PLASMA OXIDATION OF SILICON: KINETICS STUDIES
Submitted
by
DAVID TAI WAI CHAN
in Partial Fulfillment of the Requirementsfor the Degrees of
BACHELOR OF SCIENCE
and
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 19, 1984
0 David T. Chan 1984
The author hereby grants to M.I.T. permission to reproduce andof this thesis in whole or in part.
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Accepted by:S
to distribute copies
Dep~(rtment of Electrical Engineering andDepdrtment of Electrical Engineering andComputer Science, September 19, 1984
Signature Redacted
Proess r .1. Reif, Thesis Supervisor
Signature Redacted
Dr. A.K. Ray, Compa~y Supervisor
ignature RedactedProfessor A.C. Smith, ChairmanDepartmental Committee on Graduate Students
OF TECHNOLOGY
OCT 0 4 1984 ARCHIVES
LIBRARVESI
Abstract
Plasma Oxidation of Silicon : Kinetics Studies
by
David Tai Wai Chan
Submitted to the Department of Electrical Engineering and ComputerScience on September 19, 1984 in partial fulfillment of the requirements
for the degrees of Master of Science and Bachelor of Science inElectrical Engineering.
A series of studies was completed on the development of a multi-wafer plasmaoxidation system, and the kinetics of silicon dioxide grown by such a system. Thedevelopment of the multi-wafer system consisted of examining the effects ofpower(represented by the plate current), pressure, wafer spacing and coil material.At a pressure of 17 mTorr, and plate current of 0.8 A, three sets of kinetics exper-iments were performed, with 1 nm (bare wafer), 100 nm and 450 nm of thermallygrown oxide on the wafers' backside respectively. The wafers were subjected to astandard cleaning procedure prior to oxidation, and oxide thickness was measuredat selected intervals.
The results from all wafers of these runs indicated rapid initial growth rates, whichtaper off with increasing oxide thickness. The data were compared to the predictionsof various models, notably the Deal-Grove model of thermal oxidation, the constantelectric field and constant voltage models. With the assistance of correlation coeffi-cients and visual inspection, the mathematical projections of each model werematched with observations. Although all models were deficient in certain aspects,the constant electric field model emerged as the leading candidate for explaining theunderlying mechanism of plasma oxidation, with regards to its high correlation withactual data, as well as the ability to explain the non-intuitive fact of oxidation on thewafer surface facing away form the plasma.
MIT Thesis Supervisor: Prof. L.R. Reif
IBM Company Supervisor: Dr. A. K. Ray
2
Acknowledgements
There are many people without whom this thesis would never be possible. First and
foremost, I would like to express my sincere gratitude to Dr. A.K. Ray for his excel-
lent guidance through the past three summers and his patience with me all this time.
Whether it was about the research, or when I needed a ride to the local auto me-
chanic, Asit was always there to help. His superb technical knowledge, and more
important, his strong character have provided a model to look up to. Without a
doubt, the discoverer of Plasma Oxidation was, is and will be a source of inspiration
to me.
MIT is very lucky to be able to boast of professors like L.R. Reif. He has been very
kind since the day I stumbled into his office, looking for an advisor. An acknowl-
edged leader in this field, Rafael was totally supportive of the project, and I gained
a great deal from discussions with him. Upon the birth of his child, Jessica, I wish
them all the best.
Dean Eugene R. Chamberlain was the first person that I met at MIT. Since our in-
troduction in August 1979, he has been my closest friend in the administration. I
thank him sincerely for his support in the past five years. I must also acknowledge
the hard work of John Tucker and his extremely efficient assistant, Lydia
Wereminski, in running the VI-A program. They, more than any other group of
people at MIT, have made my life at IBM much more delightful.
My co-workers at IBM's T.J. Watson Research Center, especially Charles Merz and
Mel Berkenblit deserve special thanks for the time that I spent here with them. Tak
3
Ning and Shirley Coleman are two people who have also made my stay very enjoy-
able. Gottlieb Oehrlein and the late David Dong were willing to let me share their
office, something that will not be forgotten. Wai Lee was very helpful when I needed
to prepare wafers with backside pre-oxidation. My managers have been very gen-
erous, letting me work here for a total of a year's time, and agreeing to let me write
this manuscript with the help of DCF and graphics facilities at Yorktown. For this,
I wish to express my appreciation for the efforts of Nunzio Lipari and Carlton
Osburn, who invited me to join this group.
Last but not least, I wish to express my gratitude to Monica Wong, a fellow VI-A
student.
David T. Chan
4
5
List of Ilustrations
Figure 1. Interaction of Sub-systems ............................... 33
Figure 2. Oxidation Chamber (OXC) .............................. 34
Figure 3. Plasma Excitation Source (PES) ........................... 36
Figure 4. Gas Supplies Section (GSS) Structure ...................... 39
Figure 5. Pumping Network (PUN) ................................ 40
Figure 6. Control of Si0 2 Thickness Uniformity across Runs ............ 61
Figure 7. Control of Si0 2 Thickness at Lower Ip . .. ... . . . .. . . . ......... 62
Figure 8. Effect of Plate Current .................................. 63
Figure 9. Wafer-to-wafer Oxide Uniformity ......................... 64
Figure 10. Choice of Coil Material .................................. 66
Figure 11. Uniformity across Single Wafer ........................... 67
Figure 12. Growth Behavior on Bare Wafers .......................... 70
Figure 13. Growth Behavior for Wafers with various Backside Oxide Thickness 72
Figure 14. Kinetics Fitted to a Linear-parabolic Relationship ............. 75
Figure 15. Linear-parabolic Relationship with a0 Term as Parameter ....... .76
Figure 16. Purely Parabolic ....................................... 77
Figure 17. Concentration of Oxidants in Si0 2 Film ..................... 80
Figure 18. Fitting to Parabolic-Linear Kinetics ........................ 89
Figure 19. Fitting to Parabolic-Logarithmic Kinetics .................... 90
Figure 20. Constant Voltage across Si0 2 Film ......................... 93
Figure 21. Strong, Constant Voltage across Si0 2 Film .................. 94
List of Illustrations 6
CHAPTER 1 : Introduction
1.0 What is SiO2 ?
Silicon "...the second most abundant element (on earth), being exceeded only
by oxygen...
... one of man's most useful elements'..."
That last phrase is especially true today. Silicon is the starting material for the fab-
rication of most microelectronic circuitry in the modern era. It would be a major
understatement to claim that the Information Age, as defined by Sze2 , would not be
the same without it.
One of the most important properties of silicon is its ability to form silicon dioxide,
a compound with oxygen. In the microelectronics industry, this is the single attribute
that separates silicon from all the rest. For example, one of the main difficulties en-
countered in building circuits from gallium arsenide, another useful semiconductor,
is the absence of a stable oxide like SiO 2 .
CHAPTER 1 : Introduction
Before exploring its importance, it is appropriate to tabulate some of silicon dioxide's
desirable characteristics:
* Stability up to high temperatures
" Excellent electrical insulation
* High breakdown field strength
" Strong resistance to typical etches
* Strong resistance to diffusion
* High dielectric constant
* Low defect density
* Amorphous structure, i.e. isotropy
* Ease of formation/growth
Applications to microelectronics are immediately apparent. Its electrical qualities
establish its dominant role in isolation and passivation, its physical resistances to
diffusion and etching secure its function in masking. As a result, its use is pivotal in
both bipolar and MOS devices.
CHAPTER 1 : Introduction 8
VLSI Requirements
Contemporary microelectronic circuitry grows rapidly more complex and powerful,
to deal with an explosion of demand for information processing technology. Fully
integrated processors are commercially available, and memory chips with over a
million bits capacity are in the final stages of development. To counter the need for
increasing complexity, miniaturization of device dimensions is inevitable. As sizes
shrink, more devices may be placed on a wafer die of a given area. The performance
and power consumption of circuits would also be greatly improved. Together, these
facts drive the emergence of Very Large Scale Integration, VLSI.*
VLSI emphasizes device density and speed, but in doing so, places increasingly
stringent requirements on the manufacturing of the devices. All processing steps,
from crystal growth to film deposition to metallization, are pushed further against
their practical limits. Oxidation is no exception.
The silicon dioxide films of VLSI must possess all the properties listed before, as well
as many new ones. Conventional methods for the formation of Si0 2 prove increas-
ingly unsatisfactory, as problems previously negligible become significant.
This chapter surveys technologies for Si0 2 formation, both established and novel,
and details the advantages and limitations of each. Background information about
plasma oxidation is provided, and the promises that it brings along. Finally, a dis-
cussion about the goals and motivation for this thesis research ensues.
The following chapter deals with experimental techniques and practical issues.
CHAPTER 1 : Introduction 9
Chapter 3 attempts to provide a theoretical understanding of plasma oxidation
kinetics. Different models are proposed, and the data are analyzed. The single
model that fits most observations is chosen.
Conclusions and hindsights concerning the whole project comprise Chapter 4.
*Very Little Sleep Indeed
CHAPTER 1 : Introduction 10
1.1 Established Oxidation Methods--- Thermal Reaction
High quality Si0 2 is needed in integrated circuit fabrication. The method used al-
most exclusively for the past few decades centers on the chemical reaction of silicon
and a gaseous oxidizing agent at high temperatures (900-1200*C), at atmospheric
pressure. This section surveys "conventional" thermal oxidation, and its many vari-
ations. Owing to its importance, much theoretical and experimental understanding
has been achieved, as evidenced by the large number of publications3 -6 on this topic.
It remains one of the most important processes today.
1.1.1 Dry Oxidation
Ultra-high purity oxygen is passed over silicon wafers in an open tube. The temper-
ature profile of the tube is maintained carefully, typically by microprocessor-based
controllers, in multi-zone furnace heating schemes. The variation in temperature can
be better than + 0.1C7 . Oxide thus grown is dense, reproducible and desirable for
most applications of LSI (Large Scale Integration). Its drawbacks include a slow
oxidation rate and a high operating temperature. The latter causes many problems
serious to VLSI applications, and will be discussed in section 1.1.5.
The exact oxidizing species responsible for dry oxidation is as yet a matter of
controversy8 . In spite of this, a relatively reliable model, the Deal-Grove model, has
been developed3 , and is generally accepted. Many modifications9 have been offered
to supplement the main model, e.g. theories10 explaining the rapid rate of oxidation
in thin films (< 10 nm). The Deal-Grove model accurately predicts the behavior of
CHAPTER 1 : Introduction I I
Si0 2 films over 30 nm thick. A wide range of oxidation rate constants have been
published in the literature3,4 " , however.
1.1.2 Wet Oxidation
Dry oxidation is sometimes too slow to produce thick films in a practical period of
time. It was found that the presence of water molecules in the vapor stream in-
creased the oxidation rate strikingly. The same kinetic behavior was observed,
however, and the Deal-Grove model could be applied successfully to wet as well as
dry oxidation.
Si0 2 films formed by wet oxidation are much more porous, and obviously, have a
high concentration of trapped H20 molecules. In addition, the Si-Si0 2 interface is
not as "clean" as that obtained in dry oxidation. Properties are markedly improved
by a subsequent annealing step.
The water vapor can be conveniently supplied by bubbling the gaseous ambient
(oxygen, or an inert ambient, e.g. nitrogen or argon) through de-ionized water at
95*C before entrance into the oxidation tube. Since the oxidation rate is strongly
influenced by the partial pressure of water vapor, the pyrogenic method is used in
situations where the oxidation rate needs to be better controlled. Such a method
involves mixing hydrogen and oxygen in adjustable proportions to generate the ap-
propriate water vapor content.
The Si-Si0 2 interface has been the focus of many studies1 2- 5 , and it is generally
agreed that the oxidizing species migrates through the Si0 2 film to react with Si at-
CHAPTER 1 : Introduction 12
oms at the interface. To take advantage of this scenario, thick films are often grown
in three steps, in situ
1. Dry oxidation for 5-10 minutes to generate a good quality external surface,
2. wet oxidation for a longer period to grow the bulk of the oxide at a fast rate, and
3. dry oxidation for 5-10 minutes to anneal the Si-SiO 2 interface.
1.1.3 Addition of Halogen
The addition of chlorine, hydrogen chloride or trichloroethylene (TCE, C2HCl3 ) to
the oxidizing ambient enhances the oxidation rates, via mechanisms not fully
understood 6 . More important, the quality of SiO 2 films incorporating such species
show noticeable improvements. The impurities content is lowered, presumably by a
gettering effect, and the sizes of oxidation induced stacking faults are substantially
reduced. Dielectric breakdown strength is also increased.
The presence of sodium ions in the oxide causes many unwanted side-effects, nota-
bly the instability of threshold voltages. One way to avoid sodium contamination is
through the use of pure silicon tubes, or fused quartz tube reinforced with barriers
of materials in which sodium has low mobility. The use of chlorine-based additives
can also significantly minimize the problems encountered with the presence of mo-
bile sodium ions.
