plasma oxidation of silicon: kinetics studies

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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Certified by:

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

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 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


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-


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.


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,


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


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


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


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.


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)


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.


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


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


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".


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.


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.


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.


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 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 .


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.


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.


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.


__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.


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.


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


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


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.


The PUN proved to be fairly reliable. Even after periods of several months of idle-

ness, it worked much more satisfactorily than expected.


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


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.


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.


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.


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.


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


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.


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.


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


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


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.


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.


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.


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


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 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


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.


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


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


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


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.


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-


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.


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


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


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.


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


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.


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


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.


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


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


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


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-


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)


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.


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,


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


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.


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,


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.


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


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.


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


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.


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)


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.


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


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.


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


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 - -


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


(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


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.


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.


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.


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 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


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.


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plasma oxidation of silicon: kinetics studies

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