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dissertation entitled

POST-DEPOSITIONAL PROCESSING OF DIAMOND FILM
USING ELECTRON CYCLOTRON RESONANCE PLASMAS

presented by

Rabindra Nath Chakraborty

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POST-DEPOSITIONAL PROCESSING OF DIAMOND FILM USING

ELECTRON CYCLOTRON RESONANCE PLASMAS

By

Rabindra Nath Chakraborty

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering
1995

ABSTRACT

POST-DEPOSITIONAL ETCHING OF DIAMOND FILM USING
ELECTRON CYCLOTRON RESONANCE PLASMAS
By

Rabindra N ath Chakraborty

Both dc arc jet and microwave CVD grown diamond samples were successfully etched
using ECR plasmas generated from a microwave plasma disk reactor. The etch rate

obtained from argon-oxygen-SF6 ECR plasmas was an order of magnitude higher than the

rate achieved from the conventional mechanical means. This research work is the ﬁrst
report on etching 100 mm diameter, 1.5 mm thick diamond disks. For uniform etching of
100 mm diameter diamond wafers, an etch rate above 8 um/hr was achieved and up to 250
um was removed from these wafers. Etch rate as high as 12 um/hr were Obtained on
smaller samples. Response surface methodology was used to achieve this high diamond
etch rate. Statistical analysis showed that oxygen and rf bias have the strongest positive

inﬂuences on etch rate while SF6 has a negative effect. Experiments also demonstrated

that etching of diamond in an oxygen rich plasma environment is reactive ion assisted and
an approximate theoretical calculation of the etch rate for reactive ion etching of diamond
closely agreed with the experimentally obtained value. The etch rate was found to increase

steadily with microwave input power and downstream distance. The variation of pressure

showed a maximum rate around 4 mtorr. Diamond etched in absence of SF6 produced a

black ﬁlm on the etched surface which acted as a passivation layer. The etch rate was
found to decrease as the black layer became denser. Hence etching of diamond at a steady

high rate required the plasma to contain a minimum amount of SF6.

100 mm diameter, ~ 1 .5 mm thick, CVD grown polycrystalline diamond ﬁlms were
etched with as low as 5% non-uniformity over the surface. The non-uniformity of diamond
etching was observed to decrease when etching was performed under different modal pat-
terns. This observation was theoretically investigated to learn about the role of ambipolar
diffusion in determining the spatial variation of etch rate for different resonant modes at
downstream distance. The simulation results supported the hypothesis of mixing modes to
obtain higher uniformity of etching.

A part of our research was aimed at planarizing rough diamond surfaces by ﬁrst coat-
ing a sacriﬁcial layer on diamond and then etching both diamond and the layer at the same
rate. This method, referred to as the etch back method, was employed to planarize both do
arc-jet deposited and microwave CVD grown diamond samples. Different spin-on-sacriﬁ-
cial layers such as photoresist, titanium silicate emulsion in photoresist, and SOG were
used for coating the rough diamond surfaces. Experiments conducted on ﬁne grain, micro-
wave grown diamond ﬁlms with argon-oxygen-SF6 plasmas and SOG sacriﬁcial layers
showed initial success of achieving planarization although the etch back technique did not
succeed as well for coarse grain dc arc-jet deposited samples.

Patterning of the diamond ﬁlm using SOG as the masking material was also brieﬂy

investigated on a diamond coated integrated circuit. An argon, oxygen, SF6 plasma was

successfully used to remove the diamond layer from the desired locations.

Copyright by
Rabindra N ath Chakraborty

1995

However it is - good or bad,
It is for you, my Mom and Dad .’

Acknowledgments

First of all, I would like to thank my academic adviser, Professor D. K. Reinhard for
his excellent research guidance, patient understanding of my academic needs and continu-
ous support for over last three years. I have enjoyed every moment working with him and
this experience will remain an asset for me all through my life. Besides academics, his
goodness, dedication, honesty and equal respect for everyone have deeply moved me. I
would like to thank Professor J. Asmussen and Dr. T. Grotjohn for their advises in my
research. Also I was greatly beneﬁted from their remarkable teaching of plasma related
courses. I am thankful to Dr. M. Aslam and Professor B. Golding for their valuable com-
ments on my research. Thanks are extended to Dr. P. Goldman, previously at Norton Dia-
mond Film for his extensive co-operation in sending and documenting diamond samples. I
am also thankful to Mr. B. Cline and Mr. K. Gray of Norton Diamond Film for supplying
diamond samples and showing interests in transferring this diamond etching technology to
industry as a supplement or replacement for the existing methods of diamond ﬁnishing. I
sincerely acknowledge the help of my friends, Saeid Khatami for imaging SEMs, Brian
Wright for repairing the plasma reactor, Nidhan Choudhuri for consulting statistics, and
Anjan Ray for sharing his expertise in combustion. In addition, I want to thank Kuntal

Thakurta, Krishnendu Majumdar, Goutam Das, G. Srikant and Murali Sreenivasan for

vi

their silent wishes and precious friendship that gave me strength at the time of my distress.
I want to express my gratitude to my father who sent me to America for studying. I want to
share my satisfaction of completing this research with my brother Chiranjit Chakraborty,
and my lovely little sister Kaberi Sen who always remained eager for this moment.
Finally, I want to remember my ﬁrst teacher, my mother who inspired me to join the doc-
toral program and encouraged me always to continue my journey to the pursuit of knowl-

edge. TO me, this success is her achievement.

Funding for this research was provided in part by State of Michigan Research Excel-
lence fund and ARPA through Norton Diamond Film, a division of Saint Gobain/Norton
Industrial Ceramics Corporation. The microwave plasma disk reactor used for this
research is manufactured by Wavemat Inc. This reactor is integrated into a system manu-

factured by PlasmaQuest Inc.

vii

Table of Contents

List Of Tables .................................................. xi
List Of Figures ................................................. xii
Chapter I. Introduction ........................................... 1
1.1 Motivation of Etching Diamond with Plasmas ............................... 1
1.2 Research Objective ..................................................... 2
1.3 Outline of Dissertation ................................................. 3
Chapter 11. Background .......................................... 4
2.1 Diamond .............................................................. 4
2.2 Different Methods for Diamond Finishing .................................. 8
2.2.1 Mechanical Abrasion .............................................. 8
2.2.2 Laser Ablation ................................................... 9

2.2.3 Etching via Chemical Reactions with Metals ......................... 10

2.2.4 Oxidation of Diamond in Molecular Oxygen .......................... 12

2.2.5 Etching with Ion Beams and Non ECR Plasmas ........................ 13

2.2.6 Etching of Diamond using ECR Plasmas .............................. 18

2.2 General Discussion of Microwave Electron Cyclotron Resonance Plasma ....... 20
Chapter 111. Introduction to Instruments & Experimental Set-up ......... 28
3.1 Description of the Microwave ECR system ................................ 28
3.1.1 PlasmaQuest ECR Etching Machine .................................. 28

3.1.2 Operation of PlasmaQuest ECR Etching Machine ...................... 33

3.2 Description of Other Related Instruments ................................. 35

viii

Chapter IV. Theory of Etch Processes .............................. 44

4.1 Different Types of Etching ............................................. 45
4.1.1 Sputtering ....................................................... 45
4.1.2 Chemical Etching ................................................ 46
4.1.3 Ion-assisted Etching .............................................. 48
4.1.4 Ion-Enhanced Inhibitor Etching ..................................... 49

4.2 Plasma and Surface Interaction ......................................... 50
4.2.1 Generation of Species ............................................ 51
4.2.2 Diffusion of Species . ............................................. 53
4.2.3 Adsorption and Desorption ......................................... 56

4.3 Elementary Reaction Kinetics .......................................... 59

4.4 Surface Kinetics of Ion-assisted Carbon Etching ............................ 62

Chapter V. Etching Experiments and Results ......................... 71

5.1. Variable Identiﬁcation ................................................ 71

5.2. General Discussion on Experimental Design .............................. 75

5.3 Process of Optimizing the Diamond Etch Rate ............................. 80

5.4 Effect of Variables on Etch Rate ......................................... 93
5.4.1 Effect of RF Bias and RF Power on Etch Rate .......................... 94
5.4.2 Effect of Microwave Power on Etch Rate ............................ 104
5.4.3 Effect of Processing Pressure on Etch Rate ........................... 108
5.4.4. Effect of Oxygen, Sulfur Hexaﬁuoride Ratio on Etch Rate ............. 109
5.4.5 Effect of Argon, Oxygen Ratio on Etch Rate .......................... 115
5. 4. 6 Effect of Downstream Distance Etch Rate ............................ 120
5.4.7 Effect of Resonant Modes on Etch Rate ............................. 122

5.5 Black Film ......................................................... 123

5.6 Calculation of Approximate Diamond Etch Rate 1n Oxygen ECR Plasmas ...... 131

Chapter VI. Uniformity of Etching and Control of Etch Proﬁle. ........ 135

6.1 Derivation of the Modal Patterns ....................................... 136

6.2 Ambipolar Diffusion . ............................................... 145

6.3 Formulation of the Numerical Problem .................................. 149

6.4 Discussion of the Numerical Solution .................................... 153

Chapter VII. Planarization and Masking of Diamond Films . .......... 158

7.1 Planarization ....................................................... 158
7.1.1 Planarization with Photoresist on Thick Film Samples .................. 161

7.1.2 Planarization with Spin-On-Glass on Thick Film Samples .............. 162

7.1.3 Planarization with Titanium-Silicate on Thick Film Samples ............ 163

7.1.4 Planarization with SOG on Thin Film Diamonds ...................... 167

7.2 Masking ............ ; .............................................. 172
Chapter VIII. Summary and Future Research ........................ 175
8.1 Summary of Research ............................................... 175
8.2 Future Work ........................................................ 177
8.3 Conclusions ........................................................ 179
List of Appendices ............................................. 181
Appedix A ............................................................ 181
Appedix B ............................................................ 183
Appedix C ............................................................ 184
List of References .............................................. 191

List of Tables

Table 5.1 Ranges of the variables for the initial design .......................... 81
Table 5.2: The ﬁrst design of experiments .................................... 82
Table 5.3: Effect of variables on etch rate ................................... 83
Table 5.4: The choice of gas ﬂow rates ....................................... 85
Table 5.5: Exploring the gas effects on the etch rate ............................. 85
Table 5.6: Investigating the pressure effects .................................. 86
Table 5.7: Investigating the combined effect of power and argon .................. 89
Table 5.8: Experimental design for understanding the effect of argon .............. 89
Table 5.9: Variation of the operating mode and the power ........................ 91
Table 5.10: Uniformity analysis ............................................. 92
Table 5.11: Etch rate vs. rf bias: investigating the nature of dependence ............ 95
Table 5.12: The Effect of microwave power on etch rate ....................... 105
Table 5.13: Effect on SF6 to oxygen ﬂow ratio on etch rate ...................... l l 1
Table 5.14: Effect on argon to oxygen ﬂow ratio on etch rate ................... 1 16
Table 5.15: Effect of resonant mode on etch rate ............................. 123
Table 7.1: Dektak result of photoresist experiments ........................... 162
Table 7.2: Dektak result of SOG experiments ................................ 163
Table 7.3: Long range vs. short range dektak results ........................... 165
Table 7.4: Dektak result of titanium silicate experiments ........................ 166

xi

List of Figures

Figure 2.1: ECR effect .................................................. 26
Figure 3.1: A 25 cm diameter ECR system - MPDR 325i ........................ 29
Figure 4.1: Sputtering ................................................... 46
Figure 4.2: Pure chemical etching .......................................... 47
Figure 4.3: Ion-assisted etching ............................................ 48
Figure 4.4: Ion-enhanced inhibitor etching ................................... 49
Figure 4.5: Trench etching ............................................... 50
Figure 4.6: Details of RIE processes ......................................... 63
Figure 4.7: Reactive ion etching of diamond .................................. 65
Figure 4.8: Vertical and horizontal etching .................................... 70
Figure 5.1: One at-a time experimental approach ............................... 77
Figure 5.2: Results of regression analysis ................................... 84
Figure 5.3: The direction of steepest ascent ................................... 87
Figure 5.4: Role of microwave power in rf induced dc bias ..................... 100
Figure 5.5: Etch rate vs. rf induced dc bias ................................... 101
Figure 5.6: Etch rate vs. rf power ......................................... 102
Figure 5.7: Normalized etch rate vs. rf induced dc bias ........................ 103
Figure 5.8: Etch rate vs. microwave power at low power level ................... 106
Figure 5.9: Etch rate vs. microwave power at high power level ................. 107
Figure 5.10: Etch rate vs. process pressure .................................. 110
Figure 5.11: Etch rate vs. SF6 to oxygen ﬂow rate ratio ........................ 1 12
Figure 5.12: Etch rate of diamond with and without black ﬁlm .................. 1 14
Figure 5.13: Etch rate vs. oxygen to argon ratio .............................. 1 17
Figure 5.14: Sputter etch rate vs. rf power .................................... 1 19
Figure 5.15: Subsequent etching of diamond in oxygen plasma .................. 125
Figure 5.16: Etching of black ﬁlm with Ar, 02 and SF6 plasma ................... 126
Figure 5.17: Raman spectrum .............................................. 127
Figure 5.18: Globules on 02 etched sample ................................... 128

xii

Figure 5.19: Magniﬁed structures of globules ................................ 129

Figure 5.20: Pre-etched sample surface ..................................... 129
Figure 5.21: Conical structures on 02 etched sample ........................... 130
Figure 6.1: Cylindrical cavity of length c and radius a ........................ 137
Figure 6.2: Figure 6.2: Modal patterns for TE and TM modes ................... 146
Figure 6.3: The cross-section of plasma discharge ............................. 150
Figure 6.4: The numerical grid ............................................ 151
Figure 6.5: Region of solution and boundary conditions ........................ 152
Figure 6.6: Normalized downstream species density variation for mode 1 ........ 154
Figure 6.7: Normalized downstream species density variation for mode 2 ......... 155
Figure 6.8: Etching uniformity comparison for mode 1, mode 2 and mixed modes . . .156
Figure 7.1: Method of polishing diamond ................................... 159
Figure 7.2: Short and long range surface ﬂuctuations .......................... 166
Figure 7.3: Uncoated sample surface ...................................... 169
Figure 7.4: Planarized surface after processing with low 02 containing plasmas ..... 170
Figure 7.5: Planarized surface after processing with high 02 containing plasmas . . . 170
Figure 7.6: SOG coated diamond sample .................................... 171
Figure 7.7: Selectively etched diamond coated IC shows aluminum pad .......... 174

xiii

Cﬁapter I. Introduction

1.1 Motivation ot Etching Diamond using Plasmas

 

With the advancement of chemical vapor deposition (CVD) methods, polycrystalline
diamond can now be grown over relatively large substrate areas at a reasonably high
rate[1.1]. But due to thickness and surface irregularities, as-grown diamond samples often
need to be processed before they become useful for a given application. Etching diamond
mechanically or chemically is a very difﬁcult task since pure diamond is an extremely
hard and inert material.

On a different context, recently developed low pressure, low temperature, plasma dis-
charges, produced from electron cyclotron resonance (ECR) plasma reactors with micro-
wave excitation, have demonstrated excellent promise in semiconductor processing [1 .2].
For conventional semiconductor materials, these high density discharges are capable of
achieving high etch rate uniformly over a large diameter substrate with negligible surface
damage [1.3, 1.4]. Also high anisotropy and high etch selectivity are additional merits of
these discharges. Because of the excellent performance exhibited by the ECR plasmas, our
research was motivated to etch diamond with ECR plasmas and study its etch perfor-
mances as the plasma characteristics are changed.

Most of our research was conducted as part of an intense research program called
“Materials processing and manufacturing technologies for diamond substrate multi-chip
modules and reactor selection and diamond MCM process development - phase I and II”,
which was sponsored by the Advanced Research Project Agency (ARPA) and subcon-
tracted to us by Norton Diamond Film. Some part of the research was also funded by

Michigan Research Excellence Fund.

1.2. Research Objective
The focus of diamond etching research can be broadly divided into the following three

areas:

0 Removal of Diamond and Thickness Reduction

The ﬁrst part of this research was concerned with the development of a precise and
uniform plasma etching technique for 100 mm diameter diamond samples at an useful
rate. To do so, it was essential to study the effect of various plasma parameters on etch
rate. This was carried out by performing statistically designed experiments and the knowl-
edge of these effects was then utilized to methodically optimize the etch rate with ECR

plasmas.

° Uniformity of Etching and its Analysis

The second part of our research was intended to study the uniformity of etching 100
mm diameter polycrystalline diamond ﬁlms with ECR plasmas. The goal was to study and
ﬁnd methods to control the etch proﬁles in order to obtain a desired ﬁnal variation of wafer

thickness.

0 Reduction of Surface Roughness & Masking of Diamond

Surface roughness of as-deposited polycrystalline diamond ﬁlms often poses problems

for various applications, hence different methods are being employed to planarize the

3

rough surface. As a part of our research, ECR plasmas were investigated for reducing the
surface roughness of the diamond ﬁlms.

In addition, to utilize the high heat spreading capability of diamond, the possibility of
applying ECR plasmas to selectively etch the diamond layer grown on an integrated cir-

cuit wafer was brieﬂy studied in this research.

[.3 Qutline 0t Dissertation

Following the brief introduction of the technology used for growing the samples we
processed, various diamond etching methods as found in literature will be discussed in
detail in chapter 2. At the end of this chapter, the principle of ECR plasma generation and
its characteristics will be brieﬂy reviewed. The description and Operation of the speciﬁc
ECR plasma reactor used in this research will be given in chapter 3. Various other instru-
ments used for this research will also be introduced in this chapter.

Chapter 4 will discuss different plasma etching methods, surface reaction kinetics and
the phenomenon of etching carbon surfaces in oxygen plasmas. In chapter 5, the statistical
design of experiments and the optimization procedure of the diamond etch rate with ECR
plasmas will be described in detail. The effect of the investigated parameters on etch rate
and other important experimental observations will also be presented in this chapter with
graphs and tables. In chapter 6, the technique for improvement of etching uniformity will
be described along with the computer simulation results. Chapter 7 will discuss and docu-
ment the research conducted on the planarization and masking of diamond. Finally chapter

8 will conclude this thesis with a discussion of the direction of future research.

 

Chapter I I. Bar/{ground

2.] Diamond

Although artiﬁcial diamonds have to go a long way before they even begin to approach
being economically viable as acceptable gem grade single crystal diamond, synthetic
polycrystalline diamond is increasingly ﬁnding interest in industrial applications because
of its attractive physical, chemical and optical properties. The extreme hardness of dia-
mond and its chemical inertness in pure form, make it a useful material for coating
mechanical tools that are exposed to abrasive and corrosive environments. Chemical vapor
deposition (CVD) diamond coated products such as cutting tools, drills etc. are found to
have much higher longevity than the uncoated ones. They also have a longer lifetime than
tools coated with brazed or sintered diamond powder. Diamond is also being investigated
for possible applications in electronic industries because of its interesting electrical prop-
erties. The large bandgap, low dielectric constant, and high hole and electron mobility at
large electric ﬁelds are a few to name. Due to an incomparable heat dissipation capability
at room temperature, diamond appears to have a promising market in making multi-chip
modules for ICs with very high packaging density. Diamond also has some excellent opti-
cal properties including an absorption edge in the ultra—violet and a very high transparency
over the entire visible and most of the infrared spectrum.

The combination of all these properties and the potential of diamond to be used in
mechanical, Optical and electronic industries are driving the fundamental research towards
developing more inexpensive, fast, repetitive and convenient methods for growing and
processing diamond.

Naturally occurring diamonds are believed to be the result of carbonaceous materials

4

5

having been subjected to tremendous pressure and heat deep within the earth. Synthetic, or
man-made diamonds became possible in 1955 when laboratory equipment was used to
subject graphite to great pressure and heat. The theoretical basis of the modern high pres-
sure diamond synthesis rests on the calculations of the graphite-diamond equilibrium line
in a pressure-temperature phase diagram and the ﬁrst practical achievement of diamond
formation was based on the pioneering work of P.W. Bridgman and the engineering teams
in General Electric, ASEA and De Beers[2.1].

Today, diamonds are also grown under metastable conditions at low pressures using
chemical vapor deposition (CVD). In most cases, CVD methods use a mixture of hydro-
gen and a gaseous carbon compound such as methane which is activated and contacted
with the substrate to produce a diamond ﬁlm on the substrate [2.2]. The hydrogen gas is
dissociated into atomic hydrogen and then reacted with the carbon compound to form con-

densable carbon containing radicals such as CH3. The atomic hydrogen also reacts with

surface-bonded hydrogen, abstracting it and creating active surface sites. The carbon con-
taining radicals are then adsorbed onto these available surface sites. The carbon is subse-
quently incorporated into the diamond lattice, with abstraction of absorbate hydrogen,
again by atomic hydrogen. Although the exact chemistry for diamond formation in the
metastable state is complicated and still under investigation, the dissociation of the hydro—
gen molecule to atomic hydrogen is generally the key step to initiate the diamond growth.
Conceptually a principal function of a diamond growing reactor is to provide a means to
dissociate the hydrogen molecules. Hence any reactor that is capable in putting in the nec-
essary energy to produce enough atomic hydrogen should potentially be successful in

growing diamond [2.3].

6

Hot ﬁlament reactors, acetylene ﬂames, dc arc jets, dc plasma discharges, radio fre-
quency (rf) discharges and microwave discharges are some of the frequently used diamond
growing reactors. Out of these different techniques, the dc arc jet deposition method is fur-
ther elaborated on here since most of the samples processed for our research are produced
using this technique.

The deposition by conventional dc arc jet processes is usually conﬁned to small areas
and is difﬁcult to control in terms of quality, thickness and reproducibility. An improved
method of the dc arc jet, called magnetically mixed and spread arc (MMSARC) is in use
for producing large area, thick diamond wafers at high growth rates [2.4, 2.5]. In 1991,
Norton Diamond Film ﬁrst reported production of disks up to 6 inches in diameter and 1
mm thickness [1.1] using this technique. The MMSARC deposition technique utilizes a
controlled interaction of a solenoid magnetic ﬁeld and the intense electrical discharge to
alter the are properties providing a means of controlling the electron and ion characteris-
tics. As a result of the applied magnetic ﬁeld, better mixing of the hot plasma with the
cooler surrounding gas is achieved which in turn improves the homogeneity of the plasma
jet and results in more uniform deposition of diamond on a large area.

However, no deposition process using any of the reactors mentioned before, can grow
polycrystalline diamond to an exact thickness avoiding all undesired surface irregularities.
Rather, as-deposited diamond samples contain a lot of unwanted features such as surface
roughness, inappropriate thickness, pits, bowing etc. To correct these shortcomings of the
deposited diamond, wafers are often grown to more than the required thickness to keep
allowances for post-depositional processing work. Obtaining the right thickness and the

desired surface speciﬁcation from the as-grown wafer condition is not an easy task and is

7

often referred to as diamond ﬁnishing in this report.

Ever since the hardest material became a fascinating gem stone, the art and technology
of cutting and polishing natural diamond has been evolving. Research on CVD polycrys-
talline diamond ﬁnishing is relatively new and was started a little over a decade ago.

With the advent of better diamond growth technology for depositing thick ﬁlms,
reduction of thickness of a given diamond wafer to a speciﬁed dimension at a faster rate
with reasonable uniformity, has become a new requirement in diamond ﬁnishing work.
Finding a fast, uniform, repetitive and easy-to-use etching method for diamond with large
surface area is one of the important objectives of our research.

The large area diamond samples that we processed for this research work, are about

100 mm in diameter, 81 cm2 in area, 1.4 mm in thickness and approximately 32 g in
weight. Evidence of etching 100 mm diameter free-standing diamond disks prior to this
work is not found in literature. This is likely due to the fact that only recently CVD dia-
mond growth technology has progressed enough to deposit diamond on large area sub-
strates at relatively high rate. Therefore the etching experiments have now become
affordable. In addition to the 100 mm diameter free-standing diamond wafers, a few
smaller diamond disks with 50 mm diameter and 17.8 mm diameter were also processed.
Additional etching experiments were performed on some non-circular samples including
square shaped samples of dimensions 10 mm X 10 mm and 20 mm X 20 mm. Most of
these ﬁlms are optically semi-transparent in nature and have a milky or blackish surface
appearance depending upon the purity of the diamond. These samples were provided to us

by the Norton Diamond Film.

8
2.2 Different Methods for Diamond Finishing

2.2.] Mechanical Abrasion

The normal procedure in mechanical grinding is to use grit powder of a harder mate—
rial than the workpiece but there is nothing harder than diamond so diamond is lapped
with diamond. The traditional method of abrading diamond is by grinding on a ﬂat wheel
or scaife typically about 300 mm in diameter and made from cast-iron of carefully
selected porosity. This scaife is charged with diamond powder ranging in sizes from less
than 1 micrometer to about 40 micrometer, the larger sizes giving a faster removal rates
but a rougher ﬁnish. Therefore it is common practice to begin polishing with coarse pow-
der and ﬁnish off with say 0.1 micrometer powder to give a relatively smoother surface.
The diamond powder is mixed with olive oil or some other base to form a slurry or suspen-
sion which is rubbed over the metal scaife and then left for some time for the suspension
to be absorbed by the pores. The diamond to be polished is usually mounted in a metal
holder known as a dop where it is held in place by two or more metal claws, or sometimes
by a low melting point metal. The surface to be ﬁnished is placed against the scaife rotat-
ing at around 2500 rpm under a load of order 1 kg. The success in removal or polishing of
diamond depends quite critically on several things, especially the orientation of the dia-
mond, regular recharging of the diamond slurry, the vibration free running of the scaife,
and rigid holding of the diamond piece [2.6, 2.7]. Diamond removal becomes very difﬁ-
cult if presented to the scaife in certain orientations, for example, abrasion of diamond
along <100> is much easier than along <110>. The removal rates along a hard direction
depend more critically on the recharging of diamond paste.

Today the cast iron scaife is often replaced by a wheel of similar geometry in which

9

diamond powder is bonded in a metal alloy, or sometimes organic resin, on the surface of
the wheel. A diamond bonded scaife costs much more than a cast iron scaife and it can be
easily damaged but its use avoids the interruption and the labor involved in keeping the
cast iron wheel fully charged with powder. It is necessary to avoid overheating the dia-
mond piece by applying too much a load, as it is quite possible for a diamond to become
red hot under poor conditions. In this case, an outer layer of the diamond will be burnt and
damaged [2.8]. The chief draw-back of the mechanical etching methods is that they tend
to be costly and time consuming, often entailing an ablating rate of about 0.1 micrometer/
hr and requiring up to several weeks to ﬁnish a four inch diamond wafer. Obtaining a uni-
formity of etching over a large area is quite difﬁcult and at times, prominent polish lines
and sub-surface damages appear due to mechanical etching. Also an optical grade ﬁnal-
ﬁnishing of diamond surfaces virtually seems impossible to achieve through the mechani-
cal polishing means. For all these combined reasons, alternatives to mechanical etching

method are being investigated.

2.2.2 Laser Ablation

Lasers are normally used for drilling and cutting a wide variety of materials. A laser
beam can concentrate a pulse of energy on a very small area on a specimen in a very short
period of time [2.8]. Hence before the heat generated has the time to spread to the rest of
the work-piece the material under the beam receives sufﬁcient energy to vaporize. Lasers
are commonly used to drill polycrystalline diamond because it can pierce diamond with-
out causing much damage to the sample, but their ability to cause ablation and to convert

diamond to graphite can be used to etch, polish and pattern diamond as well.

10

Since graphite is much easier to remove compared to diamond, laser assisted etching
of diamond also ﬁnds application in micropatteming the nucleation sites and selective
growth of diamond ﬁlm [2.9, 2.10, 2.11]. Multi-pulse radiation from a laser, e.g, XeCl
laser [2.12], has been used for roughness reduction of the as grown diamond surfaces.

Usually the surface roughness is characterized in terms of Ra and its deﬁnition is given

later in chapter 7. However, to improve the polishing efﬁciency for a very rough diamond

ﬁlm (R3 = 250 pm), a combined method of laser induced polishing and plasma etching

was developed in which the largest defects are removed by irradiation with a powerful
YAG laser [2.13].

Although lasers can be used for cutting, drilling, smoothing or even micro-patterning
diamond as mentioned above, they would not appear very useful for bulk removal of mate-
rial from a large area diamond sample. This is mainly because of the fact that the laser
focuses on a very small area of the surface and ablates and graphitizes only that part of the

specimen on which it is incident.

2.2.3 Etching via Chemical Reactions with Metals
Diamond is extremely inert chemically and not affected by acids except those which at

high temperature act as oxidizers. However, there are some etching mechanisms. Diamond

is reported to be etched by molten sodium nitrate at a temperature as low as 427 0C [2.14].
It can also react with elemental metals which form carbides such as tungsten, tantalum,
titamium and zirconium, and act as solvents for carbon. For example, it is well known that
a diamond cutting tool suffers severe wear while cutting ferrous alloys which means that

diamond can be etched using its solubility property in some molten metals, such as iron,

ll

manganese, nickel, cobalt, chromium and platinum [2.15, 2.16] etc. In this case, the diffu-
sion of carbon atoms into hot metals is the primary key for etching. The maximum stock

removal of diamond on a 7 mm X 7 mm sample was found to be 7 micrometer / hr with an

iron plate at 950 0C in vacuum [2.17]. About 55% of the area was reported to be polished
in this method.

Both solid transition metals such as Fe, Mn and molten rare etch metals such as Ce are
found to chemical etch diamond by means of carbon solubility and are used for thinning,
polishing and patterning of diamond wafers. Free standing diamond ﬁlms are sandwiched

between two Mn or Fe sheets or powder aggregates and are heated in inert atmosphere at

about 900 0C. After the etching is complete, the wafer is cooled and the metallic material
is removed [2.18, 2.19]. Etching of CVD diamond ﬁlms by molten rare earth metals can
be accomplished either by multiple layer stacking of rare earth metal sheets and diamond
ﬁlms and heating to above the melting of the metals or by dipping of the diamond ﬁlms

into a bath of molten rare earth metals [2.20, 2.21]. In May 1995, about 70 micrometers of

diamond were reported to be etched with molten Ce at 920 0C in approximately 4 hours.
However, the area of the sample and the uniformity of the etching were not mentioned.
That report [2.22] also mentions a strong orientation dependent etching behavior of single

crystal diamond. The etching rate dependance on crystal orientations with selenium at 920

0C is reported to be in the order (1 1 1)> (100)>(110) with relative ratio of about 5:2: 1.
With molten rare earth metals, crystal grains are removed from both the growth and the
nucleation side. This high difference in etch rate from one direction to the other can be
used to advantage where the anisotropic etching is essential. However, for polycrystalline

diamond ﬁlms where grains may grow in all possible directions, this etching feature may

12

produce non-repetitive etch rate especially for different samples. The high sample to sam-

ple variation may pose difﬁculty in standardizing this processing technology.

2.2.4 Oxidation of Diamond in Molecular Oxygen

During heating, natural diamond is transformed into graphite at about 1800 OKin inert

atmosphere or in vacuum. However, in the presence of oxygen, diamond starts to be oxi-

dized at a temperature as low as 900 0K [2.23, 2.24]. From the fact that diamond loses
weight in oxygen containing atmosphere at sufﬁciently high temperature, it is known that
diamond can be removed by oxidation. Although the role of oxygen in etching diamond is
not entirely understood, several attempts have been made to understand the oxidation
behavior of polycrystalline diamond in molecular oxygen at elevated temperatures [2.25,
2.26]. A careful characterization of heating diamond at an elevated temperature reports
[2.27] that compared to other forms of carbon, diamond exhibits a relatively oxidation
resistant property. This results in a preferential removal of non-diamond content of the
sample when heated. Hence it can be expected that the etching characteristics and ﬁnish-
ing of diamond surface with oxygen will be dependent on the purity of the diamond sam-
ple. Another study [2.28] of polycrystalline diamond oxidation with air at 1073 K shows
that the oxidation of synthetic diamond ﬁlms started at lower temperature than that for nat-
ural diamond. The same study reports that the rates of oxidation of the polycrystalline dia—
mond ﬁlms synthesized by the hot ﬁlament and microwave plasma methods are found to
be intermediate between the l 1 1 and 100 planes Of natural diamond crystal. The apparent
activation energy for the oxidation of the synthetic diamond ﬁlms are reported to agree

with that for the oxidation of natural diamond at low oxygen pressure.

