.

99

large (100) silicon peak is due to the low mass absorption and
relative “thinness” (~1.5um) of the diamond film. The diamond (111)
and (400) peaks are readily distinguishable and occur at the

theoretical Bragg angles for diamond.

100

12.0 Diaphragm morphology - buckling relief of stress.

Visual observations of the diamond diaphragms A - F indicated a
“blistered and wrinkled” morphology. Visual observation of
diaphragms 6 -21 however, gave no indication of any deviation from
“flat”. The apparent shape of the buckled diamond diaphragms (A -
F) is consistent with observations of Argon et al [96] on CVD silicon
carbide films in biaxial compression, grown on single crystal silicon
substrates. The SiC films used in the study by Argon buckled upon
release from the substrate. The morphology of the delaminated
circular SiC “blisters” consisted of a single mode diametral buckling
combined with multi-modal buckling around the circumference. The
buckling of the SiC blisters is attributed to the release of biaxial
residual compressive stress in the film. Upon buckling, Argon et al.
assumed the residual compressive stresses in the SiC were almost
completely relieved [96].

The buckling behavior observed in the diamond diaphragms used
in this study is also assumed to result from the relief of biaxial
compressive residual stress. Based on the buckling criterion for a
clamped circular plate with a uniform in-plane load around the
circumference [124] and the relationship between force/unit edge
length and residual stress, the biaxial compressive stress required to
buckle the diamond diaphragms used in this study was calculated
(Equation 12.1).

NCr = critical force/unit edge length for buckling
D t D 2 plate rigidity (Equation 3.3)
oer = Ncr t = 14.68 72" r = plate radius (12.1)

t = plate thickness
on = critical residual compressive stress ,

101

For diaphragms A - F a residual compressive stress of 5MPa as
calculated from Equation 12.1 is sufficient to buckle the diamond
diaphragms. For specimens 6-12, Equation 12.1 predicts a residual
compressive stress of 15MPa is not enough to produce buckling in
any of the specimens and a compressive stress of approximately
40MPa is required to buckle the most rigid diaphragm used in this
study. Although 40MPa is a fairly substantial stress, it is an order of
magnitude less than the calculated compressive stress of
approximately 500 MPa resulting from thermal expansion mismatch
between the diamond film and substrate (Section 2.1). Due to
intrinsic factors the net residual stress in the diamond film may be
less (or more) than the thermally induced stress, but the presence of
a residual compressive stress in the diamond films sufficient to
buckle the diaphragms is very likely.

Although the rigidity of the diamond films used in this study is
significantly higher than that of the SiC films in the Argon study and
the calculated compressive stress is lower, it is assumed that the
majority of the residual compressive stress in the diamond
diaphragm is relieved upon buckling. The compressive stress in the
region around the rim of the diaphragm can not be relieved by
buckling due to the constraint imposed by the silicon substrate. The
circumferential buckling in the diaphragm was not observed in the
region close to the rim of the diaphragm due to the “clamping” of the
diamond film by the substrate. Circumferential buckling in the
diaphragm was evident in regions less than 50pm from the rim of the

diamond diaphragm. The maximum magnitude of the

102

circumferential buckles as measured by the LSCM was
approximately 311m and occurred at approximately one-third of the
distance between the rim and center of the diaphragm.

Circumferential buckles in diaphragms obtained from wafer #1
were visually observed using the naked eye or a stereographic optical
microscope by holding the specimen at a low angle with respect to the
light source. The number of circumferential buckles observed around
the rim of the diaphragms (from wafer #1) was typically 8 to 12 and
no correlation between diaphragm size and the number of
circumferential buckles was apparent for diaphragms with diameters
ranging from 1200 - 2000um and a thickness of approximately 1.5
um. Circumferential buckling was not visually observed in
diaphragms obtained from wafer #2.

Argon et al. [96] used the wavelength of the buckled SiC blisters
to predict the residual stress in the film. Due to the nature of the
“delamination front” of the growing blister and the relatively low
rigidity of the SiC thin film, the number circumferential buckles in
the SiC blister increased with increasing diameter. Blisters up to
approximately 150nm in diameter and film thickness ranging from
approximately 0.1 to lum were used in the Argon et al. study.

The diameter of the diamond diaphragms, ranging from 1200 -
2000 pm in this study, was defined by the grinding and etching
process. Based on the lack of correlation between the diaphragm
diameter and the number of observed circumferentialbuckles, it is
believed that the number of circumferential buckles which first

initiate in the diaphragm during the etching process is maintained

103

as the diameter of the diaphragm increases. The “steady state” of
circumferential buckles observed in specimens obtained from wafer
#1 may result from the magnitude of residual stress in the diamond
films being insufficient to overcome the diaphragm rigidity and
produce a new buckling wavefront for the range of diaphragm
diameters observed. The method used by Argon et al. to determine
the residual stress in thin films using the wavelength of
circumferential buckling does not seem to be applicable to the
diamond diaphragms used in this study due to the apparent “steady
state” of the diamond diaphragm circumferential buckling with
increasing diaphragm diameter.

Observations of the buckling morphology of diamond diaphragms
with larger diameters used in an associated study by Flowers [125]
showed a complex “rippled” morphology which may result from the
linkup of opposing circumferential buckles producing a multi-modal
morphology across the diameter. The complex morphology of the
diamond films with larger diameters (>3um) would make the
modeling of the deflection behavior much more difficult, thus,
diaphragm diameters were maintained between 1 and 2mm. The
“rippling” of the films was not observed in the study by Flowers for
diaphragms with diameters of 2pm or less.

The magnitude of the single mode diametral buckling in several
diaphragms measured by the LSCM technique (all from wafer #1)
was related to the diaphragm diameter (i.e. larger diaphragms had
greater central deflections due to buckling). LSCM measurement of

central deflections on several diaphragms of various diameters (1200

104

- 2000) indicated that the magnitude of the initial (stress induced)
central deflection was roughly 1% of the diaphragm diameter. The
LSCM measurements were also consistent with observations of
initial central deflections made with the nanoindenter (Section 7 .2).

The majority of the diaphragms which exhibited observable
buckling were “convex” with respect to the faceted surface of the
diamond film after buckling, but a few were observed to be “concave”.
The direction (concave or convex) of buckling had no observable effect
on the morphology of the diaphragm.

In the LSCM line scan analysis of diamond diaphragm specimen A
(Section 6), the average value for the measured strain (Equation 6.1)
in specimen A induced by the buckling of the diaphragm to relieve
the compressive residual stress in the film was ~ 5.6 x 10"4 (Table 6).

The average measured strain induced in the diaphragm due to
buckling in specimen A is very Similar to the amount of strain due to
thermal expansion mismatch predicted from thermal expansion
polynomials (Figure 10). However, the residual stress in the film is
not completely relieved by buckling of the diaphragm and the net
stress in the film is influenced by intrinsic factors as well as thermal
expansion mismatch. The calculated compressive stress in specimen
A is fairly large (>500MPa) as determined by multiplying the
measured buckling strain relief by the modulus of natural diamond.
The similarity between the measured strain relief and the estimated
thermally induced strain implies that the net intrinsic stress in
diaphragm A is relatively small, and depending upon the degree of

strain relieved by the buckling of the diaphragm, the intrinsic stress

105

may be compressive.

Differences in CVD diamond film thickness at different points
across a single substrate are commonly observed in CVD diamond
films which indicates that growth conditions can vary with wafer
location. It is therefore conceivable that significant differences in
the residual stress of the diamond film diaphragms with respect to
the relative wafer position may exist. Specimens A-F were obtained
from wafer #1 and had similar thickness (within 10%) and surface
morphologies, thus they are expected to have similar residual stress
states. Specimens 6-21 were obtained from wafer #2 and had similar
surface morphologies but diamond film thickness between the
individual diaphragms varied by as much as 40%. Therefore, the

intrinsic stress in diaphragms 6-21 may vary significantly.

106

13.0 Deflection behavior of point loaded circular glass discs

The circular glass diaphragms, described in Section 9, were used
as a rough calibration of the nanoindenter and a test of the
diaphragm deflection method in measuring the elastic modulus of a
material. The results for the deflection of the glass diaphragms are
presented in Figures 44-45

The relatively large thickness (145 - 210nm) and large deflection
(up to 27 011m) of the glass diaphragms allowed analysis of the
deflection behavior both by classical (linear) and nonlinear plate
theories (Section 4).

The load-deflection curves for the simply supported and clamped
glass discs were fit to the approximate nonlinear solutions for a point
loaded circular plate (Equation 4.2) derived by Timoshenko et al. and
Banerjee et al. (Section 4). The fitting produced a value for the elastic
modulus (E) and the constant A describing the nonlinear behavior of
the plate (Section 4, Table 4).

Fitting the simply supported circular glass plate with the general

form of the approximate plate deflection solution (Section 4, Table 4);

E 2 fit elastic modulus

Et4 ] { [W] [WP } A = fit constant (Table 4)
[—-—1'2 "' + A — = P w/t = normalized deflection (13. I)
'551 t t t = plate thickness
r = plate radius

resulted in: E = 46 GPa, A = .20, correlation = .999. The value of .20
obtained for A agrees with the values of A derived by Bannerjee and
Timoshenko (.16 and .27 respectively), but the fit modulus of 46 GPa

is substantially lower than the expected modulus of the coverslip

deflection (microns)

107

 

 

 

 

300 m 1 1 __L L l 1 I . l g 1 J 1 4 1
SIMPLY-SUPPORTED COVERSLIP
support radius = 11.1mm I"
' coverslb radius = 12.7mm m:-
250 -' thickness 3 .1450?" ”1131"" _
.1ifttl9'ji!"w
200 _ .1c.l""""" ' _
150 _ ".....'..:.‘§:":’ J
100 - ..
50 - _
' compliance
0 T I w 1 fi 1 r

r l v I v ]— V . I l—
0 200 400 600 800 1000 1200 1400
load mm

1 ' I ‘
1600 1800 2000

Figure 44. Load-deflection behavior of simply-supported circular glass
coverslip prepared by placing (no glue) the coverslip over a circular hole in
a glass plate. The compliance curve obtained from indentation into the
back of the glass plate(s) was subtracted from the data obtained for the

clamped and simply supported plates.

