II )Transport and Surface Phenomena
for
Silicon Epitaxial Growth

HITOSHI HABUKA
Iso be R &D Cent er, Shin-Etsu Ha n dotai Co. , Ltd.

A Thesis Presented tot he Faculty of Engineering
Hiroshima University

July, 1996

ABSTRACTTransport phenomena, surface chemical processes, dopant concentration profiles
and surface roughness of substrate for silicon epitaxial growth are discussed theoretically and experimentally. The objective of this thesis is to develop the models topreuict various phenomena relating to the silicon epitaxial wafer. The major part ofdiscussion is based on the calculations of the transport phenomena and the chemical
reactions at the surface. At first, the transport phenomena in a pancake reactor andin a single-wafer horizontal reactor are discussed. Secondary, the substrate rotation and the chemical reactions for the epitaxial growth are discussed to describe
the growth rate and the film thickness. For further studies, the epitaxial wafer'squalities, the dopant distribution and the surface roughness of silicon substrate, areinvestigated.
The tran 'port phenomena in a pancake reactor are di cussed based on a gas flow
vi. ualization technique using a high-sensitivity analogue can1era and numerical calculations. At room ten1perature and the epitaxial growth ten1perature of 1423 K, alarge recirculation exists in the reactor chamber, in which the gases near the susceptor flow frorn the outside toward the center of the susceptor. The profile ofthe epitaxial film growth rate observed agrees qualitatively with that predicted byvisualization and calculations.
An evaluation of silicon epitaxial thin-film growth using the SiHCb-Hz system ina single-wafer horizontal reactor is discussed by solving the transport equations forgas velocity, temperature and concentration of chemical species taking into accountof the dependence of ga properties on telnperature and c0111position assuming asimple Arrhenius-type expre sion for the chernical reaction of SiHCb and Hz on
a substrate. Non-Linear increase in the growth rate due to changes in thermal
diffusion and diffusion is found to become significant as the SiHCb concentration in
the reactor increases.
For an enhancelnent of studies, the effect of substrate rotation on transport of2

reactive gases and epitaxial growth rate is investigated for a single-wafer horizontal
reactor using a model and experiments. The rotating substrate causes a circulating
gas flow region above itself, in which an asymrnetric and nonunifonn SiHC1 3 distribution is formed by thermal dHfusion and species consumption due to the surface
chernical reaction, even when the growth rate profile on the substrate surface isnearly uniform. The good uniformity in the film thickness observed in calculationand measurement is mainly attributed to the averaging effect by integrating the
local growth rate along a concentric circle on the substrate surface, and partiallyby the species concentration distribution change, both of which are caused by therotating motion of the substrate.
For the discussion of the dependence of the epitaxial growth rate on the source
species concentrations, a transport and epitaxy model following Eley-Rideal to describe silicon epitaxial film growth in an SiHC1 3 -H 2 system is developed by numericalcalculations and comparison with experiments. The state of the surface during theepitaxial growth is also discussed considering the intermediate species, elelTICntary
reactions and rate limiting processes.
The boron concentration profile in silicon epitaxial films grown on a p-type substrate under atmospheric pressure is investigated in two types of epitaxial reactors,
a single-wafer horizontal reactor and a pancake reactor. It is concluded thst large
amounts of recirculation of gas in an epitau"'dal reactor should be avoided to obtainan abrupt boron concentration profile.
Since silicon surface after the epitaxial growth must be very smooth and flat , surface roughness of a silicon wafer heated at 800- 1100 DC under atmospheric pressure
in hydrogen ambient is studied. AFM: images show that the surface heated at 900 DC
has many small pits which are formed due to the difference in ~he chemical reacUon
rates between hydrogen-silicon and hydrogen-silicon dioxide. The behavior of surface roughness with pressure and heating time agrees well with that predicted by
the pit formation model in this study.

3

ACKNOWLEDGEMENTFirst of all, I wish to express my gratitude to Professor Kikuo Okuyama and Professor Manabu Shimada of Department of Chernical Engineering, Hiroshima University
for their continueing guidance and encouragement throughout this study. I wish to
thank Professor Yoshihiro Kikuchi and Professor Takayuki Takahagi for their helpful
suggestion and advice.
J am very rnuch grateful to all the rnembers of Isobe R&D Center and Epi Produc-tion Division of Shin-Etsu Handotai Co.) Ltd. In particular, I am deeply indebted
to Mr. Hiderni Matsuzawa, Dr. Akira Yoshinaka, Dr. Takao Takenaka and Dr.
Masatake Katayama for their continueing support in all phases of this work. I must
appreciate Mr. Takatoshi Nagoya and Mr. Masanori Mayusumi for supplying key
data of epitaxial growth rates. I am very happy to work with Mr. Hitoshi Tsunoda
having fresh idea to progress this work. I also appreciate Mr. Naoto Tate for his
n1any suggestions based on his wide and many experience on silicon epitaxial growthand charaterization.
Finally, my special thanks are due to Iny falTIily. Satoko, my wife, encouraged toproceed this work. I wish to note here that she is a skillful engineer of computer
system. Satoru and Rie, my son and daughter, always made Ine refresh and mademe very happy throughout this work.