A disadvantage with oxidation systems that use chlorine-related gases is the degree
of caution required. The halogen accelerates metallic corrosion. It is also hazardous
to human health. Several problems inherent to high processing temperatures (e.g.
dopant redistribution) are still present, as will be discussed in section 1.1.5.
CHAPTER 1 : Introduction 13
1.1.4 Modelling of Thermal Oxidation
The single model that has attracted the most attention was published in 1965, and
boasts excellent agreement with a large quantity of experimental data from inde-
pendent sources3 -'," . It is generally valid for wide ranges in temperature
(900-1200*C), pressure (0.2-1.0 atmospheres) and oxide film thickness (over 30
nm).
The Deal-Grove model' , as it is known, rests on several assumptions:
1. Henry's law for the concentration of oxidizing species at the SiO2 outer surface,
2. Ideal gas law for the concentration of the oxidant in the gaseous ambient relative
to its paitial pressure,
3. Fick's law for the transport of the oxidant through the oxide film
4. Steady state reaction at the Si-SiO 2 interface, where the oxidation rate is pro-
portional to the concentration of oxidizing species.
The resulting equation has the form
dox +Adx= B(t + T) (1.1)
where dox = oxide film thickness
t = time of oxidation
T= a constant to satisfy initial conditions
B = parabolic rate constant
B-= linear rate constantA
For thick films, i.e., do> > A,
CHAPTER 1 : Introduction 14
d2x , Bt (1.2)
i.e. the oxidation is parabolic in the long run.
In the other extreme case, when dox << A,
de B -(t + T) (1.3)ox A
This is the so-called linear regime.
The rate constants can be determined by experimental data fitting. A wide range of
values have appeared in the literature3-5 ,1 , and it is becoming apparent that these
constants can vary from system to system, and depend on wafer treatment prior to
oxidation. The linear-parabolic relationship, however, has been justified beyond any
doubt.
The nature of the oxidizing species is as yet unresolved, but various proposals have
been raised about the condition at the Si-SiO2 interface. The break down of the
simple Deal-Grove model for thin films (< 30 nm) has also been discussed in the
literature'O.
1.1.5 Problems with Conventional Oxidation
VLSI demands a much more efficient utilization of silicon real estate for denser lay-
out of circuitry than is needed in LSI levels. Device dimensions are scaled down in
CHAPTER 1 : Introduction 15
all directions to boost performance. Several problems arise when oxidation temper-
atures remain high.
Bird's Beak Effect
Thick films of Si0 2 (450 nm) are good shields for ion implantation, diffusion, etch-
ing, etc. Thus the selective oxidation of exposed areas of silicon is commonly used
in masking techniques. Silicon nitride, Si3N4 , is usually deposited and patterned to
cover regions where oxidation is not wanted. Upon thermal treatment, massive dis-
locations develop under the nitride, owing to a large discrepancy between the ther-
mal expansion coefficients of the silicon and its nitride"7 .
To remedy this situation, a thin film of Si0 2 (10-20 nm) can be grown before nitride
deposition to protect the silicon surface. Unfortunately, addition of this "pad" oxide
enhances penetration of oxide under the nitride mask. This physical extension of
oxide is known as a "bird's beak". It effectively reduces the fraction of "active" area
available for devices on the silicon surface. Its formation is linked to the lateral dif-
fusion of oxidizing species under the edge of the nitride mask at high temperatures.
Much useful "land" for VLSI can be salvaged by suppressing the formation of such
a beak, without damaging the active silicon area.
Oxidation Induced Stacking Faults
Stacking faults are structural defects in the silicon lattice. Simply put, they are dis-
ordered planes in an otherwise orderly positioned array of atoms. They are caused
by accumulation of excess interstitial silicon atoms at nucleation sites generated by
various processing steps. Thermal oxidation creates an excess of such silicon atoms
CHAPTER 1 : Introduction 16
near the Si-SiO2 interface, and some migrate into the silicon lattice, thus forcing
stacking faults. In semiconductor devices, especially MOS structures, stacking faults
lead to increased reverse-bias junction leakage, and accelerated stored charge decay,
among others. Very often, they serve as dens for the gathering of impurities, and
hence distort the electrical characteristics of hosting devices.
Extensive studies have shown that their growth with respect to temperature vari-
ations exhibits two distinct regions 8 :
* a growth region, in which new stacking faults are formed and existing ones ex-
pand, and
* a retrogrowth region, where formation is suppressed and shrinkage takes place.
The dividing line between the two depends on substrate orientation, the presence of
chlorine-bearing additives, the partial pressure of water vapor (wet or dry oxidation)
and other factors. The retrogrowth region is at higher temperatures.
At very low temperatures (below 700*C) stacking fault generation is virtually elim-
inated, as excess interstitial silicon atoms lack sufficient thermal energy to diffuse
move into the Si lattice, and condense on nucleation sites. The addition of
chlorine-related gases in controlled amounts also impede the formation of stacking
faults.
Accumulation or Depletion of Dopants at the Si-SiO 2 Interface
At equilibrium, the concentration profile of common dopants is discontinuous across
the Si-SiO 2 interface 19,20 . This is due to the establishment of an equal chemical po-
tential of the dopants on the two sides of the interface. In thermal oxidation, the
CHAPTER 1 : Introduction 17
interface marches into the Si bulk. Since the temperatures involved are sufficiently
high, the dopants may either diffuse into the oxide (boron), or accumulate on the Si
side (phosphorus). The former causes a depletion of active dopants near the Si
interface, and the latter produces a heavier doping in the Si. In either case, such de-
viations causes shifts in device parameters, and must be taken into account.
Dopant Redistribution in the Silicon Bulk
In addition to surface rejection/absorption of dopants into the oxide, high thermal
temperatures cause dopant diffusion in the silicon lattice. In MOS technology,
source and drain regions have higher levels of doping than the substrate. These areas
are effectively expanded upon thermally excited diffusion of dopants. Device char-
acteristics are severely degraded, because the junction of these regions with the
substrate contribute heavily to parasitic capacitances, and hence signal propagation
speeds. This is especially important for the small VLSI devices.
In spite of all these problems, thermal oxidation at atmospheric pressure remains a
work-horse for today's needs. But until these and other problems are solved satis-
factorily, oxidation in the traditional style may well produce results that fall far short
of the goals of VLSI.
CHAPTER 1 : Introduction 18
1.2 Other Oxidation Techniques
As discussed in the preceding section, conventional oxidation via thermal reaction
brings out several obstacles and inconveniences to the successful fabrication of VLSI
circuits. In light of this, a tremendous amount of effort is invested in research and
development to establish an alternate means of silicon dioxide formation. Of the
many existing proposals, a few stand out as the most promising. This section intro-
duces these "novel" ideas, their advantages over the conventional method, and their
limitations.
1.2.1 Anodic Oxidation --- Anodization
Little interest in this process 2' for silicon has been stirred until recently, owing to the
generally inferior quality of the resulting oxide. It plays a much more prominent role
in the fabrication of GaAs structures, where thermal oxides are unstable. Its main
attraction is derived from the feasibility of room temperature oxidation. As a result,
the many problems encountered with high oxidation temperatures are not present.
Unfortunately, some good properties of Si0 2 are lost.
Anodization acts on the principle of chemical electrolysis. The sample of silicon to
be oxidized is connected to the anode (positive terminal) of a electrolytic cell, with
a noble metal (e.g. platinum) acting as the cathode. The electrolyte (liquid in which
the anode and cathode are dipped) contains OH ions, which are attracted to the
silicon. There, they react to form SiO 2 , as in the overall equation :
Si + 2H20 + 2h -> SiO 2 + 2H+ + H2 (1.4)
CHAPTER 1 : Introduction 19
Holes, h, are provided by an external power source. In addition, light illumination
can generate some more holes to speed up the process.
The oxidation of p-type silicon is easy to understand, as holes can flow to the
Si-SiO2 interface with relative ease. It is far more complicated for n-type silicon,
where the initial contact with the electrolyte builds a Schottky-barrier-like depletion
layer. The power supply must be able to break down this "diode", and rely on ava-
lanche holes to run the oxidation. Oxide thus formed is porous, and in most respects
inferior to that obtained from conventional oxidation. In fact, anodization is seldom
used for gate oxides or device passivation and isolation. Typically, oxidation is fol-
lowed by oxide removal, in repeated steps. This provides a room-temperature, non-
destructive "cleaning" of the silicon surface.
1.2.2 High Pressure Oxidation
From the Deal-Grove model of thermal oxidation, the reaction rate at the Si-SiO 2
interface is linearly related to the concentration of oxidizing species there. In turn,
the latter is similarly related to its partial pressure in the oxidizing ambient. It is no
surprise that high pressure oxidation2 2 ,23 was recognized early on as a potentially im-
portant process. To obtain a growth rate similar to one from thermal oxidation at
atmospheric pressure, a much lower temperature is needed at high pressures. For
example, it was demonstrated that dry oxidation at 800*C and 140 atm pressure
produced a rate comparable to that at 1200*C and 1 atm 23 .
The advantages are many. Stacking faults and dopant redistribution are suppressed.
Indeed, it is gaining much more publicity in the VLSI era.
CHAPTER 1 : Introduction 20
Extreme caution must be taken to operate with the pyrogenic method. Hydrogen is
of utmost danger at high pressures and several hundred degrees Celsius. The set up
for the pumping-water method is also somewhat tricky to handle. One of the main
drawbacks in high pressure oxidation is the relatively cumbersome oxidation system.
High pressure oxidation does not, however, minimize the lengths of birds' beaks 24 .
Device density is strongly influenced by the ability to suppress bird's beak exten-
sions. This is one of the prime reasons for the reluctance of the industry to warmly
embrace high pressure oxidation processes.
1.2.3 Plasma Enhanced Oxidation
Plasma enhanced processes have begun to play increasingly prominent roles in inte-
grated circuit fabrication. Besides oxidation, examples can be drawn from etching
(Reactive Ion Etching), film deposition (Plasma Enhanced Chemical Vapor Deposi-
tion), photo-lithography (resist stripping), to name just a few. The single attractive
feature offered by plasma processes is enhanced reactivity at very low temperatures.
As can be seen from previous discussion on the disadvantages of thermal oxidation,
there exists strong motivation to bring down processing temperatures.
Plasma, the so-called fourth state of matter, is a term loosely attached to a random
collection of ionized particles and electrons in a highly energetic, gaseous-like phase.
Ions are much more reactive than their neutral counterparts, owing to the incorpo-
ration of strong electromagnetic forces.
Ionization requires acruement of energy, usually electromagnetic in nature, by neu-
tral gaseous species. The low energy plasmas used in semiconductor fabrication have
CHAPTER 1 : Introduction 21
three modes of generation, classified according to the frequency of energy input.
They are direct current (dc), radio-frequency (rf) and microwave. All require a
substantial reduction in pressure 2 -2 (typically 0.001 - 1 Torr). At atmospheric
pressures, the mean-free paths (and half-lives) of the ionized species are too short
for sustaining a plasma. They simply collide with each other, and loose their acquired
charge right away.
In dc generation26 , two electrodes are positioned in a gas stream. Upon application
of a very strong electric field between the two, the gas breaks down and causes an
electrical discharge, the plasma.
Rf excitation is achieved either by capacitive or inductive coupling. Capacitive cou-
pling is realized by applying a time varying voltage across cupped electrodes, which
act as the plates of a capacitor. A time varying current through a solenoid is the
principal means of inductive coupling. In either case, strong time varying electric and
magnetic fields are induced in selected volumes of gas (between the capacitive plates
or within the solenoid). Rf frequency ranges from several hundred kilohertz to 13.6
MHz, with certain bands prohibited by law.
Microwave plasma generation typically uses resonant cavities and
wave - guides 25 ,2 9 . Discharges obtained this way normally occupy a much smaller
volume, when compared to rf discharges. Frequencies are of the order of 2 GHz.
In general, rf and microwave plasmas are more uniform, and more efficient, in terms
of power incorporated into the plasma as a fraction of input. This is especially so for
rf plasmas. Dc plasmas have the luxury of a common reference ground voltage, and
CHAPTER 1 : Introduction 22
hence are easier to diagnose. Rf and microwave excitations possess "floating"
grounds, and are hence much harder to quantify.
Plasma diagnostic techniques, unfortunately, are not as sophisticated as one may like.
Their results are often confusing, and very difficult to interpret. This is partly due
to the complex nature of the plasma. Many differently ionized species are present,
each possessing a distinct set of characteristics. Any attempt to measure physical
parameters (except for photon emission) disturbs the existing equilibrium, leads to
drainage of certain species, and may ultimately quench the plasma.