108

150

CLAMPED CI'RCULAR' GLASS '
OVERSLIPS

deflection (microns)

L3

 

 

radius = 9.0 mm

1 = 145 microns
t=210 microns

 

 

W

1500
load (mN)

500 1000 2000

I
2500

3000

Figure 45. Load-deflection plots obtained from point loading of circular
glass coverslips clamped by applying superglue around the rim.

109

(Eglass ~ 70 GPa).
Fitting glass plate #2 (clamped) using;
A = fit constant of nonlinearity (Table 4)
[gfiilé‘z] { [‘11] + A it! 3} = P E/::ii:l::fi:§ddlelfil:ction ( 13.2)
t 2 plate thickness
r = plate radius
provided an elastic modulus (E) of 53 GPa, A = .19, and a correlation
coefficient of 0.999.

The solutions obtained by Timoshenko and Banerjee (Section 4)
predict a value of ~.43 for the constant (A) describing the
nonlinearity of the load-deflection curve for a fully clamped plate,
which is over twice that obtained by the fitting. The fit modulus of
53 GPa is also substantially lower than the expected modulus of the
glass coverslip (7 0GPa).

Loading clamped coverslip #3 (t = 210nm, r=9000um) to 1.9N (the
maximum load allowed by the nanoindenter for automatic data
collection) produced a central deflection of approximately 1/3 the
plate thickness, which is not enough to observe significant nonlinear
behavior. Classical (linear) plate theory (Section 4, Equation 4.1) for
a point loaded clamped circular plate was used to estimate the
modulus of glass coverslip #3 (Equation 13.3)

r = plate radius
E = elastic modulus

1V = 312(1-V2) v = Poissons ratio (13 3)
P 41tEt3 t = plate thickness °

wlp = slope of load-deflection curve (4.0 x 10'5 (m/N)

resulted in an estimated modulus (E) of 50 GPa.
The modulus obtained for clamped coverslip #3 using classical

(Equation 4.1) plate theory (50GPa) is similar to the modulus

110

predicted using nonlinear theory (Equation 4.2) on both the simply
supported coverslip #1 (46 GPa) and clamped coverslip #2 (53GPa).
For the coverslips which were superglued around the rim the
criterion for a fully clamped plate may not have been met, resulting
in larger deflections than predicted by theory (Equation 4.2) and a
lower estimated modulus. The value of A, the constant describing
the nonlinearity of the plate, fit to coverslip #2 (.19) was less than
one-half the value given by the approximate solutions (Section 4,
Table 4) for a fully clamped plate. The large difference in the
theoretical and fit value of A may indicate that the superglued
coverslips were not fully clamped. The coverslip which was not glued
around the rim was presumed to be simply supported with the edge
free to move. The value of A obtained from the fitting agreed with the
theoretical value of A (Section 4, Table 4) for a point loaded simply
supported circular plate with a moveable edge. For the simply
supported case, boundary conditions would not appear to be the
cause of the seemingly low estimate for the elastic modulus of the
glass coverslip. Frictional forces around the rim in the simply
supported case may give rise to an inflated measured modulus value.
Possible explanations for the “lower than expected” measured
modulus for the glass coverslips was that the balance on the
nanoindenter was improperly calibrated or that the displacements
reported by the nanoindenter were not the displacements being
induced. Both of these possibilities were investigated using the
nanoindenter calibration procedure described in Appendix B. The

results of the nanoindenter calibration (Appendix B) indicate the

111

displacements induced by the nanoindenter are 66% of the reported
displacement. Appropriate adjustment to the measured modulus
values of the glass coverslips produces values of 69, 79 and 75 GPa
for coverslips #1, #2, and #3 respectively. Only calibrated values for
nanoindenter displacement will be reported in the remainder of this
thesis.

The load-deflection behavior of the clamped circular coverslips
was normalized (Equation 13.4) following the relationship between

point load and thickness predicted by plate theory (Equation 4.1,4.2).

P P = point load

73' t = plate thickness (13.4)

normalized load =
The load-deflection curves after normalization of the load for the
- two coverslips (t = 210 and 145 um) clamped by gluing are depicted in
Figure 47. The normalized load-deflection behavior for clamped
coverslips #2 and #3 roughly coincide. The difference in the curves
after normalization may be the result of differences in the effective

clamping of the glass coverslips.

112

lCLAMPED CIRCULAR GLASS COVERSLIPS

WITH LOAD NORMALIZED .
'8 m-
2 0 °
.9 o
S 0 °
.5 D
‘6
g
‘3
radius = 9.0 m
D t = 145 microns ‘

 

 

 

0 t=210 microns
1 . , .

. , . , .
.0002 .0004 .0006 .0008 .001
normalized load (mN/ microns )

Figure 47. Load-deflection plots for clamped glass coverslips with load
normalized for radius and thickness.

 

113

14.0 Deflection behavior of point loaded diamond diaphragms

Nanoindenter-specimen compliance data collected from the
various compliance specimens (Section 7.4) was combined into a
single data set (Figure 48). The compliance behavior was described
using Equation14.1. The form of Equation 14.1 was chosen by the
author to describe the saturation to linear behavior observed inthe
compliance data. The constants in equation 14.1 were obtained by

manually fitting to the entire set of compliance data.

d = 0.01P + 0.4 [1 - exp(-P('6)] 3:333:31“ (14.1)
Equation 14.1 was used to subtract the nanoindenter-specimen
compliance contribution from the load-deflection data for the
diamond diaphragms. The relative contribution of the nanoindenter-
specimen compliance to the total deflection of the diamond
diaphragms is fairly small (<5%) for the large load (>25mN)
deflection behavior of the diamond diaphragms. At low loads (<5mM)
the contribution of the compliance to the total deflection
measurement is fairly substantial (~25%).

The diameter, thickness, load at failure, and number of data
points collected for the deflection of the diamond diaphragms used in
this study are presented in Table 7. The relative position of diamond
film diaphragm specimens 6 - 21 with respect to the silicon wafer on
which they were deposited is presented in Figure 15 (Section 5). The

measured thickness of the diaphragm specimens corresponds to the

114

displacement (microns)

 

 

 

load (mN)

Figure 48. Plot of combined compliance curves taken from various
diamond specimens and specially prepared compliance specimens. The
compliance behavior was described by Equation 14.1 which was used to
subtract the compliance contribution from the diaphragm deflection data.

 

115

Table 7: Radius, thickness, and load at fracture for point loaded
circular diamond diaphragm specimens.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

specimen radius (mm) thickness (um) fracture load (mN)
A 648 1.5 5.8
B 719 1.55 3.4
C 868 1.5 4.9
D 976 1.6 2.8
E 866 1.5 1.9
F 907 1.65 4.6
6 775 4.0 42
8 875 4.4 ' 40
9 785 4.3 31
11 890 3.1 17
12 962 4.3 36
13 865 4.3 37
14 835 4.1 37
16 895 4.0 30
17 670 3.8 32
19 905 3,5 27
21 900 3.2 ' 21

 

 

 

 

 

 

 

pl
dl.
dt

116

expected trend of thickness variation with respect to the position on
the wafer from which the specimen was obtained (i.e. thickness
decreases as distance from the center of the wafer increases). Film
thickness near the center of the wafer is expected to be greater due to
its position relative to the plasma ball generated during the
MPACVD process (Section 1.4). The portions of the wafer which were
not used in the diaphragm deflection experiments consisted of
specimens which were either destroyed during processing or
fragments which were unsuitable for the production of a diamond
diaphragm.

The load-deflection data for the circular diamond diaphragms,
corrected for nanoindenter-specimen compliance, was fit using a non-
linear least squares regression program, written by E. Case, to
Equation 14.2. Equation 14.2 is the form used by the approximate
solutions of Timoshenko et al. and Bannerjee et al. to describe the
large deflection behavior of circular plates subjected to a central
point load (Section 4). Prior to fitting, the deflection data was
normalized (divided by the diaphragm thickness) in order to comply
with the general form of Equation 14.2.

P = point load
C1 (X + C2X3) = P Cl, CZ = fitting parameters (142)

X = w/t (normalized deflection)
Results of the load-deflection data fitting is presented in Table 8 and
plots of the load deflection data and respective fits for diamond
diaphragms A - 21 are shown in Figures 49-66. Equation 14.2

described the load-deflection behavior of every one of the 17 diamond

 

w/t

Figu

117

 

SPECIMEN A

thickness =1.5 urn
‘ radius = 640

 

 

 

 

P (mN)

Figure 49. Load-deflection plot for diamond diaphragm specimen A.

118

 

SPECIMEN B

thickness = 1.55 pm
‘ radius = 719

 

 

 

—4
‘

 

P (mN)

Figure 50. Load-deflection plot for diamond diaphragm specimen B.

119

 

SPECIMEN c ‘ A 0

thickness =1.5 I4 m
‘ radius = 868 ”

 

 

 

-1

 

P (mN)

Figure 51. Load-deflection plot for diamond diaphragm specimen C.