4

1

Chapter 1 Introduction

2

1.1 Background1.1.1 Silicon crystal

2

1.1.2 Epitaxial growth2

1.1.3 Epi taxial reactors

1

1.1.4 Transport phenOlnena

61.1. 5 Surface process

81.].6 Dopant concentration profile

10

1.1.7 Process ternperature and surface roughness

13

1.2 Scope of this thesis]5

RefcTences

17

Chapter 2 Gas Flow and Heat Transfer in a Pancake Reactor

23

2.1 Introduction

24

2.2 Gas flow visualization

21

2.2.1 Reactor configuration and experirnental conditions

21

2.2.2 Solution of pl'oblelns underlying the tracer nwthoJ

2()

2.3. Basic equ ations governing the epitaxial reactor

28

2.3.1 Reactor geometry for calculations28

2.3.2 Transport equations and boundary conditions

29

2.4 Results and di scussion

31

2.4.1 Gas motions at roorn ternperature31

2.~.2 Gas flow and heat t rans fer at epitaxial growth tcrnp crature

33

2.5 Conclusions

37

Nomenclature

39

References

40

Chapter 3 Numerical Evaluation of Silicon Thin-film growth from SiHCI 3 H2 Gas Mixture in a Single-Wafer Horizontal Reactor

5

~).l

Iutroduction

42

3.2 Preparation of epitaxial silicon thin-AIrn

42

3.2.1 R.eactor configuraLlon and chemical reaction

42

3.2.2 13aHic equations governing the epitaxial reactor

44

3.3 Results and discussion

48'3.3.1 Estilnation of Lhe rate of chernical reaction [rOlll the growth rate

48

3.3.2 Transport phenorncna in the reactor

50

3.3.3 Effect of SiHC1 3 concentration on gas flow and ternperature

53

3.3.11 l ~fTecL of Sj lI C1 3 concentration and thennal J jfTusion on growth rate

5f)

3.1 Conclusions

60

N01nenclature

61

Reference

63

Chapter 4 Modeling of Epitaxial Silicon Thin-Film Growth on a Rotating
Substrate in a Single-Wafer Horizontal Reactor~.1

fntroduction

65

66

4.2 Silicon epitau-xial thin-fihn growth process

66

4.2.1 Reactor configuration for experilnents and calculations

66

4.2.2 Basic equations for transport phenomena and chemical reaction

69

4.3 Resul t and discussion

74

4.3.1 Silicon t hin-fi Inl growth and t hickness on the rotating substrate74

4.3 .2 Transport phenoIl1ena induced by rotating substrate78

4. 3. 3 Method to inlprove filnl thickness unifornlity

83

4.4 Conclusions

84

N O'lnenclature

85

References

87

Chapter 5 Model on Transport phenomena and Silicon Epitaxial Growthof Thin-Film in SiHCI 3 -H 2 Systern under Atmospheric Pressure89

5. 1 Introduction

90

5.2 Preparation of sili con epitaxial t hin-filrns

906

5.3 Basic equations governing the epitax:ial reactor

9]

5.4 Mathematical model of the rate process

95

5.4.1 Chcrnical species in the gas phase
5.4.2 Chemical species and adsorption at substrate surface

96

5.4.3 Cherillcal reactions and rate process at the surface

97]02

5.5 Reasults and discussion
5.5.1 Silicon epitaxial growth rate and grown HIDl quality

102

5.5.2 Transport phenornena in the horizontal reactor

103

5.5.3 Surface rate process

104

5.5.4 Evaluation of HCl etching effect on silicon epitaxial growth rate

106

5.5.5 State of surface during epitaxial growth107

5.5.6 Non-linear increase in epitaxial growth rate109

5.6 SUITunary111

N ornenclature

112

References

111

Chapter 6 Effect of Transport Phenonlena on Boron Concentration Profiles in Silicon Epitaxial Wafers

117

6.1 Intro duction

118

6.2 Basic equation for solid-state diffusion

11

6.3 Preparation of epitaxial silicon thin-filrn

121

6.4 Analysi s of gas flow

122

6.5 Results and discussion

123

6.5.1 Boron diffusivity

123

6.5.2 Boron concentration profiles in epitaxial wafers

125

6.6 Conclusions

130

References

1~3 I

Chapter 7 Roughness of Silicon Surface Heated in Hydrogen Ambient 13 ~3
7.1 Introduction

134

7.2 Experimental

13<1

7

7.:3 Rcsul Ls c),ncl discussjon

136

7.1 Conclusions

149

References

150

Summary and Conclusions

153

8

Chapter 1
Introduction11.1 Background1.1.1 Silicon crystal

Crystalline materials are used in many fields of science and technology.

-1

specially,

artificial crystals, such as germaniurn, silicon , gallium phosphide , gallium ar. enid ,are fascinating materials for modern and future microelectronics. Silicon is one of
the rnost popular elcrnent on earth , being included in earth's crust as silicon oxides.
Since siHcon dioxide is quite stable in air silicon crystal rnust be obtained artificiallyusing crystal growth technique. A silicon crystal ingot i grown using the Czochralsky (CZ) method or the Floating Zone (FZ) method. 1 The ingot is sliced to obtainthin wafers, which are polished to have mirror surface for the fabrication of microelectronics devkes. For microelectronic device fabrication regions layers or filn1
with various conductivity type and resistivity must be formed in a wafer using thetechnique of epitaxial growth, diffusion and ion-ilTIplantation. The epitaxi al growthof silicon has been studied and widely accepted as a key teclmology since the fir 'L report in 1957. 2 Currently, a siUcon epitaxial wafer having a very thin epitaxial £]]n1 i 'suitable especially for the fahricaton of rnetal-oxide-semkonductor (MOS) devi es 3- 6
for latch-up prevention and soft-error reduction. In the near future, the dialnet. r ofsilicon wafers become larger than 200 mm to achieve high cost perforrnance in th
fabrication of microprocessor and cornputer n1emories or other device's. Significantly
enhanced silicon microelectronic devices require the ilnprovernent of the qllaJj ty ofsilicon crystal filrns. Funclarnental researches on epitaxial growth are required for
future design of silicon crystal and devices.