At present, diagnostic tools center on the principle of Langmuir probes3 0, first pro-
posed in 1927, or its many variations. Other methods, e.g. laser spectroscopy, are
in developmental stages. With regard to the importance assigned to plasma enhanced
processes today, break-throughs in the field of diagnostics would certainly be wel-
come.
Several research groups have suggested different configurations and operations of
plasma enhanced oxidation 21- 2 8 . Generally, the sample of silicon to be oxidized is
exposed to a volume of oxygen discharge, and biassed positively with an external
circuit 25- 2 8 . This is similar to the electrochemical anodization discussed in an earlier
section, with the plasma playing the role of the electrolyte. The silicon surface facing
the discharge is continuously bombarded by ionized oxidizing agents with high en-
ergy. Although the exact species has yet to be agreed upon, present evidence points
to the negatively charged atomic oxygen ion, 0 , as the most likely candidate".
CHAPTER 1 : Introduction 23
Operating temperatures are low, usually below 500*C, but the growth rate is often
comparable to that of conventional oxidation at much higher temperatures. It is very
difficult to control plasma density uniformity, and consequently, oxide thickness
uniformity. As a result, very small samples25'3' (typically 1 cm2) are used.
Throughput is hardly a source of pride.
Most physical and chemical properties resemble that of thermal oxides. Electrical
characteristics, however, are often far inferior. But the most promising aspects come
from the absence of high temperature induced problems, including stacking faults,
birds' beaks, and dopant redistribution. Oxide trapped charge density, both in the
bulk and near the Si-SiO 2 interface, is uncomfortably high, and the break-down
strength is low.
It is anticipated that as more research is performed on plasma enhanced oxidation,
better quality oxide films can be obtained. At the present, such grown oxide films
are not practical for VLSI purposes.
CHAPTER 1 : Introduction 24
1.3 Plasma Oxidation of Silicon
Given the inadequacies of each of the mentioned processes, it is perhaps no surprise
that the industry, as a whole, has yet to endorse any single one as the successor to
conventional oxidation. Finding an oxidation process that fits most VLSI needs re-
mains a high priority.
In 1981, Dr. A.K. Ray1' 3 reported several interesting observations when exper-
imenting with electrically isolated silicon wafers in oxygen plasma. Most of the pre-
vious attempts to use plasma involved biassed substrates. Using pairs of wafers to
confine rf induced discharges, SiO 2 was found on the wafer surfaces. At pressures
below 10 mTorr, oxide was deposited on the surface facing plasma regions 2 . But
at pressures between 10 and 30 mTorr3 , contrary to intuition, SiO 2 was formed on
the surfaces facing away from the plasma. Further tests concluded that the oxide was
grown, not deposited or sputtered. Careful analysis showed that oxide quality,
physical and chemical properties, and most important, most electrical characteristics
are as good as, if not superior to, that of conventionally grown oxides. In addition,
excellent MOS devices could be built using such oxides, both as gate insulation and
for field isolation.
Being a low temperature (below 500*C) process, plasma oxidation (as opposed to
plasma enhanced oxidation) offers films free from most temperature-related prob-
lems. Being electrodeless, scaling up, both in terms of wafer size and wafer number,
was feasible.
CHAPTER 1 : Introduction 25
The process was later awarded a US patent (Number 4,323,589). As is the case with
all other plasma processes, it is not understood well. This is a common problem with
all new processes. To promote this technique, a better understanding of the under-
lying principles must be achieved.
CHAPTER 1 : Introduction 26
1.4 Objectives
The main objectives of the research performed for this thesis can conveniently be
summed up as follows :
1. contribute to the development of a viable oxidation process suitable for VLSI
needs,
2. offer a better understanding of plasma oxidation and its mechanisms, through
kinetic studies, and
3. discuss various models that may serve to explain observed phenomena.
Any new technique suffers from the problem of lack of understanding. It is essential
that a better knowledge of the mechanisms be acquired. Many approaches are pos-
sible. The most promising method of investigation follows the kinetics of oxidation,
in one sense collecting useful data, in another searching for informative clues.
Kinetic experiments are performed on silicon wafers with various pre-oxidized films
on the sides facing plasma regions. In particular, three sets of experiments inde-
pendently observe oxide growth. Each set starts off with wafers that have a certain
thickness of SiO2 pre-oxidized on one side: 1 nm (bare wafer), 100 nm and 450 nm.
Cross comparison allows deduction of the role played by self-biassed fields and
voltages. To cap off the studies, various models will be examined in the context of
providing a plausible interpretation for the observed plasma oxidation results.
CHAPTER 1 : Introduction 27
CHAPTER 1 : Introduction 28
CHAPTER 2: Experimental Techniques
2.0
Experimental techniques and details cover the bulk of the research done, and hence
deserve more than just a brief mention. Such emphasis is by no means accidental;
close attention was paid to the many "side-issues" throughout the course of research
done. Neither is the significance attached to experimentation unjustified. The topic
chosen deals directly with practical problems faced by VLSI fabrication engineers,
and demands a mastering of processing skills. Certainly, more than a theoretical
treatment is necessary.
The first portion of this chapter is devoted to a careful description of the process,
including pre-oxidation wafer treatment, apparatus, and operating conditions. The
development of a multi-wafer system follows, with oxidation kinetic studies rounding
up the rest.
CHAPTER 2: Experimental Techniques 29
2.1 Pre-Oxidation Wafer Treatment
P-type silicon wafers of 2 0-cm resistivity and <100> orientation are used. Wafer
dimensions are 3V' (83 mm) diameter and 14 mils (0.4 mm) thickness. At least one
face (the "front" side) is chem-mechanically polished, and is chosen as the surface
for plasma oxidation. In some kinetic experiments, a film of SiO 2 would be grown
thermally on the non-polished face. Both sides are examined carefully before and
after runs.
Various methods 3 ,36 have been employed in the industry to clean silicon wafers,
many of them proprietary. Generally, they include steps for the removal of
1. organic contamination, such as grease or wax, and
2. inorganic impurities, e.g. metallic ions.
All require frequent rinses in de-ionized water.
The next stage of processing is plasma oxidation. The procedure for preparing these
samples follows that recommended by Irene .
CHAPTER 2: Experimental Techniques 30
a.
b.
c.
d.
e.
f.
g.
h.
De-ionized water (diH 20) rinse Room temperature
Organic removal 950C
in solution: NH4 0H : H202 : diH2O = 1:1:5
diH20 rinse Room temperature
Inorganic removal 950 C
in solution : HCl : H202 : diH20 = 1:1:5
diH2 O rinse Room temperature
Native oxide removal Room temperature
in 9:1 Buffered Oxide Etch (HF:NH4F)
diH20 rinse Room temperature
Blow dry
Table 2.1 Pe-Oxidation Cleaning
All chemicals are electronic grade.
The resulting native oxide after cleaning was found to be very thin (about 1 nm),
well within statistical fluctuations encountered.
The wafers are then either stored in a nitrogen ambient or used directly in oxidation.
Typically, 10-12 wafers can be cleaned at a time.
Some kinetic experiments require a thermally grown SiO2 film (100 or 450 nm) on
the non-polished side of the wafers. These are prepared by coating photo-resist
(AZ1450) onto the non-polished face of wafers after appropriate oxide films are
grown on both sides. After etching in Buffered Oxide Etch and resist stripping, they
CHAPTER 2: Experimental Techniques
5 minutes
5 minutes
5 minutes
5 minutes
5 minutes
10 seconds
25 minutes
31
are subjected to the normal pre-oxidation cleaning, with the exception of the native
oxide removal (10-second dip in Buffered Oxide Etch). The 100 nm wafers are
plunged into the etching solution and pulled out immediately, while the 450 nm wa-
fers take 5 seconds.
Assuming an oxide etch rate of 100 nm per minute, and estimating that the 100 nm
wafers are in the etching solution for 1 second, roughly 2 nm of oxide has been re-
moved. This is sufficient to remove most of the native oxide on the polished surface,
but has a 2% or so effect on the thermal oxide film thickness. The 450 nm wafers
are also only slightly perturbed, as can be demonstrated with similar calculations.
These estimates were verified by ellipsometry. The native oxide thickness on the
polished faces of the three sets of wafers were indistinguishable from each other.
CHAPTER 2: Experimental Techniques 32
2.2 Experimental Set Up
GasControls
Gas GasesSuppliesSection (Ar, 02) "
(GSS)
PlasmaExcitationSource (PES)
Plasma Exci
Oxidation Chamber (C{
Plasma ControlsMeter Readings(1p. Igo Vp)
tation
XC) >Silicon)XC) Wafers
Exhaust Gases
\1/
gPumping PressureControls Network Reading
(PUN)
Figure 1. Interaction of Sub-systems
The plasma oxidation system may be conveniently divided into four sub-systems,
each being composed of several pieces of equipment. They are
1. the Oxidation Chamber (OXC),
2. the Plasma Excitation Source (PES),
3. the Gas Supplies Section (GSS), and
4. the Pumping Network (PUN).
Figure 1 illustrates the interaction between the various sub-systems. Each will be
described in detail.
CHAPTER 2: Experimental Techniques 33
2.2.1 Oxidation Chamber (OXC)
QuartzOxidation
0-ring Joint Tube
Ar,02 A 1 2 3
fIrom BoatGSS -
Clamp InductionCoil
NtoPES
O-ringSilicon Joint
r)Wafers - Clamp
ExaCap
V Shoul- -derTube
Clamp0-ri ng
Press-JonureGouge
ExhausttoPUN
/
Figure 2. Oxidation Chamber (OXC)
This section is perhaps the most important, yet the easiest to describe. The induction
coils shown in Figure 2 will be described in section 2.2.2, and again in section 2.3.
Use of the thermocouple pressure gauge is explained in section 2.2.4.
Oxidation takes place in a fused quartz tube of appropriate dimensions. Gas supplies
from the GSS enter from one end, and a narrow shoulder tube at the other functions
as an exhaust pipe. In addition, a detachable quartz cap of matching diameter allows
convenient load and unloading of silicon wafers. "O"-rings and external clamps seal
all joints to prevent gas leakage. The wafers are placed upright, and normal to the
direction of gas flow. As characterized earlier, the wafers have one polished face.
They are positioned in pairs, as shown, such that the polished sides face away from
CHAPTER 2 : Experimental Techniques 34
k
the associated coil segment. Upon excitation, high plasma densities are confined
between each pair of wafers (between wafers 1 and 2, and between 3 and 4), with
relatively weak glow in between the pairs. Two dummy wafers (A and B) are placed
further away at the two ends to provide a measure of oxidation in low plasma density
regions. The oxidation rate on A and B was found to be insignificant and non-
uniform.
The boat body is grazed with regularly spaced grids, at a spacing of 0.1 in. This al-
lows considerable flexibility in the optimization of wafer-to-wafer separation. A
quartz push-rod is used to maneuver the boat into place.
To prevent contamination, gloves need to be worn for handling. The push-rod is also
regularly wiped with ethanol to remove any dust or grease.
2.2.2 Plasma Excitation Source (PES)
Several rather bulky pieces of apparatus make up the PES. A Lepel radio-frequency
generator with output frequency 3 MHz and adjustable output power provides the
energy for plasma excitation. It has two output leads, across which an induction coil
is fitted. The current flowing through this coil, Ic, is not directly measurable in the
configuration chosen. It can be indirectly controlled by Ip, the plate current. Internal
to the rf generator, there is a vacuum tube triode, with a grid, plate (anode) and a
hot filament (cathode). Ip is interpreted as the dc value of the current emerging from
the plate.
CHAPTER 2: Experimental Techniques 35
__Rf DcFi Iter Filter- Tunaei Vc IC
InductiveTriod I ,e Network Load
C.nrCoil
Figure 3. Plasma Excitation Source (PES)
Ip, becomes the primary control parameter for power dictation. It can be contin-
uously varied between 0 and 5A, although the range used is generally no more than
1.2A.
Gauges on the front panel of the rf generator exhibit several parameters, including
plate current (Ip), plate voltage (Vp), the hot filament current, grid current (Ig) and
power control current. Ig is an especially useful variable. It's value is usually about
20-25% that of Ip,, and is a good indication of the coupling of power into the plasma.
In cases of mis-coupling, Ig drops precipitately. During experiments, all gauges were
constantly monitored to prevent any power fluctuation.
CHAPTER 2: Experimental Techniques 36
The induction coil is manually bent from hollow copper tubing. Whenever the rf
generator is turned on, water from an accessory tank is pumped through the coil to
provide cooling. At elevated temperatures, copper oxidizes to form black copper (II)
oxide, an electrical insulator. As a result, the coupling of rf power to the plasma de-
teriorates, as evidenced by drops in growth rates. Because of this, Ic ,and hence Ip,
cannot be increased arbitrarily. Gold plating was attempted, but it was discovered
that at typical Ip values, the surface of the induction coil was hot enough to allow
rapid gold migration into the copper tubing. The protective property of the gold
coating was thus lost. Stainless steel coils provided poor coupling, leading to lower
oxidation rates. In addition, they also oxidize for the same range of Ip, forming a
brown complex. An optimal range of Ip had to be found, and will be discussed in
more detail in section 2.3.