120

 

SPECIMEN o

. thickness =1.6 “m
radius = 976

 

 

c—i
—
A

 

P (mN)

Figure 52. Load-deflection plot for diamond diaphragm specimen D.

 

121

 

SPECIMEN E

thickness =1.5 um
* radius = 866

 

 

—:
--4
—

 

Figure 53. Load-deflection plot for diamond diaphragm specimen E.

 

122

 

SPECIMEN F

thickness = 1.65 gm
‘ radius = 907

 

 

—l

 

P (mN)

Figure 54. Load-deflection plot for diamond diaphragm specimen F.

 

123

 

4 . l l 1 l
SPECIMEN 6
P thickness = 4.0 “m
radius = 775
3 - ..

w/t

 

 

 

 

0 V I V ’l— 1 ‘I’ 1 I

0 10 20 30 40
load (mN)

Figure 55. Load-deflection plot for diamond diaphragm specimen 6.
Deflection to 9pm repeated three times.

124

 

4 4 1 l J l
SPECIMEN 8
_ thickness = 4.4 um
radus = 875
3 ..

w/t

 

 

 

 

o . 4 . T . f - I
0 10 20 30 40
load (mN)

Figure 56. Load-deflection plot for diamond diaphragm specimen 8.
Deflection to 9um repeated three times.

125

 

 

 

 

 

4 1 l l l I
SPECIMEN 9
_ thickness = 4.3 ,um
radus = 785
3 _
< 2 _
3
1 _
0 v I ' T . I ' 1
O 10 20 30 40

load mm

Figure 57. Load-deflection plot for diamond diaphragm specimen 9.
Deflection to 9pm repeated two times.

126

 

SPECIMEN L11
Fthickness = 3.1 ,um
radius = 890

l i

s- / -

 

 

 

f r r T y I

20 30 40
load (mN)

 

Figure 58. Load-deflection plot for diamond diaphragm specimen 11.
Deflection to 9pm repeated three times.

127

 

 

 

 

 

4 x A l L 1 l
SPECIMEN 12
_ thickness = 4.3 Hm
radus =962
3 ..
r /
K"
3
0 ' I v I ' 7 . . I .
0 10 20 30 40
load (mN)

Figure 59. Load-deflection plot for diamond diaphragm specimen 12.
Deflection to 9pm repeated three times.

128

 

4 . l l I l
SPECIMEN 13
_ “Ckness 3 4.3 “m
radus = 865
3..

w/t

 

 

 

 

O ' I . I ' F v I
O 10 20 3O 40

load (mN)

Figure 60. Load-deflection plot for diamond diaphragm specimen 13.
Deflection to 9pm repeated three times.

129

A l 4 4 A l

 

SPECIMEN 14

thickness = 4.1 um
F racius = 835

w/t

 

 

 

 

0 . r - , . ' T 1 ,
0 10 20 30 40
load (mN)

Figure 61. Load-deflection plot for diamond diaphragm specimen 14.
Deflection to 9pm repeated three times.

130

 

SPECIMEN 16

_ thickness = 4.0 pm
diameter 8 895

w/t

 

 

 

 

o r I V I Y f Y I

0 10 20 30 40
load (mN)

Figure 62. Load-deflection plot for diamond diaphragm specimen 16.
Deflection to 9pm repeated four times.

131

 

4 - 4 1 A 1 1
SPECIMEN 'I7
_ mass = 3.8 “m
radus = 670
3 r 7
g 4

 

 

 

 

0 . I . I
0 _ 10 20

load (mN)

30

40

Figure 63. Load-deflection plot for diamond diaphragm specimen 17.

Deflection to 9pm repeated three times.

132

 

SPECIMEN 19

_ thickness = 3.5 “m
racius =905

 

 

 

 

O f T w I * I * V
0 10 20 30 40
load (mN)

Figure 64. Load-deflection plot for diamond diaphragm specimen 19.
Deflection to 9pm repeated three times.

133

 

SPECIMEN 21

thickness = 32 um
radus =900

I

 

 

 

 

o ' i * T ' V j I
0 10 20 30 40
load (mN)

Figure 65. Load-deflection plot for diamond diaphragm specimen 21.
Deflection to 9pm repeated two times.

134

diaphragms included in this study with a correlation coefficient in
excess of 0.995. The nonlinear behavior exhibited by the diamond
diaphragms during loading follows the general trend predicted by
plate theory (Equation 4.2).

During the early stages of the deflection, many of the diaphragms
behaved in a manner which contradicts the predictions of plate
theory (i.e. further deflection of the plate required a less than
proportional increase'in load). The load-deflection behavior of
specimen A (Figure 49) shows a change in curvature between the
small (less than the thickness) deflection and large deflection
behavior. The small deflection behavior is believed to result from the
transition of the diaphragm morphology from that of a plate buckled
by a uniform load around its circumference (Section 11), to the
morphology of a plate deflected by a central point load. The point
loading of a buckled diaphragm may also have a “smoothing” effect
on the wrinkled morphology observed in diaphragms A - F and
expected for diaphragms 6 - 21. In any case, the initial point loading
deflection behavior is not expected to be completely explained by the
general form of nonlinear plate theory (Equation 4.2) which describes
the behavior of plates which are initially smooth and flat.

The constant C1 obtained from the fitting of the load-deflection
data for the diamond diaphragm specimens (Table 8) is predicted by
non-linear plate theory (Equation 4.2) to have the following

relationship to the diaphragm radius and thickness:

C1 = fit constant to diaphragm load-deflection data.

[ t4 ] r = diaphragm radius
C 1 = (l :2 t = diaphragm thickness (143)

a = constant function of Elastic modulus and Poissons ratio

135

Table 8: Specimen parameters and constant values for fitting of
load-deflection data to Equation 14.2*.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

specimen 1.1133111: thiifigffs 1333:; C 1 CZ R
A 648 1.5 50 1.045 .020 .998
B 719 1.55 27 1.038 -.006 .999
C 868 1.5 40 .492 .009 .998
D 976 1.6 19 .725 -.016 .997
E 866 1.5 10 .588 -.003 .999
F 907 1.65 37 .693 .017 .999
6 775 4.0 946 7,924 .022 .999
8 875 4.4 622 8.008 .017 .998
9 785 4.3 598 9,701 . .021 .999
11 890 3.1 922 1.821 .040 .998
12 962 4.3 928 7.443 .015 .999
13 865 4.3 927 8.338 .016 .997
14 835 4.1 1268 5.850 .019 .999
16 895 4.0 1095 5.840 .019 .998
17 670 3.8 1147 7.232 .019 .999
19 905 3.5 1094 4.015 .015 .999
21 900 3.2 754 2.698 .024 .999

 

 

 

 

 

 

 

 

 

* Equation 14.2: C1[ Viv + C2{%v }3] = P

w = central deflection
t = diaphragm thickness
P = point load

l

136

 

l
,(t‘ /r2 I vs. CI

specimens 8 - 21

(microns2 x 104)

2
5

thickness? Iradiu

 

 

 

 

Figure 66. Plot of C1 (Equation 14.3) versus t4/r2 for all specimens.
Dashed line represents fit forced through zero, Solid line represents best fit

with floating intercept.

137

The results of plotting C1 versus t‘I/r2 for specimens sets 6-21 and A-
F respectively are presented in Figure 66. The predicted linear
relationship (Equation 14.3) between fit constant C1 and t4/r2 for the
point-loaded diamond diaphragms is observed with a correlation of
.92 (force through zero) and .96 (not forced through zero). The initial
(residual stress induced) central deflection of the diaphragms as well
as differences in the effective diaphragm boundary conditions may
account for the scatter in the C1 versus t"‘/r2 data. Specimens A-F
were loaded on the substrate side and thus the faceted side of the
film is were the maximum tensile stress will occur. The rough
faceted surface may act to produce areas of highly concentrated
stress which would result in a significantly lower fracture stress
than a diaphragm loaded on the faceted side (6-21). The relatively
large difference between the behavior of the grouped specimens (6-21
and A-F.) may also be explained by significant differences in initial

, (residual stress induced) central deflection and boundry conditions.
Specimens A-F and 6-21 were obtained from silicon-diamond wafer#1
and wafer#2 respectively, which were grown under differing CVD
conditions and have different surface morphologies. Therefore, the
possibility of significant differences in residual stress between the
two specimen sets exists and would result in differing respective
compressive stress induced diaphragm deflections. Specimens A-F
had the point load applied to the substrate side of the diamond film
and were supported from above by the silicon substrate (i.e. diamond
film adhesion to the silicon substrate was the sole means of

diaphragm support). Specimens 6-21 were loaded on the faceted side

138

of the diamond film and were supported from below by the silicon
substrate. The silicon rim around diaphragm specimens A-F was not
as drastically “tapered” as the rim supporting specimens 6-21, which
may also effect the relative diaphragm boundary conditions.
Specimens 6-21 were roughly 2 to 3 times the thickness of specimens
A-F and therefore have a rigidity (Equation 3.3) approximately 1 to 2
orders of magnitude higher. The larger relative rigidity may make
the buckling behavior of specimens 6-21 different than that of

specimens A-F.

14.1 Repeated loading of diamond diaphragms

To evaluate the repeatability of the diaphragm deflection behavior
and address the possibility of smoothing, delamination, slippage, or
other effects which would alter the response of the point loaded
diaphragm, several specimens (6 - 19) were subjected to repeated
loadings. Loading to 911m central deflection, unloading, then
reloading to 911m, a procedure which was repeated up to 4 times, did
not alter the load / deflection behavior by more than 5%. Due to the
nature of the nanoindenter’s stage motion mechanism (gears), the
vertical location at which the indenter contacted the diaphragm upon
loading could not be accurately compared to the position at which,
upon unloading, they became separated. The repeated loadings
(Figures 6-21) of the individual diamond diaphragms were typically
indistinguishable and in the worst case (specimen 13) had a
maximum difference in load value for a given displacement of < 10%.