1.1.2 Epitaxial growth

Chemical vapor deposition (CVD) is a key technology to produce thin and uniforrn
films of semiconductor crystals or arnorphous materials. Silicon epitaxial growth is2

Olle kind of the CVD, where the filrn obtained is a single crystal over the substrate.
L~or epitaxial growth,

an epitaxial reactor, source rnaterials and substrates arenecessary. Figure 1-1 depicts various phenomena in the epitaxial reactor using gases.
The gases including the source species are introduced from the inlet of the reactor
and flow to the substrate following the transport phenomena in the reactor. In the
preparation of silicon epitaxial thin-films, SiH4 , SiH2 Cb, SiHCb, SiC14 are generally
useJ with H2 as the carrier gas. Although SiHCb is widely used for epitaxial growthof thin-fihns in industrial applications, theoretical analysis of film preparation inthis systern has b en discussed in only a f w papers,52-55 in contrast to the SiH4
11,15,16,26,47,48 and Si fT 2 C1 2 17 , 18,56-58 systenls which have been studied extensively.
In acldilion , a nlodel [or the chemical reaction between SiHCb and H2 has not yet
been fully established.

Chamber
Inlet

Gas~

Surface chemical reaction~~on ~Substrate

Transport phenomena

Fig.l-l Phenomena in an epitaxial reactor.
For Inany case in the indu trial applications the substrate usually rotates on its
axis or revolves to achieve a flat epitaxial film thickness profile. The substrate has
appropriately controlled telnperature which induces the chemical reaction to supply
silicon atorns to the substrate surface. The chamber wall of the reactor is usuallycooled with air to suppress the chemical reaction at the inside of chamber' wall.
Thi temperature environment is called cold wall, which is used in many reactors
for, ilicon epitaxial growth.
Since the analyses of film growth in the existing studies for the SiHCb systenl
were based on boundary layers and equilibrium theory, 52-55 they are limited to regions ill the vicini ty of the growth surfaces and must lnake assunlptiollS about the3

cOllcentration of the reactant gas near the surface . For an analYHis of heterogeneous
chemical reaction, such as epitaxial growth, the species concentrations are usuallyquite different from those at the reactor inlet. Thereforc, the t ransport pbenol1lCna
in a reactor have recognized a: an important subject to be studied. 19 In other words
the tram~port phenomena in an epitaxial reactor must be solved for th analysis ofchemical reactions for the epitaxial growth.
The transport phenOlnena and the chenlical reactions must be clarified for development of new technology in epitaxial growth, since a correct model on the these
phenomena can predkt an actual epitaxial growth and examine th experimental
conditions to reduce the cost of experiments. Issues or subjects to be discussed
for the development of the silicon epitaxial growth technology are so many, such (1,S
type of an epitaxial reactor , transport phenomena in a reactor including a sub traterotation , surface chelnlcal process , dopant concentration profile, process ternper(1,ture and surface roughness.

In this thesis, these are studied by theoretical andexperimental methods.

1.1.3 Epitaxial reactors

Here , types of the epitaxial reactors are reviewed briefly, since the characteristicsof the films prepared depend on the type of reactor used, for example, (a) pancake,(b) cylinder, (c) barrel, (d) horizontal, (e) single-wafer horizontal and (f) singl -waf r
vertical type as shown in Fig. 1-2.
A number of pancake reactors (Fig. 1-2 (a)) are cornmonl y lmcd worldwide toprepare silicon epitaxial thin-filrns. Pancake reactors have a large VOlUI11C and a tallcold-wall chamber in which significant natural convection is likely to occur. C as s
are introduced frorn the inlet nozzle at the center of the reactor and are exhausted
through the outlets at the bottom of the reactor.
Figures 1-2 (b) and (c) schematically show the cylinder 20 and the barrel typereactors. These reactors can perfonn the epitaxial growth on 111any substrates at4

t he same tirne ascribed to t heir large volume and tall cold-wall chamber as well as
the pall cake reactor. Gases are introduced from the top of t he reactor and go out
through the ouLlets at the bottom of the reactor.

SU\bstrate

t

....
Q)

gas

L)

E
~

~~

~ c:=

..c:

o

c::::-<-

(b)

(a)

(c)

Chamber

Chamber
Gas

Gas

Substrate

~

~

i

i

11c::~'~-Susceptor

~

(e)

(d)
Gas
(i)
L)

E
~
..c:

ttt

Substrateo(f)

Fig.1-2 Reactor types for sil icon epitaxia I growth.

(a) pancake reactor, (b) cyli nder

reactor, (c) barrel reactor, (d) horizontal reactor, (e) single-wafer horizontal reactor and(f) single-wafer vertical reactor.