13

Further investigations [2.29] to understand the oxidation kinetics with the microwave

plasma assisted diamond ﬁlms, reveal that the oxidation rate of the microwave plasma

deposited diamond ﬁlms increase directly with sp2 content of the ﬁlm, meaning the graph-
ite content of the ﬁlm inﬂuence and help increase the etch rate of polycrystalline diamond.
This observation certainly supports the oxidation resistant nature of pure diamond in con-
trast to other easy-to-oxidize forms of carbon, e. g, graphite.

Although diamond can be etched in molecular oxygen at high temperature, a more
reactive oxidizing atmosphere is one with appreciable atomic oxygen. This is achieved in

ion beams and plasma sources as described next.

2.2.5 Etching with Ion Beams and Non E CR Plasmas

Today chemically reactive plasma discharges are not only widely used for integrated
circuit manufacturing but also provide a very vital technology for processing of materials
in other industries as well. Plasmas, the collection of electrons, neutrals and ions in a
quasi-neutral environment, are used for precise etching, patterning and other surface mod-
iﬁcations. Plasmas can be generated in a laboratory in many different ways using different
sources of input energy, e. g, dc, rf, microwave and laser, required to create the plasma spe-
cies and maintain a steady state density of species by compensating the species lost in the
process of bulk recombinations in the plasma, and the surface recombinations at the walls
and on the work-piece. Such plasmas can contact a work-piece directly and be used as a
source of ions in an ion source.

In most cases, it is found that reactive ions are primarily responsible for fast anisotro-

pic etching, hence some sources are designed to extract ions from the bulk plasma using

14

high voltage grid which is then focused on a surface for processing. The Kaufman ion
source is such an apparatus that produces a high energy ion beam and is widely used in
surface treatment. An advantage of this low pressure, line of sight, beam technique is the
ﬂexibility of directional bombardment which is not available in other plasma processes.

Ion beam etching is normally classiﬁed in two categories. If the inert gas ion beam is
used for an etching it is called ion milling. If the ion beam etching uses the ions of a gas
that is chemically reactive with the work-piece, it is referred to as reactive ion beam etch-
ing (RIBE).

Reactive ion beam etching of diamond has been studied for more than a decade using
ion extracting sources similar to the Kaufman ion source. Etching of diamond with oxygen
ion beams was reported [2.30] in 1984. It was found that the sputter yield of oxygen ions
varied with the incident angle of ions and increasing the energy of oxygen ions from 0.5 to

1.0 keV did not necessarily lead to an increase in sputter yield. Ion beam assisted etching

of diamond using a 2KeV Xe+ beam and a reactive gas of nitrogen dioxide in a Kaufman

ion source has also been reported in the literature [2.31]. The etching rate was observed to

vary from 3 micrometer/hr at 500 0K to 12 micrometer/hr at O 0K. This inverse tempera-
ture dependence of etch rate is believed due to reduced adsorption of nitrogen dioxide on
the diamond surface at higher temperature. It is also noted that in ion beam assisted etch-
in g, nitrogen dioxide is reported to produce an order of magnitude higher etch rate than
oxygen. This is assumed to be due to the higher adsorption of nitrogen dioxide on the dia-
mond surface compared to oxygen. However, usage of nitrogen dioxide poses an environ—
mental hazard [2.32]. Hence the possibility of obtaining higher etch rate of diamond using

gases that creates non-hazardous products continued.

15

The surface planarization work of CVD polycrystalline diamond with ion beam irradi-
ation [2.33] shows that the etch rate and the reduction of surface roughness has a strong
dependence on the angle of ion beam incidence. In the study by Hirata et. al., smooth sur-

faces of microwave plasma CVD diamond ﬁlms were obtained when the incident angle

was set up to 0° and 800 and the sample was heated to 400 0C in an oxygen atmosphere.

The surface roughness was reported to reduce from 3 pm Rmax to 0.5 pm Rmax. Similar to
Ra, Rmam is a measure of surface roughness and will be described later in chapter 7.

A research group at the University of Arizona, Macleod et. al, reported their results on
diamond planarization techniques using oxygen ion beams in a sequence of papers [2.32,
2.34, 2.35]. Their technique of using an overcoat on diamond surface and ﬁnding an
appropriate condition of etch rate matching will be also discussed in detail in chapter 7.

Reactive ion etching (RIE), as opposed to RIBE, refers to plasma etching where reac-
tive ions cross the plasma sheath and are incident on the substrate. RIE has also been
applied to diamond etching. For example, a microwave but non Electron-Cyclotron-Reso-
nance (ECR) plasma was successfully used to etch polycrystalline diamond ﬁlm grown on
silicon substrates [2.36]. Although that paper intended to study the nature of diamond ﬁlm

regrown on an etched diamond surface, an etch rate of 24 micrometer/hour was reported

when the substrate is heated to 850 0K by the input microwave power. Room air at an
unknown ﬂow rate was introduced for etching diamond at about 53 torr of processing
pressure while about 650 watts of microwave power was put into the plasma reactor.

A study of RIE processing of diamond with oxygen and hydrogen was also carried out
using a commercial RIE system [2.37]. Most of the etching in that report was performed

with between 200-300 W rf power, a gas ﬂow of 40-80 sccm, and a processing pressure of

 

16
65-80 mtorr. Polycrystalline diamond etched with 0.4 KeV oxygen ions at an oxygen ﬂow

of 80 sccm and at 65 mtorr processing pressure gave rise to an etch rate of 1.8 - 2.4 u m/hr

as opposed to 2.1 u m/hr for natural 11 A type diamond. Use of hydrogen plasmas to etch
diamond showed a relatively lower etch rate compared to oxygen discharges.

The same paper reports the use of oxygen and argon mixtures for RIE etching of poly—
crystalline diamond. It was found that adding a substantial amount of argon in the reaction
chamber did not affect the etch rate. Also an increase of oxygen to argon ratio from O to
100% shows an initial increase in etch rate but a saturation behavior afterwards. This sug-
gests that for a given process condition, the oxygen ions available at the surface of the sub-
strate is not dependent on the number of oxygen atoms in a gas mixture as long as a
minimum supply of the oxygen is maintained. Assuming the etch rate depends only on the
number of oxygen ions, the paper explains that the number of reactive oxygen ions in
dynamic equilibrium with the argon-oxygen mixture is presumably not a strong function
of the partial pressure of oxygen in the gas mixture and this is the reason of the above
observation.

Another experiment reported the use of an rf plasma to etch diamond, diamond-like-

carbon and graphite simultaneously at about 50 mtorr, and about 100 0C. This paper sug-
gests that the selectivity of oxidation between non—diamond and diamond forms of carbon

is very high for oxygen plasmas, much higher than for molecular oxygen at a temperature

greater than 600 0C. Also according to this report, plasma oxidation at low temperatures
does not result in faceting of diamond, in contrast to high temperature oxidation in molec-

ular oxygen or plasma oxidation at elevated temperature which resulted in faceting along

(1 1 1)direction [2.38].

17
Subsequent study of RIE etching of diamond ﬁlms with applied bias to the diamond

substrate in an oxygen only plasma reported formation of columns on the diamond surface
[2.39]. Change of rf bias to the substrate or the total processing pressure was found to have
no inﬂuence on the formation of these columns. To understand the details of this phenom-

enon, etching experiments with oxygen only, oxygen - argon and oxygen - SF6 plasmas

were conducted in a parallel plate reactive ion etching plasma system. For all the experi-
ments, 200 watts of rf power, 200 mtorr of oxygen pressure and a total of 40 sccm of gas
ﬂows were maintained. With oxygen-only plasma, small cones appeared after almost 1
hour of run which developed into columns after longer etching. Once the columns were
formed, the area between the columns etched at a faster rate than the columns themselves.
Therefore, the etch rate of the layer is determined by the etch rate of the columns. The ori-
entation of the columns are found to have no connection with the growth direction of the
ﬁlm. With oxygen—argon plasma, the oxygen ﬂow rate was ﬁxed at 10 sccm and the argon
ﬂow rates were varied between 2.5 and 80 sccm keeping the rf power ﬁxed at 200 watt and
total pressure at 200 mtorr, but the columns appeared on etched surface in all cases.

However, the authors reported that diamond etched in pure SF6 produced no columns

and gave an etch rate of about 0.14 p. m/hr. Also, when SF6 was added to oxygen with a

minimum of about 1:3 ratio, the column formation was not observed. Under those condi-
tions the etch rate was 0.94 um/hr.
The composition of these columns formed after etching in oxygen only plasmas were
investigated using X-ray photoelectron spectroscopy which determined that next to carbon
and oxygen, aluminum and ﬂuorine contributed in considerable amounts to the XPS sig-

nal. The aluminum on the sample surface is believed to originate from the aluminum

18

chamber. According to the paper, the shape of the C Is peak suggests the existence of sin-
gle carbon compound. Investigating the reason for column formation during RIE etching
in an oxygen only or in oxygen - argon plasmas, the authors conclude that columns are
formed due to an micro-masking effect caused by the deposition of hard-to-etch material
from the chamber walls. They suggest that ﬂuorine causes sufﬁcient lateral etching to pre-

vent cone formation.

2.2.6 Etching of Diamond using ECR Plasmas
Recently microwave plasma reactors are being widely used because of their electrode-
less nature and their ability to create very high density excited and charged species over an
attractive range of pressure variations. An important development in low pressure and low
temperature microwave plasma processing is the electron cyclotron resonance discharge.
The advantage of the ECR approach is that much lower ion energies can be used while
retaining reasonable etch rate on any processing material. This way the processing dam-
ages are reduced signiﬁcantly and the device performances are improved. Hence the ECR
etching is ﬁnding increasing application in device fabrication [2.40].
The ﬁrst paper on dry etching of diamond with ECR plasmas came from AT&T Bell
labs [2.41] by Pearton et. al., in April 1992 and it reported the use of a Plasmatherrn 720
ECR system which has an Asmussen-type multipolar resonant cavity (Wavemat MPDR
300) Operating at 2.45 GHz. A systematic study of the dependence of etch rate on plasma
parameters were performed. The variables, pressure, microwave power and dc bias were
varied between the ranges of l and 30 mtorr, 200-700 watts, and -50 to -300 V respec-

tively. The dc biases on the substrate are induced by the 13.56 MHz rf powering Of the

l9

cathode. Etching in oxygen-only plasma at 1 mtorr, with 400 watts of input microwave
power showed a strong dependence of etch rate on rf bias. According to this paper, the
etch rate rises rapidly for biases below about 100 V and shows a saturation behavior at
higher bias region. This observed effect of improvement of etch rate with increase of bias
in the low bias zone, is explained as the ion-enhanced desorption of the etch products

which are expected to be CO and C02. At higher rf bias, with sufﬁcient supply of energy

at the surface, the removal of etch products no longer limits the mechanism, hence a satu-
ration type behavior on etch is noticed. The rise of etch rate thereafter is because of the
increase of direct physical sputtering of the diamond.

The variation of the etch rate with increasing power at a ﬁxed bias of -80 V and a pres-
sure of 1 mtorr, showed a continuous increase. This is the result of an increased density of
oxygen ions incident on the sample surface.

The diamond etch rate variation with oxygen discharge pressure at a ﬁxed bias of -80
V and microwave power of 400 watts was found to increase with increasing pressure. The
increased supply of active oxygen species on the diamond surface at higher pressure is
thought to be the reason for this. Also described in this paper is photolithographic pattem-
ing of the diamond ﬁlm using both Hunt 5209B photoresist, and dc magnetron sputtered Ti
-Pt-Au masks. The etching is reported to be highly anisotropic at 1 mtorr, -80V, and 400
watts of oxygen plasmas. Pearton et. al, reported an etch rate as high as 24 micrometer/

hour. They also noted that an addition of SF6 to the oxygen discharge increases the rate of
diamond etching from what is obtained with oxygen only, however, no explanation for this
observation is given in the paper.

S hortly after the above paper was published, another paper [2.42] in September 1992,

20

reported the dry etching of diamond using ECR plasmas for fabricating semiconductor
devices on a plasma assisted CVD homoepitaxial diamond ﬁlm. That paper described that
since neither the thickness nor the doping concentration of that CVD ﬁlms was ideally
controlled, the adjustment of the active layer thickness was taken to be an alternative
approach for fabricating recessed gate depletion MOSFETs. Because of the lesser proba-
bility of introducing surface damages, ECR plasmas were chosen for etching the active
region of the ﬁeld effect transistor with a recessed gate and also for creating the isolation
zone. Creating the electrical isolation involved patterning a 0.1 micrometer thick sputter
deposited silicon dioxide layer with photolithography to form an etch mask. The process-
ing condition of 0.4 mtorr partial pressure of oxygen, 2.7 mtorr partial pressure of Argon,
at a forward power of 1000 watts with no induced dc bias to the substrate yielded an etch
rate of about 0.5 micrometer/hr.

Etching of CVD diamond grown on a Mo substrate in a dc discharge using 50% oxy-
gen and 50% argon ECR plasma was reported from Russia [2.43]. According to the paper,
the etching of diamond in pure oxygen plasmas makes it porous but the surface is some-
what polished in oxygen-argon plasmas. The average electron temperature and the ion
energy distribution function of the plasmas were measured by a three-grid analyzer and a
Langmuir probe respectively. It was believed that the energy distribution of the oxygen

ions were inﬂuenced by the addition of argon into the plasma [2.44].

2.; general Discussion of Microwave ECR Plasma
The technology for microwave generation of plasmas has been known since the inven-

tion of high power microwave sources during World War II, but it is more recent that these

21

sources have been repeatedly modiﬁed to improve material processing technology. Elec-
tron-cyclotron-resonance discharges are in most cases excited at a commercial microwave
frequency of 2.45 GHz. These reactors differ from other microwave sources in their capa-
bility of coupling microwave power to the plasma at a very low pressure, usually in the
neighborhood of 1 mtorr. ECR sources generate very dense but low ion energy plasma
species which signiﬁcantly reduce the possibility of introducing surface and sub-surface
damages during processing. In addition to damage-free processing, ECR plasmas produce
very high anisotropic etching at reasonably high rates and with an excellent uniformity.
Because of the all these characteristics in combination, the ECR reactor is of interest today
to meet the requirements of stricter processing standards, especially in IC fabrication tech-
nology. Also as noted earlier, ECR plasmas are of interest for diamond ﬁnishing.
Therefore, background information on the mechanism and basic principles for opera-
tion of ECR discharge is discussed here in the context of the particular ECR design used in

this study, the multipolar plasma disk reactor (MPDR).

° Functioning of an Electron-Cyclotron-Resonance Plasma Source

Asmussen et.al., have described a multipolar ECR plasma source, also referred to as
the microwave plasma disk reactor, which utilizes a tunable microwave cavity designed to
create a cylindrical disk discharge that provides a large discharge cross sectional surface
for plasma processing on a large diameter substrate [2.45]. A sliding short and the cylin-
drical cavity wall form the electromagnetic excitation zone within which the quartz dis-
charge chamber conﬁnes the working gas to the discharge region. In electrodeless high-

density low-energy plasma sources, the waves are generated near a plasma surface and

22

then propagate into the plasma where they are subsequently absorbed, leading to heating
of plasma electrons and thereby exciting the discharge. For ECR discharges, the micro-
wave energy is coupled to the natural frequency of the electron gas in the presence of a

magnetic ﬁeld where the natural resonance frequency of electrons is deﬁned as:
(1)“, = — (1)

In the above expression, e is the charge of the electron, B is the strength of the static

magnetic ﬁeld, and me is the mass of an individual electron. The resonance occurs when

the electron cyclotron frequency equals to the excitation frequency a). In an actual dis-
charge this condition can be satisﬁed in a volume or surface within the discharge where

the static magnetic ﬁeld strength is appropriate for resonance, i.e a) = (I) and a compo-

ce
nent of electric ﬁeld is perpendicular to the static magnetic ﬁeld. This is called an ECR
zone. The electrons are accelerated in this zone and in turn ionize and excite the neutral
gas. The result is a plasma, the property of which can be varied with the discharge pres-
sure, the gas inﬂow rate and the microwave input power [2.46].

The time and spatially varying microwave electric ﬁeld which maintains the discharge

can be mathematically expressed as E (helm . This spatially varying electric ﬁeld pene-
trates the discharge volume and inﬂuences the movement of the electron gas. An indepen-
dent static but spatially varying magnetic ﬁeld is also impressed on this discharge volume.

Under steady state conditions of the microwave discharge, the total electromagnetic

power absorbed by the whole plasma volume Pa has to equal the total power lost by the

plasma volume P1055. The input power has a non-uniform distribution over the discharge

23

volume and thus the power absorbed by an arbitrary differential volume becomes a func-
tion of position. If the absorbed power density at position I is expressed as (P) a b 5(i') ,
then it can be related to the discharge complex tensor conductivity 6(f) and electric ﬁeld
E (7') as:
<P>.,,,,(t) = 5mm?) . admin (2)

where both the complex plasma conductivity and the electric ﬁeld are the functions of

position in co-ordinate space.

For any differential plasma volume, this absorbed power (P)abs(i) must be lost to
maintain a steady state. Hence the power balance equation at any arbitrary position is writ-
ten as:

(P)abs(;) = <P>1055(”') (3)

where the power lost by the differential volume is expressed as (P) [0550) at a position

in If the power absorbed per unit differential volume (P) a b 5(f) is integrated over the

whole discharge volume, we get the total microwave power absorbed by the plasma P 0.

Pa = [ (P)abs(r)dV = J’ (P)loss(r)dV = p10” (4)

vol vol

The absorption and the loss mechanisms in a discharge are quite complicated. The
microwave electrical energy is absorbed by the charged particles e.g, electron and the ion
gas. However, the work done on a charged particle by an electric ﬁeld varies inversely as
the particle mass, hence the energy imparted to the electron gas is much greater than the

energy to the ion gas. Thus the direct energy transfer from the input source through the

24

electric ﬁeld to the ions is usually neglected. It is important to note here that the electrons
gain energy only between the collisions and they lose energy to other particles during the
elastic and inelastic collisions. Because of electron-ion and electron-neutral elastic or
inelastic collisions, the energy of the electron gas is shared by ion gas and neutral gas.
This is the basic mechanism that heats up the ions and the neutrals. The power absorbed
term in equation (4) mainly refers to the energy gain by the electron gas and the power lost
term mainly refers to the energy interchange processes that reduce the electron energy.

In a non-ECR reactor, the time—averaged microwave power density absorbed by the

electron is given by [2.47]:

 

> 2 > 2 02
<P>ab.(i)= "m" “5"" [ " 2] (5)
U

2
Zmeve 6+0)

where n(i*) is the steady state electron density, lE(i)l is the magnitude of applied elec-

tric ﬁeld, a) is the operating frequency, m is the electron mass and De is the effective col-

e
lisional frequency. At very low pressure the mean free path of the electron-neutral and

electron-ion becomes very long and the number of probabilistic collisions between elec-

tron with neutrals or ions drastically reduces, which means De « (0. Applying this condi-

tion, we can approximate equation (5) to the following form:

 

2
(P) b a): "(hezlﬂhlng

2212». (0,] (6)

It is clear from equation (6) that at very low pressure where the effective collisional

1)
frequency is much lower than the operating frequency, 66 « 1 , the power absorbed in a

25

given differential volume (P)abs(f) falls off rapidly and sustaining the discharge

becomes extremely difﬁcult. Microwave ECR reactors overcome this difﬁculty of low
pressure processing. At very low pressures such as l mtorr, the coupling of microwave
energy to the electrons is achieved by exploiting an externally impressed static magnetic
ﬁeld. The following discussion brieﬂy shows the phenomenon of electron resonance and
its effect on the power coupling expression. The details for the ECR theory may be
obtained from [2.48].

The presence of the static but spatially varying magnetic ﬁeld inﬂuences the electron
ballistics inside a discharge and the power absorbed term of the expression (5) modiﬁes.

> 2 > 2 2
<P>abs(;)= n(r)e |E(r)l [%{ l + 1 fl] (7)

2m” 2 2 2
e e ue+(m—mce) ue+(w+w

 

 

 

The above equation shows the introduction of a)“, in the modiﬁed power absorbed expres-
sion. (1)“, is the natural resonance frequency for the electrons and was deﬁned before in

equation (1). At the resonance frequency, a)“, = a), trivial mathematical manipulation of

equation (7) shows that a very high power absorption will occur because of the presence of
the pole at that frequency. Physically, at the electron cyclotron frequency, the component
of the electron velocity that is perpendicular to both static magnetic ﬁeld and electric ﬁeld,
experiences a force, resulting into an outward spiraling motion with increasing radius. The
electron gains energy proportional to the square of time it spends inside the ECR zones.
Typically in a discharge the electron orbit radius remains limited either by the elastic or
non—elastic collisions with other particles, or moving out of the ECR zone. Sometimes the

charges are lost on the walls as well. The electron motion during ECR coupling is shown

26
in the Figure 2.1. The ECR effect is largely lost at sufﬁcient high pressures, where the time

between the collisions is small compared to an ECR cycle.

NEW

G—ECR Coupling ———-' (3 Field WI 0' P3901

Figure 2.1: ECR effect [2.48]

Through the ECR coupling mechanism, the input microwave energy is thus transferred
to the electron gas which then transfers energy with the elastic and inelastic collisions to
neutrals and ions. Some of the energy is dissipated through conduction, radiation and con-
vection losses. The complete expression for the power loss term for a given differential

volume is given as [2.48]:
(P)loss = “3,1313% 'i’ ”men[zﬁmf]%c§(Te _ Tn) + evil); + ZeVerUexj]n(;) (8)
J
In the above equation D a is the ambipolar diffusion coefﬁcient, T e is the electron tem-
perature, Tn is the neutral gas temperature, k3 is the Boltzmann’s constant, A is the dis-
charge diffusion length, ui is the ionization frequency, 1)er is the jth excitation frequency

and V ex]. 15 the excrtation potential.

At very low pressure both the conduction and convection losses are negligible since

the number of carrier particles are very few at high vacuum. In most cases, the radiation

27

loss is also neglected.

Once the plasma species are created inside the discharge, they diffuse in all directions.
In a conventional ECR etching machine, usually the substrate is independently rf biased,
inducing a negative dc voltage. Since the plasma is quasi-neutral in nature, only those pos—
itively charged species that diffuse and come close enough to the applied rf bias, experi-
ence an attracting force. A nearly collisionless plasma sheath is formed around the rf
biased substrate and the ionized species gain energy when travelling through this sheath
before striking the surface of the work-piece.

Energetic ion ﬂuxes to the substrate surface are mainly responsible for enhancing reac-
tive ion etching. Further details about the etching process on the work-piece are discussed

later in chapter 5.

Chapter III. Introduction to Instruments (’7’ fﬂrimentaléet-ug

Many instruments were used at different points to carry out the diamond etching
research. An introduction to these instruments will brieﬂy be presented in this chapter. The
general theory of ECR plasmas was already presented in section 2.3. In this chapter, sec-
tion 3.1 focuses more on the constructional and Operational details of the particular etch-
ing machine that we used for diamond processing. Section 3.2 describes other related

equipment that were often or occasionally used for our research.

3.1 Description of_ the Microwave ECR system
3.1.1 PlasmaQuest-Wavemat ECR Etching Machine
Our plasma etching machine uses a 30.5 cm internal diameter cylindrical ECR cavity
applicator. This ECR cavity, also known as a Microwave Plasma Disk Reactor (MPDR)
was developed at Michigan State University and is commercially manufactured by Wave-
mat Inc [3. 1] as their model 325i“. This ECR source and the other required components
such as the main processing chamber, the vacuum system, the microwave power source,
the computer controls, the rf biasing etc. are housed together in one embodiment and man-
ufactured by PlasmaQuest Inc. [3.2]. This whole plasma etching system is commercially
identiﬁed as the PlasmaQuest model 357 W plasma system and is schematically shown in
Fig 3.1. The discharge in this reactor is conﬁned by a 25 cm diameter microwave-transpar-
ent quartz bell jar. The height of the cavity applicator can be adjusted by varying the slid-
ing short position which gives the user a freedom to choose the vertical dimension of the
cavity and in principle ﬁx a resonant mode for a particular processing run. Usually an

appropriate resonant mode for ECR coupling was pre-established by manually changing

28

Quartz Discharge Chamber Microwave
Input Probe

ECR Surface

Sliding Short

   
  

Resonant Cavity

 

Magnet

 

—>
Load-Lock

To Pumps \F

Vacuum Chamber

‘ I —‘ Movable Chuck

To Chiller <—

 

 

 

 

Figure 3.1: MPDR 325i -An ECR System with 25 cm discharge diameter

30

the short position and was not disturbed during an experimental run. The cavity is ﬁxed to
the stainless steel main processing chamber with high vacuum seals. The main chamber
and the bell jar together form an enclosure for the plasma species. This part of the reactor
almost always stays under high vacuum which is maintained by a roughing pump and a
turbomolecular pump. The roughing pump takes the pressure down from an atmosphere to
around 100 mtorr, when the turbo pump further brings it down in the range of microtorr or
below. The turbo pump and the roughing pump are connected in sequence one after the
other. The outlet for the turbo pump is called the foreline and is the inlet to the roughing
pump. Under normal condition, when no processing is done, no gas ﬂows through the cav-
ity and the chamber remains under a high vacuum called the base pressure. The base pres-
sure is monitored by a cold cathode gauge and usually for our system, the base pressure is
around ~ 1 micro-torr. However, with gas ﬂows during processing, the pressure inside nor-
mally rises to the mtorr range and is monitored by a Pirani gauge. During processing, the
chamber pressure is automatically established at the user-set total processing pressure
which comprises of the proper partial pressures of the gases of choice. This is done by an
automatic control system which reads the measurements of the main chamber pressure
and adjusts the throttle valve opening. The throttle valve is located in between the main
chamber outlet and the inlet of turbomolecular pump. When the system is in standby
between runs, the throttle valve remains open to its maximum and the turbo pump main—
tains the system at its base pressure.
Our etching system has a microwave power source of maximum power output of 1.5
KW at 2.45 GHz frequency. The nature of electromagnetic ﬁeld patterns created inside the

cavity are determined by the cavity dimension or the position of the sliding short. To

31

create and maintain a discharge in a preselected resonating mode, both the sliding short
and coupling probe length may be adjusted to tune the discharge to a matched operating
condition [3.3] and obtain minimum reﬂected microwave power. The microwave energy is
primarily absorbed by the ECR heating mechanism described in chapter 2. To create the
necessary static magnetic ﬁeld, twelve rare-earth magnets are equally spaced in a circle
around and adjacent to the quartz chamber. The magnet pairs are arranged on a soft iron
keeper with alternate poles forming a twelve pole multipolar static magnetic ﬁeld across a

radial plane. The required static magnetic ﬁeld at 2.45 GHz can be easily calculated as:

9 —31
0) e3 :3: 2.45x10 x9.1x10 x2xn= 875 Gauss (9)

2n ’ (21E)me 1.6 X 10-19

 

 

Each magnet pole pair that is used in this reactor produces a pole face maximum ﬁeld
strength of 3000 Gauss which is well above the 875 gauss line required for coupling the
microwave energy at the excitation of 2.45 GHz. The strength and the position of these
magnets form a magnetic ﬁeld surface of 875 Gauss approximately 1 cm inside the dis-
charge zone and results in a three-dimensional radial ECR surface inside the chamber
[3.4].

A water cooled, 13.56 MHz rf biased chuck having a freedom of movement along the
z-axis is housed inside the vacuum chamber. The wafer sits on this movable stage during
processing. The chuck can stay in two different locations, one is called its home position
where it rests between processing runs and the other is a user-ﬁxed higher position to
which the chuck moves up before the beginning of a run and remains till the end of etch-
ing. The downstream distance is generally deﬁned as the distance between the generation

region of the bulk plasma and the position of the wafer while processing. For our system,

32

the downstream distance is speciﬁcally measured from the bottom of the ECR magnet
housing to the top of the chuck.

The rf bias is obtained from a 0-300 watt, 13.56 MHz variable rf power supply which
is coupled to the chuck by a matching network. Once the ions and neutral species are cre-
ated through the elastic and inelastic collisions with the ECR heated electrons, they diffuse
in all directions including towards the chuck on which the processing sample sits. When
the positively charged species diffuse close to the substrate, they are attracted by the inde-
pendently applied rf bias. The independent rf bias on the chuck provides an additional
control over the energy of the ionized species before they hit the surface of the substrate.

This ECR system is a dedicated etching apparatus and has a clear-lid load-lock exten-
sion chamber for loading and unloading convenience. The pressure of the load-lock cham-
ber is maintained by a separate mechanical pump. The main chamber pressure is cycled
between the base pressure and the processing pressure. It is not exposed to atmosphere.
The load-lock chamber, which is a small chamber compared to processing chamber, takes
considerably less time to cycle from vacuum to atmosphere for sample loading. Once the
processing sample is placed on the wafer-dish inside the load-lock chamber, the pressure
reduces to a pre-selected transfer pressure (~2 mtorr) and a robot arm carries the wafer
inside the main chamber.

Similarly when the processing ﬁnishes, the wafer is brought back to the load-lock
chamber by the robot arm, which is then sealed from the main chamber and taken up to the
atmospheric pressure for unloading. Further details of operation of this machine are

described in the following section.

33
3.1.2 Operation of the PlasmaQuest-Wavemat ECR Etching Machine

Our ECR system is a computer controlled machine and the etching conditions, includ-
ing environment such as the composition of the etching gases and the ﬂow rates, the pres-
sure inside the chamber, the input microwave power, and the rf bias are speciﬁed by the
user while programming a particular process. Also the steady state and the transient times
for each process or sub-processes can be speciﬁed while programming [3.5]. For example,
the run time for an experiment, or the separating time between establishing the gas ﬂows
and turning on the microwave power can be programmed. The machine can remain in one
of four different states, namely the sleep, edit, run or diagnostics mode as selected from
the main menu. Note that this software mode of the machine is no way related to the reso-
nant mode of the cavity.

When no etching is done, the system stays in the sleep mode. At this time, the micro-
wave and the rf power source remain turned off but the turbomolecular and roughing
pumps run in order to maintain the base pressure inside the chamber.

In the edit mode, the process sequences are programmed which are then followed dur-
ing the running of an experiment. The actual sequence is programmed by establishing var-
ious “screens” in the edit mode. Each screen in the edit mode, corresponds to speciﬁed gas
ﬂows, pressure, rf power and rf bias for a speciﬁed time duration. For a typical ﬁrst screen,
the gas ﬂows are established at a pressure slightly higher than the processing pressure.
This is useful because at higher pressure the higher collision rates among the electrons and
gas molecules facilitate initiation of a discharge. Once the plasma is initiated, it is easier to
sustain it even at lower pressure. Therefore, in most of our experiments, the plasma is

ignited at a higher pressure (about 7-10 mtorr) and later brought down to the processing

34

pressure (around 1-5 mtorr). Once the gas ﬂows are established in screen 1, an appropriate
forward microwave power is speciﬁed for screen 2. While executing this step in the run
mode, a plasma glow should appear if the sliding short position and the probe length is not
too far away from the tuned position. After allowing a short interval for settling the tran-
sients, the main chamber pressure is brought down to the desired processing pressure in
the third screen. In the fourth screen, rf bias is applied to the chuck, and the etch time is
speciﬁed. Once the etch time is elapsed, all the power supplies and gas ﬂows are pro-
grammed to zero in the ﬁnal screen, screen 5.

In summary, during the execution of an etching experiment, ﬁrst the load-lock is
vented to atmosphere for loading the wafer and then the load-lock is pumped down. The
load—lock is then purged with nitrogen and again pumped down. When the pressure is at
the pre-set transfer pressure a separating valve between the load-lock and the main-cham-
ber opens allowing a mechanical arm to place the processing wafer on to the chuck. The
robot arm comes out of the main-chamber to its home position and the valve between the
main-chamber and load-lock closes. The chuck goes up to a pre-selected height corre-
sponding to a desired down-stream distance. The gas starts to ﬂow and the pressure inside
the main-chamber increases from approximately a microtorr to the user-speciﬁed pressure
for initiating the discharge. The microwave power is turned on next and the cavity is tuned
manually if required, for the plasma to appear. The main chamber pressure then goes
down to the processing pressure and the probe length is manually varied to ensure maxi-
mum power input. The etching process continues for the speciﬁed amount of time. Upon

ﬁnishing the processing, the chuck returns to its home position, and the valve between the

load-lock and main-chamber opens. The robot lever goes inside the main-chamber to

35

collect the sample. When the sample returns to the load-lock chamber, the chamber is
vented to an atmosphere for unloading the sample. At this point, the machine can either be
re-used for another run or made to exit the run mode.