The conformity of the repeated diaphragm loading behavior indicates

139

that the effect of smoothing, delaminations, etc. either do not occur,

or have little effect on the deflection behavior.
14.2 Off-center diaphragm loading

The effect of off-center loading on the diaphragm load-deflection
behavior was investigated (Section 8). Diaphragm specimen 9 was
loaded at several points away from the center and the resulting
curves are depicted in Figure 67. The trend of the load-deflection
curves (i.e. increasing the distance from the center decreases the
deflection for a given load value) agrees with the expected load-
deflection behavior (i.e. as the distance from the center increases,
larger loads are necessary to induce a deflection equivalent to that of
the centrally loaded case).

It is also evident from the grouping of the load-deflection curves
for loadings at distances less than 100nm from the center, that the
load-deflection behavior of the diamond diaphragm will not be
significantly affected if the center is missed by even a substantial
amount (100nm or roughly 7% of the diaphragm diameter). The
method used in this study to locate the center of the diamond

diaphragms is accurate to 100nm.

140

 

 

 

 

 

‘n I————l—__I_— _ l I l I
_OFF CENTER LOADING
9 - _
8 - _
7 — _
’6 L
C
5 6 " ‘
E * DISPLACENENT‘
" 5- FROM CENTER-
g (microns)
% o centered ‘
8 4 o as -
8 . 50
3 o 75 _
v 100
n 150
2 c 200 ‘
3 250
1 ' 300 -
l 350
A 400
0 I 4 T
0 10 20 30

load (mN)

Figure 67. Load-deflection plots for off-center point loading of diamond
diaphragm specimen 9. '

141

15.0 Analysis of load at failure for the diamond diaphragms

Timoshenko et al. [113] predicts the maximum tensile stress in a
point loaded circular diaphragm will occur at the lower surface
centered directly beneath the point load. Compressive stresses in
the vicinity of the point load contact may exceed the maximum
tensile stress in the diaphragm. The strength of brittle materials
(i.e. diamond) in compression is typically several times larger than
the tensile strength [113]. Therefore, the diamond films are expected
to fail as a result of tensile stress. Timoshenko et al. describes the
relationship between maximum tensile stress in a fully clamped
plate (omax) and a highly concentrated point load (P) with the
following equation (Equation 15.1):

om,x = maximum tensile stress

P P = concentrated point load

Gmax = ?(1+V)[.485 111% + 0.52] tiplztie thlfklletses (15.1)

r — ra us 0 p a

n = Poissons ratio
A highly concentrated load is defined by the ratio of contact area (c)
and plate thickness (t) being small (~0). The point load applied to
the diaphragms using a hemi-spherical diamond indenter with a
10nm radius is not expected to apply a “highly concentrated load” to
the diamond diaphragms (t = 1.5 - 4.4 um) and may invalidate the
use of Equation 15.1 in determining the maximum tensile stress at
failure. The buckling of the diaphragms also violates the “flat plate”
assumption of Equation 15.1. Due to the aforementioned factors,

Equation 15.1 is not expected to provide an accurate estimate of the

maximum tensile stress in the diamond diaphragms. The relation-

142

ship between thickness (t2) to the maximum tensile stress (omax) is
observed in fracture behavior of the diamond thin film diaphragms

(Figure 68).

143

 

50 1 I 1
m to L = 012

_ L = load at fallue

t = fim thickness

C = 2.05

40- R = .97 _

[I

Load at iaflure (mN)

 

 

 

0 I I
0 10

film thickness2 (microns) 2

Figure 68. Plot of load at diaphragm failure versus t2.

 

144

16.0 Parameters influencing the diaphragm deflection behavior

The load-deflection behavior of the diamond diaphragms used in
this study is influenced by boundary conditions, initial (stress
induced) deflections, as well as the buckled morphology of the
diaphragm (i.e. the presence of wrinkles, etc.) [130].

The tapered silicon boundary (Figure 41) around the periphery of
the diamond diaphragm is not expected to rigidly clamp the
diaphragm during loading. Thus, the diaphragm boundary
conditions do not conform to those. specified by established plate
theory (i.e. fully clamped). The use of clamped plate theory to
describe the behavior of a “sort-of-clamped” diaphragm may bring
about significant error. However, the magnitude of the errors
introduced by the non-idealized boundry conditions was not
evaluated in this thesis and the author is not aware of an analytical
study that directly addresses this problem.

Residual stress in the diamond film is also expected to influence
the load-deflection behavior of the diaphragms. This study provided
insight into the buckling behavior of diaphragms formed from
diamond films in residual compression. The degree of residual stress
in the films, both before and after buckling, was not measured in this
study. The effect of residual stresses remaining in the diaphragm
after buckling (if any) on the diaphragm load-deflection behavior is

unknown.

145
IV. CONCLUSIONS

Circular diamond film diaphragms were prepared using a
mechanical grinding and chemical etching process. Upon release
from the substrate, buckling was observed in diamond diaphragms A-
F obtained from a single silicon wafer (wafer #1) with film thickness
less than 1.65 pm. Buckling was not visually observed in
diaphragms 6-21 obtained from wafer #2 with film thickness, in
excess of 3.1 pm (refer to Table 7). Diaphragm buckling was
attributed to the presence of residual compressive stress in the film.
Laser scanning confocal microscopy (LSCM) was used to analyze the
morphology of the buckled diaphragms from wafer #1 and estimate
the net residual strain in the films at room temperature. The LSCM
measurement of net residual strain induced in the diamond
diaphragm (5.6 x 10'“), in combination with the estimated strain at
room temperature induced by thermal‘expansion mismatch between
the silicon substrate and diamond film (~5.5 x 10'4), allowed for
speculation into the nature of the intrinsic, or deposition induced,
residual stress in the diamond films.

Centrally point loading the diamond diaphragms with thickness
ranging from 1.5 pm to 4.4 pm and diameters between 1275 um and
1925 um using a nanoindenter provided load-deflection data.
Analysis of the diaphragms based on established approximate
solutions to the point load deflection of circular plates was
performed. Plate theory (Section 4, Equation 4.2) predicts a

geometrically nonlinear behavior during point loading, which was

146

observed in the load-deflection behavior of the diamond diaphragms.
The load-deflection behavior of the 17 diamond diaphragms used in

this study was described by the form of Equation 4.2:

r = radius of plate
E = plate elastic modulus
3. P12 t = plate thickness
(N + AN )= B[-—4] P = point load (4.2)
Et N = normalized deflection (w/t)
A,B = constants (Table 4)

with a correlation coefficient in excess of .995. The effect of
thickness and radius on the diaphragm deflection behavior which
was predicted by established plate theory (Equation 14.3) was also
observed in this study. The fracture behavior of the films also
follows the predicted (Equation 15.1) diaphragm thickness
dependance. Unconventional boundary conditions and initial
(residual stress induced) deflections, however, did not allow the
point-load behavior of the diamond diaphragms to be effectively
modeled using flat plate solutions for idealized boundary
conditions. Suggestions for the improvement of the process and the
potential of the LSCM and point-load deflection techniques for the

study of polycrystalline diamond films are discussed.

147
V. FUTURE STUDIES

The magnitude and nature of the intrinsic stress for diamond
films (such as the diaphragms used in this study) needs to be
determined accurately. Future research utilizing the buckling
morphology, measurements at various temperatures, as well as
models for the degree of buckling strain relief may yield more
detailed information on the nature of intrinsic stress in
polycrystalline diamond films.

The initial, residual stress induced, deflection of the diamond
diaphragms is a significant problem to the point-load deflection
analysis. Due to buckling upon release from the substrate, the
diaphragms were not “flat plates” necessary to effectively utilize the
established plate deflection solutions. Instead, the diaphragms
assume a fairly complex “shell-like” morphology, to which solutions
for point-load deflection behavior are not currently available and
would be very difficult to develop. Again, a possible solution to this
problem would be through sample preparation. Due to the complex
residual stress state apparent in diamond films, the preparation of
“flat”, stress free diaphragms may prove challenging, but seems very
plausible.

Boundary conditions for the diaphragms used in this study do not
cOnform to those for which established plate deflection solutions
exist. It may be possible to develop a plate deflection solution for the
boundary conditions possessed by the diamond diaphragms in this

study. If boundary conditions were the only obstacle facing the point

148

load analysis of the diamond diaphragms, development of a model for
the actual diaphragm boundary conditions would be a worthwhile
effort. Such a model would be difficult to test experimentally and
would therefore be highly questionable. Another solution to the
problem of unconventional diaphragm boundary conditions is
through specimen preparation. Changing the specimen preparation
procedure to produce diamond diaphragms with boundary conditions
that conform to established plate theories would greatly improve the
results of a similar study. The fracture behavior of the diaphragm
was not fully analyzed in this study. A detailed analysis of
diaphragm fracture under point loading may prove valuable in
understanding the fracture behavior of polycrystalline diamond

films.

149
VI. CLOSING REMARKS

The ability to measure the mechanical properties (i.e. elastic
modulus and fracture stress) of diamond films will aid in the
improvement of diamond CVD processes by allowing a direct
comparison of films grown under different conditions. Growing the
“strongest” films is not a priority to the majority of current diamond
CVD researchers, due to the relative youth of the process. As an
understanding of the diamond CVD process develops and the
marketplace for diamond films expands, the concerns of diamond
“growers” will shift to the improvement of mechanical and other
properties. Methods employed to measure the macroscopic
mechanical properties of diamond films are, at this point, unable to
provide reliable information. Current methods, however, have
shown promise and with their improvement and the development of
new techniques and equipment, the ability to measure the
mechanical properties of diamond films should keep up with
advancements in CVD diamond growth.