The horizontal reactor shown in Fig. 1-2 (d) is one of the oldest reactor which has
substrates along the gas stream. Gases flow horizontally from the inlet to the outlet
over the substrates which are arranged in the gas flow direction. Since the substrates
cannot be rotated or revolved in this reactor due to its mechanical configuration ,th thickness profile is adjusted by tilting the sllsceptor 7 , 8 to obtain t he unifonn
thicknesses5

A single-wafer horizontal reactor (Fig.1-2 (e)) has only one substrate, which rotatesin the reactor chamber. Currently this type of reactor is widely used jn both researchand industry; some demonstrate excellent capabilities for preparing large-dialTlCLcr
films on substrates.
Figure. 1-2 (f) depicts a single-wafer vertical type reactor in which gases flow
vertically from the top to the bottorn of the reactor. The ubstrate can roLate withhigh rotation rate to achieve very high growth rate. 9
All reactors for silicon epitaxial growth use the ten1perature environment of cold-

wall, in which the transport phenomena are very cornplicated because of the coexistence of high and low temperatures, which affect gas density, physical constantsof gases, species transport and chemical reactions. To describ the relation betw en
the epitaxial film quality and the reactor type both the transport ph nomena andthe chernical reactions should be solved simultaneously and hould be made clear.

1.1.4 Transport phenomena

Transport of mass, momentum, energy and chernical species occurs in the epitaxial reactor and strongly affect the growth rate and the quality of epitaxial film.
Generally, the transport phenomena, especially gas flow motions, are studied mainly
by two methods, the gas flow visualization and the numerical simulation. The gas
flow visualization is an experiment by which the motions of gases are observed as
those of tracer particles or as photo images by the schlieren n1ethod. Since the gas
flow visualization clearly provides the key information on the transport phenornena
in the reactor, this technique has been commonly used for studying gas rnotions
in various fields . Io However, there exist some problems with respect to the cxperirnenLal Lechnique of the tracer rneLhod, [or example, tracer maLerial and equiprncllt
for observation. The reliability of the tracer method must be exarnined since thetracer motions sometimes disagree with the actual gas motions due to a quite higher
density of tracer particles than that of gases. For avoiding an errorneous results,6

it is quite necessary to cornpare the gas rnotions by the gas How visualization withthose by nurnerical calculations of transport phenornena, which are perforrned based
Oll the equations of the transport phenomena using a computer.

Nurnerical sill1ulatlons of transport phenonlena related to film growth by CVD
hav be 11 reported in many papers for various types of reactors. Although rnost ofthem adopted an analysis based on a two-dimensional grid, three-dimensional models
11-16 have b

com possible recently because of marked improvement in the computing

environment. The transport phenomena in pancake 17 ,18 and cylinder 20 ,21 reactors
having jet nozzles and outlets for gas, however, have not been analyzed by any threedimensional models considering the relatively complicated geometry of the reactors.
Unstable and asyrnmetric gas flows are likely to occur in such reactor chambers
because of their great height and large Rayleigh number. Although several notable'l udies on th pancake reactors have been reported such as gas flow visualization22

and nUlnerical calculations. 23-25 large part of the transport phenomena in the

pancake reactor is still unclear due to the diffuculty in the analysis. Chapter 2 ofthis the i describe' the heat and flow in a pancake reactor based on experiments
and numerical calculations.
CVD phenOlnena in horizontal reactors have been studied by many researchers.
12-16,26-33 Because of its low height and low Rayleigh number

the gas flow tends tobe table even in a cold-wall environment. Kleijn and Hoogendoorn 13 stated that theanalysis obtained by a two-dimensional model had nearly the same accuracy as thatby three-dimensional model for horizontal reactors with low Rayleigh number andhigh aspect ratio. This inlplie that a two-dimensional analysis can be, in some cases,
applied with suill ient accurac
in a horizontal reactor. In

to predict transport phenolnena and growth rates

hapt r 3 of this thesis, the transport phenomena in asingle-wafer horizoutal r actor ar focused on using the two-dilnensional calculations.
The ubstrate rotation should be discussed as well as the reactor type and geometry. The susceptor whi h holds the substrate usually rotate or revolve in theepitaxial r actors shown in Fig. 1-2 in a basic operation. The rotating substrate7

induces various changes in transport of reactive gases and ternperature above andaround itself. In vertical reactors,9, :34-39 the rotating substrate gives relatively simple laminar gas flow above the substrate which provides high growth rate and flat
thickness profile.9,37-39 The reason why the vertical reactor has simple laminar flowis that the direction of gas introduced from the reactor inlet is the same as that of
the rotating axis of the substrate. In a single-wafer horizontal reactor, however, gas
flow is very complicated because the substrate rotates around a vertical axis while
the mainstrearIl flows horizontally. In this reactor , the effect of substrate rotaUon
cannot be described by a two-dimensional model because of the gas motion inducedby the rotation. Although many works to model three-dimensional transport phenomena in a reactor have been reported both experimentally and theoretically,40-46
the rotation of the substrate in horizontal reactors has not yet been discussed. In
Chapter 4 of this thesis, the effect of the substrate rotation in a single-wafer horizontal reactor is discussed for the first time.
To evaluate correctly the transport phenomena in a reactor , the dependence ofthe physical properties of the gas on the gas composition must be considered as wellas the dependence on temperature since reactants are often introduced into reactor'
at relatively high concentrations in actual processes to achieve high productivity.
However , this dependence has been considered 13 , 17,31,47-49 but not enough. In addition, thermal diffusion l l , 13-15, 17, 18, 2G, 28-30, 47-51 is expected to affect growth rat s inchlorosilane-H 2 systen1 because the difference in rrlOlecular weight of SiH2C1 2 SiHC1 3
and SiC14 from H2 is very large. The dependence of growth rate, temperature andgas velocities on the gas compositions should be taken into account for the predictionof the silicon epitaxial growth. This issue is discussed in Chapter 3 of this thesis.