The diagnostic mode is usually not used on a regular basis. The utility of this mode is
in detecting faults or correcting the machine when it malfunctions. This mode gives the
user a lot of freedom over the drivers and controllers. However, it is advised not to use this
mode if the user is not very conﬁdent of the details of process sequences, because the sys—
tem might be damaged if wrong commands are placed.

Some more system related general safety issues are addressed in Appendix A.

3.2 Description of Other Related Instruments

0 Cleanroom, Wet Station and And Ancillary

A class 1000 cleanroom situated in C16, Research Complex for Engineering, was used
for most of the research. Several essential equipment items for our research including the
ECR plasma reactor, an ellipsometer, a microscope, a spinner, different kinds of furnaces
and a mask aligner are housed here. Except for the ECR system, the individual equipment
items are housed in class 100 individual work stations. A class 100 wet station with a hood

for safe chemical handling is also provided inside the cleanroom.

° Ellipsometer

A Gaertner WaferscanTM (Model: L115B) ellipsometer was used for measuring the

 

36

thickness of various spin-on transparent layers on the top of a diamond or diamond coated
sample. The principle of operation involves illuminating the surface of a sample with

monochromatic light having a known and controllable state of the polarization and then

analyzing the polarization state of the reﬂected light. The WaferscanTM ellipsometer uses
a Helium-Neon, l mw, 6328 Angstroms, laser as the monochromatic source of light [3.6].
The position of the stage containing the wafer can be linearly and angularly adjusted such
that the intersection of the incident, and reﬂected optical axes fall on the surface of the
wafer. A computer is used for recording the photo-detector-converted output data to ﬁnally
calculate the thickness of the transparent layer. However, for ﬁnding the thickness of the

layer, knowledge about the refractive index of the coating material is required. For all

measurements, the two angle method at 50° and 70° incident angles, was chosen.

0 Chemical Balance

Though natural diamond in pure form has an excellent transmission Of light in the vis-
ible spectrum, the polycrystalline CVD diamond samples that we processed are not per-
fectly transparent. Rather they range from being translucent to black, so the optical
devices such as an ellipsometer can not be used to precisely determine the etch rate of dia—
mond. Also for many of the samples, the polycrystalline surface is too rough to allow
e1 lipsometry.

The alternative approach taken to measure the average etch rate over the area of the

sample was simply to weigh samples before and after etching. From the weight difference

the etch rate was then computed using the simple expression stated below:

37

Weight Difference

Etched Thickness : Surface Area X Density of Diamond

 

(10)

For all our calculations, the density of diamond is assumed to be 3.515 g cm'3. Since
the samples that we processed for our experiments had regular geometrical shapes, such as
circular or rectangular, the surface area of these samples was well known in all cases.

A chemical balance (Model: Sartorius Balance A 2005) located in the Composite
Materials and Structure Center Laboratory, Research Complex For Engineering was used

for weighing samples. This balance has a digital display with a read-out resolution of 0.1

mg.

0 M icrometer

The measurement of etch rate using weight method is only good for determining the
average etch rate over the whole area of the sample, but it is not sufﬁcient to establish
whether the sample is preferentially etched in any location. A micrometer (Model: -
Scherr-Tumico-Inc. St. James, Minn. USA) was used to verify the uniformity of the etch-
ing process at MSU. For measuring the 100 mm wafers, a deep throat micrometer (Model:
Mitutyo 389) was used by colleagues at Norton Diamond Film. Different types of attach-
ments to the micrometer, namely ball and cone and ﬂat end were used to improve the mea-

suring accuracy. Finally no attachment to the micrometer was chosen giving an
approximate measurement accuracy of :10 pm.

It is noted at this point that the uniformity is generally an important criterion to make
an etching process useful in production. However, if the diamond wafer in the as-grown

state is non-uniform in thickness it may be desired to intentionally produce non-unifonn

38

etching to achieve uniform thickness. This is discussed further in chapter 6.

0 Dektak Proﬁlometer

A Dektak proﬁlometer (Sloan Model: 11 A) located in the Open Laboratory at the

Department of Physics, was mainly used for measuring the surface roughness (Ra) of a

sample. The proﬁlometer traces the surface of the sample with a ﬂoating diamond needle

that records the z-axis ﬂuctuations. The Ra computed by the instrument is an average of

line-of-sight measurements. The direction and the length of the trace is determined by the

operator where the scan length can be a maximum of 1 cm.

0 Optical Microscope and Scanning Electron Microscope

Imaging is important for surface analysis of diamond ﬁlms. Details of different
approaches for imaging characterization of diamond ﬁlms may be found in [3.7]. Various
microscopy techniques were used in this research for quantifying the uneven sample sur-
faces. A simple optical microscope, manufactured by Zeiss, (Model Axioskop), was used
for observing and taking micrographs of the diamond samples in order to characterize sur-
face morphology. The eye-piece of the microscope has a ﬁxed magniﬁcation of 10 and the
objective magniﬁcation can be varied to 2.5X, 10X, 50X, and 100x depending on choice
of the lens. The 50X and 100X objectives have differential interference contrast or Nimar—
ski capability. The microscope can also be used for an estimation of the z-axis ﬂuctuation
on the surface.

However, the optical microscope was often not adequate for viewing the detailed

39

structure of the surface. Scanning electron microscope is therefore the most widely uti-
lized technique to inspect the surface morphology of diamond. SEM operates by scanning
a focused electron beam over a surface and sensing the secondary electrons emitted from
the surface. The electron beam can be focused to an extremely small diameter (in the
range of 10-20 nm). This beam size is responsible for the resolution. The sample surface
topography is magniﬁed into an image on the monitor. SEM has many advantages over
optical microscope in its high magniﬁcations (in the range of 50X-40000 X), high resolu-
tion (2.5 - 10 nm), its extra-ordinary depth of ﬁeld (500 times greater) which results in
three dimensional imaging.

A JEOL, ISM-35 C SEM was used for getting views of the detailed features at 1000X
and 10,000X on the surface of the free standing diamond samples. Since diamond is a
non-conducting material, the samples in some cases were pre-coated with a gold ﬁlm. The
ﬁlm was then connected electrically to the conducting substrate surface with vacuum com—
patible graphite paints to avoid the charging problem while taking the micrograph. The
SEM facility is available in the Electron Optics Center at the Pesticide Research Center of

Michigan State University.

' Spinner

A spinner manufactured by Headway Research Inc. [3.8], located inside the clean-
room, was used for coating the samples with spin-on layers. Photoresist, spin-on-glass,
titanium silicate etc. were spun on the top of the process wafer. The spinner can rotate at
very high speed (about 20,000 rpm) and the time for rotation can be adjusted to a

maximum of 120 s [3.9]. In most cases, spinning work for this research required 3000 rpm

40
for 30s.

Photoresist has some inherent hazardous characteristics, so the spinner needs to be
placed under a proper ventilating hood. All necessary precautions should be followed

before using the spinner since spinner can rotate at a dangerously high speed.

0 Mask Aligner

The mask aligner, as the name suggests is generally used for aligning an optical mask
to an existing pattern developed on the process wafer from previous operational steps.
Normally the photoresist layer laid on the top of the wafer surface is exposed to ultra-vio-
let light through the mask for a pre-decided duration of time which causes the photoresist
to harden or soften depending upon the nature of the photoresist. Then the soft part of the
photoresist is etched followed by the etching of an underlying material. This is how a pat-
tern is conventionally transferred during the lithography [3.10]. For our experiment, a con-
tact printing mask aligner (Model: Karl Suss MJB3) was used which has three
independent (e.g, x, y and O) controls for moving the wafer holding chuck relative to the
mask. The process wafer mounted on the chuck is tightly held by the vacuum. The relative
positioning of the wafer can be precisely adjusted manually by looking at the TV monitor.
When the alignment is complete the mask and the wafer are clamped together for the
ultraviolet light exposure. The UV light source can operate either in constant illumination
or in constant power mode. The rated maximum output power for this UV lamp is 350 W.
In most cases, the constant power mode was chosen for operation [3.1 1]. The mask aligner
was used in this research for patterning photoresist thorough a mask for selective etching

studies. It was also used for UV—hardening photoresist layer for planarization studies.

41

The main hazard associated with the mask aligner is the exposure to the UV radiation,

hence appropriate precautions are advised before using the mask aligner.

° Ultra-sonic Cleaner

The ultrasonic cleaner, (Model: Branson 1200) was found to be extremely useful for
cleaning graphite paint from diamond samples. The graphite paint, being a conductive
adhesive was used for gluing small diamond samples to a silicon wafer so that they could
be mounted onto the chuck of the ECR system. After the etching run, the remaining car-
bon paint beneath the samples needed to be ultrasonically cleaned with acetone. As the
average diamond etch rate was calculated from the weight difference of diamond, cleaning
played an important role for getting accurate results.

It is important to mention here that water in the ultrasonic cleaner that surrounds the
beaker containing the graphite-painted diamond in acetone should always be maintained at
the speciﬁed level. Water helps cool the vibration generated heat and since acetone is ﬂam-
mable, care must be taken to avoid ﬁre hazards.

The ultrasonic vibrations generated from this equipment were also used for mixing

chemicals for our research t.

0 Heating Apparatus

There are several kinds of heating apparatus in the cleanroom. Hot plates (manufac-

tured by Corning) are normally used for heating the chemicals etc. to a maximum of

150°C. Closed heat chambers can reach up to 300 °C. To go to higher temperature

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0 Probe Station and HP parameter Analyzer

A probe-station and a HP 414SB semiconductor parameter analyzer in conjunction
were used for measuring and documenting the IC device characteristics with regard to
selective etching of diamond overcoated layers on ICs. This set-up is located in the Elec-
tronic Devices and Circuits Laboratory, of the Electrical Engineering Department.

From selected ICs on the wafer, the I-V characteristics for the resistors and the Gum-
mel plots for the transistors before the diamond coating and after diamond patterning were

made. By comparing these plots, the functioning of the devices after selective etching was

conﬁrmed.

Chapter I rV. Qheory of Etch Trocesses

Many diverse and complex phenomenon take place in a plasma etching process which
are not fully understood yet. However, some key steps of plasma etching are identiﬁed and

are broadly outlined here:
0 1. Generation of the species in the discharge
0 2. Diffusion of the species towards the substrate
- 3. Adsorption of the reactants on the substrate surface
0 4. Surface reactions
0 5. Desorption of the reaction products from the surface
0 6. Diffusion of the volatile etch products to the outlet of the chamber

0 7. Disposal of the etch products to the environment

This chapter mainly focuses on the details of steps 3, 4, and 5, i.e., adsorption, surface
kinetics of etching and desorption of products. Other related mechanisms such as the gen-
eration of species in step 1, and diffusion of species in step 2 and 6 are only brieﬂy dis-
cussed.

In some plasma processing, reaction products can be quite hazardous and proper gas
disposal measures must be taken following standard guidelines and procedures. Step 7, the

disposal of etch products to the environment is therefore an important issue and is usually

44

45

addressed when an etcher is initially installed for speciﬁc etching purposes. For our pro-
cessing, carbon in diamond form is etched in plasma whose feed gases mostly include

oxygen and SF6. In addition, C containing compounds result from substrate etching.
Therefore, the possibility exists for the production of CO, COFZ and F2, all of which are

extremely toxic.

Chapter four begins with the introduction of different types of plasma etching pro-
cesses in section 4.1. Section 4.2 discusses the diffusion, adsorption and the desorption of
neutral species. Section 4.3 reviews the reaction rate constants and the concepts of ele-
mentary reaction processes. It also describes the simple ﬁrst and second order reaction
kinetics. Section 4.4 attempts to theoretically understand the reaction processes involved
in oxygen ion-assisted diamond etching. Some fundamental reasons for etch rate limita-

tions of diamond oxidation are identiﬁed.

4.1 Diﬂerent Types of Etching

Four types of low pressure plasma processes are commonly used to remove material
from the surface of a substrate. These etching mechanisms are often identiﬁed as sputter-
ing, pure chemical etching, ion energy driven etching (also called reactive ion etching),
and ion inhibitor etching. A brief introduction to each type of etching is given here; the

details of these process may be obtained from [4.1, 4.2].

4. 1.1 Sputtering
Sputtering is basically a non-selective, physical process where the kinetic energy of

the bombarding charged particles is simply transferred to the surface molecules to liberate

46

the atoms. A noble gas which does not react chemically with target substances is often
chosen to create a discharge for sputtering. These non-reacting ions impact on the surface,

eject the atoms from the surface layer, and form the sputtered product. The mechanism is

illustrated in Figure 4.1.

Ion

/
W

Figure 4.1: Sputtering

 

Sputtered Product

 

The sputter rate is directly dependent on the surface binding energy and the masses of
the targets and projectiles. In general, at energies above 20-30 eV, heavy particles can
sputter atoms from a surface. However, the sputtering yield, deﬁned as the atoms sputtered
per incident ion, increases rapidly with energy up to a few hundred volts. Sputtering is an
anisotropic process and is strongly sensitive to the incident angle of the ions to the sub-
strate. Sputtering is used for both etching and deposition. In case of sputter-enhanced dep-

osition, the sputter product is collected on another target for growth.

4.1.2 Chemical Etching

A second etch process shown in Figure 4.2 is purely chemical etching. The discharge
supplies the gas phase etchant species, including the radical atoms and molecules, that

chemically react with the target surface and form gas phase products. It is important to

47

choose proper etchant gas species such that the chemical reaction yields gas products, that

are volatile and preferably non-hazardous.

Neutral

Volatile Product

 

Figure 4.2: Pure chemical etching

Usually this process is highly selective which means that the same discharge can pro-
duce extremely different etch rates for different substances. For example, oxygen atoms
chemically react with carbon but do not attack SiOz, so if a substrate contains both carbon
and SiOz, the carbon containing part of the substrate etches at a signiﬁcantly faster rate
than the other part in an oxygen plasma and thus etch selectivity is achieved.

Pure chemical etching, is almost in all cases, isotropic since the gas phase etchant
arrive at the substrate with near uniform angular distribution. It can be anisotropic if the
crystal orientations of the substrate promote preferential etching in certain direction. Since
more than 99% of the species in a discharge are neutrals, the ﬂux of the neutral species to
the substrate may be signiﬁcantly large, resulting in a very high etch rate. However, the
etch rate for a given material, is not limited just by the arrival of the etchant species to the

substrate but also by the complex set of reactions leading to formation of the etch products

and their desorption.

48
4.1.3 Ion-assisted Etching

In ion assisted etching the discharge supplies both neutral chemical species and ener-
getic ions to the surface. The combined effect of neutral etchant species and energetic ions
in producing etch products can be much larger than that produced by either pure chemical
etching or by sputtering alone. Ion assisted etching is a combination of chemical and phys-

ical processes and is shown in Figure 4.3.

Ion

 

Neutral
Volatile Product

\/
W

Figure 4.3: Ion-assisted etching

Products from chemical surface reactions can tend to stick to the surface shielding the
entrance for the fresh etchant species. For ion-assisted processes, the addition of high
energy ion ﬂux to the neutral ﬂux helps the etching mechanism to go in two ways. First, it
expedites the desorption of etch products from the surface, and secondly it ruptures the
surface bonds exposing the atoms of the substrate to the etchant species. These dangling
bonds often work as better active sites. Generally the etch rate increases when the ion
energy is increased beyond a certain threshold level determined by the properties of sub-
strate e.g., the bonding energy. However if the ion energy is increased sufﬁciently then a
saturation stage is reached because the rate of adsorption of the species and the formation

of etch products limit the etch rate. We know from the previous discussion that chemical

49

etching can produce very selective etching and that the physical etch process produces
extremely anisotropic etching. Ion-assisted etching is a combination of both the physical
and chemical processes. Hence the trade-off between anisotropy and selectivity become an
important consideration while designing an RIE process although the etch rate in reactive

ion etching is often much larger than either sputtering or pure chemical etching.

4.1.4 Ion-Enhanced Inhibitor Etching

Ion-enhanced inhibitor etching involves the use of the inhibitor species. The discharge
in this case supplies the etchant, the energetic ions, and the inhibitor precursor molecules
that adsorb on the substrate to form a protective layer or polymer ﬁlm. The etchant is cho—

sen to produce a high chemical etch rate of the substrate in the absence of either ion bom-

bardment or the inhibitor.

Ion
Neutral

Volatile Product
Inhibitor \ /

. _- - . - i q ‘ - ‘ -' _ . K _ -‘ ‘.
g. . . . . _ . . .' . .‘ .‘ _- _ . ‘ ‘ -‘ q ,
, .' . r _- 'r\ . . _ t -. ,
. '. - _ . . r. _ . . .' . '. A, —' . ‘. . . - . c . ‘ ' I.

 

Figure 4.4: Ion-enhanced inhibitor etching

The ion bombardment ﬂux prevents the inhibitor layer from forming or clears it as it
forms, exposing the surface to the chemical etchant. Where the ion ﬂux does not fall, the
inhibitor layer protects the surface from etching. This is illustrated in Figure 4.4. Ion

enhanced inhibitor etching is widely used in the semiconductor industry for etching

50

anisotropic trenches, where the vertical sidewalls need to be protected simultaneously

while the etching proceeds at the trench bottom, as shown in Figure 4.5.

Inhibitor layer Neutral

 

 

 

 

Figure 4.5 : Trench etching

Wafﬂe Interaction

The presence of the excited neutrals and charged species in addition to the non-excited
atomic species often give rise to very unusual chemistries in plasma. Many reactions that
are not seen otherwise are seen in a plasma environment. Also many conventional reac-
tions occur at a relatively lower temperature and at a different reaction rate inside the
plasma discharge.

In general, two different set of chemistries exist in plasma processing, one in the dis-
charge and the other at the surface of the work-piece. The discharge chemistry is responsi-
ble for maintaining a steady state concentration of different charged and neutral species
inside a bulk plasma. However, it is the interaction of plasma with the surface of the sub-

strate that provides the actual etching of the work-piece.

51
4.2.] Generation of Species

In plasma reactors, energies in non-thermal forms e. g, rf, microwave etc., are put in to
sustain the discharge mechanism. As described in chapter 3, the input energy is primarily
coupled to the electrons and then transferred to the neutrals and ions through elastic and
inelastic collisions. Scattering, excitation through momentum transfer, and ionization are
some of the important phenomena that result from collisions. Thus collisions play a signif-
icant role in generating and maintaining different species in the plasma and in determining
their energy distributions.

Broadly three distinct set of species, referred to as ions, neutrals and electrons interact
both physically and chemically inside a discharge resulting into an emission of photons
which appears as a glow of the discharge. Numerous chemical reactions that occur inside

the plasma are responsible for deciding the steady state density of each individual species.

The complexity and the number of the elementary reactions drastically increase when
more than one processing gases are ﬂown into the chamber. Non-monoatomic gases add
further complications to the discharge chemistry and the energy distribution functions.
Extensive numerical simulation is required to theoretically predict even in part the differ-
ent ionized and excited species that constitute a complex laboratory plasma. Therefore,
experimental measurement procedures, known as plasma diagnostics, are applied to iden-
tify and characterize various species in a discharge. Electrical diagnostics such as Lang-
muir probe measurements and optical diagnostic such as ﬂuorescence and spectroscopy
are some of the commonly used techniques. The probe measurement techniques are
largely used for knowing the average energy of the electron and ions, whereas actinometry

is used mainly for identifying the existence of different ions and excited neutrals in a

52

discharge. Unlike the electrical measurement techniques, most optical methods do not
introduce local perturbations in plasma and this non-destructive, non-interfering nature of
this diagnostics is often considered to be an advantage. Details of all these techniques may
be found in [4.3, 4.4, 4.5].

However, even after combining the information obtained experimentally, modelling a
discharge in reality remains quite a challenge. To brieﬂy illustrate the degree of difﬁculty
associated with the discharge chemistry, we consider here the diatomic gas oxygen which

is used for our plasma processing experiments. According to [4.6] in a pure oxygen dis—

charge, there can be signiﬁcant ground state concentrations of O, 02, 03, 0+, 02+, 04+,

- 1
03+, 0 , and electrons, as well as metastable states such as 1D and IS states of O Ag and

1 . . . .
28 states of Oz molecules. Determining the cross-sections for the binary processes

among these species are quite difﬁcult and many of these cross-section values are yet to be
precisely measured or calculated. Here the cross-section for a binary process implies the

cross-section associated with momentum transfer or ionization of any two colliding spe-
cies, say O3+and 02 for example.

Besides the complexity generated from the physical interactions such as collisions
among numerous oxygen ions and excited atoms or molecules, different types of chemical
reactions such as dissociation, recombination, attachment, excitation, resonant and non-
resonant charge transfer, etc. complicate the mechanism of species generation further.
Moreover, in actuality, our plasma for diamond etching is not a pure oxygen plasma, rather

it is composed of three gases, argon, oxygen and SF6.

Electron temperature and the species densities at the sheath and the substrate surface

53

are the main diagnostics results that we are interested in for knowing the etching mecha-
nism and the etch rate. However, plasma diagnostics was not included in this dissertation
research, and for all our theoretical calculations we rely on reasonable assumptions and
approximate values obtained from the available literature.

Later in chapter 5, we will see that even with many simpliﬁed assumptions our calcu-
lation of diamond etch rate in oxygen plasma roughly matches the experimental results

using plasma parameters within the range reported by other investigators.

4.2.2 Diffusion of Species

Diffusion is a net ﬂow of particles resulting from the spatial variation of particle con-
centrations in an environment. This common phenomenon has been studied and modeled
over many years for different particles e.g, atoms, molecules, ions, electrons, etc. in differ—
ent environments, e.g, solids, liquids, gases, and plasmas [4.7, 4.8, 4.9]. Study Of diffusion
of species in plasma has drawn signiﬁcant attention of the researchers in the area of
plasma processing since diffusion is the only means of transportation for neutrals in
plasma and an important means of transportation for charged species. Also it often con-
trols and limits many etch results e.g, etch rate and etch uniformity.

For effective etching to continue under steady state, the reactant species travel from the
generation region to the substrate surface and the etch products leave the surface and travel
through the bulk plasma to the outlet of the process-chamber where they are pumped out
as gaseous disposals. The mechanism of the charged particle diffusion in plasma is differ-
ent from that of neutrals and a separate model called ambipolar diffusion model is used to

describe the combined diffusion motion [4.10] of the ions and electrons. The ambipolar

54

diffusion mechanism is elaborated later in chapter 6 and this chapter brieﬂy discusses the
diffusion of neutral species following the discussion given in [4.11].

Random thermal motion is responsible for diffusion and the direction of the ﬂow is
determined by the gradient of concentration. The mathematical description of a diffusional

ﬂow is obtained from Fick’s expression.

FA is the ﬂux of particles of type A, D A B is the effective diffusion coefﬁcient of neutral

species A due to the collisions with B particles, and VnA is the gradient of density for par-

ticles A. The effective diffusion coefﬁcient can further be expressed as:

 

k T
B 8 (12)

D
AB
MRVAB

where kB is the Boltzmann’s constant, M R is the effective reduced mass and VAB is the

collision frequency. When the particles collide with each other, they scatter both in co-
ordinate space and in velocity space. There is a net ﬂux from regions of higher particle
concentration to regions of lower particle concentration. Often the assumption of a Max-
wellian distribution of particle velocities is used for simpliﬁcation of mathematical expres-
sions. The concept of collisional frequency can be related to the velocities of the particles

following the expression given below:
VAB = nB<GABDAB> (13)
where n B is the density of the B molecules, GAB is the collisional cross-section of A as

seen by the B molecule, and ”AB is the relative speed of the A molecule with respect to

55

the B molecule. (GABUAB> represents the average of the product of collisional cross-sec-

tion and random velocity over the velocity space. The actual cross-sections are non trivial
to compute as they are the functions of many parameters such as the temperature, the scat-
tering angle, the physical distance between colliding species etc. and it becomes more dif-
ﬁcult to calculate if the colliding species are charged particles because the presence of the
additional Coulomb force complicates the phenomenon. Important gas kinetic cross sec-
tions can be found from Tables [4.12].

However for rough calculations of diffusion coefﬁcients, charge-free species are

assumed to be hard spheres with constant cross-sections. This simpliﬁes the collision fre-
quency term and the average of (GABUAB) becomes GAB (0A3). Further simpliﬁcation

follows from the assumption of a Maxwellian distribution of neutral velocity as stated
before. Thus the collisional frequency is ﬁnally expressed in terms of more fundamental

experimental quantities such as gas temperature T and the effective neutral mass M R-

l

8kBT)2

VAB = "BGAB<UAB> = "BGABQM (14)

 

Often 1A3 = is deﬁned as the mean free path which is the average distance

”BGAB

travelled by a particle before colliding. With the assumption of hard spheres,

2 .. .
GAB = 1t(rA + r3) , where rA and r3 are the mean radrr ofA and B particles. In the case

of a homogeneous environment consisting of only one type of particles, the collisional

. 2 .
cross-section becomes 0’ = 41tr and the effective reduced mass M R becomes M/2 where

M is the mass of the particle and r is the radius of the particle respectively.

56

It can be easily seen that as the number of different species increases inside a dis-
charge, the diffusion mechanism becomes more complex. Usually a laboratory plasma is
in fact made up of more than one processing gases.

However, it is noted that for the low operating pressures in ECR processing, the mean
free paths of the species is signiﬁcantly large, on the order of a few cms, and an almost
collision-free environment is achieved. In that case, crude approximations of an effective
collisional cross-sections do not affect the calculation of the species ﬂux much, and the

calculated etch rate more or less agrees to the experimental result.

4.2.3 Adsorption and Desorption

Once the etchant species reach the vicinity of the surface by diffusion, they can with
some probability stick to the surface by a phenomenon called adsorption. This is a key
beginning step for the surface reactions that eventually produce volatile etch products. The
etch products leave the surface exposing the next layer of the substrate atoms for etching.
Thus desorption, the reverse process of adsorption also plays a crucial role for the etching
process to continue. In order to understand an etching mechanism and improve the plasma
etch rate for a certain material, both adsorption and desorption need to be carefully studied
since they often become the limiting steps for the etch rate for a particular surface process-
ing. Since the majority of the species that arrive at the surface are the neutrals, we concen-
trate here more on the adsorption phenomenon of neutrals.

Adsorption is due to an attractive force between an incoming molecule and the sub-
strate surface and can be of two kinds: Physisorption and chemisorption. Physisorption is

an exothermic process and is due to the weak Van-der-waal attractive force between a

57

molecule or atom and the surface [4.13]. When an atom comes close to the surface, typi-
cally within a distance of 0.1-0.3 nanometer, the electrons of the atom and the nucleus of
the surface material interact and form a potential well. Atoms trapped in the potential well,
remain near the surface oscillating about a mean equilibrium distance. These physisorbed
molecules are very weakly bound to the surface and can diffuse rapidly along the surface
[4.14].

Chemisorption [4.15] is due to the formation of a chemical bond between the atom or
molecule and the surface. The reaction is strongly exothermic. Chemisorption of a mole-

cule having multiple bonds can occur, for example, with breaking of one bond as a mole-

cule bonds to the surface. A molecule with a double bond shown as, A = B is
chemisorbed on a surface S when one of the bonds break and the bonding rearranges as

S — A — B — S. Often S — A — B — S is denoted by A323 and the Chemisorption process is
described by:
A = B+S—>AB:S (15)
In the case of single-bonded molecules the bonds are often torn apart as they form
bonding to the surface. This is shown in the following reaction equation.
AB+S—>A:S+B:S (16)
This process of Chemisorption following the breaking of a molecule into elemental
atoms is called the dissociative Chemisorption and requires two adsorption sites. Phys-
isorption and Chemisorption normally simultaneously exist in an etching mechanism, with
different regimes favored by individual process depending upon the surface temperature
and the nature of the energy curves that follows from the potential well formed between

the incident atoms and surface. Molecules that impinge on the surface cannot be adsorbed

58

unless both the conservation of momentum and energy is achieved. The molecules lose
their energy in the collision with the surface and those molecules for which the normal
component of the energy after collision becomes lesser than the required energy to over-
come the potential well, get trapped.

Assuming the gas neutrals in plasma follow a Maxwellian distribution, the ﬂux of the

. . 1 .. .. ,
molecules Incrdent upon the surface FA can be expressed as ZVAnAS where VA IS the

mean speed of the molecules and n A S is the gas phase volume density of the molecules at

the surface. If 5 indicates the sticking coefﬁcients, the chemisorbed molecules on the sur-

face can be written as:

r = sFA=is§AnAS (17)

ads

In general, the sticking coefﬁcient is a function of the fraction of sites covered 0 and
the gas and surface temperature. However, when thermal equilibrium is maintained, both
the surface and the gas molecules remain at the same temperature T. Generally chemisorp-
tion ceases after all the active surface sites are ﬁlled with absorbate which roughly corre-
sponds to a mono-layer of coverage. In absence of external means of creating sites,
adsorption is then continued through the physisorption mechanism where the adsorbate
trapped by physisorption diffuse along the surface to a vacant location beneath the mono-
layer. Thus many mono-layers can be physisorbed and a continuous condensation of
adsorbate can occur. However, the process comes to a steady state when the desorption
and adsorption balance each other. Under this condition, the stoichiometric equation mod-
iﬁes as:

A:S <=>A+S (18)

59

For an ion-assisted etching, the kinetic energies of the incident ions are transferred to
the adsorbed molecules upon bombardment and these molecules gain enough energy to
leave the surface. To balance the desorption rate under steady state, the adsorption rate

increases and thus a signiﬁcantly higher etch rate is achieved.

4.3 Elementary Reaction Kinetics
The phrase “chemical kinetics” is often abbreviated as kinetics and is used to describe
the quantitative study of change in concentration or pressure of reactants and products
with time brought about by the elementary chemical reactions. A reaction is called ele-
mentary if it directly proceeds in one step. In reality, the reactants may follow numerous
possible intermediate steps before the end product is formed. A signiﬁcant effort in chem-
ical kinetics has been to determine the set of elementary reactions into which a given sto-
ichiometric reaction can be broken. One type of important elementary reactions are
decomposition reactions which are often unimolecular.
A —> Products (19)
Bimolecular elementary reactions, like the one described below are also quite probable
because they require only two molecules to come close together and react:
A + B —> Products (20)
As the number of reactant molecules required for balancing a stoichiometric equation
increases, the probability of that equation being elementary reaction goes down. At high
pressure discharges, with higher concentration of gas molecules, some terrnolecular gas-
phase reactions are also found to be elementary but in low pressure discharge these types

of reactions are much less probable. However, an example of the tennolecular reaction is

60

given below.

A+B+C——)Products (21)
The reaction rate is an important parameter used for analyzing the kinetics of elemen-
tary chemical equations. It is commonly deﬁned as the per unit decrease of density of one

of the reactants or per unit increase of density of one of the products per unit time. Mathe-

matically the reaction rate R for a gas-phase reaction can be deﬁned as:

l d .
R = a32;[Aj], For allj (22)

where or]. is the stoichiometric coefﬁcients for the reaction and [A j] is the volume density

(m’3) of molecules ofjth substance. For example, the reaction rates for the stoichiometric

equation 3A + 23 —> C + D can be obtained as:

_ 1d __ _ld _ d _ d
R - 3371A] - 2El8] - EICI — mm] (23)
In case of surface reactions, the volume density [A j] is replaced by the area density

Of the jth molecule [A j'] on the surface. In general, R has a complicated form but it sim—

pliﬁes for the elementary reactions. If we deﬁne the proportionality constants K 1, K2 and
K 3 as the reaction rate constants, then the reaction rates for the elementary reactions given

by the equation (19), (20) and (21) can be expressed as equations (24), (25) and (26).

_ d -
R— dt[A]—K1[A] (24)
_ d _ d _
R— dtlAl— dtIBl—KzlAllBl (25)

_ d -1 ____9’_ _
R-EIAI— dtlBl— dthl-K3lAllBllCl (26)

61

Since equations (24), (25) and (26) are linear differential equations of ﬁrst, second and
third orders respectively, the constants K 1 (s'1 ), K2 (m3s'1) and K 3 (m°s‘l) are known as

ﬁrst-order, second-order and third-order reaction rate constants. These rate constants are
not dependent on the densities of the reactant or the product molecules but are functions of
the temperature. The thermal dependence of reaction rates is described by the Arrhenius
expression:

— /k T
KT = Koe E B (27)

where K T is the rate constant at a temperature T, K 0 is a pre-exponential factor, 8 is the

activation energy and kB is the Boltzmann’s constant. Further details related to the chemi-

cal reaction kinetics can be found in number of books [4.16, 4.17].