The load-deflection behavior of the 17 diamond diaphragms
included in this study was accurately described by the general form
of existing non-linear plate theory. Although this study met with
various difficulties and failed to produce an unquestionable value for
the modulus of the diamond films, point loading in combination with
the analysis of residual stress and buckled morphology of diamond
film diaphragms could aid in determine the mechanical properties of

CVD diamond and other brittle thin films.

APPENDICIES

APPENDIX A

Equipment parameters

1. Dow Interfacial Testing System (nanoindenter)
- Mitutoyo Finescope FS 100, Mitutoyo 50x objective
- Sony XC-57 CCD video camera, Sony Trinitron monitor
- Klinger (Garden City, NY) X-Y stepper motor
- MicroControl (France) Z stepper motor
- Klinger CC1 stepper motor controls.
- Sartorius L—610 electronic balance
- Zenith 386/20 PC
- Dow interfacial testing system III software
- Magwen Diamond Products (Lowell, MA) 10pm radius

hemispherical diamond indenter tip.

2. Laser Scanning Confocal Microscope (LSCM)
- Zeiss 1.0 LSCM (Carl Zeiss Inc., Thomwood, NY)
- Single line argon ion laser
- Silicon Graphics 4030 workstati0n

- VoxelView graphics software (Vital Images, Fairfield, I0)

150

APPENDIX B
Nanoindenter Calibration

The Sartorius 610 electronic balance was tested by measuring
three known masses (weights of which were verified using another
electronic balance). The Sartorius 610 on the nanoindenter
accurately reproduced the measured weights for the three masses.

The Z stepper motor was calibrated using a glass beam specimen
(Figure 46). The glass beam was cut from a microscope slide. The
microscope slide, from which the calibration beam was to be cut, was
chosen from a group of microscope slides used in a study by K. Lee
[129] in which the elastic modulus of over 200 microscope slides was
measured using a sonic resonance technique. The elastic modulus
measured for the 200 microscope slides was 70 + 1 GPa. The elastic
modulus and Poissons ratio of the microscope slide used for the glass
beam was measured using the sonic resonance technique (K. Lee
[129]) and found to be 69GPa and .18 for E and v respectively. The
glass beam was cut from the microscope slide using a low speed
diamond saw and the edges were ground smooth using 600 grit SiC
paper. The dimensions of the glass beam (thickness = 0.95mm, width
= 2.25mm) were measured using calipers and a micrometer. A thick

glass bar (3 x 9 x .8 cm) was used as a base and two glass plates cut

151

152

from a coverslip were used as supports for the beam specimen. The
supports were placed on the glass base and secured in place using
paper/adhesive tabs. The tabs were fixed to the surface of the base
plate and defined a square region in which the glass support was
placed in order to prevent movement. The distance between the
supports (45mm) was measured using calipers. The simply
supported glass beam calibration specimen is depicted in Figure 46.
The calibration specimen was placed on the stage of the
nanoindenter and the center point was located. The beam was
deflected using the 10pm diamond indenter tip and the
corresponding load measured. After deflection of the beam, the beam
was removed from the supports and placed directly on the glass base.
Three indentations were made near the center of the beam in order
to measure the compliance of the specimen and indenter. The
measured compliance was subtracted from the load-deflection data
obtained from the simply supported beam. The resulting load-
deflection curve is given in Figure 47. The slope of the load
deflection curve (2.5 x 10'4 m/N) for the glass beam specimen was

determined using linear regression.

d = deflection
3 P = measured load
_d_ = __I:__ 3 L=Iength ofspan (B1)
P 4Ewt E = elastic modulus of beam

w = width of beam

t = beam thickness
Equation B.1 [128] was used to determine the predicted deflection of
the beam. Equation B.1 predicts a slope of 1.7 x 10'4 m/N for the

deflection/load obtained from the beam. The measured value

153
(2.5 x 10'4 m/N) for the s10pe of the deflection/load is 50% higher than

the theoretically predicted value. The displacement value reported
by the nanoindenter (0.04 11m per step) was multiplied by .66 to bring
the measured values into agreement with beam theory. All
displacement data in this study is 66% of the values reported by the

nanoindenter.

N
S

deflection (microns)
8 S

 

B

 

154

 

0.2 0.4 0.6 0.8 1 .0

Load (Newtons)

 

glass support

\

I

I

P011113 103d glass beam

I ./

 

 

Glass Base

 

 

 

 

Figure 46. (A) Load-deflection plot for simply supported glass beam used
in the nanoindenter calibration. (B) Schematic of glass beam setup.

 

APPENDIX C

Seeding of the silicon substrate.

A homogenous mixture of diamond powder (0.1 - 0.2mm particles)
suspended in positive photoresist (Shipley 1470J) was prepared by
ultrasonic agitation. The photoresist/diamond suspension was
placed on the polished silicon substrate and spun, producing a thin,
even layer of photoresist and even distribution of diamond particles.
After the photoresist was developed, scattered diamond particles
remained on the silicon surface to act as nucleation sites for CVD

diamond [127].

155

156

APPENDIX D

Grain boundary relaxation calculations for residual stress

Windischmann et al. [94] used thermal expansion coefficients
obtained from Slack et al. [131] to produce thermal expansion curves
for silicon and diamond. The thermal expansion plots presented in
the Windischmann study are similar to the plots obtained in this
study using thermal expansion polynomials. Windischmann
determined the room temperature thermal stress in the films by
multiplying the biaxial elastic modulus of diamond (1345GPa) [94] by
the predicted thermal mismatch between diamond and silicon at the
diamond deposition temperature. The values of thermal strain used
by Windischmann et al. do not agree with the thermal expansion
plots produced in the Windishmann study or this study and are likely
the result of a miscalculation. The predicted thermal stress values
in the Windischmann study when replaced by those of Toloukian [4],

depicted in Figure 10, produce the following results:

Gin = intrinsic stress
Gin = O'T - 6th CT = total stress (D.1)
0th = thermal stress

The total stress at room temperature was determined through

measurement of the curvature induced in the silicon wafer by the

157

film combined with the Stoney equation and is believed to be
accurate to 10% [94]. For a film with an. average grain. size of
approximately 0.12pm grown at ~790°C the total residual stress was
0.2GPa. Figure 10 predicts a thermal stress (thermal strain x biaxial
elastic modulus for diamond) of (5.8 x 10'4 x 1345 GPa) = .78 GPa.
The value of .7 8 GPa is within 10% of the value (.84 GPa) predicted

by the grain boundary relaxation model (Equation 2.1).

LIST OF REFERENCES

LIST OF REFERENCES

P. D. Ownby, “Engineering Properties of Diamnd and Graphite,” ASM
Engineered Materials Handbook Volume 4, (ASM International,
1991), Pp. 821-834.

J. E. Field, “Natural Diamond: The Standard,” Diamond and
Diamond-like Films and Coatings, NATO ASI Series B. Volume 266,
edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl,
(Plenum Press, 1991), PP. 17-35.

M. D. Drory, C. F. Gardinier, and J. M. Pinneo, “Fracture Behavior of
CVD Diamond,” Thin Films: Stresses and Mechanical Properties III,
Materials Research Society Symposium Proceedings Volume 239,
edited by W. D. Nix, J. C. Bravman, E. Arzt, and L. B. Freund,
(Materials Research Society, 1992), pp. 561-566.

Y. S. Touloukian, R. E. Kirby, R. E. Taylor, and T. Y. R. Lee,
Thermophysical Properties of Matter; TPRC Series, (IFI/Plenum 1977 ).

N. K. Annamalai, R. F. Blanchard, and Joseph Chapski, “Radiation

Response of Diamond Films,” Diamond and Diamond-like Films and
Coatings, NATO ASI Series B. Volume 266, edited by R. E. Clausing, L.
L. Horton, J. C. Angus, and P. Koidl, (Plenum Press, 1991), pp. 821-828.

C. P. Beetz, C. V. Cooper, and T. A. Perry, “Ultralow Load Indentation
Hardness and Modulus of Diamond Films Deposited by Hot-Filament-
Assisted CVD,” Journal of Materials Research, 5: 2555-2561, (1990).

P. K. Bachmann and R. Messier,”Emerging Technology of Diamond
Thin Films,” Chemical and Engineering News, 70 (20):24-39, (1989).

M. N. Yoder, “Diamond: Potential and Status,” Diamond and
Diamond-like Films and Coatings, NATO ASI Series B. Volume 266,
edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl,
(Plenum Press, 1991), pp. 1-16.

K. Nishimura, K. Das, and J. T. Glass, “Material and Electrical
Characterization of Polycrystalline Boron-Doped Diamond Films

Grown By Microwave Plasma Chemical Vapor Deposition,” Journal of
Applied Physics, 69: 3142-3148, (1991).

158

10.
11.

12.

13.

14.

15.

16.
17.

-18.

19.

20.

159

R. N. Boggs, “Diamond Thin Film: Hot New Material For The 90’s,”
Design News, 45 (7): 70-75, (1989).

R. Pool, “Diamond Films Sparkle As They Come to Market,” Science,
249: 27-28, (1990).

A. E. Alexenko and B. V. Spitsyn, “Some Properties of CVD Diamond
Semiconducting Structures,” Diamond and Diamond-like Films and
Coatings, NATO ASI Series B. Volume 266, edited by R. E. Clausing, L.
L. Horton, J. C. Angus, and P. Koidl, (Plenum Press,1991), pp.789-798.