l.l.5 Surface process

An epitaxial growth is a result of chemical processes at a substrate surfac . An
appropriate model for describing the chemical reactions should be developed Lo

8calculate the epitaxial growth rate under the transport phenornena over wide rangesof the growth conditions of the species concentration and the growth temperature.
In sHicon epitaxial growth, the growth rate of silicon film increases nonlinearly within rea ing reactant concentration and finally saturates at a certain value dependingon th growth temperature. A nonlinear dependence of the growth rate on the con'entration of SiHCb in a SiHCb-H2 system is partly attributed to the changes in
the gas flow, temperature fields and the thermal diffusion in the reactor. However,the contribution of the transport phenomena are rather small to describe the entire
llolllilleu,r beha.vior of th ' fihn growth rate , because the cha.1lge ill the tru,nsport phe1l0lnena cannot predict the saturation of the growth rate. The elenlentary reactions
should be therefore investigated for an analysis of the growth rate but appropriate
and practical methods for the theoretical approach have not been established. An
allaly is of complex phenornena in sHicon epitaxial growth is quite difficult and stillr quires large arIlounts of cornputatioll tirne. The most important thing is to develop'OInpact model which can predict the actual characteristics of the epitaxial film by
the epi taxial reactor wi thin a tolerable calculation time.
At the substrate surface , the initial step of the rate limiting process is considered
to be a cherIlisorption of the reactan s on the silicon surface followed by a decomposition of the chemi orbed pede and a desorption of the by-products. 59 Based on the
di . u sion for the aturation of the ilicon growth rate 60,61 it is sugge ted that the
Eley-Rideal me hani D1 62 i applicabl to describe the epitaxial growth rate. By several rcsearchers,63-69 some lTIodified Langmuir-type models or CVD model have been
di 'cussed to describe the actual rate process for chemical vapor deposition (CVD)or etching process. However, these studies have been focused only on the surface
reaction proces es neglecting the transport phenomena including momentum, heatand species transport throughout a reactor.
To discus quantitatively the epitaxial growth rate, both surface chemical reactions
and transport phenomena in an entire reactor should be taken into account since
the concentrations of chelnical spedes at the substrate surface are usually quite9different from the concentration at the entrance of the reactor. However, this kindof studies are only a few. Hierlemann et a1. 70 calculated silicon epitaxial growthrate in a SiH 2 Ch-fb system ill a showerhead-type rapid therrnallow pre sure CVD
reactor using kinetic data from data base packages. 72, 73 Narusawa 71 show d that thesaturation of the epitaxial growth rate in a SiC1 4 -H 2 system can be described by thmodel of the transport phenomena in conjunction with the surface reaction model
66,67 considering adsorption, surface diffusion and heterogeneous chemical reaction.

For a SiHC1 3 system, theoretical studies should be performed with determining therate constants of the surface chemical processes based on the experilnental results ofthe epitaxial growth rates. Experimental and theoretical approaches to the. e topics
are discussed in Chapter 5 of this thesis.

1.1.6 Dopant concentration profile

7

c

o

~

~c..>

/

c:
o

Transition width

c..>

~

c

~

desirableoo t----~-.J
Epitaxial-film

Substrate
Depth

Fig. 1-3 Dopant concentration profile near the interface between substrate and epitaxial
film

Quality of an epitaxial wafer should be also discussed as well as the growth rate andthe film thickness profile. In an epitaxial wafer, the concentration of dopant atoms
changes at the interface between the epitaxial film and the substrate as schematicallyshown in Fig. 1-3. Although an abrupt profile is desirable, an actual profile inevitably

10has sorne width where the boron conentration changes gradually. The abruptnessof the boron concentration profile lS evaluated as the transition width. 4 The issue oftransition width is very old but has recently become a new problem, since a smalltransition width is required for the improvement of device integration. 74
Boron concentration profile in a silicon wafer is formed mainly by two nlechanisms:
autodoping 7S- 77 and solid-state diffusion 76 ,78 as schematically shown in Fig. 1-4.
There have been many reports on the autodoping of dopant species incorporated ina substrate, such as boron,4,79-81 phosphorus,76,79,82,83 arsenic,76,79,81,84-88 gallium
70 and anUmony.76, 79,83,89 For antimony, phosphorus and arsenk, reduced-pressure
epitaxiR,l growth is eO'ecLive to ohtain sharp profiles. 79,82,85,86

solid-state diffusion

Epitaxial film

Highly-doped substrate

Fig. 1-4 Major mechanism for transport of B atoms from substrate to epitaxial film