Such a high surface temperature of the coil can be explained by the "Skin Effect".
At 3 MHz, Ic flows almost entirely through a "skin" layer on the external surface of
the coil. The thickness of this "skin" is given by the "skin-depth", dp:
Idp 1 (2.1)
where f = frequency = 3 x 106 Hz
u = magnetic permeability of copper = 41Tr x 10-7 H/m
a = electrical conductivity of copper = 5.8 x 107 mho/m
This gives a value of 40 pm for dp., i.e. most of the current Ic flows through a surface
depth of 40 Mm.
CHAPTER 2: Experimental Techniques 37
2.2.3 Gas Supplies Section (GSS)
Two types of gases are needed : ultrahigh purity oxygen and argon. Both are com-
mercially available at 99.999% purity (10 ppm impurities). The flow of oxygen is
controlled to within + 0.02 standard cm3 per minute (sccm) by a Tylan flowmeter
and controller.
There are two steps taken to further purify the oxygen, as used by Ray32 ,
1. passing the gas over heated quartz beads (1000*C) to decompose any existing
hydrocarbons to carbon dioxide and water vapor, and
2. removing these impurities via a liquid nitrogen trap.
This lowers the impurity content of CO 2 to a maximum of 1 ppm and H 20 to 1 ppb.
The argon needs no further purification, as this gas is not used during plasma gener-
ation.
All connecting tubing is made from stainless steel. Valves V1 and V2 are controlled
electrically, while V3 requires manual activation. The pressures at the two ports of
the flowmeter are different. Operation of the various controls in the GSS will be
described in section 2.3.
2.2.4 Pumping Network (PUN)
Two pumps are needed. One is a mechanical pump (MP), capable of extracting large
volumes of gas, but unable to pull pressures significantly below atmospheric. The
other is a VA sorption pump (SP) with four cylinders, of which only one is needed
at a time. The SP requires liquid nitrogen chilling. It is able to pump to the desired
pressure range (10-200 mTorr), but cannot handle the large quantity of gas present
CHAPTER 2: Experimental Techniques 38
99.999% OxidationArgon 7116k
99.999% FurnaceOxygen FI FI to r )99.9999%
1000 oC ==Fo Oxygen
Liquid
Controller Trawith Display
Figure 4. Gas Supplies Section (GSS) Structure
in the oxidation tube at atmospheric pressure. Molecular sieves in the SP cylinders
absorb gas molecules at low temperatures, but re-emit them when relatively warm
(i.e. room temperature). They may be "refreshed" by heating overnight, by means
of resistive coils. All the valves in the PUN are mechanical, and allow partial flow.
Much of the preparation time for any experiment is taken up while getting the SP
ready. Prior to the first run of each day, the SP is at room temperature. The particles
absorbed in the previous runs need to be removed by 20-30 minutes of pumping by
the MP. Further details are provided in section 2.3.
Pressure in the OXC can be monitored by a thermocouple gauge. The pressure be-
fore plasma excitation can be set fairly accurately. Upon plasma ignition, pressure
CHAPTER 2: Experimental Techniques 39
shoulder tube
(O X M c la m p
press-uregouge
Mech Vpun
Pump(MI) m p Vsp5
Vsp4 VSP3
heatingcoil . P3
cuit SP4
sorption pump cylinders
Vsp 2 Vsp1
SP2 SP1
liquid nitrogen buckets
Figure 5. Pumping Network (PUN)
fluctuates for several minutes, consistent with the view that plasma takes that long
to stabilize. That stabilized pressure is typically 1 mTorr above the set value.
Rf coupling to the thermocouple probe can occasionally, though rarely, cause erro-
neous readings. This usually indicates problems with plasma confinement, and needs
to be corrected immediately. Fortunately, such incidents occur almost exclusively in
the first few minutes of operation, when the plasma is as yet unstable. Better rf
shielding, ample grounding and careful boat alignment virtually eliminated the prob-
lem.
CHAPTER 2: Experimental Techniques 40
The PUN proved to be fairly reliable. Even after periods of several months of idle-
ness, it worked much more satisfactorily than expected.
CHAPTER 2: Experimental Techniques 41
2.3 Operating Conditions
Some parameters must be specified to fully characterize any particular run. Others
are fixed for all runs. Still others are dependent on the first type of parameters. In
light of this, three types of variables are identified.
Control parameters: These characterize the experiment, and are the primary means
of control for the process. They include plate current (Ip), time of experiment (t)
and pressure of oxidation (P).
Fixed parameters: These do not change from run-to-run after optimization. They
are needed, however, to characterize the run. Oxygen flow rate is fixed, and wafer-
to-wafer spacings are all fixed.
Dependent parameters: For a chosen set of control parameters, they are also fixed.
Examples include plate voltage (Vp), and grid current (Ig). Although they provide
interesting insights about the behavior of the system, they cannot be directly con-
trolled.
2.3.1 Control Parameters
Plate Current --- Ip
Limits on Ip are discussed in section 2.2.2. Three values of Ip are chosen : 0.8, 1.0
and 1.2 A. Preliminary data concerning oxidation rates are compared, and 0.8 A is
chosen for all later kinetic studies. Degradation of oxidation rates, a measure of the
induction coil deterioration, is least severe for the lowest value of Ip Still lower Ip
would lead to impractical oxidation rates, however, and non-uniform growth. This
CHAPTER 2: Experimental Techniques 42
holds for both inter- and intra- wafer oxidation, and is consistent with the opinion
that lower input power leads to non-uniform spatial plasma excitation. Long term
reproducibility and reliability become over-riding issues. In addition to decaying
oxidation rates, large Ip causes high oxidation rates, especially for thin films. The
initial phases of oxidation provides many useful insights to the development of a
theoretical model, and merits extra attention. Short oxidation times and low
oxidation rates are called for. Since the plasma takes several minutes to stabilize,
oxidation duration cannot be shortened arbitrarily. Lower Ip helps in this regard.
Duration of Experiment --- t
Comparisons of oxidation rates for different sets of parameters are best made for
equal t. Instability of the plasma, assumed to occur in the initial few minutes of
excitation, can be taken into account by cross-comparing. For kinetic studies, the
primary parameter is t, which may be varied depending on the oxidation rate. For
thin films, t may be of the order of 10-15 minutes. For thicker films, experiments
may take up to 4 hours. The rules of thumb for choosing t is that
1. the changes in oxide thickness are significant (i.e. much greater than statistical
noise), and
2. the changes in oxide thickness are not too large.
The first rule ensures that statistical fluctuations do not influence conclusions, and
the second avoids missing periods of changing mechanisms, such as the gradual
dominance of a logarithmic growth rate over a parabolic one.
CHAPTER 2: Experimental Techniques 43
As expressed in the preceding discussion about Ip, t cannot be arbitrarily small.
Oxidation pressure, taken as a measure of plasma stability, fluctuates for about 5
minutes before settling. Clearly, t should be soundly more than that. On the other
hand, by the second rule of thumb, the initial phases of oxidation may be masked by
a long t, especially for thin films (less than 5 nm), when oxidation rate is higher.
The approach, then, is to choose t as a function of SiO2 film thickness. Several ex-
periments for the same t must be performed, to provide cross-reference. More on
this will be discussed in section 2.6.2, in conjunction with the role of a control wafer.
Pressure --- P
Pressure has an astounding effect on the total mechanism of the oxidation, as re-
ported by Ray, et ap2 33 . Below 10 mTorr, deposition seems to be the prevailing
mechanism, whereas above 10 mTorr, actual growth accounts for the formation of
SiO 2 . Even the surface of oxide emergence depends on the pressure. The rate of
formation, however, is relatively stable for pressures above 10 mTorr. It is also
conveniently high for practical oxidation, yet low enough to satisfy the rules in the
preceding section.
Another practical issue affects the choice of operating pressure. Although the GSS
can supply oxygen at a fairly accurate rate, the PUN is unable to control the pressure
below a certain value (about 5 mTorr). This is partly due to the air-tightness of the
whole system. Small leakages are extremely hard to prevent. The limitations of the
sorption pump may be another cause. With all GSS valves off, i.e. no gas input, the
PUN can only pull the system pressure down to about 5 mTorr at full strength.
CHAPTER 2: Experimental Techniques 44
2.3.2 Dependent Parameters
Plate Voltage Vp and Grid Current 1g
Once Ip is specified, the plate voltage and grid current are fixed, for normal opera-
tion.
Table 2.2 Plate Current, Plate Voltage and Grid Current
VP and Ip are indicators of the internal operating conditions of the rf generator. They
also provide an indirect measure of the operation of the induction coil. There is no
direct measure of the induction coil current, Ic, or voltage, Vc.
The percentage of power coupled into the plasma is also unknown. An estimate
would be around 50%, with the rest of the power dissipated into the surrounding
room. The absence of a match box further complicates optimizing the power ab-
sorption. Shielding and frequent grounding were expected to boost plasma power
incorporation, although this was not verified in the studies. Little change, with or
without shielding, could be detected.
CHAPTER 2: Experimental Techniques 45
Ip(A) Vp(kW) Ig(A)
0.8 1.80 0.22
1.0 2.25 0.29
1.2 2.60 0.36
Ig, as are Ip and Vp, are read off meters provided on the rf generator's front panel.
They are all measures of the internal operating condition of the generator. For
normal operation, Ig does not deviate appreciably. It does drop sharply, however,
when plasma confinement between wafer pairs breaks down. This observation
serves as a good indicator for mistakes in wafer alignment, pressure, etc. Ig does not
seem to have a direct role in the oxidation process.
CHAPTER 2: Experimental Techniques 46
2.4 Measurement Techniques
Two approaches are used for the measurement of SiO 2 film thickness, depending on
how thick that film is. Thin films are measured by standard ellipsometry (oxide
thickness below 30 nm). Thicker films are more conveniently examined by an IBM
7840 Film Thickness Analyzer (FTA).
Thin Films
(do, < 30 nm)
A semi-automatic ellipsometer is used. The technique offers accuracy, but its use is
handicapped by latency. One point at a time is measured. Film uniformity cali-
bration calls for as many points per wafer as possible. The compromise struck out
deals with 5 points per wafer. The center and 4 points, each one inch away from the
center are chosen. Because of the number of data points taken per wafer is rather
small, uniformity is not as accurate. For thin films, however, this is the only method
with valid results.
Thicker Films
(do, > 30 nm)
The FTA38 is an especially convenient instrument for measurement of SiO 2 film
thickness. It allows for the rapid acquisition of 21 data points from selected spots
on each wafer. Mathematical analysis (such as averages, standard deviations, etc.)
is automatically performed. The FTA measures combined reflectance of the film and
substrate in the optical range of 0.38 - 0.75 Am, and calculates the film thickness
from constants associated with the film and substrate properties. Results from
CHAPTER 2: Experimental Techniques 47
ellipsometry and the FTA agree to better than +5% for films beyond 30 nm. In
view of its much higher throughput, the later is the preferred means of measurement
for thicker films. Seventeen points per wafer are measured. The outermost points
were about V" from the edge of the wafer.
CHAPTER 2: Experimental Techniques 48
2.5 Multi- Wafer System Development
To gain prominence as a desirable VLSI fabrication process, several goals must be
met by any plasma oxidation process.
1. A better understanding of the process is needed,
2. Fast throughput, and
3. Cost-effective, when compared with conventional processes.
The general goal of the studies done concerns gathering more information about the
underlying mechanisms and the behavior of the oxidation. It is hoped that, as more
facts are uncovered, the process can be further optimized.
The immediate concern in the industry, however, is its practical application to VLSI
fabrication. One of the main attractions of this process is the feasibility of scaling
up, with respect to both wafer size, and number of wafers for a single run. The fol-
lowing sections deal with the development of a commercially viable multi-wafer
oxidation system, and the limitations encountered. The final choice of a system for
kinetic studies is then outlined.
2.5.1 Wafer Size Scajing
The discovery of plasma oxidation in its present form was made in the late 1970's,
and reported in the literature in 1981. The initial set-up could oxidize a single 2%"
(57 mm) silicon wafer per run. Typically it took several hours to grow around 200
nm SiO2 films.
CHAPTER 2: Experimental Techniques 49
Clearly, this would not satisfy the demands of the semiconductor industry for fast
throughput.