H, Kiyota, K. Okano, T. Iwasaki, H. Izumiya, Y. Akiba, T. Kurosu, and
M. Iida, “Fabrication of Metal-Insulator-Semiconductor Devices Using
Polycrystalline Diamond Film,” Japanese Journal of Applied Physics,
30: L2015-L2017, (1991).

K. Okano, H. Kiyota, T. Iwasaki, T. Kurosu, M Iida, and T. Nakamura,
“p-n Junction Diode Made of Semiconducting Diamond Films,”
Applied Physics Letters, 58: 840-841, (1990).

R. C. McCune, D. W. Hoffman, T. J. Whalen, and C. O. McHugh,
“Adherence of Diamond Films Produced by Microwave Plasma
Deposition on SiAlON Tool Inserts,” Thin Films: Stresses and
Mechanical Properties, Materials Research Society Symposium
Proceedings Volume 130, edited by J. C. Bravman, W. D. Nix, D. M.
Barnett, and D. A. Smith, (Materials Research Society, 1989),pp. 261-266.

P. W. Bridgman, “Synthetic Diamonds,” Scientific American, 193: 42-
46, (1955). ’

F. P. Bundy, H. T. Hall, H. M. Strong, and R. J. Wentorf, “Manmade
Diamond,” Nature, 176: 51-55, (1955).

W. Zhu, B. R. Stoner, B. E. Williams, and J. T. Glass, “Growth and
Characterization of Diamond Films on Nondiamond Substrates for
Electronic Applications,” Proceedings of the IEEE: 79: 621-646, ( 1991).

J. C. Angus and C. C. Hayman, “Low-Pressure, Metastable Growth of
Diamond and Diamondlike Phases,” Science, 241: 913-921, (1988).

K. E. Spear, “Diamond- Ceramic Coating of the Future,” Journal of the
American Ceramic Society, 72: 171-191, (1989).

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

160

T. R. Anthony, “Methods of Diamond Making,” Diamond and
Diamond-like Films and Coatings, NATO ASI Series B. Volume 266,
edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl,
(Plenum Press, 1991), pp. 555-577.

W. G. Eversole, “Synthesis of Diamond by Deposition on Seed
Crystals,” U. S. Patent #3030187, (1962).

W. A. Yarbrough and R. Messier, “Current Issues and Problems in the
Chemical Vapor Deposition of Diamond,” Science, 247 :688-695, (1990).

J. C. Angus, H. A. Will, and W. S. Stanko, “Growth of Diamond Seed
Crystals by Vapor Deposition,” Journal of Applied Physics, 3922915-
2922, (1968).

N. Setaka, “Critical Assessment of State-of-the-Art of Growing
Diamond,” Diamond and Diamond-like Films and Coatings, NATO
ASI Series B. Volume 266, edited by R. E. Clausing, L. L. Horton, J. C.
Angus, and P. Koidl, (Plenum Press, 1991), pp. 875-888.

B. V. Spitsyn, L. L. Bouilov, and B. V. Derjaguin, “Vapor Growth of
Diamond on Diamond and Other Surfaces,” Journal of Crystal
Growth, 52: 219-226, (1981).

P. K. Bachmann and H. Lydtin, “High Rate Versus Low Rate Diamond
CVD Methods,” Diamond and Diamond-like Films and Coatings,
NATO ASI Series B. Volume 266, edited by R. E. Clausing, L. L.
Horton, J. C. Angus, and P. Koidl, (Plenum Press, 1991), pp. 829-854.

B. V. Spitsyn, “Origin and Evolution of the Science and Technology of
Diamond Synthesis in the USSR,” Diamond and Diamond-like Films
and Coatings, NATO ASI Series B. Volume 266, edited by R. E.
Clausing, L. L. Horton, J. C. Angus, and P. Koidl, (Plenum Press,
1991). pp. 855-873.

A. R. Badzian and R. C. DeVries, “Crystallization of Diamond From
the Gas Phase; Part 1,” Materials Research Bulletin, 23: 385-400, (1988).

J. Mercier, A. M. Bonnot, E. Caignol, and E. Gheeraert,
“Investigations of Growth Mechanisms of Diamond Thin Films by Hot
Filament Assisted CVD,” Diamond and Diamond-like Films and
Coatings, NATO ASI Series B. Volume 266, edited by R. E. Clausing, L.
L. Horton, J. C. Angus, and P. Koidl, (Plenum Press, 1991), pp. 533-
540.

31.

32.

33.

34.

35.

36.

37.

38.

39.

161

S. J. Harris, A. M. Weiner, and T. A. Perry,“ Filament-Assisted
Diamond Growth Kinetics,” Journal of Applied Physics, 70: 1385-
1391, (1991).

K. Baba, Y. Aikawa, and N. Shohata, “Thermal Conductivity of Dia-
mond Films,” Journal of Applied Physics, 69: 7313-7315, (1991).

P. K. Bachamnn and D. U. Wechert, “Characterization and Properties
of Artificially Grown Diamond,” Diamond and Diamond-Like Films
and Coatings, NATO ASI Series B. Volume 266, edited by R. E.
Clausing, L. L. Horton, J. C. Angus, and P. Koidl, (Plenum Press,
1991). pp. 677-714.

P. Bou and L. Vandenbulcke, “Raman Investigations on Diamond
Films and Crystals Deposited by Plasma-Assisted CVD,” Journal of
the Electrochemical Society, 138: 2991-3000, (1991).

F. G. Celii, D. White, and A. J. Purdes, “Effect of Residence Time on
Microwave Plasma Chemical Vapor Deposition of Diamond,” Journal
oprplied Physics, 70: 5636-5646, (1991).

Y. Saito, S. Matsuda, and S. N ogita, “Synthesis of Diamond by
Decomposition of Methane in Microwave Plasma,” Journal of
Materials Science Letters, 5: 565-568, (1986).

Y. Liou, A. Inspektor, R. Weimer, D. Knight, and R. Messier, “The
Effect of Oxygen in Diamond Deposition by Microwave Plasma
Enhanced Chemical Vapor Deposition,” Journal of Materials Research,
5: 2305-2312, (1990).

T. Mitomo, T. Ohta, E. Kondoh, and K. ohtsuka, “An Investigation of
Product Distributions in Microwave Plasma for Diamond Growth,”
Journal of Applied Physics, 70: 4532-4539, (1991).

M. Nunotanim M. Komori, M. Yamasawa, Y. Fujiwara, K. Sakuta, T.
Kobayashi, S. Nakashima, S. Minomo, M. Taniguchi, and M. Sugiyo,
“Effects of Oxygen Addition on Diamond Film Growth by Electron-
Clyclotron-Resonance Microwave Plasma CVD Apparatus,” Japanese
Journal of Applied Physics, 30: L1199-L1202, (1991).

J. J. Chang, T. D. Mantei, R. Vuppuladhadium, and H. E. Johnson,
“Low Temperature and Low Pressure Diamond Systhesis in a
Microwave Electron Cyclotron Resonance Discharge,” Applied Physics
Letters, 59: 1170-1172, (1991).

41.

42.

43.

45.

46.

47.

48.

49.

50.

51.

162

H. Kawarada, K. S. Mar, and A Hiraki, “Large Area Deposition of
Diamond Particles and Films Using Magneto-Microwave Plasma,”
Japanese Journal of Applied Physics, 26: L1032-L 1034, (1987).

M. Kawarada, K. Kurihara, and K. Sasaki, “Synthesis of a Diamond
and Metal Mixture by the Chemical Vapor Deposition Process,”
Journal of Applied Physics, 71: 1442-1445, (1992).

F. Akatsuka, Y. Hirose, and K. Komaki, “Rapid Growth of Diamond
Films by Arc Discharge Plasma CVD,” Japanese Journal of Applied
Physics, 27: L1600-L1602, (1988).

K. Kurihara, K. Sasaki, M. Kawarada, N. Koshino, “High Rate
Synthesis of Diamond by DC Plasma Jet Chemical Vapor Depositon,”
Applied Physics Letters, 52: 437-438, (1988).

Y. Hirose, S. Amanuma, and K. Komaki, “The Synthesis of High-
Quality Diamond in Combustion Flames,” Journal of Applied Physics,
68: 6401-6405, (1990).

K. V. Ravi, C. A. Koch, H. S. Hu, and A. J oshi, “The Nucleation and
Morphology of Diamond Crystals and Films Synthesized by the

Combusiton Flame Technique,” Journal of Materials Research, 5:
2356-2366, (1990).

M. Frenklach, “The Role of Hydrogen in Vapor Deposition of
Diamond,” Journal of Applied Physics, 65: 5142-5149, ( 1989).

M. Frenklach, “Theory and Models for Nucleation and Growth of
Diamond Films,” Diamond and Diamond-like Films and Coatings,
NATO ASI Series B. Volume 266, edited by R. E. Clausing, L. L.
Horton, J. C. Angus, and P. Koidl, (Plenum Press, 1991). Pp. 499-524.

Z. Chen, G. P. Wirtz, and S. D. Brown, “Chemical Kinetic Calculation
of the Gas Phase in Filament-Assisted Chemical Vapor Deposition of
Diamond,” Journal of the American Ceramic Society, 75: 2107-2115,
(1992). .

C. J. Chu, M. P. D’Evelyn, R. H. Hauge, and J. L. Margrave,
“Mechanism of Diamond Growth by Chemical Vapor Depositon on
Diamond (110), (111), and (110) surfaces: Carbon-13 Studies,” Journal
of Applied Physics, 70: 1695-1705, (1991).