The epitaxial wafers for NIOS devices generally have a high-resistivity p-type epitaxial film on a low-resistivity p-type substrate, and have boron atoms as dopantsin both the epitaxial film and the substrate. Studies have been made on boron
autodoping (1) by reduced-pres ure epitaxial growth,4, 79, 90 (2) by addition of Hel
to the anlbient during epitaxial growth using silane 80 or (3) by masking the backof the substrate with, ili '0 11 dioxide. 76,87,88 (1) is reported to enhance autodoping79
and (2) cannot b applied to th widely used chloro ilane system. (3) is effective
and wid ly us d but in 'ufficient.
11

The boron concentration profile can be sharpened by decreasing the growth telnperature, where soHd-state diffusion is d0111inant rather than autodoping. ~urth -rmore, the problern of crystal qualit y4 in atrrlosphcri -pressure low-tcrnpcraLurc epitaxial growth has been solved by using very high purity ga: es. 82,91-94 However, thegrowth rate and the throughput are decreased with decrea.'3ing growth temperature.
Therefore, atmospheric-pressure epitaxial growth at reasonably high telnperature
should be pursued to achieve both an abrupt boron concentration profile and a highcost performance.
From the viewpoint of fluid dynamics, especially under atmospheric pressure, gas
recirculation due to natural and forced convection occurs easily to transport the
dopant species via the gas phase. These conditions may enhance C1utodoping andbroaden the dopant concentration profile since the convection carrie the dopant
species to and from the substrate via the gas strealn in the reactor. Such a flow
field increases the gas residence time which must be short to obtain all aorupt
interface 95 ,96 in a compound ,semiconductor hetero-epitaxial wafer.
Natural convection can be suppressed when the height of gas flow region in thereactor is very small. Although such a configuration is currently employed in modern
single-wafer horizontal reactors, autodoping and boron concentration profile in theepitaxial wafer grown in such an environment have not been sufficiently discus d.
The sharper doping profile was reported 97 to be observed in a single-wafer epitaxial
reactor rather than in a batch-type reactor; however , the rnechanisrn has not yet heen
made clear. Moreover, although autodoping has been discussed [or the gas phas inclose proximity to the substrate 75- 77 ,80, 98-]02 or in relation to the growth condition,such as the substrate rotation rate,9 the difference in the dopant concentration profile
between epitaxial reactors having various rnain gas flow conditions has not been
discussed. Therefore, the boron concentration profiles are studied in Chapter 6 ofthis thesis mainly from the viewpoint of the transport phenornena.

12

L.l.7 Process Le1nperaLurt and surface roughnes5

For silicon wafers with srnall diarneter, the processes with temperatures up to1473 K have been often used for the improvement of Czochralski silicon wafers as
high-temperature annealing.103 In the near future, the diameter of silicon wafers is
xpected to become larger than 200 rnm to achieve high cost performance in device
fabrication.

In processes for wafers larger than 300 mm, thernlal stress and slip

generation will pose serious problems, because slip generation of a large-diameter
wafer is very sensitive to the ten1perature distribution within the wafer. 104 However,
it is very difficult to develop a heating rnethod that has a very uniform temperature profile over the entire wafer. To achieve a slip-free process, the wafer process
teTnperature should be shifted to near or lower than 1000°C where the mechanicalstrength, such as the yield stress, is high. 105
Recently several researchers 106 - 110 have discussed surface roughness of a siliconsurface heated below 1000°C in hydrogen ambient.

For silicon epitaxial growth

proce s the heat treatlllent in hydrogen ambient is desirable to remove the nativeoxide film on the slicon substrate.

Ohkura et al. 106 reported that prebaking inhydrogen ambient under 100 torr led to a minimum degree of microroughening, andthat the native oxide films acted as a protective film against roughening at the siliconsurface. However, Ueda et al. 107 showed that many pits on the silicon surface were
fonned at 1000°C through a heating process in hydrogen ambient. They proposedthat surface roughening might be due to the behavior of oxygen atoms incorporated
in the silicon crystal. Muraoka et al. 108 showed that the low-ternperature prebaking
process used in epitaxial growth resulted in a rough epitaxial silicon filn1 surface.
Yanase et a1. 109 studied the silicon surface after hydrogen annealing in detail, andfound that the surface annealed at 900°C had lnany pits which might be due tothe reaction of silicon with snlall all10unts of moisture and oxygen in hydrogen gas
in conjunction with the incomplete rellloval of the native oxide film. Although thechernical reaction between silicon and hydrogen gas was -ignored in these studies,13

Gallois et al. 110 recently showed that the etch rates of silkon by hydrogen gas atvarious ternperatures were considerably fast.
To realize a desirable heat treatment process , roughening of the silicon surface
during the removal of the native oxide film at the ternperatures lower than 1000°C
should be studied. Moreover, surface roughening under atmospheric pressure must
be investigated because atmospheric-pressure epitau'<:ial growth can be applied to
improve cost performance in microelectrk device fabrication. The rnechanisn1 ofsurface roughening is investigated in Chapter 7 of this thesis, since it has been
unfortunately unknown in spite of the importance of such research.