However, to understand the etching related surface kinetics, the concepts of the ele-
mentary reactions and reaction rates are applied to gas—solid reactions. The simplest math-
ematical model for gas-solid reactions was ﬁrst developed by Langmuir for a single site
mechanisms which was later extended for dual site mechanism by Hanshelwood [4.18,
4.19]. Active site theory is the basis for this kinetics which proposes that the reactions
occur at the favored sites on the surface. It also presumes that the surface is not fully cov-
ered by a mono-layer of adsorbed species and one atom or molecule is adsorbed per active
site due to strong valence bond. The Langmuir kinetics theory further assumes the follow-
ing conditions:

1. The surface is homogeneous, i.e., a uniform average activity can be deﬁned over the
entire surface. This assumption clearly requires an uniform distribution of sites.

2. No interaction occurs among the adsorbed species, i.e., the amount adsorbed has no

35“

Km.

L.
l H

62

effect on the adsorption rate per site.

3. Surface migration is either non-existent or so rapid that only adsorption and desorp-
tion can be the rate-controlling mechanism.

It is important to mention here that the homogeneous, non-interacting surface implies

that both the activation energy for adsorption Ea and desorption Ed remain constant in time

as well as from site to site.

The next section utilizes the concepts of the Langmuir kinetics to develop a model for

an ion assisted surface etching of carbon with oxygen only plasma.

4.4 Surface Kinetics of Ion-assisted Carbon Etching

In this section, we attempt to understand the ion-assisted mechanism of diamond etch-
ing in pure oxygen plasmas and ﬁnd an expression for etch rate of carbon based on some
practical assumptions. The approach presented here for development of this expression
closely follows the method given in [4.20].

Although etching of diamond in oxygen plasma may be a relatively new topic of study,
burning of carbon in molecular oxygen is a phenomenon known to mankind since the
beginning of the civilization. Surprisingly, even after knowing this phenomenon for ages,
the reaction mechanism of carbon and oxygen is not well understood. Whether direct oxi-

dation of carbon yields CO or C02 or both as the primary products remained a question
for many years [4.21, 4.22]. Finally researchers came to a consensus that both CO and
C02 are formed as primary products from carbon-oxygen reactions and the CO/C02 ratio

increases substantially with higher temperature and lower pressure [4.23, 4.24, 4.25]. An

accepted model for calculating the ratio of CO/C02 from direct oxidation of carbon is

63
given by equation (28) [4.26]:

[col/[c021 = Ae-ﬁ (28)

At low pressures A E 102'5 , and E E 6 — 9 kcal/mol . R and T in the above equation are the
universal gas constant and gas temperature respectively.

In the case of ECR etching, the processing pressure is usually in the order of a few
mtorr and the gas temperature is about 300 K. Therefore an approximate volume density
ratio of CO to C02 becomes 300:1 which suggests that at low pressure very little C02 is
directly formed from oxidation of carbon. C02 is rather formed in the gas-phase indepen-
dently through the oxidation of CO. So we can simplify the problem of the ﬁnding carbon
etch rate with oxygen ECR plasma by neglecting the formation of C02 from the chemical
etching of carbon. We also assume that the necessary conditions for Langmuir kinetics
hold true on the surface of carbon and the positive oxygen ions that strike the substrate

either help in desorption of CO molecules or sputter the carbon atoms depending on where

the ions are incident.

 

 

 

Figure 4.6: Details of RIE processes

64

Several important intermediate steps numbered as 1 through 10 in Figure 4.6 show dif-
ferent processes that take place between the generation of atomic oxygen in an oxygen
plasma and completion of the etching process by producing CO. These processes are
explained below along with their appropriate rate constants.

1: Diffusion of the etchant oxygen atoms to the surface at a rate constant Kn

2: Adsorption of O atoms are on the surface at a rate constant K0

3: Desorption of etchant species without reaction at a rate constant KW

4: Reaction of O atoms with the surface C at a reaction rate K ,. to form CO.

5. Thermal desorption of CO from the surface at a rate K d-

6: Ions are incident on the surface at a rate constant of K ,-.

7: Carbon atoms are sputtered at a rate constant of yiKi.

8: Ions assisted desorption process at an effective rate constant YiKi.

9: Adsorption Of etch products in gas phase back to the surface at a rate constant Kb-
10. Diffusion of CO through the bulk plasma to be pumped out at a rate constant K0

Following Langmuir kinetics we assume that all 0 atoms incident on the available
sites react instantaneously with the surface carbon to form a surface bond. Therefore, step

3 is neglected and reaction rate Kr in step 4 is assumed to be very large. Also we neglect

the processes such as 1, 9, and 10 that are not directly related to the surface kinetics and
assume that the effective etching of carbon in oxygen plasma is given by the following

four reactions:

0(g) + C(s) —> CO Adsorption rate constant 2 K (29)

a

C :O —> C 0 Thermal desorption rate constant 2 K d (30)

65

ion + C :O —) C O Ion-assisted desorption rate constant = Y1K ,- (31)
ion + C(s) —-) C(g) Sputtering rate constant = yiKi (32)

Equation 29 describes the adsorption of O atom species on the surface, equation 30
features the regular thermal desorption phenomenon, equation 31 describes the ion—
assisted desorption in case of reactive etching, and equation 32 represents the sputtering of
carbon atoms due to high energy oxygen ion bombardment. The (g) and (s) notation refer

to the gas and surface respectively and CO indicates a surface carbon-oxygen bond. Here

yi is the carbon atoms sputtered per incident oxygen ion on the uncovered carbon sites and

Y,- is the yield of the CO molecules desorbed per incident ion on a fully covered surface in

the absence of other desorption mechanism. Often Y,- is approximated by a simple model

E.
“”113: for Ei>>Eb (33)

where Eb is the energy binding the CO molecule to the surface, E,- is the ion energy and n

is the bond breaking efﬁciency factor where I] S 1 .

0.0696)

 

Figure 4.7: Reactive ion etching of diamond

66

Let us assume that the carbon substrate shown in Figure 4.7, has a surface site area-

density no’ of which 0 fraction is covered with CO bonds. Then the area-density for the

uncovered carbon atoms and oxygen-bonded carbon atoms [CD] on the surface becomes

n0'(1 — O) and nO’O respectively. We assume that "05 is the density of the oxygen atoms

in gas phase near the surface of the carbon substrate and n ,- 5 is the oxygen ion density at

the boundary of the plasma sheath.

Reactive ion etching of carbon with pure oxygen plasmas is achieved in two ways; by
forming the CO bonds through the surface reactions and desorbing the CO molecules
from the surface and by physically sputtering the carbon atoms by the positive ions of oxy-
gen. Both these processes contribute to the removal of the carbon from the surface.

Here we ﬁrst consider the etching mechanism following the formation of CO which is
described by the equations 29, 30, and 31. The rate of [C20] formation, and the thermal

and ion-assisted desorption of [C20] can be calculated using the relation given in equation

 

 

 

25.
dC'O -KOC—K '19 34
El - If . — a[ ][ ]_ anOSno( _ ) ( )
ormatton
d , ,
t thermal — desorption
d . I
330°] . _ 1 = -YiKl.[C:O][ion] = —YiKin0 9,2,5 (36)
ion - (ISSISIE(

Adding all the effects described by the above three equations, the rate of change Of

surface coverage can be calculated:

67

d d I I I I
E[C:O] = 217"“ 0 = KanOSno (l —O)—Kdn0 O—YiKino Onis (37)

I18!

Finally equation 37 can be rearranged in the following form.

Applying the steady state condition d—i) = 0 , we can further simplify equation 38, and cal-

culate O.

O = Kanos

Kan05+Kd+ YiKinl-S

 

(39)

The steady state CO desorption ﬂux can be easily found by adding the two different

desorption phenomenon (thermal and ion-assisted):
Now, we focus on the etching contributed by the sputtering of carbon atoms described

by the equation (32). The rate of carbon sputtering can be calculated as:

37mm = $011-9) = —y,K,.IC<s)IIionI = —v,-K,.n0’(l —e)n,-S (41>

sputter
The carbon atoms are ejected only when an energetic ion hits an uncovered carbon atom
on the surface. (1 — 0) portion of the total substrate area on the surface sites is not covered

with CO, therefore the ﬂux of sputtered carbon atoms can be calculated as:

yiKino'U —O)ni5 ’
- (1 —O) = 'yiKino "is (42)

 

rc = —%IC(S)1

sputter

Usually the sputter—yield y, increases as the energy of the incident ions increases. The

vertical etch rate is directly related to the ﬂux of CO molecules and the sputter ejected

68
carbon atoms that are leaving the surface and is given by:

F + F
Ev : co c (43)

where n C is the carbon atom volume-density of the substrate. Combining and rearranging

the equations 29, 30, 42 and 43, we obtain the vertical etch rate of carbon due to the for-

mation of CO and sputtering of carbon atoms:

 

1
EV = [L0] I ] mixing. (44)
Kd+ YiKinl-S Kanos

 

In order to calculate the total vertical carbon etch rate, the rate constants need to be
evaluated from the plasma characteristics which can be approximately related to some of
the plasma properties such as the electron and neutral temperatures, ion density at the
sheath etc. From the previous assumption that all 0 atoms reaching the surface are imme-
diately adsorbed, and the adsorption rate /site does not depend on the density of covered

sites, we can ﬁnd an expression for the adsorption rate coefﬁcient K a. This expression is

given below:

Average velocity of O-atom _ F0 (45)
Surface density of open C—sites n ’

 

(I

 

0
If a Maxwell-Boltzmann’s distribution is assumed for the neural 0 species inside the

bulk plasma then the ﬂux of the O-atom can be related to the neutral O temperature To and

the mass of oxygen atom MO through the following expression.

 

1 8kBT0 i I
Ka=Z[ .]/no (46)

69

Similarly the rate constant for the ion driven desorption K, is related to the electron

temperature Te, mass of the ion M i, Bohm velocity uB and the surface carbon sites density
n 0’. Equation (47) describes the relation.

1

i
k r /M.
K,- = “B, = (( B e), ’) (47)

no no

 

 

The vertical etch rate given by equation 44, describes a combined effect of both chem-
ical and ion-assisted processes. If the ion—assisted contributions e. g, ion-enhanced desorp—
tion and sputtering parts in the equation 44 are equated to zero, the equation modiﬁes to
give only the rate of chemical etch process. From section 4.3, we know that pure chemical

etching is an isotropic process and thus has the same etch rate for both horizontal and ver-

tical direction. Therefore, with Y IX 1. and yiKl. = 0 we get the following expression for

chemical etching:

E - E — ['10—] ' (48)
H _ V chemical — nC _L + l
Kd Kanos

 

 

In case of reactive ion etching of a side—wall structures as shown in Figure 4.8, equa-

tion 44 describes the vertical etch rate E v since ion-assisted etching is mainly vertically

directed for low pressure processing and equation 48 describes the horizontal etch rate

E H. Often in plasma processing, anisotropy, ah becomes an important factor and in math-

ematical terms it is deﬁned as:

a h = — (49)

7O

Ion Flux

l i

     

Figure 4.8: Vertical and horizontal etching

It is important to note that under steady state conditions, the horizontal and vertical etch
rate and thus the anisotropy are functions of temperature and can widely vary as the tem-
perature of the substrate changes. At low temperature and low pressure processing, e. g, in
ECR reactors, the etching is usually extremely anisotropic.

The following chapter utilizes the surface kinetics and the etch rate expression devel—

oped in this section for calculating the diamond etch rate in an ECR oxygen plasma.

Chapter ‘V. Etching Wriments and Results

5.]. Variable Identification

Usually development of a process involves a detailed exploration of the experimental
parameters with an aim to set them at appropriate values such that an Optimum yield of
interest is achieved. Because of the large number of combinations of experimental vari-
ables, this is not always easy. In our case, a high and uniform etch rate of diamond was

deﬁned as the primary yield of interest. We ﬁxed our attention only to the ECR type of

reactor with cylindrical discharge, speciﬁcally a Wavemat reactor of model 325iTM. Since
the reactor geometry plays an important role on the etch rate, the sliding short height was
set at the beginning of an experiment and kept unchanged for the duration of the whole
run.

With repetitive observation of relatively low diamond etch rates during early pilot
experiments, it was realized that a better insight into the major rate-affecting variables was
needed. Therefore, the following list of external variables was investigated based on the

existing knowledge of plasma and material processing theory.

1. Gas Composition: Use of the right gas composition enhances the plasma chemistry
for the etching reactions, hence the etch rate is expected to vary strongly with the gas com-
position. As described before, an ECR plasma consisting of varying proportions of argon,
oxygen and sulfur—hexaﬂuoride was chosen for our purpose. The reason for choosing oxy-
gen is obvious, as diamond is elementally carbon, and one easy way of etching diamond is

to oxidize it. However, the choice of SF6 and argon came more from experience which

71

72

will be described later. From the theory of etching, a higher proportion of oxygen in
plasma is expected to produce a higher diamond etch rate, hence an oxygen rich environ-

ment was chosen for most of the etching experiments.

2. F low rate of the etching gas and their proportion: For a given gas composition, the
total gas ﬂow rate can also be an important variable. For a given pressure, ﬂow rate deter-
mines the residence time of the gas molecules inside the main chamber. The average resi-

dence time of a gas molecule decreases with high gas feed, as is quantized by the simple

relation [5.1] given by t: % where t , p V and Q are the residence time, operating pres-

sure, main chamber volume and gas ﬂow rate respectively. Thus the ﬂow rate plays a criti-
cal role in determining the probability Of the species to react with the work-piece.

Also at low gas feed rates, etch rates often decrease as the area of the substrate
increases. This happens due to the lack of adequate etchant species. Hence a minimum
amount of ﬂow rate is required to avoid this phenomenon known as the wafer loading

effect.

3. RF bias to the substrate: The ﬂux of ions is deﬁned as F: n(i) (v) where F is the

ﬂux, n(I) is the spatially varying average number density of the species, and (v) is the
velocity of the species averaged in the velocity space. The independently applied rf bias
inﬂuences the average velocity, and the kinetic energy of the ionized species incident upon
the substrate. The energy of the impinging species is very important to both sputtering

effects and reactive ion etching.

73

4. Microwave input power: Microwave power is required to ionize the gas atoms and
molecules in order to sustain the generation of ion-electron pairs under steady state condi-
tions. It is easy to imagine following the discussion in section 2.3, that more input power
in a discharge would cause more ionization yielding a higher ion density in the bulk
plasma and a higher ﬂux of ions to strike the substrate surface. Therefore, the etch rate is

expected to increase with the increase of microwave input power.

5. Down stream substrate distance from the plasma: Previous work has experimentally
shown [5.2] that the sputter rate decreases as the distance between the substrate and the
plasma generation region increases. The experimental results agree with the theoretically
derived expression for the spatial distribution of species in the downstream region [5.3].

This expression for a cylindrical discharge is given below.

 

 

J xomb

2b Do I ]( a ) xomr (-l\'::)

"ed-(I32): Ill/0(7) 2 x—- '2— JO( a )k' (50)
m=l om Jl(xom)

In equation (50), ne, ,(r, 2:) represents the electron and ion density at a radial location r and

downstream distance 2. Here, 2:0 is taken to be the plane where a constant species con-

centration of N0 is maintained. In comparison with the experiments, 2:0 is taken to be the
bottom of the ECR base plate. r=0 implies the central axis of the cylindrical cavity.
a and b in the above expression, represent the radius of the downstream chamber and the

plasma discharge respectively. J 0 and J 1 are the bessel functions of order zero and one.

74

xom are the mlh zeros of the zero-order bessel function and k; is given by

 

D

a

x 2 1)-
k, = J(ﬂ) — (4) . The terms 1),. and Da are already deﬁned and are known as the

collisional frequency and the diffusion coefﬁcient.

Derivation of equation (50) assumes a spatially uniform species density N 0 at the gen-

eration region. Also the species density is taken to be zero at the metallic walls, and the
charged particles are assumed to follow the ambipolar diffusion theory. Equation (50)
clearly shows that the species density decreases exponentially with the downstream dis-
tance. Consequently the etch rate will increase as the downstream distance decreases.

However, this must be balanced against the uniformity concerns.

6. Main chamber processing pressure: The processing pressure directly affects the

mean free path of the species and the frequency of the species collision. From the

Te—CpA curve [5.4], it is known that for a given gas mixture and reactor geometry, lower

pressure results in a higher electron temperature, corresponding to a higher ionization rate
due to more energetic electrons. On the other hand, a lower pressure corresponds to a
reduced number of particles to be ionized. These contradictory contributions to production
of ionized species complicate the etch rate dependence on pressure.

In addition, the sheath potential across the rf biased chuck is known to vary with the
change of pressure which further complicates the dependence of etch rate on pressure.
Besides the etch rate, the etch uniformin is also affected by the processing pressure. At

lower pressures, say 1 mtorr, one expects a more uniform plasma environment and a

75

higher etch uniformity than compared to 20 mtorr. Thus it is apparent that the processing

pressure is a vital variable for both etch rate and etch uniformity.

7. Operating mode of the plasma: The operating mode in a microwave reactor deter-

—> ->

mines the patterns of E and B ﬁelds inside the circular metal cavity. These modal patterns
inﬂuence the spatial distribution of the species and are therefore expected to have effects
on etch uniformity. The spatial distribution of patterns for different TE and TM modes and

its effects on uniformity are explained in more detail in chapter 6.

5.2. General Discussion on Experimental Design

A typical approach to ﬁnd the dependence of etch rate on the each variables, is to vary
each variable one at a time keeping others ﬁxed at certain values. But this method leads to
performing a huge number of experiments. If a set of experiments is designed in which

each of our seven variables takes 5 independent values, then the number of necessary runs

becomes 57 = 78,125. If each experiment takes two hours to perform and analyze, nearly 1
or more years of round the clock experiments would be required. This unacceptably large
number of experiments and experimental hours do not even include the experiments
needed to test the repeatability. Obviously this inefﬁcient approach is not useful and needs
to be modiﬁed. At this point, a tempting compromise would be to maximize etch rate for
only one variable keeping others constant. Then ﬁxing this variable at that value, other
variables are investigated for their corresponding maxima. The process continues until all
the variables are maximized. Though this method results in a reasonably lower number of

experiments to perform, at times the method can fail miserably. The example illustrated in

76

Figure 5.1 shows that the success of this method totally depends on the nature of the
response surface. Referring to the hypothetical response curve shown in Figure 5.1, it can
be seen that while a single-variable-at-a-time optimization could lead to an apparent max-
imum of ~ 6 um/hr the actual maximum of etch rate of about 15 urn/hr exists under a dif-
ferent set of parameter values. The experimentalist would need to be lucky to reach this
correct global maximum with the technique described. However, various methodical
design approaches address this problem and are available in statistics books [5.5, 5.6, 5.7].
Statistically designed experiments help to evaluate the etch performances based on rela-
tively fewer experiments. Some of these commonly adopted design structures are listed
below.

1. One-way treatment structure: Often in statistical language, the treatments refer to
effects over which the experimenter has full control such as, the power, bias etc. in our
case. The one-way treatment structure consists of a set of treatments where no relationship
between the treatments is assumed and each treatment is analyzed independently. This is
essentially a one-variable-at-a time technique, described before.

2. Factorial arrangement treatment structure: A full factorial arrangement of treat-
ments structure consists of the set of treatment combinations constructed by combining
two or more levels of treatments. This is a very general way of constructing the experi-

mental design. If there are n treatments or variables to be analyzed with each having 3 dif-

ferent levels then sn becomes the total number of combined experiments. A special case of
factorial arrangement is the two-way treatment structure consists of the set of treatments
constructed by the levels of two different types of treatments. In general, if the ﬁrst treat-

ment type has 5 levels and the second treatment has r levels then they produce sr treatment

Variable 2

 

77

Etch Rate Proﬁles

 

 

Variable 1

Figure 5.1: One at-a time experimental approach

78

combinations. As previously noted this approach can lead to a very large number of exper-
iments.

3. Fractional factorial arrangement treatment structure: A fractional factorial arrange-
ment treatment structure consists of only a part or fraction of the possible treatment com-
binations in a full factorial treatment structure, described before. There are many
techniques for selecting an appropriate fraction, most of which depend on the assumptions
the experimenter makes about the interactions between the various types of treatments in
the treatment structure.

Recently, statistical designs of experiments, especially fractional factorial designs
have been largely used in the area of plasma etching [5.8, 5.9]. This approach commonly
begins with two distinct levels of treatments about a center point, one higher and one
lower value for each treatment. The purpose of the initial experiments is to determine the

slope of the response curve. In the case of n variables, the number of the experiments sug-

gested by the full factorial design is 2". Often the number of treatments in a plasma pro-
cessing is large e.g, n = 5 or 6, and the number of initial experiments suggested by the full
factorial design becomes unaffordable so a fraction of the experiments are usually elimi-
nated using appropriate statistical elimination formats.

During simultaneous variation of different factors, the level of response changes
because of main treatment effects and different combination of treatment interactions.
Mathematically, the difference between the average responses at the two levels of a factor
is deﬁned as the main effects. Interaction effects result from the presence of joint factor
effects. When the nature of response change with one factor depends on the levels of other

factors, then the interaction is said to exist between the prime factor and the other factors.

 

I:

t O

79

Interactions between two factors are called two-factor interaction effects, interactions
between three factors are called three-factor interaction effects and so on. Mathematically,
half the difference between the main effects of one factor at the two levels of a second fac-
tor is known as the two-factor interaction effects.

Interaction effects are not necessarily present between two given factors. Also the
experimentalist may not be interested in knowing about all interaction effects. Therefore,
while designing the fractional factorial design, the experimentalist can choose to confound
the unimportant effects in order to reduce the total number of experiments. Resolution for-
mats e. g, resolution III, IV, V etc. are different standard formats that can be used to con-
found different effects and eliminate half or more number of the experiments. With half of
the experiments eliminated from the full factorial design, a resolution III design ensures
that main-effects are not confounded with other main-effects but some main-effects may
confound with two—factor interaction effects. A resolution IV does not confound one
main-effect with other main-effects or two-factor interaction effects but does confound
two-factor interaction effects with other two-factor interaction effects. Similarly, a resolu-
tion V does not confound main effects and two-factor interaction effects with each other,
but does confound two factor interactions with three-factor interaction effects and so on.
The details of design aspects of experiments and use of different formats may be found
from [5.10].

However, once the initial experiments are performed following the design, the results
are linearly regressed to ﬁnd a best linear ﬁt for the output function which is to be opti-
mized; etch rate for our case. Common computer packages for statistical analysis such as,

SPSS [5.11] may be used for the purpose of regression [5.12]. The coefﬁcient of each of

80

the variables in the obtained linear equation determines the weight of that variable for the
output function. These response surfaces are plotted using the linear equation and the
direction of steepest ascent is chosen as the direction to further vary the variables to deter-
mine a new center point. This way the improvement of the result is continued at each iter-
ation till the global maxima of the function is reached.

The repeated use of fractional factorial design technique with two levels of treatments
about a center point to determine the direction of the steepest ascent in order to optimize

an yield is Often referred to as response surface methodology (RSM). This method sug-

gests a total of 2"'1 initial experiments to perform, where n implies the number of vari-
ables to be investigated. With this method, half the number of experiments suggested by

the full factorial designs are eliminated.

5.3 Process of Qotimizing the Diamond Etch Rate

The general response surface method was applied to our speciﬁc problem of maximiz-
ing the plasma etching rate for diamond while avoiding the non-uniformity of etching and
other undesirable effects. In the very beginning of this study, microwave input power, rf
bias to the substrate, and gas composition as determined by individual ﬂow rate were

thought to be the most important variables and the rest were kept constant. A full factorial
experiment to determine all effects would require 24 or 16 experimental runs. In order to

reduce the number of runs, a 24" fractional design was used, requiring only 8 experiments
to be identiﬁed from the initial design of 16 experiments. This elimination based on reso-
lution IV formats, guaranteed no confounding between the main effects with other main

effects or two-factor interaction effects. However, at this point, we were simply interested

81
in the main effects.

In addition to these 8 experiments the center point experiment was run thrice to learn
about the standard error of the process. The order of the experiments was randomized to
avoid hidden time effects. For all these experiments, the factors were varied between a
high value and low value which are shown in Table 5.1.

Table 5.1: Ranges of the variables for the initial design

 

 

 

 

 

 

 

 

 

 

Factor Center Higher Lower
Value Value value
Power 650 700 600
Bias 94 1 02 85
02 4 6 2
SF6 4 6 2

 

 

 

 

 

 

 

 

 

 

 

 

All these etching experiments were performed on a 50 mm diameter semi-transparent
diamond sample NTA1—005. This sample was initially 250 micron thick and 1.2518 grams
in weight and was cut out of a 100 mm diamond wafer. Our aim was to precisely and uni-
formly etch 25 microns from the 50 mm diameter diamond wafer at a reasonably high rate.

Each etching operation was 1 hour in length, with the main chamber process pressure
maintained at 7 mtorr, the Argon gas ﬂow ﬁxed at 12 sccm, and the downstream distance
at 11 cm. The etching thus Obtained during the time period of March-April 1994 is pre-
sented in the Table 5.2. Here the average etch rate was determined by weighing the sample
before and after the etching.

From the output of the statistical software SPSS/PC+ described in Appendix B, the
dominance of the chosen variables on the etch rate over the random error can be recog-

nized. The value of signif F identiﬁes the signiﬁcance of the factors considered for the

82

analysis. For our case, the SPSS output shows the value of (l-signif F) is almost 1, which
implies that bias, oxygen ﬂow rate, microwave power and SF6 ﬂow rate in combination
showed have a signiﬁcant effect (~100%) on etch rate over the uncontrolled random exper-
imental error. Thus we conclude that our initial choice of variables was appropriate.

Table 5.2: The ﬁrst design of experiments

0
N

Run # Order Power Bias

600 85
700
600
700
600
700

~

2
3
4
5
6
7
8
9

—
O
#beOOQNNNN

H
_

 

The analysis of variance (ANOVA) performed with SPSS was found helpful in identi-
fying the signiﬁcance of individual variable on the etch rate. This effects of individual fac-
tors are ranked in the descending order of inﬂuence in Table 5.3 which shows that the
effect of the ﬁrst three variables, bias, oxygen ﬂow rate, microwave power was positive on

the etch rate whereas the effect of the SF6 was negative.

From the linear multiple regression of the data reported in Table 5.2 the following

equation of etch rate was generated.

 

83
Etch Rate = 0.0338(bias) + 0.139(02) + 0.00198(power) - 0.0651(SF6) - 2.94

In the above equation, etch rate, ﬂow rates, power, and bias are expressed in micrometer/
hr, sccm, watts, and volts respectively. MATLAB software was used to plot different con-

stant etch rates with oxygen ﬂow rate and SF6 ﬂow rate as the two axes. These plots,
shown in Figure 5.2, assume 650 watts of microwave power and 2 seem of SF6 ﬂow rate.

Table 5.3: Effect of variables on etch rate

 

 

Variable Effect

 

 

Bias positive

 

 

Oxygen positive

 

 

Power positive

 

 

SF6 negative

 

 

 

 

 

 

 

 

The direction of steepest ascent suggests moving towards a higher rf bias. However,
the maximum value of the bias for the present conﬁguration of the plasma reactor in the
constant bias mode is a set point of 150 V, which induces around 120 V dc bias during etch
experiments. Hence it was clearly understood that for obtaining higher etch rate of dia-
mond we cannot follow the steepest ascent indeﬁnitely. To Obtain higher etch rate for a dc
bias of ~ 120 V, the oxygen ﬂow rate has to be increased. Figure 5.2 shows that for achiev-
ing higher etch rate, say 4 um/hr or above, the oxygen ﬂow rate has to be greater than
about 12 sccm. Hence from this analysis, increasing the rate of oxygen ﬂow was identiﬁed
as an important step for increasing the etch rate.

However, the ﬂow rate of SF6 and its combined effect with 02 on etch rate was thought

to be equally important to analyze at this point. A next set of new experiments were

designed involving 02 and SF6 gas ﬂow rates about a center point.

Oxygen Flow Rate in sccm

84

 

 

  

1

 

 

 

25
20 -
15 -
4
ﬂow rate
10 ' required for
obtaining
4 urn/hr rate
with 120 V bias
5 -
0 l
0 50

100

150 200

RF Induced DC Bias

Figure 5.2: Results of regression analysis

250

85

During these experiments, oxygen ﬂow rate was increased to 10 sccm from the 6 seem
in order to verify the prediction of increased rate with increased oxygen ﬂow. Table 5.4
shows the new values chosen for the center point, lower and upper bound for the gas ﬂow
rates. While performing the experiments, microwave power was ﬁxed at 600 W, the rf
induced bias was recorded as ~120 V, the downstream distance was held at 11 cm and the
pressure was set to 7 mtorr.

Table 5.4: The choice of gas ﬂow rates

 

 

 

 

 

 

 

 

Factor Center Higher Lower
Value Value value
02 8 1 O 6
SF6 2 3 1

 

 

 

 

 

 

 

 

 

 

These experiments were performed in April-May, 1994 and the results are shown in
the Table 5.5.

Table 5.5: Exploring the gas effects on the etch rate

Run #

Order 02 SF6

um/hr
6 6 1 4.0
6 3.0
10 4.7
10 3.5
8 3.7
8 4.1

 

For these experiments, the microwave power, the rf induced dc bias and the processing
pressure were ﬁxed at 600 watt, 122 volt, and 7 mtorr respectively. The downstream dis-

tance was held at 1 1 cm and the argon ﬂow rate was maintained at 12 sccm. The multiple

86

regression analysis on the above data yields an expression which is described as:

Etch Rate = 0.155(02) - 0.54 (SF6) + 3.68.
Constant etch rate surfaces e. g, 4, 6, 8 um/hr were plotted on an SF6-oxygen axis

using this linear equation. This plot is shown in Figure 5.3. The direction of steepest
ascent is easy to determine from plots and the plots suggest to move in the direction of as

small SF6 percentage as possible. But a separate problem crops up if this ratio Of oxygen
to SF6 is continually increased. A black ﬁlm starts forming when this ratio exceeds a cer-

tain value (about 14:1) which appears to be slightly dependent on the diamond sample and

perhaps on the diamond quality. Hence ﬁnally a direction of 10% SF6 was chosen in order
to increase the etch rate without forming the black ﬁlm. The new value of 02 and SF6 ﬂow

rates became 20 and 2 sccm.

At this point it was felt the variables that were initially neglected needed more atten-
tion. The pressure was varied between 3 and 10 mtorr which gave the etch rates shown in
Table 5.6. It should be noted that the maximum etch rate occurs at about 4 mtorr. To con-
ﬁrm this Observation, a set of 10 experiments involving pressure as one of the variables
were further designed on a fresh sample NTAl-Ol 1.

Table 5.6: Investigating the pressure effects

 

Run # Pressure [rm/hr

1 7 4.56
4 5.78
10 4.15

2
3
4 5.16
5 5.86

 

 

 

 

SF6 Flow Rate in sccm

 

87

4 micron/hr
6 micron/hr

  
 
 
 

SPSS Model

   
 
 
 

20% SF6 8 micron/hr

Data points

10% SF6

   

 

3.0 um/hr . This direction

0 is chosen to
avoid the side
effects of
etching.

O

4.0 um/hr 4.7um/hr Steepest Ascent
i »
8 16 24 32 40

Oxygen Flow Rate in sccm

Figure 5.3: The direction Of steepest ascent

88
This sample weighing 1.5988 g was very similar in appearance to NTAl-OOS and had

thickness ranging from 360 to 440 microns. It was also cut from a 100 mm diamond sam-
ple. The experiments conﬁrmed the existence of a maximum at 4 mtorr. From these pre-

liminary experiments, four Of the major variables, bias, 02 ﬂow rate, SF6 ﬂow rate, and

pressure were optimized and ﬁxed at 120 V, 20 sccm, 2 seem and 4 mtorr respectively.
With the help of the statistical design of experiments we reached an etch rate close to 6
urn/hr from an initial low etch rate of l um/hr or less.

With repeatable etch rate results and satisfactory uniformity on 50 mm wafers, 100
mm diameter samples were considered for etching. The ﬁrst 100 mm sample etched was
NTAl-60 which had a thickness of 1.29 mm and a weight of 35.69 g. It was blackish in
appearance. In the beginning, 10 runs shown in Table 5.7, were conducted to remove 50
micrometer from the substrate side. For all runs except Run 9, the substrate height was 12

cm downstream from the plasma, the 02 ﬂow rate was at ﬁxed 20 sccm and SF6 at 2 sccm.