L. R. Martin, “Diamond Film Growth in a Flowtube: A Temperature
Dependance Study,” Journal of Applied Physics, 70: 5667-5674, (1991).

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

163

M. Frenklach and K. E. Spear, “Growth Mechanism of Vapor-
Deposited Diamond,” Journal of Materials Research, 3: 133-140,
(1988). ‘

L. Vandenbulcke, P. Bou, and G. Moreau, “On the Control of Diamond
Deposition Structure and Morphology,” Journal of the Electrochemical
Society, 139: 2985-2991, (1991).

S. J. Harris, “Gas-Phase Kinetics During Diamond Growth: CH4 As-
Growth Species,” Journal of Applied Physics, 65: 3044-3048, (1989).

S. J. Harris, L. R. Martin, “Methys Versus Acetylene as Diamond
Growth Species,” Journal of Materials Research, 5: 2313-2319, (1990).

L. R. Martin, M. W. Hill, “A Flow-Tube Study of Diamond Film
Growth: Methane Versus Acetylene,” Journal of Materials Science
Letters, 9: 621-623, (1990).

D. G. Goodwin and G. G. Gavillet, “Numerical Modeling of the
Filament-Assisted Diamond Growth Environment,” Journal of
Applied Physics, 68: 6393-6400, (1990).

T. Kawato and K. Kondo, “Effects of Oxygen on CVD Diamond
Synthesis,” Japanese Journal of Applied Physics, 26: 1429-1432,
(1987 ).

J. A. Mucha, D. L. Flamm, and D. E. Ibbotson, “On The Role of Oxygen
and Hydrogen in Diamond-Forming Discharges,” Journal of Applied
Physics, 65: 3448—3452, (1989).

B. Lux and R. Haubner, “Nucleation and Growth of Low Pressure
Diamond,” Diamond and Diamond-like Films and Coatings, NATO
ASI Series B. Volume 266, edited by R. E. Clausing, L. L. Horton, J. C.
Angus, and P. Koidl, (Plenum Press, 1991), pp. 57 9-609.

M. Frenklach, R. Kamatick, D. Huang, W. Howard, K. E. Spear, A. W.
Phelps, and R. Koba, “Homogeneous Nucleation of Diamond Powder in
the Gas Phase,” Journal of Applied Physics, 66: 395-398, (1989).

C. P. Chang, D. L. Flamm, D. E. Ibbotson, and J. A. Mucha, “Diamond
Crystal Growth by Plasma Chemical Vapor Deposition,” Journal of
Applied Physics, 63: 1744-1748, ( 1988).

63.

64.

66.

67.

68.

69.

70.

71.

72.

73.

74.

164

Y. Muranaka, H. Yamashita, and H. Miyadera, “Characterization of
Diamond Films Synthesized in the Microwave Plasmas of CO/H2 and
CO/Oz/Hg Systems at Low Temperatures (403-1023 K),” Journal of
Applied Physics, 68: 8145-8153, (1991). '

Y. Saito, K. Sato, H. Tanaka, K. Fujita, and S. Matuda, “Diamond
Synthesis from Methand-Hydrogen-Water Mixed Gas Using a

Microwave Plasma,” Journal of Materials Science Letters, 23: 842-846,
(1988).

C. J. Tomg, J. M. Sivertsen, J. H. Judy, and C. Chang, “Structure and
Bonding Studies of the C:N Thin Films Produced by RF SPuttering
Method,” Journal of Materials Research, 5: 2490-2496, (1990).

R. Meilunas, R. Chang, S. Liu, and M. Kappes, “Nucleation Control of
Diamond Films on Surfaces Using Carbon Clusters,” Applied Physics
Letters, 59: 3461-3463, (1991).

H. Itoh, T. Osaki, H. Iwahara, and S. Sakamoto, “Nucleation Control
of Diamond Synthesized by Microwave Plasma CVD on Cemented
Carbide Substrate,” Journal of Materials Science, 26: 3763-37 68,
(1991).

D. J. Pickrell, W. Zhu, A. R. Badzian, R. E. N ewnham, and R. Messier,
“Near Interface Characterization of Diamond Films on Silica and
Silicon,” Journal of Materials Research, 6: 1264-127 7, (1991).

S. Iijima, Y. Aikawa, and K. Baba, “Growth of Diamond Particles in
Chemical Vapor Deposition,” Journal of Materials Research, 6: 1491-
1497, (1991).

K. Hirabayashi, Y. Taniguchi, O. Takamatsu, T. Ikeda, K Ikoma, and
N. Iwasaki-Kurihara, “Selective Depositon of Diamond Crystals by
Chemical Vapor Depositon Using a Tungsten-Filament Method,”
Applied Physics Letters, 53: 1815-1817, (1988).

S. Matsumoto, Y. Matsui, “Electron Microscopic Observation of
Diamond Particles Grown From the Vapour Phase,” Journal of
Materials Science, 18: 1785-1793, (1983).

M. A. Tamor and K. C. Hass, “Hypothetical Superhard Carbon Metal,”
Journal of Materials Research, 5: 2273-227 6, (1990).

B. E. Williams and J. T. Glass, “Characterization of Diamond Thin
Films: Diamond Phase Identification, Surface Morphology, and Defect
Structures,” Journal of Materials Research, 4: 373-384, (1989).

75.

76.

77.

78.
79.
80.
81.
82.

83.

84.

165

J. Narayan, A. R. Srivatsa, M. Peters, S. Yokota, and K. V. Ravi, “On
Epitaxial Growth of Diamond Films on (100) Silicon Substrates,”
Applied Physics Letters, 53: 1823-1825, (1988).

D. G. K. Jeng, H. S. Than, J. E. Butler, R. F. Salat, and G. J. Fricano,
“Local Heteroepitaxial Diamond Growth on (100) Silicon,” Diamond
and Diamond-like Films and Coatings, NATO ASI Series B. Volume
266, edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl,
(Plenum Press, 1991), pp. 627-634. I

A. R. Badzian, “Defect Structure of Synthetic Diamond and Related
Phases,” Advances in X-Ray Analysis, Volume 31, edited by C. B.
Barrett, J. V. Gilfrich, R. Jenkins, J. W. Richardson, and P. K.
Predecki, (Pleneum Press, 1988), pp. 113-128.

D. E. Peebles and L .E. Pope, “Analytical and Mechanical Evaluation
of Diamond Films on Silicon,” Journal of Materials Research. 5: 2589-
2598, (1990).

C. T. Kuo, T. Y. Yen, T. H. Huang, and S. E. Hsu, “Adhesion and
'I‘ribological Properties of Diamond Films on Various Substrates,”
Journal of Materials Research, 5: 2515-2523, (1990).

D. W. Kweon and J. Y. Lee, “The Interface Morphology of Diamond
Film Grown on Si,” Journal of Applied Physics, 68:4272-4275, (1990).

K Kobashi, K. Nishimura, Y. Kawate, and T. Horiuchi, “Synthesis of
Diamonds By the Use of Microwave Plasma Chemical-Vapor
Deposition; Morphology and Growth of Diamond Films,” Physical
Review B, 38: 4067—4084, (1988). ‘

C. Wild, N. Herres, and P. Koidl, “Texture Formation in
Polycrystalline Diamond Films,” Journal of Applied Physics, 68: 973-
978, (1990).

C. Tsai, J. Nelson, W. Gerberich, J. Heberlein, and E. Pfender, “Metal
Reinforced Diamond Composite Films,” Thin Films: Stresses and
Mechanical Properties III, Materials Research Society Symposium Pro-
ceedings Volume 239, edited by W. D. Nix, J. C. Bravman, E. Arzt, and
L. B. Freund, (Materials Research Society, 1992), pp. 275-280.

J. Narayan, “Dislocations, Twins, and Grain Boundaries in CVD
Diamond Thin Films: Atomic Structure and Properties,” Journal of
Materials Research, 5: 2414-2423, (1990).

85.

86.

87.

88.

89.

90.

91.

92.

93.

166

E. D. Specht, R. E. Clausing, and L. Heatherly, “Measurement of
Crystalline Strain and Orientatin in Diamond Films Grown By
Chemical Vapor Deposition,” Journal of Materials Research, 5: 2351-
2355, (1990).

Y. Ohsawa, Y. Tamou, N. Kikuchi, K. Hiraga, T. Oku, “TEM Observa-
tions of Diamond Films Produced by Hot Filament Thermal CVD,”
Journal ofMaterials Science, 26: 3748-3752, (1991).

S. J. Harris, D. N. Belton, R. J. Blint, “Thermochemistry on the
Hydrogenated Diamond (111) Surface,” Journal of Applied Physics, 7 0:
2654-2659, (1991).

H. Hirai, O. Fukunaga, and O. Odawara, “Effect of Microwave Power
on Hydrogen Content in Chemically Vapor Deposited Diamond Films,”
Journal of the American Ceramic Society, 74: 1715-1718, (1991).

D. S. Knight and W. B. White, “Characterization of Diamond Films by
Raman Spectroscopy,” Journal of Materials Research, 4: 385-393,
(1989).

T. Anthony, W. Banholzer, J. Fleischer, L. Wei, P. Kuo, R. Thomas, and
R. Pryor, “Thermal Diffusivity of Isotopically Enriched 12C Diamond,”
Physical Review B, 42: 1104-1111, (1990).

K. M. McNamara and K. G. Gleason, “Carbon Bonding Environments
in CVD Diamond Films Investigated Via Solid-State NMR”, Diamond
and Diamond-like Films and Coatings, NATO ASI Series B. Volume
266, edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P. Koidl,
(Plenum Press, 1991), pp. 541-547.