141.2 Scope of this thesis
After this chapter of introductioll , silicon epitaxial growth and epitaxial wafer
are discussed [rorn the viewpoints of transport phenomena and surface chemical
reacUons.
In Chap. 2, gas flow and heat transfer in a pancake reactor for silicon epitaxial
film growth are discussed based on a gas flow visualization technique, numericalcalculations and growth rate profile of silkon epitaxial film. In the gas flow visualizatioll, rnotions o[ NH 4 CI or Si0 2 particles are observed using a high-sensitivity
analogue camera. The observed gas How motions are compared with those obtainedby three-dimensional calculations of Lhe transport equations o[ the mass, momentum
and encrgy.
In Chap. 3, an evaluation of sili con epitaxial thin-film growth using the SiHChTT2 systelll ill a single-wafer hori:0ontal reactor is discusscd. Since SiHCl:3 is widelyused for the epitaxial growth of silicon thin-films in industrial applications, thetrarl port equations for gas velocity temperature and concentration of chemicalpecies in SiHCI 3 -H2 systen1 are solved, taking into account of the dependence ofgas properties on temperature and composition. By comparing the measured andcalculated growth rates under atmospheric pressure, the increase in growth rate withternperature and SiHCh concentration are discussed by assUllling an Arrhenius-type
expression for the chenli 'al reaction of SiHCb and H2 on a substrate. Transportphenomena in the 'ingle-wafer horizontal reactor are discussed in detail.
In Chap. 4, the effect of sub trate rotation on transport of reactive gases andepitaxial growth rate is investigated for a single-wafer horizontal reactor using amodel and experiInents. The govenling equations for gas velocity, temperature andchemical species tran port are solved for the SiHCh-H2 systern for silicon thin-film
preparation. The eff ct of the rotating Illotion of the substrate is discus 'ed under
the conditions giving nearly unifornl filnl thickne s profile.
In Chap. 5 a transport and epita..'{y model to describe silicon epitaxial filn1 growth
in a SiIIC1 3 -II 2 system is developed by nUIuerical calculations aI1d cOlnparison with15

experiments. The rate of epitaxinJ growth is calculated by cOlnputing the transport of rnomenturn, heat and chemical species ill a reactor incorporating ch rnicalreactions at a substrate surface described by the Eley-Rideal 1110cl 1.

The reac-tion processes determining the growth rate consist of chemisorption of SiHCh anddecomposition by H 2 , rate constants of which are evaluated from the model andmeasured results. The state of the surface during the epitaxial growth is also discussed considering the intern1ediate species, elementary reactions and rate linliting
processes.
In Chap. 6, the boron concentration profile in silicon epitaxial wafers grown underatmospheric pressure is investigated in two types of epitaxial reactors, a singlewafer horizontal reactor and a pancake reactor. Transport phenomena are studied
in these reactors by numerical calculations or by a gas flow visualization technique.
The difference between the measured boron concentration profile and the calculated
one using Fick's law is assumed to be due to autodoping which is mainly due torecirculation of gas in an epitaxial reactor.
In Chap. 7, surface roughness of a silicon wafer heated at 800- 1100 DC underatmospheric pressure in hydrogen ambient is studied. Haze of the surface is discussed
from the viewpoint of the competitive etching reactions of silicon and silicon dioxidewith hydrogen gas. The behavior of surface roughness wi th pressure and heatingtime agrees well with that predicted by the pit fonnatioll lTIodel in this study.

16

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(1994).

22

Chapter 2
Gas Flow and Heat Transfer
in a Pancake Reactor

232.1 Introduction

In this chapter, the transport phenomena in a pancake reactor, especially gas flow
motions, are visualized and calculated using a three-dimensional model including
the inlet, the outlets, the susceptor and the bell jar as the crucial parts . The
silicon epitaxial thin film is actually prepared in the pancake reactor under the same
conditions as those in the gas flow visualization and the numerical calculations since
the growth rate profile also provides information on the gas flow direction especiallyin a single-wafer horizontal reactorl.
The aim of this investigation is to study correctly the gas flow and heat transfer
in a pancake reactor in a steady state. The resul ts from gas flow visualization,
numerical calculations and growth rate profile observed in the pancake reactor underatmospheric pressure are compared with each other for the first time. Additionally,
the gas flow motions in a pancake reactor are discussed in conlparison with those ina single-wafer horizontal reactor.

2.2 Gas flow visualization

2.2.1 Reactor configuration and experimental conditions

Figure 2-1 shows the pancake reactor used [or thjs study. Substrates from 3- to
6-inches in diameter are held on a 0.42 rn diarneter susceptor. This reactor has one
inlet nozzle at the center of the susceptor frorn which the gases flow to the topof the quartz charnber. The reactor also has two outlets connected to the baseplate, through which the gases flow out of the reactor chamber. Gas motions arevisualized and observed under atmospheric pressure at room teluperature and 1423K
when the susceptor was not rotated. The gas velocity and the pressure at the inlet
were l.0 TIl S-1 and l.013~3 x 10 5 Pa, respectively.
Small tracer partidet:l of S102 and NH4 CI were generated in the reactor to observe24

Lhcir rnotions in the gas strcam. At room temperature, NH 4 Cl particles were produced from the chemical reaction of NH 4 0H and HC!. A small plate containing
NH 4 0H aqueous solution was placed on the susceptor, then HCl gas flowing at 0.521/111in was introduced from the inlet nozzle. As HCl gas approached the susceptor)
tracer particles of NH4 Cl were generated. The motions of the transported tracer particles were observed under the hydrogen flow rate of 40 l/min from the inlet nozzle.
The temperature of the susceptor was raised to the epitaxial growth temperature of1423 K, under a hydrogen gas environment with a flow rate of 40 l/min. The gases of
SiIICh and CO 2 were introduced through the inlet nozzle at the flow rate of II/min.
Small tracer particles of Si0 2 were generated from the chemical reaction between
SiHCb and CO 2 in the gas phase.