The first step was to bring wafer dimensions up. The procedure appears deceptively
straightforward : use larger oxidation tubes and optimize parameters. The biggest
challenge comes upon retaining plasma uniformity over an extended volume. Rf
coupling is much more efficient in this regard. Wafer size scaling, as this is known,
was developed at the beginning of this decade. The wafers used in the kinetic studies
are 3" in diameter, an oxidization area increase of over 100%. This translates to
a doubling of effective integrated circuitry area per wafer. More important, the oxide
properties were in no way degraded. In fact, in many aspects, the SiO 2 films on the
larger wafers show better characteristics than that on earlier versions. Details will
be discussed in Chapter 3.
2.5.2 Wafer Number Scaling
In addition to having the capability to oxidize larger wafers, it is important to be able
to process several wafers simultaneously. The advantages are many. More wafers
per run means much higher throughput, and allows the existence of "quality control"
wafers, which function to monitor the process itself. However, quality must not be
substituted by quantity. One of the most challenging tasks, then, is to perfect a
multi-wafer system capable of producing excellent quality oxides in reasonable time
frames.
The oxidation of interest takes place on the side of the wafer facing away from high
plasma density regions. The insertion of an identical wafer as a mirror image on the
CHAPTER 2: Experimental Techniques 50
other side of the plasma doubles the oxidation area. The same induction coil segment
would provide coupling to the entrapped plasma.
From here, two geometrical configurations can be considered. The first resembles a
common Reactive Ion Reactor, where several wafers are fit into a large frame, in a
bell-jar like-oxidation tube. Unfortunately, plasma uniformity cannot be easily
maintained with such a structure.
The other alternative is to cascade several double wafer structures, together with
associated coil segments, in series. This is the final set up chosen. Intuitively, the
current flowing through the coil, Ic, would need to be increased in proportion to the
number of segments, to first order, so as to incorporate the same energy for each
plasma section. To a qualitative extent, this holds true. Fortunately, not 100% of
the power output from the rf generator is absorbed into each plasma segment. Ex-
cess energy, presumably, may be extracted by subsequent stages. All this was veri-
fied by experimental observation.
As discussed in an earlier section, excess Ic, and indirectly, Ip, degrades coupling by
causing oxidation of the external surface of the copper coil. A reasonable limit is to
place Ip below 1.0 A, where reproducible rates can be obtained. As consecutive
sections are added, the oxidation rate for each wafer would be seriously constrained.
Oxidation uniformity across a single wafer and from wafer-to-wafer suffers as more
sections are added. One plausible explanation is the non-uniform distribution of
plasma energy for the different sections. The wafers on either end tend to have lower
rates than those positioned more toward the center of the chain. This observation
CHAPTER 2: Experimental Techniques 51
is consistent with the view that the coupling is stronger in the plasma segments near
the middle of the coil, and that fringing is more severe at the two ends.
Another problem is encountered in wafer number scaling. Plasma confinement is
relatively simple to achieve in two- or four-wafer systems. It is not so for systems
with many more wafers. Apparently, the geometry of the cascaded sections
produces much stronger fringing fields, which also have longer range. For a ten- or
more wafer system, plasma ignition and confinement are almost impossible.
The most promising system, then, consists of 4 sections (8 wafers). The oxidation
rates are acceptably high, and throughput is much improved. Such a system was re-
ported in May 198339 .
Choice of a System for Kinetic Studies
The kinetic studies are performed on 'a four-wafer (2 plasma segments) system as
shown in the OXC section.
There are many considerations for this choice.
1. Provision of more data points per experiment. Each wafer is an independent
testing ground. The resultant phenomena should be consistent across the wa-
fers, thus allowing for verification.
2. Possibility of including a "control" wafer. A control wafer is needed to monitor
experimental parameters. Fluctuations in power, pressure, etc may cause erro-
neous results. As a safe-guard, a fresh control wafer is inserted in every kinetics
experiment, to allow for run-to-run comparisons, or to provide indications of
experimental malfunctions.
CHAPTER 2: Experimental Techniques 52
3. Reasonably good quality control. Inter- and intra-wafer SiO2 thickness uni-
formity is much easier to control for a four-wafer system. The oxidation rate is
neither too fast nor too slow with a plate current of 0.8 A, which does not cause
rapid aging of the coil.
4. Fairly straightforward experimental techniques. The problems encountered with
many-wafer systems are not prevalent. Plasma confinement, in particular, was
almost always achieved.
5. Simplicity of experimental set up. Building the induction coil is much simpler,
and the OXC (boat and oxidation tube) need not be exceedingly bulky.
There are no apparent reasons against the choice of a four-wafer system, for the
purpose of studying oxidation kinetics.
CHAPTER 2: Experimental Techniques 53
2.6 Kinetic Studies
The motives for such studies have been described. This section will describe the ex-
perimental approaches chosen to pursue them. A key issue is the unambiguous in-
terpretation of data. Here, the use of a control wafer is pivotal.
2.6.1 Series of Experiments
All parameters except experiment duration, t, have been selected. They are Ip, VP,
Ig, pressure, oxygen flow rate and spacing between wafers. These parameters are
discussed in section 2.3.
Three series of experiments are performed. They use:
1. bare silicon wafers,
2. wafers with back side oxide of 100 nm, and
3. wafers with back side oxide of 450 nm.
The back side oxide films are thermally grown. In all cases, the polished side has only
a very thin film of native oxide ( ~ 1 nm) to start off the series.
The wafers are oxidized for a certain period, examined (including measurement),
re-inserted into their original positions, and re-oxidized. The cycle repeats until
growth is almost insignificant for 4 additional hours of oxidation. To examine ac-
tivity in the very fast range, when the films are very thin, experiments may only be
of the order of 15 minutes. The experimentation time is increased as the oxidation
rates decrease.
CHAPTER 2: Experimental Techniques 54
The oxide thickness for wafers at positions 1, 3 and 4 are then plotted against accu-
mulated oxidation time. Wafer 2 serves as the control wafer, whose role will be
discussed in the following section.
The feasibility of using accumulated time is justified by the results of previous ex-
periments. The oxide film thickness after two one-hour runs is identical to that for
a single two-hour run.
The three series of experiments are designed to look into the effect of back side
oxidation on that of the front. This will provide a useful clue for the theoretical de-
duction of a model.
2.6.2 Role of the Control Wafer
Wafer 2 is replaced with a fresh bare wafer for every run. Its function is to provide
an indicator for the fluctuations of experimental parameters. Its use is designed to
detect power slippage, pressure instability, and other hazards. For a certain set of
parameters, the oxide thickness on wafer 2 allows cross-comparison between run,
and lends credibility to the interpretation of data.
Si0 2 thickness on the control wafers after experiments of equal duration should be
similar, allowing for small variations in other parameters. Several runs with the same
duration need to be performed for statistical comparison. Since coil aging is signif-
icant at high plate currents, it is important to use the control wafer to monitor sup-
pressed growth rates due to coil degradation.
Experimental data verified the reproducibility of the process, on which the whole
idea of the control wafer is based. Moreover, excellent results were obtained on the
CHAPTER 2: Experimental Techniques 55
various runs, with the fluctuation of oxide thickness on the control wafer never ex-
ceeding 5% of its mean value for any given run time. This may be one of the most
attractive features of the process itself, and is a tribute to the caution heeded
throughout experimentation.
CHAPTER 2: Experimental Techniques 56
CHAPTER 2: Experimental Techniques 57
CHAPTER 3: Results and Discussions
3.0
The purpose of this chapter is two-fold. First of all, experimental results are pre-
sented, accompanied by relevant observations and comments. Secondly, the data are
discussed in the context of various theoretical interpretations. The model that best
fits experimental results is chosen, and examined further for possible implications.
To start off, the quality, reproducibility and other characteristics of the SiO 2 films
from multi-wafer systems are shown.
3.1 Multi- Wafer System
As mentioned in Chapter 2, the oxide films grown by plasma oxidation must be of
high quality, have a fast throughput, and be reproducible, in order for the process to
gain credibility as a viable step in integrated circuit fabrication. This section aims to
address each of these concerns, and hence establish the attractiveness of the process.
3.1.1 Quality of Plasma Oxide Films
Extensive studies on the properties of plasma grown SiO 2 films were reported by
Ray, et al 3 . Table 3.1 lists the major physical and electrical characteristics of par-
ticular interest.
CHAPTER 3: Results and Discussions 58
Plama SiO 2 Thermal SiO2Pnqperties 500*C growth 11000 C growth
tempeatwm tanperiut
Etch rate in 1:9 BHF (nm/min) 74-76 75
Refractive index 1.461-1.465 1.462
Stress (dynes/cm 2 ) 1.5-1.6 x 109 3.1-3.4 x 109
Fixed charge (No./cm 2) 2-6x 1010 2x 1010
Interface states (No./cm 2eV) 2-6x 1010 2x 1010
Retention time (sec.) ~ 100 >500
Breakdown strength (MV/cm) 4-8 10
Boron depletion Absent Present
Bird's beak effect Absent Present
Oxidation-induced defects Absent Present
Table 3.1 Properti of Plwma SiO2 grOw at 500 Ccompared to thermal SiO2 grown at 11000 C
(Ray, et al 3l.,-- reprinted withpermwion from the author)
As-grown plasma oxide films possessed high fixed charge and surface-state densities
(6 x 101 0cm- 2 and 6 x 101 0cm- 2eV- 1 respectively). With post-oxidation annealing
(10000, 15 min. 02, followed by 5 min. of Ar), the values dropped to 2 x 1010.
Breakdown strength also improved from 3-4 MVcm-1 as grown to 7-8 MVcm-1 with
that heat-treatment.
In a companion paper, Ray et aP 4. discussed the application of plasma oxide films in
the fabrication of polysilicon gate NMOS devices, and the resulting device charac-
teristics. Of special interest was the potential applications of plasma oxide films as
CHAPTER 3: Results and Discussions 59
gate insulation and field isolation. With standard thermally grown SiO2 films as ref-
erence, plasma oxides showed great promise, especially as field isolation in
semi-ROX structures. The conclusion reached was that plasma oxide films had se-
veral advantages, namely the absence of boron depletion, bird's beaks and oxidation
induced defects, mostly stemming from their low formation temperature, over
thermally grown films of comparable thickness in MOS technology, while no obvious
disadvantage, besides in-depth understanding of the mechanisms involved, existed.
CHAPTER 3: Results and Discussions 60
3.1.2 Reproducibility
I I I I I I I I I
400 -01.2 A, 2.6 kV
....................................................... +5% ----0--------- ------------------------------------- average----
.. ................................................................. - 5% ......--
0 300 - 1.0 A, 2.3 kV......................................... . .... .......-- ------------------... + 5 % .-------------------- ---------- -------- - ---- average----
C 200 wafer 3 (no backside oxidation)4 hours
IIIIII I I I j
0 5 10 15 20 25
Run Number
Figure 6. Control of SiO 2 Thickness Uniformity across Runs
Reproducibility deals with the ability to control the growth of films to a certain target
thickness in different runs, their uniformity across wafers, and the variation of their
thickness across any single wafer. A production and yield issue, it is of immense
concern to the ultimate goal of integrating the technique into the main process flow.
Figure 6 shows the resulting thickness of oxide films grown after 4 hours on bare
wafers at position 3, for different runs, and at two values of Ip (1.0 A and 1.2 A).
At the higher value of Ip, d., tends to fluctuate much more, and decays rapidly with
prolonged use of the coil. With Ip=1.0 A, however, the variation, especially after a
CHAPTER 3: Results and Discussions 61
200
4 hours
1500 2 hurs
cu 100
1 hour
E-1 -wafer 2 (Control wafer)
0L~0.8 A, V 2.3 kV
0 5 10 15 20
Run Number
Figure 7. Control of SiO 2 Thickness at Lower Ip
period of "breaking-in" a freshly built coil, is well within + 5% of the average value.
This is due to coil aging, as discussed in Chapter 2. At higher Ip values, the coil
oxidizes much faster, leading to unstable coupling to plasma segments. As a direct
result, control is compromised by faster oxidation.
At Ip=0.8 A, as shown in Figure 7, the variations are even less pronounced. Con-
trary to intuition, longer oxidation durations lead to larger fluctuations in oxide
thickness. Although the rate of increase for thicker films is markedly less than that
for thinner ones, longer oxidation durations magnify errors in "set" parameters, such
as power input, as referenced by Ip. The importance of controlling Ip can be seen
CHAPTER 3: Results and Discussions 62
from Figure 8 on page 63. At a nominal value of Ip=1.0 A, variations of + 20%
leads to a + 34% uncertainty in do,. Oxide thickness is very close to being linearly
related to Ip, so a + 5% change in Ip can cause a variation of + 8.5% in do0 .
dox is also dependent on wafer position, both with respect to plasma segments, and
to the separation between pairs. The latter dictates the intensity and uniformity of
plasma generated. Ray, et a1 2 . has reported the dependence of do. on wafer distance
from rf coil excitation at pressures below 10 mTorr. In the pressure range of above
10 mTorr, similar dependence holds. Thus, to obtain the best results, wafer posi-
400
o 300
(D
0
200E-1
00 F-
1000.8 1.0
Ip (A)
1.2
Figure 8. Effect of Plate Current
CHAPTER 3: Results and Discussions
4 hours,
AK- wafer 2 (Control wafer)
.000,I
63
I I I I I I I I
280 4 wafer system I,=1 A, Vp=2.3 kV, 4 hoursaverage
0
D 240
- 8 wafer systernm
E-=1.25 A, V,=3.4 kV, 3 hoursCi)
. 200
I I I I I I I I
0 2 4 6 8
Wafer Number
Figure 9. Wafer-to-wafer Oxide Uniformity
tioning needs to be optimized. As a consequence, inter-wafer d., uniformity may be
regulated.