G. J. Lewinsink, T. G. M. Oosterlaken, G. C. A. M. Janssen, and S.
Radelaar, “Evolution of Intrinsic Stress During Nucleation and
Growth of Polycrystalline Tungsten Films by Chemical Vapor
Deposition,” Thin Films: Stresses and Mechanical Properties III,
Materials Research Society Symposium Proceedings Volume 239,
edited by W. D. Nix, J. C. Bravman, E. Arzt, and L. B. Freund,
(Materials Research Society, 1992), pp. 139-144.

R. S. Fisher, J. Z. Duan, and A. G. Fox, “Stress Gradients and
Anisotropy in Thin Films,” Thin Films: Stresses and Mechanical
Properties, Materials Research Society Symposium Proceedings
Volume 130, edited by J. C. Bravman, W. D. Nix, D. M. Barnett, and D.
A.'Smith, (Materials Research Society, 1989), pp. 249-254.

94.

95.

96.

97.

98.

99.

100.

101.

102.

103.

104.

167

H. Windischmann, G. F. Epps, Y. Cong, and R. W. Collins, “Intrinsic
Stress in Diamond Films Prepared by Microwave Plasma CVD,”
Journal of Applied Physics, 69: 2231-2237, (1991).

B. S. Berry, W. C. Pritchet, J. J. Cuomo, C. R. Guarnieri, and S. J.
Whitehair, “Intrinsic Stress and Elasticity of Synthetic Diamond
Films,” Applied Physics Letters, 57: 302-303, (1990).

A. S. Argon, V. Gupta, H. S. Landis, J. A. Cornie, “Intrinsic Toughness
of Interfaces Between SiC Coatings and Substrates of Si or C Fibre,”
Journal ofMaterials Science, 24: 1207-1218, (1988).

S. Hong, T. P. Wheis, J. C. Bravman, and W. D. Nix, “Measuring
Stiffnesses and Residual Stresses of Silicon Nitride Thin Films,”
Journal of Electronic Materials, 19: 903-909, (1990).

H. Windischmann, “Intrinsic Stress in Sputter Deposited Thin Films,”
Critical Reviews in Solid State and Materials Science, 17: 547-592,
(1992).

J. L. Davidson, R. Ramesham, and C. Ellis, “Synthetic Diamond
Micromechanical Membranes, Cantilever Beams, and Bridges,”
Journal of the Electrochemical Society, 137: 3206-3210, (1990).

G. F. Cardinale and R. W. Tustison, “Biaxial Modulus Measurement of
Chemical Vapor Deposited Polycrystalline Diamond Films,” Journal of
Vacuum Science and Technology A, 9: 2204-2209, (1991).

CT. Rosenmayer, F. R. Brotzen, and R. J. Gale, “Mechanical Testing of
Thin Films,” Thin Films: Stresses and Mechanical Properties,
Materials Research Society Symposium Proceedings Volume 130,
edited by J. C. Bravman, W. D. Nix, D. M. Barnett, and D. A. Smith,
(Materials Research Society, 1989), DP. 7 7-86.

D. S. Stone, K. B. Yoder, and W. D. Sproul, “Hardness and Elastic
Modulus of TiN Based on Continuous Indentation Technique and New
Correlation,” Journal of Vacuum Science and Thchnology A, 9: 2543-
2547, (1991).

D. L. J oslin and W. C. Oliver, “A New Method for Analyzing Data
From Continuous Depth-Sensing Microindentation Tests,” Journal of
Materials Research, 5: 123-126, (1990).

W. W. Weiler, “Dynamic Loading: A New Microhardness Test Method,”
Journal of Testing and Evaluation, 18 (4): 229-239, (1990).

105.

106.

107.

108.

109.

110.

111.

113.

168

M. E. O’Hern and C. J. McHargue, “Mechanical Properties Testing of
Diamond and Diamond-like Films by Ultra-Low Load Indentation,”
Diamond and Diamond-like Films and Coatings, NATO ASI Series B.
Volume 266, edited by R. E. Clausing, L. L. Horton, J. C. Angus, and P.
Koidl, (Plenum Press, 1991), pp. 715-722.

B. S. Berry and W. C. Pritchet, “Internal Stress and Internal Friction
in Thin-Layer Microelectronic Materials,” Journal of Applied Physics,
67: 3661-3668, (1990).

X. Jiang, J. V. Harzer, B. Hillebrands, Ch. Wild, and P. Koidl,
“Brillouin Light Scattering on Chemical-Vapor-Deposited
Polycrystalline Diamond, Evaluation of the Elastic Moduli,” Applied
Physics Letters, 59: 1055-1057, (1991).

X. Jiang, “Brillouin Light Scattering on Diamond and Diamondlike
Carbon Films,” Thin Films: Stresses and Mechanical Properties III,
Materials Research Society Symposium Proceedings Volume 239,
edited by W. D. Nix, J. C. Bravman, E. Arzt, and L. B. Freund,
(Materials Research Society, 1992), pp. 269-274.

T. P. Weihs, S. Hong, J. C. Bravman, and W. D. Nix, “Measuring the
Strength and Stiffness of Thin Film Materials by Mechanically
Deflecting Cantilever Microbeams,” Thin Films: Stresses and
Mechanical Properties, Materials Research Society Symposium
Proceedings Volume 130, edited by J. C. Bravman, W. D. Nix, D. M.
Barnett, and D. A. Smith, (Materials Research Society,1989), PP.87-92.

S. Hong, T. P. Weihs, J. C. Bravman, and W. D. Nix, “The
Determination of Mechanical Parameters and Residual Stresses for
Thin Films Using Micro-Cantilever Beams,” Thin Films: Stresses and
Mechanical Properties, Materials Research Society Symposium
Proceedings Volume 130, edited by J. C. Bravman, W. D. Nix, D. M.
Barnett, and D. A. Smith, (Materials Research Society, 1989), PP.93-98.

M. K. Small, J. J. Vlassak, and W. D. Nix, “Re-Examining the Bulge
Test: Methods for Improving Accuracy and Reliability,” Thin Films:
Stresses and Mechanical Properties III, Materials Research Society
Symposium Proceedings Volume 239, edited by W. D. Nix, J. C.
Bravman, E. Arzt, and L. B. Freund, (Materials Research Society,
1992), PP. 257-262.

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and
Shells, (McGraw Hill, 1959).

114.

115.

116.

117.

118.

119.

120.

121.

122.

123.

124.

125.

169

H. Reismann, Elastic Plates: Theory and Application, (John Wiley &
Sons, 1988).

S. Way, “Bending of Circular Plates With Large Deflection,”
Transactions of the American Society of Mechanical Engineers, 56:
627-636, (1934).

C. W. Bert and J. L. Martindale, “An Accurate, Simplified Method for
Analyzing Thin Plates Undergoing Large Deflections,” AIAA Journal,
26 (2): 235-241, (1988).

B. Banerjee, “Large Deflection of a Circular Plate Under A
Concentrated Load - A New Approach,” Journal of the Industrial
Mathematics Society, 33(1): 57-61, ( 1983).

R. Schmidt, “Large Deflections of a Clamped Circular Plate,” Journal
of Engineering Mechanics Division, Proceedings of The AS CE, 94:
1603-1606, (1968).

C. Y. Chia, Nonlinear Analysis of Plates, (McGraw Hill, 1980).

B. Banerjee and S. Datta, “A New Approach to an Analysis of Large
Deflections of Thin Elastic Plates,” International Journal of Non-
Linear Mechanics, 16(1): 47-51, (1981).

B. Banerjee, “Large Deflections of Circular Plates of Variable
Thickness,” International Journal of Solid Structures, 19(2): 179-182,
(1983).

J. Mattavi, “Modeling of the Strain of Diamond Thin-Films on Silicon
Substrates,” Senior Research and Design Project, Depatement of
Materials Science and Mechanics, Michigan State University, (1993).

G. M. Pharr, “The Anomalous Behavior of Silicon During

N anoindentation,” Thin Films: Stresses and Mechanical Properties
III, Materials Research Society Symposium Proceedings Volume 239,
edited by W. D. Nix, J. C. Bravman, E. Arzt, and L. B. Freund,
(Materials Research Society, 1992), pp. 301-312.

S. Timoshenko and J. Gere, Theory of Elastic Stability, (McGraw-Hill,
1961), pp. 390.

L. E. D. Flowers, Graduate Student, Michigan State University,
Department of Materials Science and Mechanics, Personal
Communication, (1992).

126.

127.

128.

129.

130.

131.

170

J. Zhang, Graduate Student, Michigan State University, Department
of Electrical Engineering, Personal Communication (1993‘).

A. Masood, M. Aslam, M. Tamor, and T. Potter, “Techniques for
Patterning of CVD Diamond Films on Non-Diamond Substrates,”
Journal of the Electrochemical Society, 138: L67-L71, (1991).

Y. Ku, Deflections of Beams for all Spans and Cross Sections, (McGraw-
Hill, 1986), pp. 17.

K Lee, “Dependance of the Effective Young’s Modulus of Glass/Epoxy and
Glass/Glue Laminants on Adhesion Area and Glue Bond Thickness”,
Masters Thesis, Department of Materials Science and Mechanics, Michi-
gan State University, 1993.

R. Averill, Professor of Materials Science and Mechanics, Michigan State
University, Personal Communication, (1993).

G. A. Slack and S. F. Bartram, “Thermal Expansion of Some Diamondlike
Crystals”, Journal of Applied Physics, 46:89-98, 1975.

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