For Run 9, the gas ﬂow rates were doubled. The aim of these experiments was to investi-
gate the combined effect of argon and power on the etch rate. These experiments were not
center point experiments. The microwave power was varied at two levels Of argon ﬂow
rate. Doubling the gas ﬂow rates did not affect the etch rate much which indicated that the
etch rate does not depend on the ﬂow rates of the individual gas as long as the mutual
ratios among the feed gas are unchanged. This experiment also conﬁrmed that the initial
gas settings did not suffer from any wafer loading effect. From the results presented in
Table 5.7, no clear combined effect of argon and power on etch rate was identiﬁed. Hence
a next set of 7 experiments were planned for etching 50 microns at a ﬁxed microwave

power level but with two levels of argon.

89

Table 5.7: Investigating the combined effect of power and argon

Run # Power Ar Run time um/hr

#

650 18
650 12
700 18
12
18
18
12
12
24
12

3.96
5.42
3.83
4.36
4.31
4.15
4.00

\OOOQGUI-RhUJN
NNNNNNNNNN

O

 

The experiments shown in Table 5.8 were also intended to test the repeatability of
etching runs under similar parameter conditions. This time the attention was focussed on
etching the growth side of the sample mainly to know the etching behavior Of the growth

side. During the etching runs, relevant parameters such as pressure, rf bias, Oz and SF6

Table 5.8: Experimental design for understanding the effect of argon

Run # Power Ar Run time [rm/hr
1 650 1 2 2 4.52

2 650 12 4.31
650 12 4.23
650 12 4.52
650 18 4.17

650 18 4.21

650 18 , 4.40

 

90

were kept at their Optimized values Of 4 mtorr, 150 volts, 2O sccm and 2 sccm respectively.

It can be seen from the results of these experiments that the effect of argon on the etch
rate was found insigniﬁcant over the range investigated. However, the etch repeatability on
the same sample under the same plasma parameters was found to be very satisfactory.
Improvements in post-etched uniformity of the samples thickness was observed. The
peripheral sides Of the samples became rougher after etching.

At this point it was decided to further remove 100 microns from the growth sides with
an intention of varying the Operating modes. This was one of the variables left untouched.
In our reactor the modes are difﬁcult to identify with certainty because the diameter of
MPDR 325i is relatively large [5.4]. For this large diameter cavity, some of the existing
modes may be degenerate or overlapped. However, for our experiments, the height Of the
sliding short and therefore the height of the cavity was taken as the variable. For every
unique resonant position of the sliding short, an unique modal pattern is generated, may it
be single, multiple or degenerate.

Initially three different cavity heights corresponding to sliding short positions 236.54,
225.00 and 248.08 mms were chosen. Table 5.9 shows the details of the design of experi-
ments and their corresponding results. Although the results do not apparently show any
signiﬁcant inﬂuence Of the modes on the etch rate, an intriguing result was obtained from
the analysis of etch uniformity. Processing with one mode (236.54) yielded a standard
deviation of about 18% (8 mm standard deviation around an average of 45 pm) which is
reduced to 5% (5 um standard deviation around an average of 103 pm) with all three
modes shown in Table 5.9. Since the total amount of etching was limited and speciﬁed by

the Norton Diamond Film, more investigations on uniformity with individual modes were

91

not possible on the same sample.

Table 5.9: Variation of the operating mode and the power

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sliding
Run # Milezovvzlave £323“ Run time um/hr
(mm)
1 650 236.54 2 5.04
2 600 236.54 2 4.74
3 600 225.00 2 3.59
4 700 225.00 2 5.12
5 600 248.08 2 4.45
6 700 248.08 2 4.84
7 650 236.54 2 4.89
8 650 236.54 2 4.82
9 600 248.08 2 4.53
10 600 225.00 2 3.49
1 1 700 236.54 2 3.24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Therefore, experiments continued on other samples to identify the overall uniformity
of etching on a 100 mm wafer with different modes and their associated etching patterns.
After quite a lot of effort we failed to recognize any statistically signiﬁcant and unique
spatial etching pattern for any individual mode. However typical uniformity data as col-
lected from measuring 21 points on a 100 mm wafer are presented in Table 5.10. These
points were varied radially and angularly on the surface. All the thickness measurements
on different 100 mm diameter wafers were obtained from Dr. Paul Goldman, previously at
Norton Diamond Film. The measurements were taken using a Mitutyo 389 deep-throat

micrometer and the measurements were repeatable only within an error bar of 10 um.

92
Table 5.10: Uniformity analysis

 

 

 

 

 

 

 

 

Sample Dates Modes unify“), %
NTAl-60 07/06/94 - 07/09/94 236.54 45 i 8 18%
NTAl-63 08/29/94 - 08/30/94 248.08 49 i 17 35%
TA-1484 09/01/94 - 09/02/94 225.00 59i7 12%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.10 shows that the standard deviation of etching was 18%, 35%, and 12% of the
mean value for modes corresponding to 236.54, 248.08, and 225.00 mm of cavity height.
The standard deviation, implying the non-uniformity of etching, in the case of mixed
modes experiments was reduced to 5% of the mean value which suggests that the etch uni-
formity can be improved with an appropriate combination of different resonant modes.
But this hypothesis was not proved statistically because the error associated with the
micrometer measurements was comparable with the uniformity improvement claimed.
Therefore, we decided to further investigate the mixing modes phenomenon from the the-
ory and simulation of the species distribution in the downstream distance. This has been
discussed in detail in chapter 6.

In the meantime, etching experiments were continued in the context of improving etch

rate and with 1.1 kW of microwave power and ﬂow rate ratio of oxygen to SF6 (28:2),

ﬁnally an etch rate of around 7 um/hr on 100 mm diameter wafers, and ~12 um/hr for 2
cm X 2 cm wafers were obtained. At this point, the bell jar showed a crack which we think
may have resulted from the high microwave power.

When the system was fully repaired, it was modiﬁed to a great extent. The rf biased

chuck was rebuilt, a new bell jar was put in and the water cooling of the rf chuck was

93

changed to a.closed loop cooling system with a chiller circulating a mixture of ethylene
glycol and de-ionized water which has a much higher electrical impedance. The results
obtained from the modiﬁed system set up are reported separately in this work.

The focus of the experimental research at this point was shifted from obtaining a fur-
ther high diamond etch rate to investigate effects of individual variables on etch rate. The
results of these investigations along with some more interesting observations are reported

in the next section.

5.4 Eﬁfect of Variables 0n Etch Rate

During performing the statistically designed experiments, we observed that oxygen,

argon, SF6 ECR plasmas can etch diamond from both the substrate and growth side, and

that the etch rate is not signiﬁcantly different from one side to the other under the same
plasma conditions. However, the etch rate does vary from one sample to the other under
the same plasma processing conditions. The reason for this observation is not yet clear but
to avoid the possibility of introducing errors due to some unknown reasons that attribute to
the property of an individual CVD diamond sample, in this section the etch rate obtained
from etching two different samples are not combined for studying the effects of individual
parameters on etch rate.

Most of the previous etching work following the factorial design concepts involved
experimental designs with simultaneous variation of multiple variables. Hence conclu—
sions about the effect of one independent variable on the etch rate was difﬁcult to draw
from these results. A fresh set of experiments was therefore designed and performed to

document single variable dependence. In most cases, every experiment was performed

94
twice to check the repeatability. The repeatability of the etch rate for polycrystalline dia-

mond ﬁlms in our system was found very satisfactory. The standard deviation is almost

always calculated to be less than 10% of the mean etch rate, and typically 3-4%.

5.4.1 Eﬂect of RF Bias and RF Power on Etch Rate

From the result of statistical analysis, rf bias was concluded to be the most dominating
factor in determining the etch rate of diamond. To explore this further, three samples, TF
271 , TF 254 A, and TF 267 were simultaneously etched with the rf power varied between
0 W and 235 W. The variation of the rf power in that range resulted in a variation of

induced negative dc substrate biasing from 0 V to 138 V for argon-oxygen-SF6 plasma.

Out of the three samples etched, TF 271 was a 92 mm diameter semi-transparent sample
with a beginning weight of 12.9346 gram; the other two samples, TF 254 A and TF 267
were 1 cm diameter semi-transparent samples with initial weights of 0. l759g and 0.0445 g
respectively.

For the experiments to study the effect of the rf induced dc bias on diamond etch rate

an argon, oxygen, SF6 plasma with ﬂow rates of 6, 28, and 2 seem at 4 mtorr processing

pressure was used. The actual absorbed microwave power was about 400 W and the mode
was ﬁxed corresponding to 248.08 mm of sliding short height. The runs were 1.5 hours
long and during processing, the wafer was placed at 5.5 cm downstream distance from the
baseplate position. Table 5.11 summarizes the results obtained from these experiments. At
the end of 16 runs used for studying the effect of bias on etch rate, a total of 73.8 mm, 84.2
um and 85.6 um were removed from TF 271, TF 254 A and T F 267 respectively.

Careful study of the experimental results in Table 5.1 I shows that at higher values of

95

dc bias (> 120V), signiﬁcant increase in rf power leads only to a very little increase in rf
induced negative dc voltage.

Table 5.11: Etch rate vs. rf bias: investigating the nature of dependence

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RF Power Induced urn/hr um/hr tun/hr
(Watts) DC Bias TF 271 TF 254A TF 267
230 -138 6.94i0. 12 7.48 i 0.99 7.67 1r 0.16
198 -136 6.38i0.05 6.19 i 0.16 6.73 i 0.16
150 -134 5.55i0.l7 6.19i0.16 6.37 i066
95 -125 3.04:0.15 4.21 i 0.33 3.54:0.66
45 -86 1.26 i 0.09 1.75 i- 0.165 2.00 i 0.16
25 -42 1.01 i 0.08 1.651000 1.77 i0. 167
l7 -23 0.52 i 0.02 0.590i0. 16 0.70:0.035
0 0 0.074 i 0.01 0 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In practice, matching the rf power to the substrate at a given dc bias requires a two-
fold adjustment. The ﬁrst part is associated with controlling the amplitude of the 13.56
MHz rf sinusoidal signal in such a way that a speciﬁed dc bias appears at the substrate and
the second part is concerned with matching the dynamic plasma load to the 50 Q imped—
ance of the rf generator for minimizing reﬂected power and maximizing the rf power ﬂow
to the substrate. The amplitude of the rf voltage is adjusted through computer control and
matching of the generator impedance to the plasma is achieved using a matching network
which can either be manually operated or computer controlled. As seen from Table 5.1 l,
the relationship between the dc bias and the corresponding rf power is clearly non-linear.

To understand this better, let us follow the analysis given by Lieberman [5.13] and

96

consider a discharge modeled as a load impedance Z D = R D + jXD where RD and XD are

the discharge resistance and react‘ances respectively. The rf power source connected to ZD

is modeled by its Thevenin’s equivalent circuit, consisting of a voltage source with com-

plex amplitude VT in series with a source resistance RT. The time average power ﬂowing

into the discharge iszPRF = %R8( V R F] R F*) , where VRF is the complex voltage across

ZD, and IRF is the complex conjugate of the complex current ﬂowing through the series

VT
RT+RD+jXD

 

circuit. Solving for VRF and IRF from the series elements we get I R F =

and V R F = I R F(R D + jXD) . Therefore we can express the rf power ﬂow through the dis-

charge as:

 

R
PRF = élvrl2 D2 2 (51)
(RT+RD) +XD

Under a perfect impedance matching which is assumed to be achieved with the match-

ing network, the reactance part of the equation (51) becomes zero and RT equals to RD.

1/2
(RDRT)

For a lossless matching network, we get |VT| = X
D

V R F from Lieberman [5.13].

Therefore, in a matched condition the maximum rf power ﬂow to the discharge becomes:

2
IIVTI 1[RD] 2
PRFI = "— = ' — VRF (52)
ma 2 R 2 2
X T XD
Equation (53) describes a parabolic dependence between the rf power ﬂow and the rf

voltage if RD and XD are assumed to be constant.

A relation between the amplitude of rf voltage, VRF and the induced dc bias, Vdc can

97

be obtained from the following expression [5.14].

 

kBTe (27“ka)

Equation (53) is valid for eVRF >> KTe, which is usually true for rf substrate biasing. In
equation (53) k3 is the Boltzmann’s constant, Te is the electron temperature, and Vf is the
ﬂoating potential. Vf can be calculated relative to the plasma potential Vp from the follow-

ing expression [5.14].

 

 

kBTe Mi
V = V ln( ) (54)

+
P f 2e 21tme
In equation (52) Mi and me are the mass of the ions and mass of electrons respectively. If
T8 is assumed to be 6 eV for our reactor, then for oxygen plasma V12 — V f becomes ~28 V.

Although equation (53) suggests a non-linear relationship between VRF and Vdc, the

 

 

part kBTe “(21teVRF

) in equation (53) is relatively small for the range of VRF we are
2e kBTe

interested in. Therefore, for all our purposes, |Vdc| is slightly less than the peak voltage

VRF and proportional to it. Hence, equation (52) can now be rewritten as equation (55)

which indicates a non-linear parabolic relationship between rf power and induced dc

voltage.
P RF °‘ Vdc (55)

It is important to note that for the derivation of the above relation, RD and XD are assumed

to be constant under all rf power levels but in reality, this assumption does not hold true.

To further document the relation between the rf power and the dc bias in an microwave

98

reactor, an interesting experiment was conducted. An argon-oxygen-SF6 plasma was gen-

erated with only rf power input in the absence of microwave power, and the rf induced dc
bias was measured as the rf input power was varied. In a similar experiment rf induced dc
bias was measured at the same values of rf input power but in the presence of 500 watts of
microwave input power. The rf power vs. measured induced dc bias with no microwave
power and with 500 watts of microwave power are plotted in Figure 5.4. The shape of the
curves showing the dependence of dc bias on rf power looked similar in both cases, but the
with-microwave curve is shifted lower by about 50 V. The non-linear dependence of rf
power on the dc bias is not the simple square relation of equation (55). This may be in part
because the discharge impedance decreases as the level of rf power ﬂow increases. Such a
decrease would be due to the local generation of species around the rf biased substrate
which is effectively decreases RD as the rf power increases. Note that for the higher den—
sity with microwaves, a given rf power creates less dc voltage than with rf only.

With this understanding of if power ﬂow and the induced dc bias, we turn our attention
to study their effect on etch rate. From Table 5.1 1, it can be seen that the for the same
applied rf bias or power, the etch rate varies from sample to sample, although a similar
nature of etch rate dependencies with both rf power and dc bias were shown by all three
samples. The data of etch rate vs. dc bias and etch rate vs. rf power for TF 271 were picked
for plotting in Figure 5.5 and 5.6. This sample was chosen particularly because the mea-
surements of weight difference for the larger diameter and heavier sample TF 271 are
more accurate. The solid line of the Figure 5.6 represents the best cubic ﬁt to the experi-
mental data. Analysis of the Figure 5.5 and 5 .6 shows that diamond etch rate improves

with both rf power and induced dc bias which means that higher ion energy or higher ion

99

ﬂux or both can increase the etch rate. This is expected because higher ion energy
increases the ion-energy driven desorption of C20 bonds from a location on the carbon
surface and an increased ion ﬂux on the surface increases the rate of incident ions and
yields a faster etch rate.

Although Figure 5.5 and 5.6 are very useful to know the behavior of etch rate with dc
bias or the rf power, these plots are not adequate to understand the dependence of etch rate
on only ion energy. As mentioned before, the rf power level inﬂuences the discharge
impedance, so the increase in etch rate may be due to both increased energy of the species
and increased number of species. To account for the effect of increased species density
around the substrate, a normalized etch rate is considered for plotting. Since the actual ion
ﬂux is not measured, the normalization is done by dividing the etch rate with a quantity
proportional to the ion ﬂux. The ratio of rf power to induced dc voltage is proportional to
the ion ﬂux, hence the effect of increased species density can be eliminated when the etch
rate is divided by this quantity. Figure 5.7 shows the normalized etch rate for different val-
ues of rf induced dc bias. The plot approximately supports a linear dependence of etch rate
with the ion energy. The distinction between the ion-energy driven etching processes
namely, the sputtering and RIE, is not possible until the sputtering results are discussed
later in this dissertation: at this point however, note that the linear dependence of etch rate
on ion energy agrees with a key assumption made in section 4.4 while deriving the theory
for reactive ion etching of diamond. This assumption described that the etch rate of dia-
mond in a pure oxygen plasma is mainly limited by the desorption rate of C20 and not by

the arrival rate of the ﬂux of O atoms, therefore the etch rate linearly increases with the

RF Power in Watts

100

 

    

 

 

 

250 l I l I I I I I I
0 :X
l
200- ‘\ x -
l
l
l
l
\
150 ' x .
l
\
\
\3" In Presence of 500 W
\\ of Microwave Power
100 _ \X / 7
\
\
\
if
\
\
50- \ \ .
\ \X
Only RF Power
0 l I l I i
-200 -180 -160 -140 -120 -100 -80 -60 -4O -20 0

RF Induced DC bias in Volt

Figure 5.4: Role of microwave power in rf induced dc bias

Etch Rate in ttm/hr

101

 

 

 

 

I I I I l

0 l l
-140 -120 -100 -80 -60 -40 -20 0

RF Induced DC Bias

 

Figure 5.5: Etch rate vs. rf induced dc bias

Etch Rate in urn/hr

102

 

 

 

 

 

50

l l
100 150
RF Power in Watts

Figure 5.6: Etch rate vs. rf power

200

250

Normalized Etch Rate(um-V/hr-W)

103

 

 

 

 

L l l l L l

20 4O 6O 80 100 120 140

RF Induced DC Bias in Volts

Figure 5.7: Normalized etch rate vs. rf induced dc bias

104

energy of incident ions. Evidence supports this assumption and conﬁrms that the rate of
formation of CO was not exceeded by the ion—energy driven desorption process at least in

the region of our experimental investigations.

5.4.2 Eﬂ‘ect of Microwave Power on Etch Rate

We have discussed before that the microwave input power plays a determinant role in
establishing the density of the ions inside a discharge. Although the species generation
zone is mainly conﬁned around the static ECR magnetic ﬁelds, the increased species den-
sity in this region is redistributed in the volume of the discharge by the diffusion process.
Thus, at steady state, for higher microwave input power, the ion density at the sheath
boundary is expected to increase with increased power causing the etch rate to go up. A set
of experiments was carried out on a 92 mm wafer TF 271 to conﬁrm the diamond etch rate
dependence on microwave power, the results of which are presented in Table 5.12. Param-
eters other than the microwave power were kept at constant values. The absorbed rf power
was kept at 95 watts with an induced dc bias of ~ -l25 V, the ﬂow rates of argon, oxygen

and SF6 were ﬁxed at 6, 28, and 2 seem respectively, the pressure and the mode were cho-

sen at 4 mtorr and 248.08 mm of sliding short height, the downstream distance was ﬁxed
at 5.5 cm from the base-plate position. Table 5.12 shows that over this range of power,
increasing the power by a factor of 2.5 increases the etch rate by a factor of 1.8. The varia-
tion of the etch rate with microwave input power is shown in Figure 5.8 with the solid line
representing the best cubic polynomial ﬁt to the data points.

A separate set of experiments was also conducted on a different sample at a different

mode to explore the higher region of the microwave power. During these new experiments,

105

Table 5.12: The Effect of microwave power on etch rate

 

 

 

 

 

 

 

 

 

 

Microwave um/hr
”we” TF 271
(Watts)
200 2.14 i 0.02
300 2.55 i 0.05
400 2.99 i 0.07
500 3.81 i018

 

 

 

 

 

 

 

 

the power was varied between 600 and 800 watts. Other variables, e.g, the rf induced dc
bias to the substrate, the pressure, the downstream distance and the cavity mode were held
constant at ~120V, 4 mtorr, 5.5 cm. and 236.54 mm cavity height respectively. The ﬂows

of Ar, 02, and SF6 were kept constant at 6. 25 and. 2 sccm. The data obtained from these

experiments are plotted in Figure 5.9 and the results show a very similar characteristic as
obtained from the previously stated experiments conducted on lower microwave power
region. Over this range of power, increasing the power by a factor of 1.33 increases the
etch rate by a factor of 1.3. In short, for the overall range of power explored, increase in
microwave power increases the etch rate of diamond at a more or less steady rate.

On a different context, the role of microwave input power was investigated by etching
diamond with and without the input of microwave power. With only rf and no microwave
power input, a plasma is generated inside the processing chamber. Etching experiments
were carried out with the rf only plasma at two different levels of rf power, 100 watts and
200 watts which induced -156 V and -l7l V respectively. The experiments were con-

ducted in an argon, oxygen, SF6 plasma with individual gas ﬂow rates of 6, 28 and 2 seem.

Etch Rate in um/hr

106

 

 

 

 

l l l l

 

250

Figure 5.8:

300 350 400 450 500

Microwave Power in Watts

Etch rate vs. microwave power at low power level

Etch Rate in pm/hr

446
600

6/1

107

 

 

 

 

l

l l l l l l l

 

620 640 660 680 700 720 740 760 780 800

Microwave Power in Watts

Figure 5.9: Etch rate vs. microwave power at high power level

108

The main chamber processing pressure was kept at 4 mtorr and the operating resonant
mode corresponded to 248.08 mm of cavity height. The substrate height was ﬁxed at 5.5
cm below the base plate.

Etching with 100 watts of absorbed rf power at the substrate in absence of any micro-
wave input power produced an etch rate of ~0.57 um/hr, which in the presence of 500
watts of microwave and 100 watts of rf power improved to ~3.68 um/hr. This shows that
the etch rate increases by more than a factor of 6.45 in presence of 500 watts of microwave
power. Similarly with only 200 watts of rf input power in absence of any microwave
power, the etch rate became 0.91 um/hr which with an input of 500 watts of microwave
power and 200 watts of Rf power increased to ~6.33 um/hr. In this case, the ratio of etch
rates with 500 watts of microwave power to zero microwave power becomes 6.94.

Two important observations can be made from these experiments. One, the presence of
microwave power is important in producing a higher ion ﬂux to the substrate and thus a
higher etch rate of diamond. Two, the plasma generated from only rf input is capable of
etching diamond, although at a very low rate. The poor rate is mainly attributed to the low
species density generated by the rf only plasma in contrast to the ECR microwave gener-
ated plasma. Note that from Figure 5.4 the substrate bias and therefore incident ion energy

was actually somewhat higher with rf only plasma.

5.4.3 Eﬂect of Processing Pressure on Etch Rate
The processing pressure inside a ﬁxed-volume main chamber determines many char-
acteristics of the plasma, the most important being the species density and their tempera-

ture. Other characteristics such as the residence time of the species, the sheath voltage etc.,

109

are also inﬂuenced by the processing pressure.

Since the microwave energy is coupled to the electrons ﬁrst which through collisions
ionize the gas to ignite the plasma, the effect of the pressure can be easily seen during
igniting a discharge. Often a discharge cannot be created at a very low pressure e.g., l
mtorr, hence a common practice is to initiate a discharge at a higher pressure such as 7
mtorr and bring it down to the lower processing pressures. However, the effect of pressure
on etch rate was experimentally explored on a 50 mm wafer NTAl-005 with an argon,

oxygen and SF6 plasma having corresponding ﬂow rates of 12, 20 and 2 seem. For all the

experiments, the mode was ﬁxed to 236.54 mm of sliding short height, the downstream
distance was 5.5 cm and the microwave power was 600 watts. The rf induced dc bias was
held constant about 120 V and the pressure was varied between 2 and 10 mtorr. The varia-
tion of etch rate with main chamber pressure is plotted in Figure 5.10.

The result shows a maximum etch rate around 4 mtorr. The reason for this is thought to
be due to a counter—acting effect of pressure on sheath potential and the species density.
For an ECR plasma, the plasma species density increases with increasing pressure [5.15]
but sheath potential and hence the incident ion energy decreases with the increasing pres-
sure [5.16]. Etch rate being a function of the ion energy and incident species concentra—
tion, a combination of these two effects are likely to produce the observed maximum in
etch rate vs. pressure. Since 4 mtorr produces the maximum etch rate, most of the etching

runs were conducted with pressure ﬁxed at this value.

5.4.4. Eﬂect of Oxygen, Sulfur Hexaﬂuoride Ratio on Etch Rate

SF6 became a part of the gas composition for diamond etching because a black ﬁlm

Etch Rate in urn/hr

5.8

5.6

5.4

5.2

4.8

4.6

4.4

4.2

110

 

I

T

T

I

 

Pressure in mtorr

Figure 5.10: Etch rate vs. process pressure

 

lll

was found to form on the etched surface when oxygen only plasma was used for etching.
Later it was found that sputtering with argon only plasma also forms the black ﬁlm. How-
ever, addition of a little amount of SF6 in the plasma environment prevented the formation
of the black layer.

It was noticed that SF6 containing plasma can also clean an already formed black layer
as well. Thus a ﬂuorine containing plasma was chosen for etching diamond although the

statistical analysis showed that SF6 has a negative effect on diamond etch rate. To investi-
gate the effect of SF6 on the etch rate more carefully, a set of experiments was designed
where the oxygen ﬂow rate was kept ﬁxed at 28 sccm and the SF6 ﬂow rate was changed

from O to 8 seem. Argon was not ﬂown through the system. All experiments were repeated
and the results obtained are presented in the Table 5.13. The plot in Figure 5.11 supports

the negative effect SF6 on etch rate. The etch rate was found to decrease as the SF6 to oxy-
gen ratio was increased. For these experiments pressure and the downstream distance were

kept at 4 mtorr and 5.5 cm respectively.

Table 5.13: Effect on SF6 to oxygen ﬂow ratio on etch rate

 

 

 

 

 

 

 

 

 

 

 

 

SF6 Flow 02 Flow SF6: 02 um/hr
Rate Rates Ratio TF 271

8 28 0.28 0.76 i 0.03

6 28 0.21 1.67:0.05

4 28 0.14 2.85i0.03

2 28 0.07 3.9222022

0 28 0 5.51 i0. 141

 

 

 

 

 

 

 

 

 

 

 

 

 

Etch Rate in um/hr

0
0

112

 

 

(A)
I

l l

 

 

0.05 0.1 0.15 0.2 0.25

SF6: Oxygen Ratio

Figure 5.11: Etch rate vs. SF6 to oxygen ﬂow rate ratio

0.3

113

The microwave input power was 500 watts and the rf power was 100 watts which

induced a dc bias of ~128 V. The reason for the negative effect of SF6 is not clear. Addi-
tion of SF6 may modify the internal plasma chemistry in a complex way. Also ﬂuorine and

oxygen may compete for the surface sites on the diamond substrate. The value of rate con-
stants of carbon-oxygen and carbon-ﬂuorine reactions differ in magnitude which would
contribute to the change in etch rate.

However, an exception to the negative effect of SF6 on etch rate was noticed while

etching a diamond ﬁlm with an already-formed black ﬁlm on the surface. It was found that

an addition of 2 sccm of SF6 in a 6 sccm to 28 sccm of argon-oxygen plasma increases the
etch rate by about 33%. This is apparently contradictory of the negative effect SF6 as seen

in Figure 5.1 1. But the experiment was repeated three times and etch rate of the black lay-

ered diamond was conﬁrmed to increase with slight addition of SF6. These preliminary
results tend to imply that the black ﬁlm etches at a slower rate in absence of SF6, although
diamond without any black ﬁlm etches at a faster rate in absence of SF6. However, a ques-

tion about the possible role of argon remains because Figure 5.1 l was generated for an

oxygen2SF6 plasma as opposed to the argon—oxygen-SF6 plasma.
Hence a fresh set of experiments was conducted with argon-oxygen-SF6 plasmas. For

these experiments, the argon and oxygen ﬂows were kept constant at 6 and 28 sccm, and

the SF6 ﬂow rate was varied between 0 and 8 sccm at a ﬁxed processing pressure of 4

mtorr. Thus the proportional content of ﬂuorine atoms and ions were changed in the

plasma as the ﬂow rate of SF6 varied from experiment to experiment. The microwave and

rf input power were ﬁxed at 500 watts and 100 watts respectively for all experiments.

Etch Rate in urn/hr

ll4

 

 

 

   

No Black Film

 

 

3h-
/ /X
/
/
Black Film \ X
\ ..
2)? \
\
\
\
\
\
\
1- \ -
\
\
\X
0 4 l l l l l l
0 1 2 3 4 5 6 7 8

SF6 Flow Rates

Figure 5.12: Etch rate of diamond with and without black ﬁlm

115

The downstream distance was chosen to be 5.5 cm and the mode was ﬁxed at 251.71 mm
of cavity height. The 92 mm diameter sample TF 271 with no black ﬁlm on the substrate

side was etched in the argon-oxygen-SF6 plasma and the etch rate was indeed found to
decrease with increase in SF6 ﬂow rates supporting the similar observation obtained while
etching in an only oxygen-SF6 plasma. Thus argon was eliminated as the source of an
anomaly seen with regard to the increase in etch rate with addition of SF6 while a black-

layered diamond was etched.

To study how the etch rate of the black ﬁlm changes with the content of SF6 in plasma,

black ﬁlm was grown on the substrate side by sputtering with an argon only plasma and

then the sample etched in the same argon-oxygen-SF6 plasma used to etch the sample
without the black layer. Figure 5.12 shows that as the SF6 ﬂow ratio increased, the etch
rate ﬁrst increased and then decreased. This indicates that the presence of SF6 is important
to keep the etch rate up but beyond a certain point, a higher concentration of SF6 does not
aid the etching mechanism. An initial conclusion, that in absence of SF6, a black ﬁlm layer

grows on the diamond which acts as a passivation layer and reduces the etch rate was
drawn from these experiments. However, more experiments were required to conﬁrm the

hypothesis. These experiments were performed and are described in section 5.5.

5.4.5 Effect of Argon, Oxygen Ratio on Etch Rate

The mode corresponding to 248.08, which was used most often for Ar, 02 and SF6 plas-

mas did not seem to be an appropriate resonant mode for argon-oxygen plasma, especially

for high argon content, because the returned microwave power was observed to be quite

116
high regardless of the probe length. The plasma was also found to ﬂicker at times. The

sliding short was therefore changed to 251.71 mm of cavity height which seemed to pro-
duce a steady, bright discharge with less microwave returned power.

Table 5.14: Effect on argon to oxygen ﬂow ratio on etch rate

 

 

 

 

 

 

 

 

 

 

 

 

unm-
ow Rate Rates Ratio TF 271

6 0 0 0.14 i 0.08

6 2 0.33 0.64 i 0.18

6 6 1 1.22 i 0.04

6 14 2.33 1.37:0.02

6 28 4.66 1.49 i 0.04

 

 

 

 

 

 

 

 

 

 

 

 

In order to investigate the effect of argon to oxygen ratio on the etch rate of diamond,
the microwave absorbed power was kept constant at about 400 watts and argon gas ﬂow
was ﬁxed at 6 seem. The absorbed rf power was ﬁxed around 95 watts with an induced dc
bias of -l25V. The downstream distance was chosen to be 5.5 cm and the pressure was
kept constant at 4 mtorr.

The results of the experiments are shown in Table 5.14 which are plotted in Figure
5.13. The etch rate initially showed a drastic increase with oxygen ﬂow ratio but as the
oxygen content is increased beyond a certain ratio of the total gas ﬂow, the etch rate
showed a saturation behavior. The reason for this observation lies with the change in
nature of etching from sputtering to RIE. Argon being a noble gas does not participate in

reactive ion etching, hence in an argon only plasma, etching becomes purely sputtering

Etch Rate in um/hr

1.6

117

 

 

l 1 l l l l l

1 1.5 22.5 3 3.5 4
OxygenzArgon Flow Ratio

Figure 5.13: Etch rate vs. oxygen to argon ratio

 

 

118

and an extremely low etch rate is produced. As oxygen is introduced to the discharge, the
etching changes from sputtering to RIE showing a drastic improvement in etch rate. With
gradual increase of oxygen ﬂow ratio to argon, the density of oxygen atoms and ions starts
dominating the plasma and the rate of etching shows a continuous improvement. However,
increase in oxygen ﬂow beyond a point does not help in increasing the proportion of oxy-
gen content in plasma signiﬁcantly, therefore the etch rate shows a saturation phenome-
non. It might be useful to indicate here that although the etch rate was found to increase
with oxygen content ratio in the etching plasma, the etch rate of diamond ﬁlm was unusu-
ally low, in an argon-oxygen plasma. In fact, with other parameters being constant, the
plasma etching experiment with 6 seem of argon and 28 sccm of oxygen shows that the
etch rate obtained is less than a factor of 4 compared to the etch rate obtained in an argon—

oxygen-SF6 plasma with ﬂow rates of 6, 28 and 2 seem. It is believed that this happens

because during each step of argon-oxygen etch experiments, a black ﬁlm is formed due to

the absence of SF6 which etches at a lower rate than a non-black-layered diamond. The

effect of changing the ﬂow rate of argon in an oxygen rich plasma environment was not
explored in detail. A few experiments were conducted, but the etch results were not found
very conclusive. However, we believe that the presence of argon in an oxygen plasma
seems to stabilize the plasma and reduce the return microwave power.