Figure 9 shows dx across wafers for 4- and 8-wafer systems respectively. The first
and most obvious conclusion that can be deduced from Figure 9 is that the 4-wafer
system produces more uniform dx across wafers. This can be attributed to the dif-
ficulty of controlling plasma densities for many-wafer systems. As more wafers and
plasma segments are encountered, the harder it is to obtain good wafer-to-wafer dox
uniformity. This is one of the most serious limitations against scaling up wafer
numbers indefinitely.
CHAPTER 3: Results and Discussions 64
Secondly, do,, on the two end wafers of the 8-wafer system (wafers 1 and 8) tend to
be lower than that on others. This observation may be explained by considering the
geometric configuration of the rf induction coils. The rf field is much weaker at the
two ends of the coil, which resembles a large-size dipole antenna. do, on the end
wafers, hence, tend to be lower. The same can be observed, to a much less obvious
extent, in the profile for a 4-wafer system.
Another issue of relevance to reproducibility is focussed on the material of the rf
induction coil. As discussed in Chapter 2, a large current flows through the coil, at
3 MHz. At large Ip, the copper coil oxidizes, and adversely affects oxidation rate
through decreased coupling efficiency. Gold plating, it was discovered, did not pre-
vent this, because the surface temperature on the coil was so high that gold atoms
migrated into the copper bulk. In fact, compared to pure copper coils, gold-plated
coils decayed even faster. The presence of gold atoms seems to enhance coil aging
at moderate Ip (1.0 A), as illustrated in Figure 10 on page 66. Stainless steel coils
offer much lower oxidation rates at similar power inputs, through less effective cou-
pling. What is worse, they are not immune to age-related decay, and are relatively
hard to control. At higher Ip, all such effects are accelerated.
Also of related interest is the variation in do0 across any single wafer. Wafers are
circular, and the oxide profile is actually symmetrical with respect to the center of the
wafer. FTA measurements done on 17 spots on a wafer are used to determine the
profile, as shown in Figure 11 on page 67. In general, the central disk of about 2
inches in diameter is relatively flat, while do, on the portions within an inch of the rim
is somewhat higher. At moderate power input, with Ip at 1.0 A, the variation is al-
CHAPTER 3: Results and Discussions 65
4 6
Run Number
Figure 10. Choice of Coil Material
most negligible, well within + 5% of the average thickness. Integrated circuit fab-
rication tolerances are easily satisfied by such uniformity.
CHAPTER 3: Results and Discussions
280
240
200
160
0
C.)
0
B----
Copper coil
Gold plated copper coilV--
'10' Stainless steel coil
IP= 1.0 A, 4 hours
I I I I I I I I I1200 2 8 10
66
3.2 Kinetics Data
The most important aspect of this thesis is the interpretation of data, and under-
standing their implications. The resources of IBM's T.J. Watson Research Center,
where the investigation was carried out, are of immense value in this respect. Soft-
ware packages of analytical mathematics, computer hardware and CPU usage are all
in abundant supply, not to mention the assistance of consultants in the various dis-
ciplines.
Kinetics data were stored in variables in APL workspaces, and various programs,
based on existing general-purpose software tools, were written to fully analyze the
300 1 1 1 1 I
% +5%
0 0-- -- -- -------- -- -- -- --- r- - - -r-a-
0 6a
aD 260
-240 wafer 1, 4-wafer system0 = 1 A, V =2.3 kv 4 hours
2200 0.5 1.0 1.5 2.0
Distance from center (in)
Figure 11. Uniformity across Single Wafer
CHAPTER 3: Results and Discussions 67
different figures and trends. With the help of Tektronix 618 Storage Display Units,
graphs were plotted and visually inspected. To further facilitate the inference of
conclusions, a single statistical measure, namely the correlation coefficient40 , c, was
relied on extensively.
N(N N
f (xiyi) - N
C - (3.1)
(N NNF 2N2
( x )i - N 9 -V{5 N(y2) i( )
where
xi = set of N data points of variable x
yi = set of N data points of variable y
c provides a measure of the correlation between actual data (xi), and theoretically
derived values (y). The latter is obtained by least-square-fitting of experimental re-
sults, represented by xi, to pre-determined equations, which are demanded by the
various physical models deemed plausible.
Visual inspection, correlation coefficients and physical intuition played the most im-
portant roles in the analysis.
Three sets of d0 X versus time values are obtained. The first is the thickness of oxide
plasma-grown on bare wafers. The second type of wafer has 450 nm of thermal
CHAPTER 3: Results and Discussions 68
SiO 2 pre-grown on its backside (the surface in direct contact with high plasma den-
sity regions). The last batch has 100 nm of pre-grown oxide on each backside.
As mentioned in Chapter 2, the validity of the chosen method of gathering such data
was upheld by previous experimentation. The alternate solution, using fresh wafers
after each increasingly long oxidation, would be impractical, in terms of time con-
sumption, control of "set" parameters, and the endurance of the different pieces of
equipment. The tolerance of the rf generator for such marathon runs, for example,
is subject to much suspicion.
CHAPTER 3: Results and Discussions 69
3.2.1 Bare Wafers (No Backside Oxidation)
I I
I-=0.8 A, Vp= 1.8 kV
V
W
VV
VV 7 U ~
77 W~V
0_
no backside oxidation
o position 1
* position 3
V position 4
20
Time, t40
(Hours)
Figure 12. Growth Behavior on Bare Wafers
In the first series of kinetics-related experiments, the wafers started off after a thor-
ough cleaning, with practically no oxide on either surface (native oxide, of the order
of 1 nm in thickness, is inevitably present). Figure 12 shows the behavior of these
three wafers. From this, several conclusions can be drawn. The first is that their
inter-wafer do0 uniformity does not degrade appreciably, for accumulated oxidation
times in excess of 50 odd hours. Secondly, the same oxidation mechanism takes
place at all three sites, as evidenced by the close correlation among the growth
curves. Finally, the oxidation is extremely fast for thin films (Ado, = 29.7 nm from
CHAPTER 3: Results and Discussions 70
600
400
200
0
0
FI-
CQ
I
iI
010 60
I I I-
0.5 to 1.0 hours at position 3, when d.. is below 100 nm), while tapering off, as if
approaching certain practical limits after much longer accumulated oxidation dura-
tions (from 46 to 58 hours, d., grew a mere 29.1 nm at position 1, when close to half
a micron).
It is this last observation that serves to indicate termination of the series. Further
growth would be negligible, with the increase in do0 of the order of magnitude as the
standard deviation in film thickness.
The surfaces directly in contact with plasma glow have a thin film of SiO 2 grown
also, confirming previous observations. However, these backside oxide layers tend
to stabilize below 100 nm, and are quite non-uniform, compared with the films on
the other side. Hence no effort was made to obtain thickness versus time data for
the surface in contact with the plasma.
CHAPTER 3: Results and Discussions 71
3.2.2 Wafers with 450 nm and 100 nm Backside Oxide
Since the behavior of wafers at all three positions (1, 3 and 4; position 2 is occupied
by the control wafer) are almost identical, those placed at position 3 (wafers 3, 7 and
11) will be used to illustrate the various kinetic properties.
I I
Position 3
I,=0.8 A, Vp=1.8 kV
0
00
0 V
ivv
LaoooD 0
C3
V
S*
V
20
Time,
no backside
0
oxidation
v 100 nm backside SiO2V
600
10400
200
0
40
t (Hours)
Figure 13. Growth Behavior for Wafers with various Backside Oxide
Thickness
Figure 13 shows the behavior of SiO2 growth on wafers at position 3. Wafer 3 has
no significant backside oxidation to start off. Wafer 7 and 11 have, respectively, 450
and 100 nm of thermal SiO 2 pre-grown on those surfaces facing the plasma. In
CHAPTER 3: Results and Discussions
450 nm backside SiO 2
0C 60
72
I I I
I I
conjunction with Figure 12 on page 70, the major conclusions are also attributable
to the pre-oxidized wafers.
In addition, several interesting characteristics are immediately apparent. The
oxidation rates, short and long term, decrease with increasing thermal pre-oxidation.
The thickness at which further growth becomes negligible also decreases, as limiting
do drops from over 500 nm, to just below 300, and finally to about 70. The time
taken to approach stabilization is another factor that decreases, with wafer 3 taking
over 50 hours, wafer 7 needing 35, and wafer 11 just over 20. In effect, these figures
combine to provide a potentially useful way of controlling the oxidation process.
Since the oxidation rate depends on the thickness of pre-deposited SiO 2 film, one can
conclude that the oxidizing species is charged. If neutral species like 0 or 02 are
responsible for oxidation, the oxidation rate should not be linked to the thickness of
SiO 2 film on the wafer backside. The hypothesis of charged species will be clarified
when the analysis of the kinetics data is done.
Although parameters and constants may vary, it is clear that the same underlying
mechanism takes place in all three cases, in order to explain the similarity of the
curves in Figure 13 on page 72. Oxide uniformity across wafers is not affected by
much. In addition, the backside films of thermal SiO2 do not demonstrate significant
change throughout the oxidation series. The uncertainty in do, across the same wa-
fer, however, suffers drastically, with increasing pre-oxidation.
CHAPTER 3: Results and Discussions 73
3.3 Modelling
The previous section has led to the conclusion that, with or without backside pre-
oxidation, the same mechanism is at work in plasma oxidation. In turn, this allows
concentration of efforts in the examining the behavior of one selected wafer. Wafer
3, starting off with no backside SiO 2 , is a logical choice, owing to the longer accu-
mulated time of oxidation, and that the features that deserve particular attention are
more apparent. In this section, various models will be introduced, kicking off with
the familiar Deal-Grove model of thermal oxidation, which has already been pre-
sented in Chapter 1. Not surprisingly, plasma SiO 2 growth does not conform best
to the Deal-Grove model. Two other more exotic models, both taking into account
the effects of electromagnetic interactions, will cap off the discussion. After a thor-
ough examination, the model that best suits the observations will emerge.
3.3.1 Deal-Grove's Linear-Parabolic Model
As introduced in Chapter 1, conventional oxidation of silicon at high temperatures
can be relatively well-modelled by that proposed by Deal and Grove'. The model
makes several assumptions (see Chapter 1) about the various phases of oxidant
transport. Perhaps the most far-reaching concerns the claim that the oxidants drift
through the the SiO 2 film to the Si-SiO 2 interface, where they react with the silicon.
The outcome can be neatly summarized by the equation
2dox + Adox = B(t + T) (1.1)
Rewriting (1.1), one obtains
CHAPTER 3: Results and Discussions 74
600
_ I,=0.8 A, VP=1.8 kV ----
0400
Corr. coeff.* = 0.99728
t = 2.2 - 4.25x10- d0x + 2.73x10-4 do 2
0200E-1/
C%2o /9 wafer 3
(no backside oxidation)* with respect to time, t
0 10 20 40 60
Time, t (Hours)
Figure 14. Kinetics Fitted to a Linear-parabolic Relationship
t = ao + aidox + a2d 2 (3.2)
where ai are constants.
The task is to fit the kinetics data of wafer 3 to equation (3.2), and deduce the con-
stants (al), and the corresponding correlation coefficients, c, according to equation
(3.1).
At first glance, this seems simply an exercise in multiple linear regression. However,
the form of equation (3.2) signifies that do. is the independent variable, although the
data contain much more confidence in the accuracy of t. In addition, the correlation
CHAPTER 3: Results and Discussions 75
1 .......A 0 A IT __ 4 0 1.17.u a, ~D1 0 RLY
--
Linear-parabolic fitting0--
.,3 -0
0
C)
0
* with reipect to time, t
20 40 60
Time, t (Hours)
Figure 15. Linear-parabolic Relationship with a0 Term as Parameter
coefficient, as defined, compares theoretical and actual values of the dependent vari-
able, in this case, t. With this in mind, great care is taken to ensure the establishment
of concrete conclusions.