Argon-only sputtering experiments were also performed. Our previous experiments
studying the effect of rf bias on the etch rate of diamond, successfully demonstrated that

etching of diamond in argon-oxygen-SF6 plasma was deﬁnitely ion assisted. The argon

only etching experiments allow differentiating between sputtering and RIE. With argon

sputtering experiments, 400 watts of absorbed microwave power at 4 mtorr pressure, and

119

 

012

01'-

1108"

EB

Etch Rate in um/hr

(104-

 

 

L l l l l 1

 

 

100 110 120 130 140 150 160 170

RF Power in Watts

Figure 5.14: Sputter etch rate vs. rf power

180

120
an input of 100 watts of rf power produced a diamond removal which was only about 0.4%

of the etch rate produced by an argon-oxygen-SF6 plasma under similar parameter speciﬁ-
cations. This clearly demonstrates that the etching mechanism in an argon-oxygen-SF6

plasma is reactive ion etching dominated. As an extension of the sputtering experiments,
the bias dependence of sputtering in an microwave ECR was explored and the results are
shown in Figure 5.14. 500 watts of microwave input power, 4 mtorr pressure, 5.5 cm of
downstream distance and the mode corresponding to 251.71 were chosen as the parame-
ters for these sputter-experiments.

Figure 5.14 shows that rf power increases the sputtering rate although the rate always

remained in the order of a tenth of a micrometer/hr even with at the highest value of rf

power investigated.

5.4.6 Effect of Downstream Distance on Etch Rate

We have seen from the previous discussion in section 5.1, that the steady state spatial
distribution of species density decreases along the downstream distance, which was exper-
imentally veriﬁed by Gopinath et.al., for argon sputtering and theoretically derived using
simpliﬁed assumptions by Hopwood et.al., [5 .2, 5.3]. The effect of downstream distance
on etch rate due to reactive ion etching is expected to be similar to the that of the sputter-
ing, However, experiments were conducted to quantify this effect.

An argon, oxygen, SF6 plasma at 4 mtorr was used for etching the wafer. The ﬂow

r ates were 6, 28 and 2 sccm for argon, oxygen and SF6 respectively. The input microwave

and the rf power were ﬁxed at 500 watts and 200 watts. The induced dc voltage from the

ff Power was about -140 V. The etch rate of a 92 mm diameter diamond disk TF 271 at

121
10.2 cm downstream distance was found to be 4.06 urn/hr as compared to 6.33 um/hr at

5.5 cm downstream distance. The experiment showed an average increase in etch rate by a
factor of 1.56 when the downstream distance is decreased from 10.2 cm to 5.5 cm. For the
same change of downstream distance, the theoretical expression from Hopwood [5.3] pre-
dicts the average etch rate to improve by a factor of 1.58 which closely matches our exper-
imental observation.

Since, the etch rate strongly depends on the downstream distance for obtaining higher
etch rate, the etching must be performed as close to the plasma generation region as possi-
ble. However, that is not always done because of some other reasons. The uniformity of
the etching may suffer over a larger area substrate at lesser downstream distance because
the etching proﬁles may follow the spatial patterns of the resonant modes. At larger pro-
cessing distances, the modal effects are washed away and similar etch proﬁles would be
obtained from all modes independent of the individual modal patterns.

Another practical problem arises when processing is performed at shorter downstream
distance. Since, the rf power ﬂowing through the substrate for a given induced dc voltage

is dependent on the species density, the rf power ﬂow through the substrate for a given
induced dc bias and given absorbed microwave power increases as the downstream dis-
tance becomes shorter. For a given maximum power handling capability of the rf power
generator and the matching network, the applied dc bias or the setting value of the rf
Power and the absorbed microwave power together determines a cut-off distance between
the Substrate and the plasma. If the substrate is forcibly brought closer than this minimum
downstream distance, the rf power tends to ﬂow more than the power handling limit,

Which initiates a protective circuitry in the rf matching network and shuts the system. Thus

122

the substrate must not be brought too close to plasma in order to keep a high substrate

bias.

5.4.7 Eﬂect of Resonant Modes on Etch Rate

Not all electromagnetic resonating modes are suitable for ECR energy coupling [5.4]
and the mode appears to shift with loading of the cavity. During the argon-oxygen experi-
ments shown in Figure 5.13, the cavity height corresponding to 248.08 was not found
appropriate for argon only and high argon/low oxygen containing experiments. The
plasma was found to ﬂicker although the 248.08 mode was consistently successful in cre-
ating argon—oxygen SF6 plasma especially for high oxygen and low argon contents. The
mode corresponding to 251.71 was found quite stable for argon-oxygen experiments as
well as only oxygen experiments. The individual electromagnetic modes for MPDR 325i
are difﬁcult to uniquely identify because of its large discharge diameter. Therefore, in this
work, the modes are described in terms of the cavity height. The scope of our research at
this point was not to identify the operating modes and we assumed that a ﬁxed cavity
height represents a unique mode or a unique combination of modes which are repeatedly
obtained when the cavity height was adjusted to that value. Such an assumption neglects
hysteresis or mode related instability effects [5.17] that might occur in practice.

We know that the spatial distribution of the density of species is determined by the
Operating mode and that the ions that reside over a given area of the substrate mainly par-
tiCipate in etching. Therefore the average etch rate which is related to the total ions over
the Work-piece area, can certainly be expected to vary from mode to mode. However, large

area processing with MPDR 325i does not appear to produce a very widely varying

123

average etch rate for different ECR resonating modes. An example of the etch rate varia-
tion is given in the Table 5.15. In this case, the plasma and the wafer conditions were more
or less identical and two modes were chosen corresponding to 251.71 and 248.08 mm of

cavity height respectively.

Table 5.15: Effect of resonant mode on etch rate

 

 

 

 

 

 

 

 

 

 

 

 

 

Plasma Mode ﬁrs;
Ar202:SF6 => 6:28:2 248.08 3.15
Ar:02:SF6 => 6:28:2 251.71 3.64

02 => 28 248.08 5.51

02 => 28 251 .71 5.64

 

 

 

 

 

 

 

The etching runs were conducted with 400 watts of absorbed microwave power and
l 00 watts of rf power with the downstream distance ﬁxed at 5.5 cm. The pressure was kept

constant at 4 mtorr.

5.5 Black Film
In the last section, we noted that diamond etched in an only oxygen, only argon, or in
argon-oxygen mixed plasma showed a black ﬁlm on the etched surface. Also the diamond
With a black ﬁlm etched at a lower rate than diamond with no black ﬁlm. Moreover, some
initial results indicated that the presence of SF6 was necessary to keep the diamond etch
rate from falling from run to run due to the formation of the black ﬁlm. To investigate this
ful‘ther, a diamond sample with no initial black ﬁlm was etched successively in a plasma

cotltaining no SF6. For this investigation, an oxygen only plasma was chosen with an input

 

1.1m

124

microwave power of 500 watts. The rf power was set at 100 watts and the pressure was
ﬁxed at 4 mtorr. The wafer TF 271 was placed 5.5 cm below the base—plate. The etch rate
dropped with successive runs. This is shown in Figure 5.15. The decreasing nature of the
etch rate implies that at the end of each run the surface of the diamond was becoming
more and more etch resistant to oxygen plasma causing the etch rate to go down. To the
naked eye, the ﬁlm appeared to grow as black dots on the surface which became more and
more intense as the etch hours proceeded. This clearly suggested that the black ﬁlm was
ac ting as a passivation layer on the diamond surface and for unknown reasons, the pres-
ence of SF6 prohibited the growth of this passivation layer. Also as noted earlier, SF6
cleans the passivation layer in case it was already grown. To verify this hypothesis, a
reverse experiment was conducted. The same wafer TF 271 with an already—grown black
ﬁ 1 rn was now etched in an argon-oxygen-SF6 plasma successively. The gas ﬂow rates were
6, 28 and 2 sccm for argon, oxygen and SF6 respectively. Other parameters were ﬁxed
exactly at the same speciﬁcations as the above-mentioned only oxygen plasma experi-
ment. As expected, the etch rate increased with successive runs which can be seen from
Figure 5.16. In conclusion, the presence of SF6 is found essential to keep a constant high
etch rate of diamond although if the proportion of SF6 is continually increased in the
Plasma, the etch rate starts falling beyond a certain SF6 to oxygen ratio (approximately
8%). In all experiments, the etch rate of the black ﬁlm coated diamond was always found
loWer than the etch rate for diamond with no black ﬁlm under the same plasma speciﬁca-
tions. It was also noted that the actual etch rate of the black ﬁlm is dependent on how the
ﬁlm was grown. For example, visual inspection showed that argon sputtering produced a

mote blackish ﬁlm than oxygen plasma etching for the semi-transparent black-ﬁlm-less

Etch Rate in um/hr

125

 

5.5

P
01

 

3.5
1

 

l l

 

2 3

Number of Runs

Figure 5.15: Subsequent etching of diamond in oxygen plasma

 

Etch Rate in um/hr

3.8

3.6

3.4

SA)
[\3

(A)

[\D
C!)

2.6

2.4

126

 

 

 

l l l l
x
' x
I
l l 1 l
1 2 3 4 5

Number of Runs

Figure 5.16: Etching of black ﬁlm with Ar, 02 and SF6 plasma

 

127

sample TF 271. The black ﬁlm visually appeared to become increasingly prominent as the
total etching hours increased both for argon sputtering and oxygen etching. This observa-
tion led to some obvious questions, such as whether the black ﬁlms produced by an oxy-
gen only, argon only and argon-oxygen mixed plasma were identical and whether the
nature of the black ﬁlm produced at the end of one hour run was same as the ﬁlm produced
at the end of two hour runs. The answers to these questions are actually related to quanti-
fying the black ﬁlm and understanding the cause of its formation. We have not done an
extensive study of the black ﬁlm. However, some initial results and some possible hypoth-
esis based on our initial work are presented next.

An independent study reported the use of SF6 containing plasma to clean metal parts
[5.18]. Using Ar, 02, SF6 plasmas, it was found that SF6 was necessary to remove graphite

containing lubricant. This report together with our observation of cleaning the black ﬁlm

in SF6 containing plasma, lead to a possibility that the black layer is possibly a graphitic

layer. As a preliminary investigation, Raman spectrum was taken on an argon sputtered

x 10‘

 

1.8“

16*

 

Counts per second

   

 

 

 

.2 1 1 l l l l 1
1200 1250 1300 1350 1400 1450 1500 1550 1600
Shift Wavenumber 1/cm

Figure 5.17: Raman spectrum

128
black layer coated diamond ﬁlm. The result of this investigation, presented in Figure 5.17,

did not show graphite sp2 bonds. However, Raman analysis as used for Figure 5.17 is not
speciﬁcally a surface analysis method.

An alternative explanation for black surfaces following plasma treatment is found in
Chapman [5.19]. When surface treatment results in a surface morphology with a high scat-
tering coefﬁcient for visible light, a black velvet appearance may result. A speciﬁc exam—
ple is the sputtering of copper substrates which under certain conditions can result in a
surface covered with sub-micron cone-like structures. It was noted that the pictures of
such surfaces in Chapman were reminiscent of SEM images obtained from Dr. Paul Gold-
man previously at Norton, on samples which had been etched in this study at Michigan
State University. This prompted further SEM examination of the surface morphology of
black ﬁlm coated samples. Since our SEM facility cannot load 92 mm diameter sample, a
dc arc-jet deposited 1cm X 1 cm diamond sample MSU—3, was micrographed after remov-
ing 50 um from the substrate side in pure oxygen plasmas. The SEM shown in Figure

5.18, shows globules to appear on the etched surface at a magniﬁcation of 1000X.

 

En

Figure 5.18: Globules on 02 etched sample

129
When magniﬁed at 10000X, the SEM shown in Figure 5.19, revealed numerous irreg-

ular structures on the etched side of the diamond surface.

 

lum

Figure 5.19: Magniﬁed structures of globules

These structures were not seen in a pre—etched sample (Figure 5.20).

 

lum

Figure 5.20: Pre-etched sample surface

130
As noted, SEMs of etched surfaces were also investigated by Dr. Goldman of Norton

Diamond Film. One of such micrographs on an oxygen plasma etched semi-transparent 50
cm diameter sample is shown in Figure 5.21. This sample had 50 um removed from the
substrate side in a pure oxygen discharge. The SEM again showed roughly cone shaped

formations on the etched surface.

 

Figure 5.21: Conical structures on 02 etched sample

Evidence in literature shows that these cones are usually formed from high anisotropic
etching such as sputtering. Dorsch et.al., [2.39] postulated that the black ﬁlm on diamond
surface observed from their etching in an rf oxygen plasma, was an optical effect caused
by the surface cones. They believed the reason for the formation of cones is micro-mask-
ing. According to them, tiny deposits from the wall-chamber fall on the sample and act as
micro-masks which are ﬁnally responsible for the development of the conical structures
seen after etching.

More surface analysis is required to determine for certain the nature of the black ﬁlm.
However, the explanation of cone formation and its optical effect is highly plausible. The

nature of both argon sputtering and oxygen only etching are extremely anisotropic which

131

could result in the formation of the surface cones. However, addition of SF6 may change

the nature of etching to more chemical and less anisotropic. The lateral etching in pres-

ence of SF6 would then be responsible for both cleaning the already—formed cones and

preventing the new cones from formation. However, the reason for the initial cone forma-
tion, micromasking or other, is not established by our work.

The reduced etch rate of diamond-with-black-ﬁlm in oxygen plasma could also be
explained in the light of the cone formation. In RIE, sidewall etching is low. As the cones
form, much of the diamond surface is in the form of angled walls, not receiving the RIE
effect. Therefore, a gradual fall in etch rate is seen as the diamond surface grows more and

more black during successive oxygen plasma etching runs.

5.6 Calculation Qf Approximate Diamond Etch Rate in Oxygen ECR Plasmas

In section 5.3, we concluded that the diamond etching in an argon-oxygen—SF6 plasma

with higher oxygen content is mainly RIE. The conclusion can surely be extended for
etching in an oxygen only plasma. In this section, we try to relate the theory of reactive ion
etching of diamond explained in section 4.4, with the experimental results obtained. This
is done by theoretically calculating the diamond etch rate under certain typical plasma
conditions for a pure oxygen plasma and comparing the same with the value obtained
from the experiments performed in a similar oxygen discharge. The calculation is based
on assumptions about the plasma density and species temperature which were not experi-
mentally veriﬁed, hence the accuracy of this calculation may be questioned. However, the
usefulness of this calculation is to gain an understanding in the reactive ion etching phe-

nomenon for ECR etching.

132

A typical oxygen only plasma condition is assumed at 400 watts of absorbed micro-

wave power at a ﬁxed processing pressure of 4 mtorr. The absorbed rf power is assumed to

induce a typical dc voltage of 120V. Using external cooling, the substrate temperature Ts

is normally held at about 300 C or 300 K. ECR plasmas are known as cold plasmas, and
from experience we know that the temperature of the cavity does not go very high even
without cavity cooling for only 400 watts input. Therefore the temperature of the gas and
the ions can be thought to be quite low, say 350 K.

The ions in a processing discharge contribute negligible proportion of the species, usu-
ally less than 0.1%, hence most of the species remain neutral the density of which can be

calculated using the simple gas law relations shown as follows:

 

= (56)

 

In expression (56), P], T], n], represent the atmospheric pressure, ambient temperature
(300 K) and gas particle density at STP and P2, T2, n2 represent the processing pressure,

gas temperature, and the oxygen molecule density inside the plasma. For 4 mtorr of pro-

cessing pressure and 350 K of gas temperature the density of oxygen molecule is calcu-

lated as 4.1 1X1019 m'3. We further assume that 10% of the gas molecules, or 4.11><1018

m'3, are dissociated inside the discharge and remain in the form of neutral oxygen atoms.
It is also assumed that the density of the oxygen atoms at the surface of the diamond sub-

strate has is same as anywhere else inside the discharge and is therefore equal to

4.11x1018 m'3.

The ions are assumed to be mostly singly charged and with an incident energy of 120

133

eV since the rf induced dc bias of 120 V comes across the chuck sheath. To be consistent
with our previous assumptions made in connection with discussing the effect of rf power

on etch rate, we keep the section 5.4.1 value for the electron temperature which was 6 eV.

. . . 16 _
The values for the downstream Ion densrty nis 1S assumed to be and 4x10 m 3.

The atomic volume-density of the diamond n C is known as 1.79><1029 m'3. The acti-

vation energy for the diamond oxidation E b is approximately calculated to be 230 kJ/mol

or 2.39 ev per bond from [2.8]. Assuming I] ~ 0.2 for equation (33) we get the ion-

enhanced sputter desorption yield Y1. as 10.

Now, the thermal desorption rate constant Kd is related to binding energy of diamond

through the following expression:

”Eb
Kd = Koexp(-k7) (57)
S

where TS is the substrate temperature and K 0, the pre-exponential factor represents the
number of attempted escapes per second and for Chemisorption processes ranges from

1013 to 1015. Considering a mean value of K0 to be 1014, Kd is calculated to 8.4x10_27 5'].
Taking the surface state density no' for diamond to be 1.58>~<1019 m‘2 for the (11 1)

surface, Ka is determined from equation (46). The value of Ka is 1.08X10_ll cm3s'1.

For an electron temperature of 6eV, the Bohm velocity of oxygen ions uB=

 

5993 m/s, so from equation (47), Ki becomes 3.82x10_10 cm3s'l.

134

With all these assumptions, we turn our attention to equation (44) for calculating the
etch rate of diamond in a pure oxygen plasma. Based on our argon sputtering experiences

and information given by Chapman [5.19] the sputter rate related term of the equation (44)

can be neglected for all practical purposes. Usually the sputter yield factor 7;“ for carbon is

negligibly small producing a carbon sputter rate in the order of 3% of the RIE rate or

lower. Therefore, the equation (44) is modiﬁed to:

o 1
EV - E2] 1 + l (58)

Kd+ YiKiniS Kanos

 

Using equation (57), the etch rate of diamond in an oxygen plasma can be ﬁnally cal-
culated as ~ 10.8 um/hr.

Experimentally an etch rate of 6-8 um/hr on a black—ﬁlm-less 100 mm diameter wafer
is achieved under the similar plasma conditions for which the etch rate is calculated. It is
important to remember that the etch rate varies from sample to sample. Also the diamond

2 varies with

wafers are polycrystalline and since the number of the surface atoms per m
the crystal plane. Hence, considering the various assumptions, an average etch rate of 6-8

um/hr over a 100 mm wafer is actually quite a close agreement to the predicted value.

Chapter rVI. Uniformig; o: Etchng and Control 01 Etc/i Troﬁle

In chapter 5, based on micrometer measurements we noticed that etching with mixing
modes yielded better uniformity than etching in any single mode on a 100 mm diameter
diamond wafer. This chapter attempts to explain this interesting experimental observation
with theoretical reasoning and simulation. Since our reactor MPDR 325i, is a microwave
resonant cavity, the spatial distribution of electric and magnetic ﬁelds, also called modal
patterns, inﬂuences the spatial distribution of the charged species in the generation region.
In section 6.1, mathematical expressions relating different possible spatial patterns for dif-
ferent microwave resonant modes for a free—space cylindrical cavity are derived.

The proﬁle of the diffused charged species distribution in the downstream distance fol-
lows from the solution of the ambipolar diffusion equations. The ambipolar diffusion
equations model the simultaneous motion of the ions and electrons in the discharge and
this is reviewed in section 6.2. If the species in the generation zone are assumed to have a
spatially uniform species density distribution, then the downstream species density distri-
bution can be obtained by analytically solving the ambipolar diffusion equation. This ana-
lytical solution given in equation (50), shows that the species density takes a Bessel
function variation along the radial distance and an exponential decay along the down-
stream distance. The assumption of spatially uniform species density in the generation
zone is simple and useful in terms of getting an initial understanding of the species distri-
bution, but it needs to be modiﬁed to model the real discharge more accurately. In section
6.3, a radially varying species density is assumed in the generation region. To solve for the

downstream species density the differential equation describing the diffusion phenomenon

are translated into appropriate difference equations. The numerical technique to solve

135

136

these difference equations is also discussed in this section.

In section 6.4, the MATLAB generated plots are presented and discussed. These plots
show that sequential etching using different modes can indeed achieve higher etch unifor-
mity. The actual MATLAB programs are attached in Appendix C. At the end of this sec-
tion, the idea of mixing modes is brieﬂy extended to explore the possibility of controlling
the etch rate proﬁle in order to a achieve desired ﬁnal surface speciﬁcation for a given

sample.

6.1 Derivation of the Modal Patterns

The species generation in an ECR reactor is mainly conﬁned to a three dimensional
volume with cusps which for a 2.45 GHz microwave etching system, is determined by the
location of 875 Gauss lines generated by the externally impressed static magnetic ﬁelds.
This zone is also known as the ECR zone and for the MPDR 325i exists about 1 cm inside
the discharge [3.4] from the circumference of the conﬁning bell-jar.

To study the uniformity in etching with an ECR reactor, the distribution of the species
in the bell jar would ideally be experimentally measured. However, in this work, we have
not measured the spatially varying ion densities for different modes. In a microwave ECR

cylindrical reactor like ours, the generation of species at the ECR regions depends on the

strength of the cavity E ﬁeld and its orientation relative to the external magnetic ﬁeld. The

cavity ﬁelds are dependent on the selection of the individual mode by the choice of appro-

priate cavity height. The spatial variation of the E and H ﬁeld structures inside a free-
Space cylindrical cavity can be theoretically derived by solving the Helmholtz’s wave

equation. Although these solutions for an empty cavity will change in presence of the

137

dielectric materials, or plasma, the solutions are still useful as a guideline. Solving the
Helmholtz’s equation in a plasma-ﬁlled cavity is a much more complicated task.

Figure 6.1 shows a free-space cylindrical cavity of radius a and length c for which the
modal patterns for TE and TM modes are derived in the following subsection. The details

of this derivation may be obtained from [6. 1, 6.2].

E

Figure 6.1: Cylindrical cavity of length c and radius a

6.1.1 TE modes
For the derivation of the modal patterns for TB modes, we ﬁrst consider an electro-

magnetic vector quantity called the magnetic Hertz potential. The deﬁnition of the mag-
netic Hertz potential may be obtained from [6.3]. The magnetic Hertz potential T—t;

satisﬁes the Helmholtz’s wave equation. To ﬁnd the expressions describing E and Pi

ﬁelds for a certain TE mode in a cylindrical cavity conﬁguration, Helmholtz’s wave equa-

tion is ﬁrst solved for magnetic Hertz potential. The Hertz potential is then manipulated to

obtain expressions for the E and H ﬁelds in an empty cylindrical cavity.

138

We assume that the axis of the cylinder shown in Figure 6.1, is aligned along the z-axis

o u o o o o A u
and that the magnetic Hertz potential ex13ts only along this dIrection. Then 1th can be writ-

._\
ten as 1th: 21th, where 1th(r, 0, z) is a spatially varying scalar quantity representing the

magnitude of the magnetic Hertz potential.
The Helmholtz’s wave equation can be expressed in terms of the magnitude of the

magnetic Hertz potential, as equation (59).
V211,, + 1310.: 0 (59)

In the cylindrical co-ordinate system, equation (59) modiﬁes to equation (60):

2
a 8 82
—§—(r alt/9+2 -1- 12"4- 12th+k21th= 0 (60)
;a r r 2280 dz

Solution of equation (60) provides the spatial variation of 1th. Once equation (60) is
solved, the expression for 1th is used to ﬁnd the expressions for E and H ﬁelds. The rela-

tion between 1th and the E , and H ﬁelds can be obtained from equation (61) and (62).

These relations are directly derived from the deﬁnition of the magnetic Hertz potential

3 a
E: jwqunhz jwu(— r—l-a—gh+0a—1:h) = i‘Er+0E6 (61)
2 2
H: k2f+V(V-1?) = >113 :mlai’: +2k,,+_—1th =>H +0H +211 (62)
h h nae raeaz h+azz r 0 z

where (0 and u in equation (61) and (62), represent the excitation frequency and the

permeability of the cavity. To obtain the expression for if; by solving equation (60), we

139

further assume that no mutual interactions exist between the directional components of

1th. Therefore the method of separation of variables is applied and 1: h is written as:
1th = R(r)O(0)Z(z) (63)

where R, O and Z are only dependent on radial distance r, angular measure 0, and axial

distance 2. Combining the equation (60) and (63) we get the following equation,

 

2 2
1 a 8R 1 80 1371;. 2_
rRar(rar)+ rzeaez +Zaz2 +k — 0 (64)

An introduction of a new constant k: simpliﬁes the equation (64) by splitting it into

two simple differential equations of known forms.

2 2
13(311) _1_a_o 2_—_-15_1th:k2

713; W +rzoaez _ Zaz2 ‘ (65)

The right part of equation (65) describes the simple harmonic oscillator which is rewritten

below as

— +kz z: 0 (66)

The solution of equation (66) is well known and takes a form:
Z(z)= Aocoskzz + Basinkzz (67)
where A0, and BO are two z-independent quantities. The remaining part of the equation

(65) is written as equation (68) which can be further simpliﬁed by deﬁning a new constant

k9.

140
1 8 8R 1 89 _
IRE(r$)+[ 760—02]+(k2 —k 2)— (68)

Introducing kg and grouping the terms properly we again obtain a solution which has two

parts.

r8 0R 1829 2
Rar —( ar WE“ ”2’2) ' “'63—‘92 k9 (69)

The right part describes the angular dependence and the left part describes the radial

dependence of 1th . The right part takes the simple harmonic oscillator form as described

before in equation (66) giving

2
B_E-2) + k99= 0 (70)
802
Equation (70) has the solution as:
(9(0): Alcosk90+Blsink90 (71)

where A] and B1 are constants with respect to 0. Since rotational symmetry exists in
cylindrical cavity, a condition 9(0) = 9(0 + 2n1t) has to be satisﬁed by equation (71)
which produces k8 = n . Therefore, the remaining part of the differential equation in

equation (69) becomes:

233103—1344“ —k 22—)r - n2 (72)

Equation (72) is rearranged and equation (73) is obtained.

18R 2
3.2.12? + '13— +1(k2_k2)_%1R= 0 (73)

141

The form of equation (73) has a well known solution which is expressed as a combination
of Bessel and Hankel function of order n given by

R(r)= A21n(krr) + BzYn(krr) (74)

where

k, = ,/(k2—k:2) (75)

Equation (74) is now simpliﬁed again using the property of Hankel functions. Since the

value of zero order Hankel function YO(0) is inﬁnite at r=0, B2 in equation (74) has to be

zero. Thus the ﬁnal radial dependence of magnetic Hertz potential becomes:
R(r)= Aan(k,r) (76)

Combining Z, O and R from equation (67), (71) and (76) we construct the full expression

for the magnetic Hertz potential using equation (63) which is given below.
1th(r, 0, z) = ROZ = AZJ,,(krr)(Alcosn0 + Bl sinn0)(A0cosk:z + Basinkzz) (77)
Equation (77) can be further simpliﬁed using boundary conditions. The tangential

component of the E goes to zero at the metallic cavity boundary which is expressed in the

following equation

thl -0 (78)

metal —

where n is the unit normal vector to the surface. If equation (78) is applied to equation

I

x
(61) at r=a, we get, k, = ~11"— where, xnm’ is the mth zero of the ﬁrst derivative of the 11th
a

order bessel function, shown as J n’(xm) = aa—x[Jn(xm)] = 0. Similarly, if equation (78)

142

is applied to equation (61) at z=0 and z=C, we get Z(z) = Basin(kzz) and kZ = {Z—t where
l is any positive integer. Finally, the simpliﬁed expression for the magnetic Hertz potential

becomes:

xn

1th(r, 0, z) = AJn(

 

am r)(Alcosn0 + Bl sinn9)(sin-l-:—tz) (79)

The above expression is true for any arbitrary mode TE , where, the subscripts n, m,

run
and 1, denote the 0, r, and z variation respectively. The arbitrary constants A, A1, B1 are

the related to the microwave power input and the reactor characteristics.
However, for a given cavity dimension, not all operating frequencies can excite a TE

mode and the expression for an appropriate resonant frequency is obtained from equation

(75). Since k = (ox/Ire is always true for a wave of frequency (0 that travels through a

medium with permeability u and permittivity 8, equation (75) is rewritten as equation (80).

 

x ’2 2
k2 = ki+k2 = ( m") +(lﬂ) = (02118 (80)

Z a c

Rearranging equation (80) we get,

vc xnm’ 2 11C 2
fTEm, '- Q‘E‘K a ) +05) (81)

where vc is the velocity of light in free space and fTEm’ is the resonant frequency. It is

 

 

important to note here that for a given input frequency, different TE modes can be excited
in the cavity by changing either the length c or the radius a. For our cavity, the length c is

ﬂexible and can be adjusted by changing the sliding short position.

Finally, the expressions for the E and H ﬁelds for TE "m , modes are developed using

143

equation (79), (61), and (62). The derivation is straight forward and hence is not shown

here. However, the ﬁnal expressions for the r and 0 component of E ﬁeld e.g, E r, E9 and

r, 0, 2 components of H ﬁelds, e.g, Hr, H9 and H3 are listed below.

 

 

 

xnm [TC
E=—j(1)un(% )AJ"1a r)(A sinn0— B cosn0)(sin—z) (82)
nm xnm 111?
E0 = jtoufca )AJn ’( a r)(A cosn0+B sinn0)(sin—C—z) (83)

m
l

 

 

, - (IE-“XXL: m" )AJn '(xnm r)(Al cosn0+B lsinn0)(cos{:—tz) (84)
H9 = —(?X%)An] "C": r)(A sinn0— B Icosn0)(cosl%tz) (85)
”z ‘ 1 1’“) 141,111"

Note that for TE modes, E ﬁeld does not have an axial or 2 component. Similarly, for

 

 

r)(A cosn0 + B lsinn0)(sin£§z) (86)

transverse magnetic ﬁelds or TM modes, we expect to ﬁnd no component of the magnetic

ﬁeld along the z-direction and expect the E ﬁeld to have components in all directions. In

the next part, we discuss how the above approach is extended for solving the TM modes.

6.1.2 TM modes

For TM modes, the same Helmholtz’s wave equation is solved in cylindrical co-ordi-
nate but for the electric Hertz potential 11:8. Similar to magnetic Hertz potential, electric

Hertz potential is also an electromagnetic vector quantity. We again consider that the

direction of electric Hertz potential is aligned to the z-axis, or the axis of the cylindrical

144

. ._\
cav1ty and ne = 211e,.
With mathematical manipulation as carried out in the last section and with proper

application of boundary conditions, an expression for the electric Hertz potential is

obtained which is given in equation (87).

 

x I
Ite(r, 0,z) = BJn( '2" r)(Alcosn0+Blsinn0)(cosl%tz) (87)

Again B, A1 and B1 in equation (87) are constants and are related to the input microwave
power and the reactor characteristics. As before, the expression for the resonant frequency
for the TM modes is developed. Surprisingly this expression, as given in the earlier equa-
tion (81), remains the same for both TE and TM modes. The E and H ﬁeld components

for the TM "m 1 modes are ﬁnally expressed in the following ﬁve equations.

 

 

 

 

X

—(l—:—tX 2'")BJn a m" r)(A cosn0+B sinn0)(sinlitz) (88)

[TC 1 mnr . [TC
Ea = — — -)Ber "a AsinnB—Blcosne) sm—z (89)

c r c

2 l7: 2 . l1:
Ez = k — : J" Alcosn0+Blsmn0) cosgz (90)

. 1 11:
= -](08n(;)B./n (EJ- r)(A sinn0— B cosn0)(cos—z) (91)

. xnm I xnm . [71:
”0 = —](08(-21—-)B.1n( a r)(A1cosn0+Bls1nn0)(cos-;z) (92)

th

Here, xnm represents the m zero of the nth order bessel function, J n(x).