Figure 14 on page 75 shows the result of such an attempt to optimize c. The re-
sulting equation has the form
2 10-4 2t =2.2 -4.25 x 10- do. + 2.73 x 10d0 x (3.3)
The maximum correlation coefficient of 0.99728 is not high, and visual inspection
of Figure 14 on page 76 rules out the possibility of this being the best fit. More
CHAPTER 3: Results and Discussions
600
i -
400 F-
0 Corr. coeff. = 0.99373* .
t = -0.199+1.04x10- 7 xdx+1.80x10- 4xds2
wafer 3
(no backside oxidation) -
200
000
0-~
/
I'0
0
76
, I
I
600
Purely parabolic fit
0 400 - *ro* &
do =8705.9 + 5095.4 x t. Corr. coeff. = 0.98891
00
3 200
* wafer 3(no backside oxidation)
0 I
0 20 40 60
Time, t (Hours)
Figure 16. Purely Parabolic
significant, the linear coefficient a1 in equation (3.3) is negative, while ao and a2 are
positive. This translates into a negative linear rate constant, which is incompatible
with any reasonable deduction, from a physical standpoint.
The method chosen for the regression fitting is based on the standard non-weighted
least-squares approach. Hence, slight uncertainties in the thick film regime, with
Ado, insignificant relative to do., can skew the thin-film coefficients a and a, appre-
ciably. To avoid this, two mathematical approaches are possible. One is to use
normalized least squares, where the sum of the variations are normalized by the ab-
CHAPTER 3: Results and Discussions
solute value of dox. This method, however, is highly sensitive to matrix inversion
convergence uncertainties. The other is to rewrite equation (3.2)
t - a0
d = a + a2dox (3.4)
The left-hand side of equation (3.4) is renamed with a new variable, y(a) ,
y(ao) = a, + a2dox (3.5)
y(a0 ) would depend on the externally fixed parameter ao , and allow some leeway in
determining the best fit that also satisfies physical intuition.
Upon iteration, the value of ao that leads to the highest correlation, as well as a non-
negative linear oxidation rate, also happens to cause a, to be extremely small (prac-
tically zero), as can be seen from Figure 15 on page 76. The resulting c of 0.99273
is worse than that in Figure 14 on page 75 (0.99728), and is low by most standards.
Moreover, visual inspection also allows discarding this model for the plasma
oxidation process.
A null a, term also necessitates the conclusion that the kinetics is at best parabolic.
With this assumption, equation (3.2) is rewritten
d = - + (3.6)
CHAPTER 3: Results and Discussions 78
Equation (3.6) produces, from simple linear regression, the fit shown in Figure 16
on page 77, this time with d. as the dependent variable, and thus should be closer to
actual observation.
2dX ~ 8705.9 + 5095.4 x t (3.7)
The correlation is far from perfection. It is interesting to note that the discrepancies
between observed and predicted values are largest for films thinner than 200 nm and
thicker than 400 nm. This strongly contrasts with thermal oxidation, where the fit-
ting to parabolic kinetics is better for thicker films. The above analysis confirms an
earlier indication that oxidizing species are charged. Since charged species diffuse in
the presence of an electric field, it is now appropriate to consider various models that
describe the kinetics of oxide growth in the presence of an electric field, either con-
stant or variable.
CHAPTER 3: Results and Discussions 79
3.3.2 Constant Electric Field Model
H
............
............
............
Gas(or Plasma)
x=0
Figure 17. Concentration of Oxidants in SiO2 Film
Before dealing with the effects of electric fields on the growth kinetics of plasma
SiO2, it is appropriate to consider the simpler situation where no fields exist. In
Figure 17,the Si-SiO 2 interface is located at x=O, for convenience. The SiO2 film
thickness is d.x, i.e., the SiO2-gas (or plasma) interface is at x = dx. The concen-
tration, c, of oxidants in the SiO 2 bulk is co at x=O, and c, at x=do.
If the oxidation is due to uncharged species, with no electric field present, assump-
tions that will be relaxed later, diffusion of these uncharged oxidants takes place,
CHAPTER 3: Results and Discussions
S 10 2
CS
zzco
x=do X
80
owing to a concentration gradient of the oxidant in the SiO2 film. In one-
dimensional steady-state analysis, the flux, J, of oxidants is given by Fick's law:
clc(x)J = - c I (3.8)
Ox
where c(x) is the concentration and D is the diffusion coefficient of the oxidant
through SiO2 . D is assumed to be independent of concentration and x. In the ab-
sence of sources or sinks of oxidants in the bulk of the oxide, the flux must be inde-
pendent of the position, i.e., J does not vary with x. This allows direct integration
of equation (3.8). Incorporating the boundary conditions on c(x) at x=0 and at x=
do,, and then re-arranging,
D[c0 - cj]J = (3.9)
Note that J, as given by equation (3.9) is negative, owing to the coordinates of ref-
erence that was chosen. The growth rate of the SiO 2 film is assumed to be directly
proportional to the incoming flux at the Si-SiO2 interface,
= -sDJ (3.10)
at
where 9 = volume of SiO2 formed per mole of oxidant.
Substituting equation (3.9) into (3.10),
c =dox D[c, - co]
at dox
CHAPTER 3: Results and Discussions 81
Odox K, 3.1=t d (311
where K, = QD[cS - co].
Further integration of equation (3.11) from initial conditions of t = to, and do, =do
yields
2 2dox d + 2K,(t - to) (3.12)
Equation (3.12) has exactly the same form as equation (3.6), which should come as
no surprise. The Deal-Grove model makes assumptions that are identical to the ones
followed in this derivation. When the process is diffusion limited, as required in
equations (3.8) and (3.10), the oxidation is parabolic. This is the case in thick ther-
mal films.
CHAPTER 3: Results and Discussions 82
In the presence of a constant electric field
The plasma state is a collection of ionized particles. Intuitively, some of these
charges may be absorbed at the SiO2 -plasma interface, at x=dox in Figure 17 on
page 80. If this absorbed surface charge density is uniform, a reasonable assumption
for a spatially uniform plasma, a constant electric field is set up by this charge sheet
in the bulk of the SiO 2 . Furthermore, if the space charge within the oxide is suffi-
ciently low, the total electric field, E, is predominantly produced by the surface ab-
sorbed charge layer, and is to first order constant throughout the SiO2 film.
In the presence of and electric field, equation (3.8), which describes the flux of
oxidants, is modified by a term describing their interaction to the electric field.
Assuming that the oxidants have a mobility M in response to this field, E, the total
flux is
Oc(x)J = -D - +MEc(x) (3.13)Ox
Again assuming no sources or sinks in the oxide bulk, the flux of the oxidants in the
steady state should be independent of x, and constant. Re-arranging (3.13),
D Oc(x) _ j7~7 Ox - c(x)- EpuE lx - yE
dc(x) IE= -- dX
J Dc(x) JE
Integrating,
CHAPTER 3: Results and Discussions 83
log, c(x) - A + xILE D
where A is a constant of integration.
A uExc(x) = LE + e D
Applying the boundary conditions at x=0 and do. (see Figure 17 on page 80), and
re-arranging,
I.Edo
AECs -Coe D (-4= ____E____I(3.14) ILEdox
L e D
Substituting equation (3.14) into equation (3.10) yields
AEdoxadox c5 - coe D
t - E Edox (3.15)
L - e D
Equation (3.15) is far more complex than its no-field counterpart, equation (3.11).
However, there are several limiting cases where equation (3.15) can be simplified.
They are:
1. c. >> c5, with assisting field,
2. co >> cs, with retarding field,
3. c. << c,, with assisting field, and
4. c, << cs, with retarding field.
CHAPTER 3: Results and Discussions 84
Of the four, the first two cases correspond to the migration of silicon-related species
to the Si0 2 -plasma surface. The other two, to be examined in more detail, represent
the diffusion of oxygen-related species through the film to the Si-SiO 2 interface.
Now consider the third situation of an assisting field, and co << c,. Such a situation
may be provided by positively charged oxidants, e.g. cation interstitials or anion va-
cancies, drifting under the influence of a field pointing into the silicon substrate (E
negative). This field is produced by a positive surface charge layer at x=do, or a
negative charge Si-SiO 2 interface. Alternately, negatively charged oxidants can drift
against a field pointing away from the silicon bulk. In either scenario, the product
IE is negative, with the sign convention adopted in Figure 17 on page 80.
pAEd.So, if co << cs, then c, > coe D , and equation (3.15) simplifies accordingly.
Odo 1~- %LEc~at s LEdox
1-e D
( pEdox( - e D d(dox) = - 12Ecsdt (3.16)
DFor small values of dox, i.e. do < i< , the left hand side of equation (3.16) can
tLE
be expanded by a Taylor's series, and higher order terms may be dropped,
doxd(dox) e DQcsdt
fdox t
d0 to
CHAPTER 3: Results and Discussions 85
x= d + 2DS2c5(t - to) (3.17)
Note that the electric field, E, drops out.
The form of equation (3.17) is again identical to those of equations (3.6) and (3.12).
The difference, however, is that equation (3.17) is valid for thin films, whereas (3.6)
is applied to thick films, and (3.12) for all films.
In the constant electric field model, then, the initial growth follows parabolic kinetics.
The growth behavior of thick films can be deduced upon returning to equation
(3.16). Since 1E is negative and D >> 1, the left hand side of (3.16) be-
comes simply d(do),
d(dox) ~ - GEcdt
Integration yields
dox -d 0 = Q( - LE)cs(t - to) (3.18)
The thick film growth is linear, for charged species moving under the influence of an
assisting field.
CHAPTER 3: Results and Discussions 86
Parabolic-logarithmic Kinetics
The last case of co << c, and a retarding field can be examined under a similar light.
The major difference is that the product uE is now positive, and the requirement
pEd..Cs >> coe D
places much more severe constraints on the ratio of cs to c.. Thus for very thin films,
the growth is parabolic, as in equation (3.17), with the exact same derivation as that
in the previous case of an assisting field. For thick films, however,
sEdO0e D >>1,
and hence, equation (3.16) becomes
sAEdOXe D d(dox) ~ 2tEcsdt
f dox dE A
t
de D dA = IzEcS t dT
= QtLEc5(t - to)
MEdoxe D
ILEdO (gE) 2c5e + D (t-to)
sEdoxe D = a+ft
CHAPTER 3: Results and Discussions 87
D IEdox ILEdO
IELe D - e D I
A~d. 2(,uE)2cst2where a = e D - D
0(ME)2C,and (3= D
D
dx -- loge(a + t)ILE
If ft >> a,
dex ~ Y + 8 loget (3.19)
where y loge3, and 8 = .AE AE
In the long run, oxidation due to oxidants in a retarding electric field follows loga-
rithmic kinetics.
Figure 16 on page 77 shows the result of fitting of growth behavior of wafer 3 to a
purely parabolic equation, with the consequent coefficients in equation (3.7). It is
sufficient to say that the "no-field" model does not describe the process kinetics to
a satisfactory level. However, the actual data do seem to confirm the existence of
an initial parabolic phase. Figure 18 on page 89 depicts the comparison of observed
data with the predictions of the parabolic-linear model of charged oxidants drifting
in an accelerating field. The parabolic correlation coefficient is outstanding, but the
linear version leave much to be desired. It is clear to the naked eye that the growth
in the long run does not agree with the drawn straight line.
CHAPTER 3: Results and Discussions 88
20 40
Time, t (Hours)
Figure 18. Fitting to Parabolic-Linear Kinetics
Figure 19 on page 90 illustrates the result of fitting the same data to parabolic-
logarithmic kinetics. The high correlation factors (0.99923 for the parabolic section,
an amazing 0.99997 for the logarithmic) agree nicely with visual inspection. The
equations are
d2, a151.9 + 6617.2 x t (3.20)
for thin films (do. < 300 nm), and
dox ~i - 107.2 + 153.6 x loget (3.21)
CHAPTER 3: Results and Discussions
600
0400V
0
200E-
0
0
de,2 =151.9 + 6617.2 x t
Corr. coeff. = 0.9992 .- ....--
- do1 = 301.7 + 3.86 x t
..... * Corr. coeff. = 0.99580
Parabolic--linear fitting
wafer 3
(no backside oxidation)
0 60
89
600 I I I I I
d 151.9 6617.2 x t....
Corr. coeff. = 0.99923... .-- s04- d00 = -107.2 + 153.6 x loget
Corr. coeff. = 0.99997
S200
CQ wafer 3(no backside oxidation)
I I
00 20 40 60
Time, t (Hours)
Figure 19. Fitting to Parabolic-Logarithmic Kinetics
for films beyond 300 nm.
All other wafers exhibit the same behavior. Table 3.2 illustrates the results of at-
tempts to fit the data from all wafers to the parabolic-logarithmic model. Wafer 8 is
the lone exception, appearing to be purely parabolic. This may be due to a much
later than expected transition into the logarithmic stage. Wafer 8 notwithstanding,
there is little doubt that the observed growth rates across all wafers conform to
parabolic-logarithmic kinetics.