Equations (82) through (86) for TEM, and equation (88) through (92) for TM ”m , can

145

be used to plot the variation of E and H ﬁelds in a cavity as a function of r and 0. Usually

the z component variation is not plotted since the z-dependence is periodic (sinusoidal).
Plots of various modal patterns are available in references [6.4], and several of them are
shown in Figure 6.2. Obviously some modal patterns seen at z=0, show a great deal of
radial variations.

At relatively low pressures, where the ECR mechanism is primarily responsible for
species generation, the plasma density variation from mode to mode will be mainly due to
the different generation rates at the ECR zones. As described earlier, the ECR mechanism
is due to the interaction of the external magnetic ﬁeld with the perpendicular component
of the microwave electric ﬁeld. This will clearly be different from mode to mode, resulting
in different modes having different numbers of ECR excitation zones and different genera-
tion rates. The generated species will diffuse away from the excitation zones creating dif-
ferent species density distribution in space for different modes. This is described in the
following sections.

At higher pressures, on the order of 100 mtorr and above, species generation due to
Joule heating becomes appreciable. For such cases, the plasma tends to visually represent

the ﬁeld patterns shown in Figure 6.2. For example, at higher pressures the TE211 mode

shows four bright plasma regions corresponding to the four electric ﬁeld lobe patterns for

that mode. The TMOH mode shows a bright plasma located in the center. In this work,

however, our attention was limited to low pressures and ECR plasmas.

6.2 Ambipolar Diffusion

Ambipolar diffusion, or Schottky diffusion, assumes that the mean free path for the

146

 

   
 

  
  

—
'

«‘9;
’55!- a .

       

Figure 6.2: Modal patterns for TB and TM modes

147

carriers is much smaller than the discharge volume. Since electrons move much faster than
the ions, a space charge electric ﬁeld is established which accelerates the ions but slows
down the electrons. As a result, under steady state conditions, both electrons and ions dif-
fuse with the same diffusion coefﬁcient Da, which is known as ambipolar or Schottky dif-
fusion coefﬁcient.

Considering an inﬁnitesimal volume of discharge with a non-zero space-charge elec-
tric ﬁeld E, the ﬂux of ions 1“,. and electrons Fe going out of the discharge boundary can

be written as:

F = -niuiE— DiVni (93)

l

r, = neueE—DeVne (94)

i
where n, u and D in the above equations denote the charged species density, mobility and
the diffusion constants for the species. The subscript i, and e refer to ions and electrons
respectively. The mobility and the diffusion constants for both ions and electrons are

related to plasma characteristics e. g, the temperature of electrons and ions, Te, Ti and the
collisional frequency for momentum transfer, vim, and vem. These relations are shown in

equation (95) through (98).

 

 

 

“i = Mivim (95)
e

“e — mevem (96)

D kT‘ 97

i — M-V ( )

De = e (98)

 

where me and Mi in the above equations represent the mass of electrons and ions respec-
tively.

Because, the plasma is quasi-neutral, we can assume n e = n,- = n . Further, under
steady state conditions, the macroscopic densities of the ions and electrons in a small vol-

ume remain constant which implies that the ﬂux of ions equals the ﬂux of electrons across

the boundary of the small volume considered. Therefore, we can also assume

F- = I‘ = F. Applying these two conditions to equations (93) and (94), one can show

 

that
F = —DaVn (99)
where
.D + D.
Da = “I e “e I (100)
“fl-“e

This simply indicates that under steady state conditions, the electrons and ions diffuse

together and the effective ambipolar diffusion constant is Da. Moreover, the transient con-

dition for the charge ﬂow through a small volume has to satisfy the continuity equation

which is given as:

%—VI"+V'F = 0 (101)

where v,- is the ionization frequency. Combining equation (99) and (101) we get:

girl-vin+DaV2n = O (102)

149

Under steady state condition, equation (102) can be rearranged as:

Vi
Vzn—b—n = O (103)

Equation (103) is the key equation for modelling the transport of the species inside the
discharge. Note that the density of the species 11 is a function of spatial co-ordinates and is
assumed to be spatially non-uniform at the edge of the generation region corresponding to

2:0. For a cylindrical co-ordinate system, the equation (103) can be written as:

18 an 182n+
?ar1’arl+—2923:2+D1—:,=)' O (104)

To make the problem less complicated we assume that the species density does not

 

vary with 0. Therefore, equation (105) changes to:

:— 9—2 +0 :,=)o

V .
The term (DI-)1 in the above equation, represents the effective generation of carriers

a

per unit volume in the bulk plasma. Usually this term is very small for the low pressure

discharge, and may be neglected to a ﬁrst approximation.

6.3 Formulation of the Numerical Problem

Since angular symmetry is assumed in the model, the actual three-dimensional dis-
charge is simpliﬁed to a two-dimensional cross section taken along the r-z plane. More-
over, the radial variation of the species density from the center to the discharge

circumference is symmetrical about its axis, hence, it is sufﬁcient to consider only half the

150

discharge, extended from the center to the periphery. Figure 6.3 represents the modeled

structure of the discharge.

Edge of Generation

Region Discharge_>l
\ Radius

2:0 (0,0)

  

Downstream
Distance

\

 

 

 

 

 

 

 

Wafer -———— I' ——>

Chamber _,I
Radius

 

Figure 6.3: The cross-section of plasma discharge

A uniform numerical grid is established for the entire diffusion region, in which the spe-
cies densities at discrete locations are represented by individual grid points.

A part of the grid is enlarged and shown in Figure 6.4. The numerical solution is car-
ried out using the ﬁnite difference method [6.5] and MATLAB software [6.6]. n(i,j) in Fig-
ure 6.4 represents the species density at the grid location (i,j). The ambipolar diffusion
equation shown in (105) is translated into a difference equation using the notation

described in Figure 6.4.

151

“(iJ'll

 

AZ

 

n i-l,’ ' " n i+l,'
( J) Ar n(1,J) ( J)

 

 

 

 

n(i,j+l)

Figure 6.4: The numerical grid

The important steps showing the trend of the derivations are shown below.

 

 

 

 

 

 

2 "(i+1,j)—N(i,j)_n(i,j)—n(i-1,j)
an __ a an Ar Ar
d_r- _ FEB—r): Ar (106)
2 n(i,j+l)—n(i,j)_n(i,j)—n(i,j—l)
a n a an _ Az A2
8::- 7(37) — Az (107)
la_n _ l n(i+l,j)-n(i—1,j)
rdr _ i(Ar)|: 2Ar :l (108)

The above equations, combined with equation (105) gives the ﬁnal expression for the

species density at the location (i,j) in terms of its neighbor locations:

(n(i+l,j)+n(i—1,j j) +n(i,j+l)+n(i,j—l))
(Ar)2 (A2) (109)

[2 + 2 +31]
(Ar)2 (Az)2 Da

Equation (109) is the difference equation which has been numerically solved for the

"(i,j) =

 

 

appropriate boundary conditions. The discharge has four boundaries, hence four boundary
conditions are needed to solve the set of equations shown in equation (109). The cavity
periphery is metallic, hence the density of ions and electrons becomes zero along the

boundaries. Therefore 11 at ma, and z=c are assumed to be zero. At z=O, the spatially

152

varying density of the generated species serves as one boundary condition. Since the
chamber radius is much bigger than the discharge radius, only a part of this boundary has
non-zero species density. This is shown in Figure 6.5. The species density goes to zero for

the portion of grid that is outside the bell —jar since that corresponds to the top metallic sur-

face of the vacuum chamber. Also by symmetry 3_n
r

 

may be assumed. The Figure 6.5
0

r:

shows two regions.

Non-uniform n “=0

(0,0) —‘>i /

 

% n=0

l

n=0

 

 

 

Figure 6.5: Region of solution and boundary conditions

The shaded region is where the iterative search for the correct solution continues and
the clear region represents the ﬁxed valued boundaries. After every iteration the new den-
sity at each physical location namely, each matrix element is compared with its old value.
The maximum and the total difference between the old and the new density in the whole
shaded matrix is calculated after each iteration. When both these differences reach below a

pre-determined value, an acceptable accuracy level is ensured and the iteration is stopped.

153

6.4 Discussion of the NyLmerical Solgtion

For testing purpose, the numerical solution was ﬁrst carried out with an uniform spe-
cies density at 1:0. The plot of the downstream species density obtained from the numeri-
cal solution matched well with the plot obtained from the analytical solution given by
equation (50). Then the simulation was carried out for two different non-uniform hypo-
thetical species distribution at the source region. The results of the simulations are shown
in Figure 6.6 and 6.7. Usually the species density in the ECR reactor increases from the
center to the periphery since the actual ECR zone, i.e, the 875 Gauss line region exists
closer to the periphery. Therefore two species distributions are chosen both of which show
an increase in species density along the radial distance but distribution 1 shows a larger
radial variation than distribution 2. For the purpose of this discussion, the two different
distributions are referred to as different modes. Although they do not necessarily corre-
spond to any two speciﬁc modes discussed in section 6.2, they represent in a qualitative
way how species variations may change as modes and pressures are changed.

The species densities at various locations are normalized and plotted in Figure 6.6 and
6.7. The downstream distance for mode 1 and mode 2 were chosen to be 2.5 cm and 10 cm
respectively. Since the proﬁle at the downstream distance for mode 1 shows a radial
increase in species density, etching in mode 1 will result in removal of more material from
the periphery than from the center. However, mode 2 will show an opposite effect. Hence,
if appropriate amount of etching is performed with mode 1 and mode 2 sequentially, the
total removal at the end of combined etching may be very uniform along the radius. This is

shown in ﬁgure 6.8. The percent variation in etch rate for mode 1 is 23.6%, for mode 2

Normalized Species Density

154

Processing at Mode 1

 

0.9 ~

  
     

Species density
at generation
0-8 region

0.7

0.6

Downstream species it
0.5 ” density at 2.5 cm below \

the generation region \

l

0.4

0.2 -

0.1 -

 

 

 

Radial Distance

Figure 6.6: Normalized downstream species density variation for mode 1

10

Normalized Species Density

155

Processing at Mode 2

 

 

 

l T ﬂ l ‘l
0.9 ~ Species density at —
generation region
0.8 L -
0.7 ~ 2
0.6 - .
0.5 ~ -
0.4 - -
0.3 ’- \ \ h \ ' \_ 4
Downstream species \ ' \ . \
0.2 * density at 10 cm below x. -
the generation region \.
0.1 - ‘x w . ~ \ -
1‘ ‘ ' ‘ 1~ A

 

 

Radial Distance

Figure 6.7: Normalized downstream species density variation for mode 2

10

156

Processing at mixed modes: Mode l + Mode 2

 

0.7 l I f l l f l
0.65" ,”’ a
0-6" ,’ Model ‘
0.55:____,’”’ .

>5

E 0.5

93

ED Mode l + Mode 2

.C

5 0.4L (50% on each mode) J
0.35—_._._._._g_p_ ‘7‘ .1
0'3? Mode2 \\"\.\ ‘
0.25" "x.\_ -

"'2

02 l l l l J I l

 

 

 

Wafer Radius

Figure 6.8: Etching uniformity comparison for mode 1, mode 2 and mixed modes

157

is 34.7%, and the mixed modes is 2.9%. For this example, the etching was assumed to be
done for equal amount of time in each mode. These calculations are done over a 100 mm
radius wafer. For achieving even higher uniformity, relative run times may be optimized.
Also more modes may be introduced for etching. However, from this discussion it is seen,
that the etching in mixed modes can result in higher uniformity that etching in any one
mode. It may be noted that initial experiments in chapter 5 supported this hypothesis.

As an extension of this concept, the method of mixing modes may be found useful for
further controlling the etch proﬁles as desired. For examples, the wafers may be preferen-
tially etched with intention to make a non-uniform wafer, uniform or to achieve a ﬁnal
desired thickness variation for a wafer. In fact, for the CVD grown free-standing polycrys-
talline diamond wafers, the as-grown wafers are often of non-uniform thickness and there-
fore require non-uniform removal of material to create a ﬁnal structure of uniform

thickness.

Cﬁagter ’VII. Tlanarz’zation (twill/[asking Oiﬂiamomf films

7.] Planarization

Reduction of surface roughness on an as-grown polycrystalline diamond ﬁlm is a well-
known problem in diamond research. Many different methods are proposed in the litera-
ture for planarizing rough ﬁlms, some of which are already reviewed in detail in chapter 2.
However, before going into the description of the polishing techniques, it is useful to
brieﬂy introduce different measures of surface roughness that are commonly used in char-

acterizing a rough diamond surface [7.1]. Ra, Rmax, and R2 are three of such measures. Ra

is known as the mean roughness of a surface and is deﬁned by equation l 10.

 

LILX
l
R, — L 1. j jlf(x,y)ldxdy (110)

x y 0 0
f(x,y) in the above equation is the surface height relative to the center plane and Lx and 1.3,
are the dimensions of the surface. Rmax is deﬁned as the difference in the height between

the highest and lowest points on the surface relative to the mean plane, and RZ is the aver-

age difference in the ﬁve highest peaks and ﬁve lowest valleys relative to the mean plane.
ln general, different diamond polishing methods vary in their efﬁciency and often the

initial roughness of the ﬁlm plays a critical role in determining the success of a method.

Some polishing techniques work better for the gross reduction of roughness, say for ﬁlms

with beginning Ra ~ 10 um, and some others work better for ﬁner polishing, say for ~ 0.5
um of beginning Ra.
In this section, we focus on results from the planarization technique using a sacriﬁcial

planar coating. This process is described in Figure 7.1. The idea of ﬁrst coating the rough

158

159

Overcoat

/ Desired Surface

 

 

Poly-Crystalline Diamond

 

1. After spinning on the sacriﬁcial layer

 

 

Poly-Crystalline Diamond

 

2. After etch back using ECR plasma

Figure 7.1: Method of polishing diamond

 

 

160

diamond surface with a planarized layer, and then etching both the diamond and the
coated layer at the same rate to obtain a ﬂat diamond surface at the end, has been investi-
gated by several researchers [7.2, 7.3, 7.4, 7.5]. However, the methods differed in the pla-
narizing material and the technique used to coat the diamond surface. Also different
etching mechanisms and etching apparatus have been reported by different researchers.
Our planarization technique was restricted mainly to the investigation of different spin-on-
materials as the sacriﬁcial layer.

A Wavemat 325i ECR plasma reactor was used as the etching apparatus for all pla-
narizing experiments. Finding a proper spin-on-material that forms a crack-free, continu-
ous, uniform, and smooth surface on a rough diamond surface and which etches at a low
comparable rate as diamond was the ﬁrst main challenge to face. Once a material was
found, the next task was to ﬁnd the correct plasma etching condition and the time of etch—
ing. The etching condition was mainly controlled by changing the gas chemistry. This was
similar in concept to controlling the selectivity of etching in conventional semiconductor
processing, except that in diamond planarization, a non-selective plasma was generated
intentionally to etch both the diamond and the sacriﬁcial layer at the same rate. Since,
sputtering by nature is a relatively non-selective etching process, both sputtering and RIE
with proper gas mixtures was applied for this purpose.

We have seen in the previous chapter that even plain etching on an uncoated diamond
sample increases the surface roughness, hence no over-etching was desired in order to
make the method effective. Deciding the etch time was not easy as the surface roughness
varied spatially and the height of the over-coat ﬁlling the surface peaks and valleys, was

necessarily different at different places. For best success, the etch time had to be just

161

appropriate to etch the maximum height of the spin-on-material without over-etching.
The following sections discuss various planarization results obtained from using dif-

ferent overcoats and ECR plasmas consisting of various mixtures of Ar, 02,and SF6.

7.1.1 Planarization with Photoresist on Thick Film Samples

It is well known that photoresist can smooth rough surfaces and Pearton et.al., reported
that UV hardened photoresist, Hunt 5209B [7.6] can be used as a masking material for dia-
mond in an oxygen containing plasma [2.41]. Since, a material used as mask has a much
lower etch ratio than the masked materiel, Hunt AZ 5209B was thought to be a potential
overcoat for yielding an etch rate at least comparable to that of diamond. The samples

treated for polishing experiments with a photoresist overcoat, had an initial Ra between
0.4 and 0.8 microns. These 1 cm X 1cm square shaped samples were are jet deposited and
had a blackish appearance. Initially two samples MSU-l and MSU-7 afﬁxed in the middle

of a 50 mm silicon wafer by graphitic paint, were spin-coated with AZ 5209-E at 4000

rpm for 30 seconds. Then the samples were soft—baked for 30 minutes at 85 0C and UV
hardened at 300 watts for 15 minutes using the SUSS MJB 3 mask aligner as the UV
source. The thickness of the photoresist layer was measured to be ~ 0.9 pm by an ellip-
someter. The samples were then sputtered for half-hour in Argon only plasma. The pre-
processing, post-coating and the post-etching dektak proﬁlometer scans showed that some
degree of surface planarization was achieved after the photoresist coating, but the rough-

ness after the plasma etching went back to a value close to the pre-processing Ra. These

results are given below in Table 7.1.

162
Table 7.1: Dektak result of photoresist experiments

 

 

s I Initial Ra Ra aft" 6 50 min Post
amp e Scan layer t etching Ra
(Dektak) 33:22:) (Dektak)

 

 

MSU-7 6213 i 1412 4718 i 1034 5812 i1405

 

 

 

 

 

 

 

 

 

 

 

 

Another sample, MSU-S was coated similarly with 5209 E photoresist but was etched
with an argon/oxygen plasma for 96 minutes. This caused the post-etch processing Ra to
actually increase beyond the initial Ra. Next, experiments were performed that showed
that UV hardened photoresist AZ 5209B actually etches much faster (about 8 times) in our
system than diamond with an argon & oxygen plasma ECR plasma. The adjustment of the
plasma parameters did not seem to affect this etch ratio to a great extent, so it became clear
that photoresist was not a good choice for the diamond planarization at least for the
plasma chemistry and the photoresist investigated. Therefore the research turned to the

investigations of other spin-on-materials.

7.1.2 Planarization with Spin-On-Glass on Thick Film Samples

First, in order to establish the etch rate of SOG, a 3 inch Si wafer was coated with 51 1
F spin-on-glass [7.7] at 3000 rpm for 30 s, followed by a 30 s bake at 150 oC and 1 hour
bake at 420 0C in N 2 atmosphere. The thickness of one SOG layer ranged between 1800 —

3500 angstrom, depending upon the spinning speed. Typically the thickness was found to
be around 2000 angstrom from ellipsometer measurements, when spun at 3000 rpm. The

etch rate of SOG in an argon only plasma was appreciably lower than photoresist, and was

163

found closer to diamond. However, as the thickness of the SOG ﬁlm was grown to more

than 4000 Angstroms with multiple layers, the ﬁlm showed surface scaling at the end of 1

hour heating in 420°C.

However, arc jet deposited samples were coated with SOG and treated in ECR plas-
mas. MSU-2, received two layers of SOG coating following the technique discussed above
and was sputtered in an argon only (20 sccm) plasma. Dektak measurements did not show
much improvement in Ra with two layers of SOG coating or at the end of sputter etching.
The standard deviation showing the variation of surface roughness from one spatial loca-

tion to other, increased after the sample was coated with SOG and the higher standard

deviation was maintained after etching. Table 7.2 shows the results obtained from Dektak

 

 

 

 

measurements.
Table 7.2: Dektak result of SOG experiments
Sample Initial R8 111::- 6 50 min Post
Scan etching Ra
(Dektak) 33:12:23 (Dektak)
MSU-2 3287 i 253 3054 i 721 2882 i 667

 

 

 

 

 

 

 

 

 

 

 

 

 

Since, SOG results did not show much encouraging results with argon sputtering we

decided to use titanium silicate-photoresist emulsion for our next set of experiments.

7.1.3 Planarization with Titanium-Silicate on Thick Film Samgles
Earlier work on diamond planarization using an argon/oxygen ECR ion beam irradia-
tion with no sacriﬁcial coating was reported to reduce the surface roughness from 3 pm

Rmax to 0.5 pm Rmax [2.33]. Zhao, Grogan et al., [2.32, 2.34, 2.35] from the University of

164

Arizona reported to improve the method of ion beam smoothing by coating the rough dia-
mond surface with a layer of titanium silicate mixed in an appropriate proportion of photo-
resist. Depending upon the initial roughness of the diamond ﬁlm, often several layers of
coatings were applied to make the coated surface smooth to the desired scale. According
to the report, the coating was hardened by baking, and etched with an oxygen ion beam of
various energy and various incidence angle of the ion beam. The etching was reported to
result into a smooth diamond surface with appropriate energy and incident angle.

The ion-beam in their case was derived from a Kaufman ion source and the use of a
Faraday cup allowed them to monitor and maintain a constant beam flux. The ability to
adjust the incident angle of the beam with respect to the macroscopic surface of the dia-

mond substrate was claimed to be very important in achieving a polished surface and an

incident angle of 470 was reported to produce the best polishing result.

We attempted to planarize diamond using the same concept of adding a titanium sili-
cate—photoresist layer on the rough surface of diamond but etching in an ECR plasma reac-
tor MPDR 325i instead of an ECR ion beam apparatus or Kaufman source. The main
difference between the MPDR 325i and an ion beam source is that the ion ﬂux from an
ECR plasma reactor strikes the surface of the substrate perpendicularly and the incidence
angle of the ion ﬁux can not be controlled. Therefore, etching in an ECR plasma reactor is
expected to produce different results than what was obtained from ion beam etching at a
non-perpendicular angle of incidence.

To carry out the experiments, titanium-silicate was mixed in a 1: 1 proportion with both
SC1400—l7 and SC 1400-28 [7.8] photoresists and agitated using ultra-sound waves for 15

minutes following the technique described by Zhao et. al. This mixture was then spun on

165
different samples which produced an effectively plane surface, supported by the Dektak

measurements but the post-etching Dektak measurements for Ra in almost all cases were
comparable to the beginning Ra implying no signiﬁcant ﬁnal planarization.

Many attempts were successively made for months to equalize the etch rate of titanium
silicate with diamond under different plasma conditions but no condition was found to
produce a satisfactory result. During one set of Dektak measurements, the short range (0.1

mm) Dektak scans of etched samples were noticed to be less than the Ra from a long range
(1 mm) Dektak scans for the coated sample, whereas the R8 measurements for the

uncoated sample did not differ much from short range to long range measurements. The
results of these scans are presented in Table 7.3 and are thought to be key observations in
terms of understanding our post-etching results. From the scans, it seemed to us that the
overcoat layer planarizes the samples over short ranges but fails over long ranges.

Table 7.3: Long range Vs. short range dektak results

 

 

Sample 0.1 mm 1 mm

Sample Condition Scan scan

 

 

MSU-l6 4* Uncoated 3281:521 39442444

 

 

MSU—ll Coated with 6 599:382 1830 i 820
layers

 

 

 

 

 

 

 

 

 

 

 

 

In other words, the uncoated surface appears to have two kinds of roughness, one
results from rapidly changing peaks and valleys and the other is produced from variation
of surface topography over several hundreds of micrometers. The Dektak proﬁlometer
picked up both these types of roughness while tracing the surface. We think that the pla-

narization coating successfully reduces the short-range roughness, although it follows the

166

long range topography variation of the surface. This is better explained in Figure 7.2.

Overcoat follows the
surface topography

/\//\

 

Diamond with rough surface

 

Figure 7.2: Short and long range surface fluctuations

Since the planarization occurs only in short ranges upon coating, it is believed that at
the end of etching the surface roughness for small regions are reduced although the long
range roughness remains unaffected. A typical result based on 0.1 mm Dektak scan is
shown in the Table 7.4 below.

Table 7.4: Dektak result of titanium silicate experiments

 

 

 

 

 

 

 

 

 

 

 

 

s I Initial R, Ra 3“" 6 50 min Post
amp 2 Scan lay er t etching Ra
overcoa
(Dektak) (Dektak) (Dektak)
MSU-14 3406 i 442 432 i 231 2135 i 821

 

 

 

 

Another interesting phenomenon was observed which was not reported by Zhao et.al.,
[2.32, 2.34, 2.35]. Titanium silicate appeared to exhibit a two-phase etching process. In all
cases the photoresist was etched away at a very high rate leaving behind numerous small

dot-like particles on the diamond surface. This remaining material appeared to be

167

relatively etch-resistant. We believe that the photoresist served as the carrier for the sus-
pended titanium silicate particles which deposit on the surface of the diamond as the pho-
toresist is etched away by the oxygen plasma.

At this point a new set of planarizing experiments were planned with spin-on-glass
(SOG). This was motivated by an observation made on an SEM of SOG coated sample
used in the masking work reported later in section 7.2. Since the arc-jet deposited diamond
thick ﬁlms appeared to have prominent long range surface variations compared to the
microwave grown thin ﬁlm samples, we chose to carry out our experiments with the
microwave CVD grown diamond ﬁlms. These are thin ﬁlms grown on silicon substrate
which have grain sizes not more than about 1-2 pm.

Since this time our interests were more concentrated in seeing the effect of our pla-
narizing technique on small areas (say ~ 50 um X 50 pm), the SEM was thought useful to
document the surface features as opposed to Dektak proﬁlometer. The result of these

experiments are described in the next section.

7.1.4 Planarization with SQG on Thin Film Diamond

Although SOG experiments performed earlier did not show much improvement in Ra,

we still chose SOG as the planarizing layer due to several reasons. First of all, it is a spin-
on-material which acts as a planarizing layer. It is regularly used for planarizing the multi-
level interconnects in IC manufacturing due to the ﬂowability of glass at high temperature.
Secondly, SOG is a homogeneous material unlike the suspension of titanium-silicate in
photoresist, which is not expected to show a two-phase etching. Thirdly, SOG is an

already oxidized inorganic compound, and therefore does not etch at a very high rate in an

168

oxygen plasma. Also it is known that a ﬂuorine containing plasma etches SiOZ. Thus the

etch ratio of diamond to SOG in an RIE process may be expected to be controlled by
changing the ratio of oxygen content to the ﬂuorine content in the etching discharge.

From some initial experiences of coating arc-jet samples with SOG as reported in sec-
tion 7.1.2, we knew that the SOG coated surface shows cracks for multiple layers, in most
cases when the number of layers is more than two, and in some cases when it is even more
than one. The cracks seen on surface are thought to be mainly due to mismatching of ther-
mal expansion between diamond and SOG. Since two layers of SOG at spinning speed of
3000 rpm refer to a total of 0.4 um thick ﬁlm, the SOG technique appeared to be limited to
samples with surface roughness less than 0.4 micrometers.

However, in order to study the planarization experimentally, a microwave grown dia-

mond-on-silicon sample was SOG spun at 3000 rpm for 30 seconds followed by a soft

bake for 60 s at 150 °C and hard bake for 1 hour at 400°C. The process was repeated to
add another layer of SOG and the total thickness of the masking material was determined
about 4000 An gstroms from the ellipsometer. Then the sample was broken into two pieces
and each piece was etched under different plasma conditions. For both the discharges, the
input microwave power, rf power, process pressure, downstream distance and the duration
of the runs were same and were ﬁxed at 500 watts, 100 watts, 4 mtorr and 45 minutes

respectively. The oxygen to SF6 gas ﬂow ratio was changed intentionally to exploit the

freedom of balancing the etch rate of SOG to diamond. One piece was etched in an argon-

oxygen-SF6 plasma with 12, 6, 2 seem of gas ﬂows and the other piece was etched with
argon-oxygen-SF6 plasma at ﬂow rates of 12, 12, 2 seems. Then the samples were cleaned

with 50% hydroﬂuoric acid to wash away any remaining SOG.

169
SEMs were taken to document the uncoated, spun-on and post-etched surfaces of the

sample. Figure 7.3 shows the uncoated microwave grown diamond sample at a magniﬁca-
tion of 9000X. Typical grain sizes of this sample appear to be about ~l mm which is likely
to produce a “short range” type of surface roughness which is needed to verify our hypoth-

esis.

 

Figure 7.3: Uncoated sample surface

Figure 7.4 at 7500X, shows the result after etching with lower oxygen containing
plasma, and Figure 7.5 at 7500X, shows the surface after etching in higher oxygen con-
taining plasma. It is obvious from the SEMs that peaks of the diamond surface are indeed
affected by the etching and some degree of planarization is achieved. The SEMs show that
the planarization result improves when the oxygen ﬂow rate was changed from 6 to 12
sccm. Figure 7.4 shows some planarization but Figure 7.5 shows an improvement. This
indicates that the oxygen content in the 12:6:2 sccm of argon oxygen SF6 plasma was not

adequate.

170

 

Figure 7.4: Planarized surface after processing with low 02 containing plasmas

The comparison of Figure 7.4 with 7.5 seems to give an idea of the process evolution
indicating how the peaks of the polycrystalline diamond have somewhat been “melted

away” due to etching and a relatively planar surface have slowly evolved.

 

Figure 7.5: Planarized surface after processing with high 02 containing plasmas

171

However, the surface morphology after planarization is still far away from what would
be an ideal plane surface. There are several reasons behind it. A look at the two—layer of

SOG coated sample in Figure 7.6 is informative in this regard.

 

Figure 7.6: SOG coated diamond sample

The SEM of the SOG coated sample in Figure 7.6, reveals that although SOG has been
successful in covering almost all the peaks on the surface, it could not really produce a
perfect planarized layer. The scales seem to come off from the surface. Since the etch back
method even under the perfect matched etch rate condition, can only retain the same
degree of surface smoothness as achieved from the planarizing coating, a very smooth sur-
face at the end of spin-on is desired. But in case of SOG, we do not ﬁnd a very smooth
post—spun-on surface to begin with, hence the ﬁnal etched result was not very satisfactory.

Also after the etching runs were completed, pin-holes and voids are noticed to appear
on the surface. Presently these are thought to be caused by the lack of ﬁlm continuity for
these very thin ﬁlms (< 100 micrometers).

Our initial attempt has been helpful in gaining a better insight on the principle of the

172

etch-back method and its use for diamond planarization. The results support our hypothe-
sis of short range planarization. However, a search for a better sacriﬁcial coating needs to
continue for a higher surface planarization outcome and to achieve planarization on a wide

variety of samples irrespective of how they are produced.

7.2 Masking

One of the motivations for exploring the new diamond technology is to utilize its
incomparably high thermal conductivity. Diamond used as a coating on silicon chips could
mean a larger integration and smaller device spacings. This is because the heat produced
by the chip which becomes a larger and larger concern with increased chip integration is
carried away by the diamond layer. For producing this heat managing diamond layer, dia-
mond needs to be ﬁrst grown on the top of the IC and then patterned.

Masking polycrystalline diamond is a known technique although the problem becomes
more difﬁcult when the pattern needs to be transferred on a diamond-coated IC rather than
a plain diamond surface. The complications mainly arise from the IC metallization layer
that is underneath the diamond surface. Our research mainly concentrated on ﬁnding a
masking material that could be easily patterned and removed without etching the underly-
ing aluminum contact layer. Patterning diamond ﬁlms can involve selective growing of the
diamond seeds [7.9] as well as selective etching of a continuous thin ﬁlm. Many studies on
selective growth phenomenon of diamond and microstructural control of nucleation can be
found [7.10, 7.1 l, 7.12] in literature. Selective etching of diamond has also been reported.
The conventional method of transferring a pattern on the surface of a diamond-coated IC

was successfully tried and reported [7.13] in 1990. The selective etching work in [7.13]

173

used an aluminum metal mask to pattern the diamond ﬁlm grown on the top of an ampli-
ﬁer IC, which showed perfect functioning before the diamond growth and after the dia-
mond etching. However the metal contact layer for the IC in this case was not aluminum.
For our research, a diamond layer was grown by Ulczynski et al., [7.14, 7.15] on the
top of a 50 mm silicon wafer containing ICs of resistors, BJTs, FETs, and MOS capaci-
tors. The metal layer was aluminum and our aim was to etch the diamond layer only from
the metal contacts of the ICs in order to test the functioning of the devices. The diamond
covered wafer had approximately 0.65 micrometer of diamond grown over the devices.
This wafer was micrographically characterized at many different phases of operations. For
this initial attempt, Spin-On-Glass was chosen as the masking material. It was known from
the previous experiences that SOG can produce a thin (~4000 A) ﬁlm which can exhibit an
etch rate lower than that of diamond under certain plasma conditions. SOG was spun at

3000 rpm for 30 seconds over the diamond surface followed by a soft bake for 60 s at

150°C and hard bake for 1 hour at 400°C. The same process was repeated to add another
layer of SOG such that the total thickness of the masking material was determined to be
about 4000 Angstroms by the ellipsometer. Then a photoresist layer was spun, baked and
patterned to in a standard way to make the wafer ready for the plasma etching. The SOG
was etched with a 50:1 buffer oxide etch. From the plasma etch data established before,
SOG and the diamond etch rates were found to be ~325 A/min and ~475 A/min in a 800

W, 110 V rf bias, 7 mtorr, Ar, Oxygen and SF6 plasma. The gas ﬂow rates in this case for
Argon, Oxygen and SF6 were 12, 6, and 2 sccm respectively. A total of 25 minutes of

plasma etch was thought to be sufﬁcient. Remaining SOG was etched using chemicals and

the devices were inspected using a microsc0pe.

174
An SEM shown in Figure 7.7, shows the removal of the diamond from the aluminum

metal pads.

Diamond

Aluminum

 

Figure 7.7: Selectively etched diamond coated IC shows aluminum pad

Some of the devices were successfully tested using the probe station and device
parameter analyzer assembly. However, this experiment represents an initial attempt
which can be further improved with the use of better mask material. In this ﬁrst attempt,

over-etching was noticed although the diamond was seen to be patterned.

Chapter (VI I I . ,gummag and future Research

8.] Summary ofResearch
The dc arc jet and microwave CVD grown samples were successfully etched using

ECR plasmas generated from MPDR 325i reactor. Etching was mainly carried out with 02

containing plasmas although some sputtering experiments were performed with only
argon. Initial plasma etching experiments exhibited a low etch rate of diamond but with
the help of statistically designed experiments the etch rate was increased by an order of
magnitude. An etch rate of about 8 um/hr on 100 mm wafers and 12 um/hr on smaller
samples were ﬁnally obtained. Statistical analysis showed that oxygen and rf bias have the

strongest positive inﬂuences on etch rate while SF6 has a negative effect. However, dia-
mond etched in absence of SF6 produced a black ﬁlm on the etched surface. This black

layer acted as a passivation layer, and the etch rate was found to decrease as the black ﬁlm
became denser. Hence etching of diamond at a steady high rate required the plasma to

contain a minimum amount of SF6.

Experiments demonstrated that plasma composition with higher oxygen contents pro-
duces higher etch rate and the etching nature was shown to be reactive ion assisted. The
sputtering rate was found to be extremely low compared to the rate of reactive etching. An
etch rate equation of diamond was also calculated from the theory of reactive etching and
compared with the rate obtained from the experiments. These values agreed quite closely.
A maximum of about 250 um was removed from one single diamond wafer. The etch rate
of diamond did not differ much from substrate side to the growth side.

Four inch, ~l.5 mm thick CVD grown polycrystalline diamond ﬁlms were processed

175

176

with as low as 5% non-uniformity over the surface. The uniformity of diamond etching
was observed to increase when etching was performed with more than one mode in
sequence of time. This observation was theoretically investigated to learn about the role of
modal patterns and ambipolar diffusion on the etching behavior. The simulation result
supported the hypothesis of mixing modes to obtain higher uniformity of etching.

Another part of our research was aimed at planarizing rough diamond surfaces. The
etch back method was employed to reduce the surface roughness of the arc-jet deposited
and microwave CVD grown diamond samples. Different spin-on-sacriﬁcial layers such as
photoresist, titanium silicate emulsion in photoresist, and SOG were spun on diamond and
used as planar coatings. UV-hardened photoresist in oxygen containing plasma environ-
ment showed a much higher etch rate compared to diamond in our system for all condi-
tions investigated. Titanium silicate in photoresist showed a two phase etching mechanism
with photoresist being etched away at a very high rate leaving behind the titanium silicate
particles on the uneven surface of diamond. Both spin-on-layers of titanium silicate-pho-
toresist emulsion and SOG resulted into planarizing the short range surface roughness.
The long-range (order of 100 um) surface variations were more or less followed by the
coated layer. However, planarization experiments conducted on microwave grown dia-
mond ﬁlms with short range surface variation (order of 1 mm), showed initial success of
achieving some degree of planarization using etch back technique.

Masking of diamond ﬁlms using SOG was brieﬂy investigated. An integrated circuit
coated with diamond, was patterned with SOG and selectively etched with ECR plasmas.
The aim of this work was to etch the diamond layer from the metal pads of the ICs. An

argon, oxygen, SF6 plasma was successfully used to remove the diamond layer from the

177

desired locations.

8.2 [injure Work

Further development of ECR etching of diamond may go in many directions. A few of

these potential research areas are highlighted below.

A. Obtaining higher etch rate

Etch rate of diamond may still be increased several folds if higher rf bias and higher
microwave power are applied for etching. With an rf induced dc bias of 300V and the
microwave power of 1.5 KW, the speculated etch rate becomes over 40 um/hr if the etch
rate increased linearly with both bias and microwave power. The etch rate is unlikely to
depend linearly on the microwave power and rf bias over an indeﬁnite range, still one can

reasonably expect to obtain an etch rate of about 25 um/hr using ECR oxygen plasmas.

B. Relation of If power and induced dc bias in MPDR

Preliminary experiments showed that the rf induced dc bias is related to rf power in a
complicated way for a microwave cavity. Detailed experimental or theoretical investiga-
tions were not performed to understand how the rf power (rf induced dc bias), microwave
power, and the downstream distance are mutually related in a microwave ECR reactor.
Investigation of this would be an important in order to understand the etching behavior of

these microwave discharges with rf biasing.

178
C. Black ﬁlm investigation

Although we were successful in preventing the formation of black ﬁlm on diamond

surface using SF6 in plasma, we have not quantiﬁed the ﬁlm. Black ﬁlms grown under dif-

ferent etching conditions were not investigated or compared. Research can be directed
with proper surface analysis techniques to identify the chemical composition of the black

ﬁlm in order to ﬁnd the nature of the black ﬁlm and the reason for its formation.

D. Relating etch rate to the quality of the diamond ﬁlm

Different diamond samples showed different etch rate when etched simultaneously
under same plasma conditions. The reason behind this observation has remained unex-
plored. Investigations relating the dependence of etch rate on the quality of the ﬁlm
namely, electrical conductivity, optical transparency, grain size and orientation may be
quite helpful in answering the sample-to sample variation.

Also experiments with single diamond crystal will be an important contribution in
ﬁnding the directional dependence of diamond etching with ECR plasmas. At this point, it
is believed that plasma etching does not show large variation in etch rate from one direc-

tion to other.

E. Surface planarization

Although etch back technique following a coating of SOG on diamond showed some
improvement of surface roughness, SOG is not an excellent material for planarization. As
multiple layers are spun, cracks and scales are seen on the surface. Therefore, for an

improved surface smoothening, search for a better planarizing material should continue.

179

Ideally this material should exhibit the ability to form a thick coating to planarize both
long range and short range surface variations and show an etch rate comparable to dia-

mond under attainable plasma conditions of the reactor.

F Uniformity analysis and experimental veriﬁcation
Further work is required to correlate etch uniformity in r and 0 with different cavity
modes. A more precise measurement technique than the micrometer would be useful. For

example, the etching experiments could be conducted on smooth wafers such as, Si02

coated Si wafers and a wafer scanning ellipsometer can be used to record etch uniformity.
This way the uncertainty of thickness measurement that arises from the roughness of a

polycrystalline diamond wafer can be avoided.

8.3 Conclusions

In conclusion, ECR post-process etching was found to offer signiﬁcant improvement
as a diamond removal method as compared to conventional mechanical post-processing.
The rate of material removal is over an order of magnitude higher than that obtained by the
older method. This research represents the ﬁrst report of high rate and uniform ECR
plasma etching on large free standing diamond substrates. As a result, there is interest in
transferring the technology to industry in order to supplement or replace the existing
methods of diamond ﬁnishing. Also, the research describes a new method for controlling
etch uniformity through mixed mode etching.

A signiﬁcant challenge for future work is to achieve not only rapid material removal,

but also improve the quality of the ﬁnished surface by reducing the surface roughness.

180

This involves the uses of sacriﬁcial over-layers on diamond and will be the subject of

ongoing research.

List of Appendices

ﬂggendix Fl: ,gategu and Maintenance affCK sistem

Some important safety issues for the users and the ECR plasma etching system are
addressed here.

The plasma radiates UV light, hence looking directly into the plasma without having
proper eye-protection should be avoided. The ECR system runs under high vacuum, hence
caution must be taken to avoid all risks of implosion. If the pressure inside the main-cham-
ber for any reason goes up, then the system should be immediately shut down for investi-
gation before further processing. For example, a cracked bell jar can lead to dangerous
accidents. As the system operates with microwave energy, microwave leak detection is
necessary before processing. Proper and safe handling of gas cylinders is also a part of
operating this system. If ever, the system is opened for maintenance, all necessary precau-
tions must be taken to avoid inhaling any hazardous gas that may be used or generated
during processing.

Preventive maintenance on a regular interval is suggested to reduce the chance of sys-
tem failure. The mechanical pumps need an oil change, bearing lubrication etc. on a regu-
lar basis. Nitrogen should ﬂow for purging the alcatel mechanical pump especially if

ﬂuorine contained gas e.g, SF6 etc. is ﬂown through the cavity. Presently the microwave

cavity and the turbo pump is open-end water cooled using tap water. However, the turbo
pump runs always and water should always ﬂow through the pump. Water cooling lines
get eventually clogged because of the sediment deposits and use of common cleaning
agents for removal of sediments may be very damaging for the system at times. Therefore,
closed loop cooling arrangement with cooling agents other than water is recommended.

Usually mixture of ethylene glycol and de-ionized water is circulated through the chiller

181

182

for cooling. Presently the rf biased chuck is cooled this way, other parts that need cooling
especially the microwave cavity may be recommended to switch over to closed-loop cool-

ing system using chiller in future.

Mend/i213: gig; Ougut

 

27 Oct 94 SPSS for MS WINDOWS Release 6.0 Page 1
This software is functional through January 31, 1995.

**** MULTIPLE REGRESSION ****
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable. RATE
Block Number 1. Method: Enter POWER SF6 O2 BIAS
Variable(s) Entered on Step Number 1.. SF6 2.. BIAS

3.. 02 4.. SF6

Multiple R .98505

R Square .97033

Adjusted R Square .95549

Standard Error .10438

Analysis of Variance DF Sum of Squares Mean Square
Regression 4 2.85047 .71262

Residual 8 .08716 .01090

F = 65.40646 Signif F = .0000

 

Variables in the Equation ..................

Variable B SE B 95% Confdnce Intrvl B
BIAS .033841 .004142 .024289 .043394
02 . 138801 .017585 .098250 .179351

POWER .001983 5.5480E-04 7.03893E-O4 .003263
SF6 -.O65051 .017585 -. 105601 -.O24500
(Constant) -2.937349 .491688 -4.071 183 -1 .803515

End Block Number 1 All requested variables entered.

183

431$)ch C: Matlaﬁ Trograms

The following Matlab program generates Figure 6.5

% Ambipolar Diffusion Simulation
% Initialize the matrix and problem size
% Assume that there is no recombination in the plasma; i.e,
% Vi/D =0% Down-stream Distance distl=l; dist2=2;
% Collisional term: col = vi/D
col=0.0;
a=zeros(20,20);
nr=20;
nz=20;
delr=l .0;
delz=l .0;
delr2=delr*delr;
delz2=delz*delz;
% Initialize the boundary
for m=l :nz
a(20,m)=0.0;
end
for m = lznr
if m>10
a(m,1)=0.0;
else a(m,l)=l+(0.09*m)"2;
a(m,20)=0.0;
end
end
% Set up the matrix : Use the iterative method
for k = 1:100
maxerr=0.0;
sumen:0.0;
for i=2:nr—1
for j=2:nz-1
r=i*delr;
adev=(2./delr2+2./delz2+col);
apr2=a(i+ l ,j)./delr2;
amr2=a(i- l ,j)./delr2;
aprl=a(i+l,j)./(2.*r*delr);
amrl=-a(i—1,j)./(2.*r*delr);
ap22=a(i,j+1)./de122;
am22=a(i,j- l )./de122;
anew=(apr2+aprl+amr2+amrl+apz2+am22)/adev;
eri=abs(anew-a(i,j));
maxerr=max(err,'maxerr);

184

185

sumerr=sumerr+err;
a(i,j)=anew;
end
end
for m=l :nz
a( l ,m)=a(2,m);
end
end
sumerr;
maxerr;
for m=l :nr

cone 1 (m)=a(m,distl )/a(10, l );
conc2(m)=a(m,dist2)/a( 10,1 );
rad(m)=0.5*(m- l );
end
plot(rad,conc l ,'-',rad,conc2,'-.')
title ('Figure 6.5 : Diffusion of Species in Mode l')
ylabel ('Species Concentration') xlabel (’Radial Distance in inches')
gtext ('_ Concentration : at source')
gtext ('-.- Concentration : 5 cm below')
print mesh 1 .ps

The following Malab program generates Figure 6.6

% Ambipolar Diffusion Simulation
% Initialize the matrix and problem size
% Assume for that there is no generation-recombination in the plasma; i.e, % Vi/D =0
% Down-stream Distance distl=l; dist2=8;
% Collisional term : col = vi/D
col=0.0;
a=zeros(20,20);
n1=20;
nz=20;
delr=l.0;
delz=l.0;
delr2=delr*delr;
delz2=delz*delz;
% Initialize the boundary
for m=l :nz
a(20,m)w.0;

end
for m = lznr

if m>10

186

a(m,1)=0.0;
else a(m, l )=1+(0.02*m)"2;
a(m,20)=0.0;
end
end
% Set up the matrix : Use the iterative method
for k = 1:100
maxerr=0.0;
sumerr=0.0;
for i=2:nr-l
for j=2:nz-l
I=i*delr;
adev=(2./delr2+2./delz2+col);
apr2=a(i+] ,j)./delr2;
amr2=a(i- 1 ,j)./delr2;
aprl=a(i+1,j)./(2.*r*delr);
amrl=-a(i-l,j)./(2.*r*delr);
ap22=a(i,j+1)./de122;
am22=a(i,j- l )./de122;
anew=(apr2+aprl +amr2+amrl +ap22+am22)/adev;
eri=abs(anew-a(i,j));
maxerr=max(err,maxerr);
sumerr=sumerr+err;
a(i,j)=anew;
end
end
for m=l :nz
a( l ,m)=a(2,m);
end
end
sumerr;
maxerr;
for m=l :nr
conc l(m)=a(m,distl)/a( 10,1 );
conc3(m)=a(m,dist2)/a( 10,1);
rad(m)=0.5*(m-l);
end plot(rad,conc l ,'-',rad,conc3,'-.')
title ('Figure 6.6 : Diffusion of Species in Mode 2')
ylabel ('Species Concentration')
xlabel ('Radial Distance in inches')
gtext ('_ Concentration: at source')
gtext ('-.- Concentration: 20 cm below’)
print mesh2.ps

187

To generate Figure 6.7, three Matlab programs are to be run in sequence. These three
programs are numbered as Program I, Program 2 and Program 3, These programs are

given below.

Program 1

% Ambipolar Diffusion Simulation
% Initialize the matrix and problem size
% Assume that there is no generation-recombination in the plasma; i.e, % Vi/D =0
% Down-stream Distance distl= l; dist2=2;
% Collisional term : col = vi/D
col=0.0;
a=zeros(20,20);
ni=20;
nz=20;
delr=l.0;
delz=l.0;
delr2=delr*delr;
de122=delz*delz;
edge=9;
% Initialize the boundary
for m=1 :nz
a(20,m)=0.0;
end
for m = 1:nr
if m>10
a(m,l)=0.0;
else a(m,l)=l+(0.09*m)"2;
a(m,20)=0.0;
end
end
% Set up the matrix : Use the iterative method
for k = 1:100
maxerr=0.0;
sumerr=0.0;
for i=2:nr-l
for j=2:nz-1
mi*delr;
adev=(2./delr2+2./de122+col);
apr2=a(i+] ,j)./delr2;
amr2=a(i-1,j)./delr2;
apr1=a(i+l,j)./(2.*r*delr);
amrl=-a(i- l ,j)./(2.*r*delr);
ap22=a(i,j+ 1 )./de122;

188

am22=a(i,j-1)./de122;
anew=(apr2+apr1+amr2+amr1+ap22+am22)/adev;
err=abs(anew-a(i,j));

maxerr=max(err,maxerr);

sumerr=sumerr+err;
a(i,j )=anew;
end
end
for m=1:nz
a( l ,m)=a(2,m);
end
end
sumerr;
maxerr;
for m=1:nr

conc l(m)=a(m,distl)/a(10, l );
conc2(m)=a(m,dist2)/a(10,1 );
rad(m)=0.5 *(m- 1 );

end

etch 1 =conc2( l :edge);
radius=rad(12edge);
plot(radius,etch ,'-.')

Program 2

% Ambipolar Diffusion Simulation
% Initialize the matrix and problem size
% Assume that ther is no generation-recombination in the plasma; i.e, % Vi/D =0
% Down-stream Distance distl=l; dist2=8;
% Collisional term : col = vi/D
col=0.0; a=zeros(20,20);
nm20;
nz=20;
dell=1.0;
delz=l .0;
delr2=delr*delr;
de122=delz*delz;
edge=9;
% Initialize the boundary
for m=1:nz

a(20,m)=0.0;
end for m = 1:nr

if m>10
a(m,l)=0.0;
else a(m, l )=l+(0.02*m)"2;

189

a(m,20)=0.0;
end
end
% Set up the matrix : Use the iterative method
for k = 1:100
maxerr=0.0;
sumeri=0.0;
for i=2:nr-l
for j=2:nz-1
r=i*delr;
adev=(2./delr2+2./de122+col);
apr2=a(i+] ,j)./delr2;
amr2=a(i- 1 ,j)./delr2;
aprl=a(i+l ,j)./(2.*r*de1r);
amrl=-a(i-1,j)./(2.*r*delr);
ap22=a(i,j+1)./de122;
am22=a(i,j-1)./de122;
anew=(apr2+apr 1 +amr2+amr l +apz2+amz2)/adev;
err=abs(anew-a(i,j));
maxerr=max(err,maxerr);
sumerr=sumerr+err;
a(i,j)=anew;
end
end
for m=1:nz
a(1,m)=a(2.m);
end
end
sumerr;
maxerr;
for m=1:nr
concl(m)=a(m,distl)/a(10,1 );
conc3(m)=a(m,dist2)/a( 10,1 );
rad(m)=0.5*(m-l);
end
etch2=conc3( l :edge);
radius=rad( l :edge);
plot(radius,etch2,'-—')

Program 3

etch3=(etch l +etch2)/2;

plot(radius,etch l ,’--',radius,etch2,'—.',radius,etch3,'-')
title ('Comparison of Etching Proﬁles')

ylabel ('Etching Proﬁle')

190

xlabel ('Radial Distance on Wafer Surface (inches)')

gtext ('Etching proﬁle in Mode 1 alone')

gtext ('Etching proﬁle in Mode 2 alone')

gtext ('Etching in mixed modes : Mode l for 50% and Mode 2 for 50% time')
print etch.ps

List of References

List at geterences

$113641

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Qhapter 2

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[2.25] L.S. Plano, S. Yokota, and K.V. Ravi, Proceedings of First International Sympo-
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[2.26] “Oxidation Kinetics of Diamond, Graphite and Chemical Vapor Deposited Dia-
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[2.27] “Post-depositional Diamond Etching”, P.K. Bachmann, D. Leers, D.U.
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[2.29] “The Role of Microstructure on the Oxidation Behavior of Microwave Plasma

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195
Hsu, Journal of Material Research, Vol. 5, Nov 1990, pp 2445-2450.

[2.30] “Etching of Diamond with Argon and Oxygen Ion Beams”, T.J. Whetten, A. A.
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196
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[2.44] Private Conversation with Dr. N. V. Suetin at the Conference of The Electro-
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[2.45] J Asmussen, J. Hopwood, and F. C. Sze, Review of Scientiﬁc Instruments, Vol
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197
[2.47] Gaseous Electronics and Gas Lasers, B. E. Cherrington, Perrnagon Press, 1974.

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June 1989, pp 883-893.

Chapter 3

[3.1] Wavemat Inc., 44191 Plymouth Oaks Blvd., Suite 100, MI 48170, USA.

[3.2] PlasmaQuest Inc., 850 N. Dorothy Drive, Suite 504, Richardson, TX 75081,
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[3.3] “Electron Cyclotron Resonance Microwave Discharge for Etching and Thin Film
Deposition”, J. Asmussen, Chapter 1 l of Handbook of Plasma Processing Technology:
Fundamentals of Etching, Deposition, and Surface Interegtions. Park Ridge, N.J., Noyce
Publication, 1990.

[3.4] “Plasma Diagonistics Modeling and Etching Application of the Multipolar ECR
Plasma Reactor”, J. Asmussen, paper distributed as a part of class notes for BB 989, 1993.

[3.5] Basic Operation Instruction for PlasmaQuest 357 W Electron Cyclotron Reso-
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[3.6] User Manual for Gaertner WaferSkanTM Ellipsometer L 1 15 B, Gaertner Scien-
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[3.7] “Characterization of Diamond Films”, W. Zhu, H. S. Kong, J. T. Glass, Chapter
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198

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[3.10] Semiconductor Integrated Circuit Technology, W. R. Runyan Addison-Wesley,
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[3.11] User Manual pf MJB 3 Mask Aligner, Karl Suss.

[3.12] R. J. Nemanich and J. T. Glass, Journal of Vacuum Science and Technology, A
6, 1988, 1783-1787.

[3.13] User Manual for HP 4145 B parameter analyzer and the omrating diskette,

Hewlett Packard.

Chapter 4

[4.1] Glow Discharge Processes: Sputtering and Plasma Etching, B. Chapman, Wiley,

New York, 1980, Chapter 7, pp 297-342.

[4.2] Plasma Etching: an Introduction, D. L. Flamm and D. M. Manos, Academic
Press, Boston, 1989, Chapter 2, pp 91-182.

[4.3] Plasma Diagonistics Techniques, R. H. Huddlestno and S. L. Leonard, Academic
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[4.4] “Optical Emission Spectroscopy of Reactive Plasmas: A Method for Correlating
Emission Intensities to Reactive Particle Density”, J. W. Coburn, and M. Chen, Journal of
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[4.5] “Positive Ion currents in the Positive Column of the Mercury Arc”. I. Langmuir,

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[4.6] A Theoretical and Experimental Investigation of the Chemical Kinetics of an

199
Oxygen Microwave Discharge, M. L. Brake, Ph.D dissertation, 1983, MSU, pp20-25.

[4.7] Diffusion Process. M. H. Jacobs, Springer-Verlag, 1967.
[4.8] The Diffusion and Drift of Electrons in Gases, L. G. H. Huxley, Wiley, 1974.

[4.9] Diffusion Kinetics for Atoms in ngstals, J. R. Randoloph, Van Nostrand, 1968.

[4.10] The Mobility and Diffusion of Ions in Gases, E. W. Wadsworth, Wiley, 1973.

[4.1 1] Principles of Plasma Discharge and Materials Processing, M. A. Lieberman and
A. J. Lichtenberg, John Wiley and Sons, 1994, Chapter 9, pp 290-297.

[4.12] Introduction to Plasma Physics, B. M. Smirov, Mir Publisher, 1977.

[4.13] The Adsogption of Gases on Solids, N. Feather and D. Shoneberg, Cambridge
university Press, 1949.

|4.14| Physisomtion Kinetics, H. J. Kreuzer, Springer-Verlag, 1986.

[4.15] Theom of Chemisogption, Springer Verlag, 1980.

[4.16] Elementary Chemical Kinetics. J. L. Latham and A. e. Burgess, Butterworths,
1962.

[4.17] Basic Chemical Kinetics, H. Eyring, Wiley, New York, 1980.

[4.18] Chemisorption, D. O. Hayward and B. M. W. Trapnell, Butterworths, London,
1964.

[4.19] Diffusion and heat transfer in chemical kinetics, D. A. Frank-kamenskii, Ple-
num Press, New York, 1969.

[4.20] Principles of Plasma Discharge and Materials Processing, M. A. Lieberman and
A. J. Lichtenberg, John Wiley and Sons, 1994, Chapter 15, pp 472-510.

[4.21] “Measured Temperatures of Burning Pulverized Particles and the Nature of the

Primary reaction Products”, A. B. Ayling, and I. W. Smith, Combustion and Flame, Vol

200
18, 1972. pp 172.

[4.22] “The Role of Surface Complex in the Carbon-Oxygen Reaction”, N. R. Laine,
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magon Press, New York, 1963.

[4.23] Combustion. 1. Glassman, Academic Press, 1987, pp 391-395.

[4.24] “Factors Affecting the Product Ratio of the Carbon-Oxygen Reaction- II. Reac-
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[4.25] “Combustion and Mass Transfer Characteristics of Large Carbon Particle in the
Grid Region of a Fluidized Bed Combustor”, A. S. Choi, Ph.D dissertation, 1988, Section
2-2, pp 1-30.

[4.26] “Heterogeneous Kinetics of Coal Char Gasiﬁcation and Combustion”, N. M.

Laurendeau, Progress in Energy and combustion science, Vol 4, 1978, pp 221-270.

m

[5.1] Glow Discharge Processes, B. Chapman, John Wiley & Sons, 1980, Chapter 1,
pp 1-19.

[5.2] “ECR sputter removal of S102 on Silicon Wafers”, V. Gopinath, G. T. Salbert, T.
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6, Nov/Dec 1993, pp 2067-2070.

[5 .3] Macroscopic Properties of a Multipolar Electron Cyclotrgn Resonance Micro-

wave Plasma Source for Anisotropic Silicon Etching, J. A. Hopwood, Ph.D desertion,

MSU, 1990, Chapter 5, Section 5.6.3, pp 99-108.

[5.4] Design and Experimental Investigation of a Large Diameter Electron Cyclotron

201
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[5.5] Statistics for Exxriments: An Introduction to Design, Analysis, and Model
Building, G.E. P. Box, Willey, 1978.

[5.6] Analysis of Messy Data, G. A. Milliken, Lifetime Learning Publication, 1984.

[5.7] Response Surface Methodology. R. H. Myers, Allyn and Bacon, 1971.

[5.8] “Statistical Experimental Design in Plasma Etch Modeling”, G. S. May & C. J.
Spanos, IEEE Transaction on Semiconductor Manufacturing, Vol 4, No. 2, May 1991, pp
83-98.

[5.9] “Optimization of a Low Damage, High Resolution SiNx Etch Process in an Elec-
tron Cyclotron Resonance (ECR) Reactor with Multipolar Conﬁnement”, R. J. Olson, T.
E. Kaizor, B. Lane, W. M. Hobler, and L. Bourget, Presented at The Electrochemical Soci-
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[5.10] Statistical Design and Analysis of Experiments with Applications to Engineer-
ing and Science, R. L. Mason, R. F. Gunst, and J. L. Hess, John Wiley and Sons, Chapter
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[5.1 1] SPSS for Windows Made Simple P. R. Kinner, Lawrence Erlbaum, 1994.

[5.12] Temperature and Concentration of Ionic and Neutral Smcies in Resonant

Microwave Cavity Plasma Discharges, G. L. King, Ph.D Desertion, MSU, 1994.

[5.13] Principles of Plasma Discharges and Materials Processing, M. A. Lieberman
and A. J. Lichtenberg, John Wiley and Sons, 1994, Chapter 11, pp 327-386.

[5.14] “High Frequency Sustained Multipolar Plasmas”, C. Pomot and J. Pelletier,
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1992, pp 385-418.

202

[5.15] “Investigation of Inﬂuence of Electromagnetic Excitation on Electron Cyclotron
Resonance Discharge Properties”, P. Mak, G. King, T.A. Grotjohn, and J. Asmussen, Jour-
nal of Vacuum Science and Technology, A 10, No. 4, 1992, pp 1281-1287.

[5.16] “Ion and Neutral Energies in a Multipolar Electron Cyclotron Resonance
Plasma Source”, G. King, F. C. Sze, P. Mak, T. A. Grotjohn, and J. Asmussen, Journal of
Vacuum Science and Technology, A 10, No. 4, 1992, pp 1265-1269.

[5.17] “Investigation of Multipolar ECR Plasma Source Sensors and Models for Pro-
cess Control”, P. U. Mak, M. H. Natarajan, B. L. Wright, T. A. Grotjohn, F. Salam, M. Sie-
gel, and J. Asmussen, presented at 42nd National Symposium of the American Vacuum
Society, Minneapolis, Minnesota, Oct 1995.

[5. 18] “Cleaning of Metal Parts in Oxygen Radio Frequency PLasma: Process Study”,
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nology, A 12, 1994, pp 369.

[5.19] Glow Discharge Prpcesses, B. Chapman, John Willey & Sons, 1980, Chapter 6,

pp 250.

(,fliapter 6

[6.1] EE 836 Lecture Notes, K. M.Chen, Chapter 2, MSU, 1994.

[6.2] Field and Wave Electromagnetics, D. Cheng, Addison-Wesley, 1992.

[6.3] Elements of Engineering Electromagnetics, N. N. Rao, Prentice Hall, 1991.

[6.4] “Plot of Modal Field Distribution in Rectangular and Circular Waveguides”, C.
S. Lee, W. Lee, and S. Chuang, IEEE Transactions on Microwave Theory and Techniques,

Vol 33, pp 271, 1985.

203
[6.5] Numerical Solution of Differential Equation, 1. Fried, Academic Press, 1979.

[6.6] The Student Edition of MATLAB: Student User Guide, Prentice Hall, 1992.

Chapter 7

[7.1] Manual for Atomic Force Microscope, 1993, pp 243.

[7.2] “Method for Leveling Diamond Film”, Patent Application No. 62-220052, J apa-
nese Patent Ofﬁce, Sep 2, 1987.

[7.3] “Surface Smoothing of Diamond Membranes by Reactive Ion Etching Process”
C. Vivensang, L. Ferlazzo-Manin, M. F. Ravet, G. Turban, F. Rousseaux, and A. Gicquel,
to be published in Diamond and Related Materials.

[7.4] “ECR Plasma Polishing of CVD Diamond Films”, H. Buchkremer-Hermanns, C.
Long, and H. WeiB, presented at Diamond Films 1995, Barcelona.

[7.5] “Experimental Study of Diamond Surface Planarization”, D. K. Reinhard,
research proposal submitted to Norton Diamond Film, 1993.

[7.6] Hoechst Celanese Group, Somerville, NJ, USA.

[7.7] Filmtronics Inc., P. O. Box 1521, Butter, PA 16003, USA.

[7.8] Shipley Inc., 500 Nickerson Road, Marlboro, MA 01752, USA.

[7.9] “Techniques for patterning of CVD diamond ﬁlms on non-diamond substrates”,
Masood A, Aslam M, Tamor M.A, Journal of the Electrochemical Society, Vol 138: L67-
8, Nov 1991.

[7.10] “Microstructural control of diamond thin ﬁlms by microlithographic pattem-
ing”, J. F. DeNatale, J. F. Flintoff and AB. Harker, J. Appl. Phys., Vol. 68 (8), 15 October

1990, pp 4014-4019.

204

[7.11] “Selected area nucleation and patterning of diamond thin ﬁlms by electro-
phoretic seeding”, J. L. Valdes, J.W. Mitchel, J. A. Mucha, L. Seibles, and H. Huggins,
Journal of Materials Science, 27, 1992, pp 553-556.

[7.12] “Micropatterned diamond substrate”, J.W. Glesener, and R. J. Tonucci, J. Appl.
Phys., Vol. 74, No. 8, 1993, pp 5280-5281.

[7.13] “Processes for the preparation of Polycrystalline Diamond Films”, F. Jansen
and M. A. Machonkin, Xerox Inc. US. Patent # 4925701, May 15, 1990.

[7.14] “M. Ulczynski, D. K. Reinhard, M. Prystajko, and J. Asmussen, Advances in
New Diamond Science and Technology, edited by S. Saito, N. Fujimori, O. Fukunaga, M.
Kamo, K. Kobashi, and M. Yoshikawa, pp 41, M.Y.U., Tokyo, 1994.

[7.15] “Diamond Coatings on Integrated Circuits”, D. K. Reinhard, M. Ulczynski, and
R. N. Chakraborty, presented at 3rd International Conference on Applications of Diamond

Films and Related Materials, Gaithersburg, Maryland, August 21-24, 1995.