Perhaps the most pivotal piece of evidence in support of the constant-field approach
is the observation that little oxidation occurs on the surface adhering to the plasma.
CHAPTER 3: Results and Discussions 90
Parabolic2
dox= al +
Logarithmic
a 2 t dox= a 3 + a4 loget
nobacksideSiO2
450 nmbacksideSiO
2
100 nmbacksideSiO2
1
3
4
342.7
151.9
212.3
7752.6
6617.2
7752.5
0.99890
0.99923
0.99878
137.2
153.6
170.1
Corr. a Corr.WAFER a 1 a 2 coeff. a 3 a 4 coeff.
- 45.2
-107.2
-131.5
5 54.4 156.8 0.99782 -8.8 20.3 0.99969
7 18.3 236.2 0.99771 3.6x10 2 18.8 0.99940
8* 32.3 242.7 0.99978 -- --- ---
9 291.6 3695.0 0.99517 -0.657 80.95 0.99858
11 11.8 2777.5 0.99688 -47.96 91.82 0.99987
12 171.9 3183.3 0.99653 -83.10 111.1 0.99929
* wafer 8
Table 3.2
0.99974
0.99997
0.99988
seems to be purely parabolic
Parabolic-logarithmic Coefficients
The initial parabolic phase of growth requires that dox<< --- . On the surfacetLE
facing the plasma, the electric field, E, would presumably be much higher, owing to
the relative abundance of ionized particles. The above constraints, then, would lower
the parabolic-logarithmic dividing line, by a factor equal to the inverse ratio of the
two electric fields. In other words, the kinetics would enter the long run logarithmic
regime much earlier.
The long run logarithmic growth rate, expressed by 8 in equation (3.19), depends on
the electric field also, as
CHAPTER 3: Results and Discussions 91
DAE
Since E is higher on the surface touching the plasma, 8 would be lower by the inverse
ratio of the electric fields. Combining the two factors of early transition into the
logarithmic regime, and lower logarithmic growth rates, it can be deduced that an
insignificant amount of SiO 2 would be grown on the face in touch with the plasma.
However, some questions do remain. Equation (3.17), which describes the initial
phase of growth, claims that the parabolic rate constant, 2Mc, , is independent of the
electric field. Table 3.2, however, suggests that it drops drastically with increasing
backside SiO2 thickness. This would require c, to vary by the same factor as the ratio
of parabolic rate constants (0 is the volume of SiO2 produced per mole of oxidants,
and is not likely to vary by much), for wafers placed at the same position. This is
difficult to rationalize. since c5 would seem to be controlled by the local plasma
density, and not by the thickness of oxide on the other side. The variation of 20c, (
a2 in Table 3.2) across wafers, in contrast, is much simpler to acknowledge, given
unequal plasma densities at the surfaces of wafers at different positions.
CHAPTER 3: Results and Discussions 92
3.3.3 Constant Voltage Model
V
Cs
C0S *O2 Plasma
X=O
Figure 20. Constant Voltage across SiO2 Film
Another plausible model that takes into account electr field interactions assumes a
constant voltage across the growing SiO 2 film. This potential difference can be ex-
plained by the presence of ions absorbed from the plasma at the SiO2 outer surface.
In Figure 20, the reference zero potential is set at x=0, i.e., at the Si-SiO 2 interface.
At x=dOX, the potential is then V0 , as assumed to be constant. Following the steps
CHAPTER 3: Results and Discussions
V=V-
93
X=dOX
Inverse-log/parabolic fit
9.5x10- 3 -
coeff. = 0.9
-. 9-.--- 0
1.4x10- 2 loget . -
7545 .-- !'0 d1 2 = 1.6x104 + 4.9x10 3
600
o400
a)0
2 200
CQ20E-
t
Corr. coeff. = 0.99118
dor- Corr.
~'1- *I -
J *wafer 3
(no backside oxidation)
20 40 60
Time, t (Hours)
Figure 21. Strong, Constant Voltage across SiO2 Film
taken in the previous section on the constant electric field model, the flux is given
by
49c(x) VOJ = - I c - t I c(x)
ax dox(3.22)
V0since the electric field, E, is just .
dox
With similar assumptions of the absence of sinks and sources in the SiO 2 bulk, the
V0resulting equation for J resembles (3.14), with E replaced by - -
CHAPTER 3: Results and Discussions
I I I I I
* -0 ~
9 -9-
0
10 ."
0i i
I I
94
Vo
do
cs -Coe D
c - e D
The growth rate, analogous to equation (3.15), is
__ OVo cs- coe D
e D
ado_ KP
at do
juvo
=1 - oe D
[-e D]
Simple integration of (3.24) yields a parabolic relationship,
= d0 + 2KP(t - to)
The limiting case of small potential difference is useful for verification of the model.
With VO approaching zero, (3.25) gives
CHAPTER 3: Results and Discussions
(3.23)
ado
at
or
where
(3.24)
(3.25)
d 2 (3.26)
J = A (
95
~~ILpo~v
= G2D[c - c ]
Hence
dox =d0 + 2 SDLCS - c0](t - to) (3.27)
This is identical to equation (3.12), which was derived for the diffusion of uncharged
species in zero-field, and hence, zero voltage.
The fitting of data to parabolic relationships has been done in Figure 16 on page 77,
yielding equation (3.7). The correlations that are formed do not support the sug-
gestion that plasma oxidation follows parabolic kinetics. This model, clearly, does
not satisfy the main criteria for selection. It does, however, provide a spring-board
for the construction of more complex models that incorporate voltages across the
oxide film.
In particular, one sophisticated model assumes a strong, constant potential difference
across the SiO2 film. The electric field thus created would be sufficiently large to
skew any existing concentration profile, dwarfing the concentration gradient term,
and leaving the flux with just the electrical second term on the right hand side of
equation (3.22). Such assumptions lead to inverse-logarithmic short run behavior,
of the form
CHAPTER 3: Results and Discussions 96
1d - A-Blo&t (3.28)
and long run parabolic relationships as in equation (3.26). Figure 21 on page 94 il-
lustrates the effects of examining the growth of SiO 2 on wafer 3 in the context of this
model. Neither visual inspection nor mathematical judgement lend credibility to the
validity of this model, however. It provides valuable experience in dealing with
voltage-controlled phenomena, and should not be discarded lightly.
CHAPTER 3: Results and Discussions 97
3.3.4 Other Models
It must be emphasized that there is no shortage of possible theoretical interpreta-
tions. Wu, et alP. have suggested a "half-life" model for thermal nitridation of
silicon, that leads to linear-parabolic- logarithmic growth. Their major assumption
was the inclusion of a "characteristic diffusion length" of nitridants through the
nitride film. Modifications of the Wu, et alP. approach would be to assume "half-
lives" for oxidants. The physical basis for proposing such conditions is, as yet, not
on firm grounds. This does mean that there is plenty of room for creativity and in-
genuity.
One of the most devastating obstacles in the development of a viable theory is the
lack of understanding of plasma properties, especially charge and voltage effects on
adhering surfaces. As plasma processes become more common, it is hoped, by many
in the ranks of integrated circuit fabrication engineers, that much improved know-
ledge flows from the increasing experience of handling plasma. Only then can
plasma-related processes, in this case oxidation, be further comprehended.
CHAPTER 3: Results and Discussions 98
3.4 The Correct Model
After the preceding discussion of the various models, one may safely assume that
there are deficiencies in each and every one of them. The Deal-Grove model pre-
sented in section 3.3.1, with widespread support for its application to thermal
oxidation, does not appear to describe plasma oxidation satisfactorily. The constant
voltage model, a simple version of which is examined in section 3.3.3, does not seem
to explain the phenomena any better. Others, such as the "half-life" model proposed
by Wu, et a14 ., and the advanced constant "high voltage" approach touched upon in
section 3.3.3, also do not meet most demands. The former lacks physical backing,
with the only support enjoyed being purely mathematical. The latter predicts a be-
havior different from that observed.
That leaves the constant electric field model, which was fully discussed in section
3.3.2. The presence of the word "plasma" suggests immediately likely roles for
electromagnetic forces and charged particles. The assumptions made are fair and
reasonable, but more important, the predictions match observations extremely well.
The kinetics behavior can be divided, in this model, into two regimes with distinct
characteristics. The thin film region obeys parabolic growth, while long run thick
films follow logarithmic rates. The curious phenomena of oxidation on the "wrong"
side can be explained, with the consideration of the effects of the constant electric
field. Some questions are bound to remain, as in the problem of parabolic rate con-
stants. At present, it is not clear if this deviation from the implications of the model
is irreconcilable.
CHAPTER 3: Results and Discussions 99
Wafer 3 (no backside oxidation)
MODEL NEoQUATypN Co . COMMENTS
Deal-- (3.2) Zpaolic 0.99728* Poor fit; negative linear rate constantGrove (3.5) parabolic 0.99373* Worse fit; null linear rate term
(3-8) parabolic 0.98891 Even worse fit; no linear rate term
Const (3.2) Parabolic 0.98891 Zero field
Field (3.17) parabolic 0.99923 Thin films, very good fit(3.18) linear 0.99409 Thick films, assisting field; poor fit(3.19) logorithmic 0.99997 Thick films, retarding field; excellent fit
nverse-Const (3.28) ogarithmic 0.97545 Thin films, strong field; worst fitVoltage (3.28) >rabolic 0.99118 Thick films or low voltage; poor fit
Others -0 -923 Two parabolic processes in parallel-- - -- "Half-life" model
*with respect to time, t
Table 3 . 3 Comparison ofVarious Models
Table 3.3 lists the results of applications of the various models to the growth of
SiO2 on wafer 3. The comments column summarizes the conclusions of the dis-
cussion thus far. Whether in tabular or prose form, the results all point to the se-
lection of the constant, retarding field model as the most logical candidate for
explaining the process.
CHAPTER 3: Results and Discussions 100
CHAPTER 3: Results and Discussions 101
CHAPTER 4 : Conclusions
4.0
The goals of this thesis, as stated in section 1.4, are broad, and by many accounts,
aggressive. To a certain extent, all three major objectives were met. But from an-
other angle, much more needs to be done in this field. As Dr. Sun Yat-sen, the father
of the modern Chinese Republic, once said :
"...Comrades, we still need to work hard,
the Revolution is not yet successful..."
In a similar light, the road to the establishment of plasma oxidation as a work horse
for VLSI needs is long and full of obstacles. It is hoped that a considerable portion
of that road has been travelled over in this thesis, paving the way to even further
advances.
The experimental work related to this thesis took over two summers and one semes-
ter. By itself, the experience gained is invaluable. With regards to the stated claim
of contributing to the development of a viable plasma oxidation process, the function
of experimentation is unquestionable. The experiments also provided unique data
for analysis, and from this point of view, supplied the necessary ingredients for a
better understanding of the process. Much more needs to be done, however. The
kinetics of the backside is the logical next step. External biassing of wafers, an ex-
tremely difficult and tricky task, is another example of possible things-to-do.
CHAPTER 4: Conclusions 102
On the theoretical side, the models that were discussed in Chapter 3 are by no means
fully refined and complete. Nonetheless, they do possess a definite amount of value
as proto-types for the final version. These first-order scenarios are possible simpli-
fications of the real thing. When examined more carefully, these present drafts are
likely to metamorphose. Such is the path of development. The celebrated Deal-
Grove model clearly does not suit the needs, since it does not take into account the
roles of electromagnetic fields and charges. The constant electric field hypothesis,
which has emerged as the prime candidate, appears to fit comfortably with most ob-
servations to date, but does not explain others. The constant voltage approach in the
presented form, while appealing because of its roots in plasma theory, is unable to
demonstrate the excellent correlation between predictions and data that marks the
constant field model.
On a more optimistic note, the existence of the non-intuitive phenomena of oxidation
on the "wrong" side was not even suspected less than a decade ago. In the space of
a few years, its kinetics and other characteristics have been deduced. Simple models
have already appeared. The productivity of the research members involved cannot
be challenged. They have brought the development of the process a long way. With
a proven track record, there is little doubt that they same researchers can furnish a
complete account if given reasonable time.
The two phases of this thesis are combined without conflict. The problem of which
comes first does not arise. Experimentation supports theory, which in turn drives
more experiments. This intertwining is important; one could easily have performed
laboratory work without theoretical direction, or developed a hypothesis that has no
CHAPTER 4: Conclusions 103
real life support. Fortunately, the rules at IBM's Yorktown Heights Laboratories do
not restrict the scientists and engineers to follow one and not the other approach.
This thesis could not be done at most other places. It is a tribute to the IBM Corpo-
ration.
CHAPTER 4: Conclusions 104
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CHAPTER 4: Conclusions 106