Symmetry Plane

Inlet Nozzle

Susceptor
Skirt

for calculations,

Z

Ba~p:ly

X

OutlettOutletFig.2- 1 Schematic diagram of a pa ncake reactor for gas flow observation . One-fourth of
the reactor is used for the calculation .

As shown in Fig. 2-2, the n10tions of Si0 2 or NH 4 Cl small particles were observed
under a two-dimensional sheet of Ar+ laser (4W) light and were recorded on video by
a high-perfonnance analogue camera and an image processing system composed of25

SUPER EYE C2847 and DVS-3000 (Hamamatsu Photonics Co. , Ltd. , Hamarnatsu).
The SUPER EYE system has been used for optical observation in various fields , suchas air flow analysis in a clean roorn 2 and cell biol ogy 3. The sheet of Ar+ laser Hght
enabled visualization of the tracer motions at an angle of about 15 degrees from thefront of the reactor chamber. Because the video image of this system included weaknoises from the radio induction heating system of the reactor, the video image wastaken immediately after cutting off the heat induction current.

SUPER EYE(VTR camera)

4w Ar+ion
Laser

Image
processor
OutletOutletH2 + HCI (R. T.)
H2 + SiHCI3 + CO2 (1423K)
Fig.2-2 The observation system for the smoke tracer method .

2.2.2 Solution of problems underlying the tracer method

Gas flow visualization at high temperature in such a large reactor is very di fFicult because of problems such as the influences of temperature, gas composition ,observation period and therrnophoresis of the tracer particles in nonisothermal flow .
Under inappropriate conditions, tracer motions may show a completely different behavior from that of the actual gas motions. These problems must be solved prior toperforming the gas flow observations.
Observations of gas motions at a temperature higher than 1273 K are often dan-26

gerous because equiprnent located near the susceptor as well as the operators are
exposed to intense heat radiation frOITl the heated susceptor through the large window designed for the observations. To avoid this, some parts of the reactor and theequipment are modified to assure safe operation when the susceptor is heated tothe epitaxial growth temperature. The upper half of the charnber window rnade oftransparent quarLz glass is concealed by a cloor equipped wi th waLer cooling pipes,
h n 'c the observation is concenLrated on the region near the susceptor where theepitaxial film growth occurs.
The gas COITlposition for observaUons cannot be exactly the sarne as that· for theactual epitaxial growth. The gas flow visualization requires the 8i0 2 or NH 4CI trac-en; in L11 , present method; however, these particles do not exisL during epitaxial
growth. 8ince tracer particles weigh several orders of magnitude more than a carrier
gas uch as hydrogen, they occasionally show quite different motions from those ofcarrier gases, for example tracers travel to the bottom due to gravity even in a horizontal tream. Thermophoresis 4 also causes a problem' the different motions of theparticle fron1 the gas tream are due to a temperature gradient 5 . Thermophoretic
force tran 'ports the tracer particles away from the hot surface of the susceptor andleads to a layer near the surface having a very small amount of tracer particles, which
is ,om time incorrectly a umed to be a stagnant layer 4 , 6. Very small 8i0 2 particles
in hydrogen gas at atmospheric pressure have nearly the same thermophoretic coefficient as that of Ti0 2 particles 4 which are usually used for gas flow visualization 4 , 7.
Additionally 8i0 2 desirably ha n1uch lower density than Ti0 2 . For these reasons,8i0 2 par'ticles are chosen as tracers for the observations at high temperature. At
room temperatur , NH 4 CI particles are used for the visualization, because NH4CI
has lower d nsity than 8i0 2 and 8i0 2 cannot be produced at room temperature
frOll1 8iHCl 3 andO 2 , NH 4 CI particles are used only at room temperature because

they d conlpos at high temperature, Another reason for using 8i0 2 and NH4 Cl
inst ad of Ti0 2 i that th source gases, such as NH4 0H, HCI, 8iHCb and CO 2 )do not cause any 111eLalhc contanlination in the reactor, thus allowing an accurate
27

epitaxial growth rate with excellent film and without unexpected perturbations.
Immediately after introducing and generating the tracer particles, the tracer rnotions at various regions in the reactor chamber can be observed clearly sinc theconcentration of the tracer particles is still low. However, this situation lasts only
for several seconds after the introduction of the tracer particles B since the tracer particles increase in concentration and begin to appear as a dense white cloud. Because
a high amount of reactant is necessary to produce the tracer particles, the concentration of the generated particles is rather high and it is often difficult to continue
the observation for a long period of time. Furthermore, it is quite difficult to adjust
the concentration of the tracer particles. Therfore, the steady-state gas motions
cannot be observed by any ordinary method, the naked eye or a normal-sensitivity
camera. In this study, the high-sensitivity analogue camera makes it possible toperform the observation for more than 20 minutes after stopping the generation of
8i0 2 or NH 4 CI particles. This observation reveals a state with a very low concentration of small-diameter tracer particles, which can be assumed to be the motionsof hydrogen gas without any tracers.
The tracer rnotions should be compared with the calculated motions of gases
cornposed of hydrogen. By showhlg the agreement between the observed tracer
motions and the calculated gas rnotions, the gas flow motions during the epitaxial
growth can be clarified.

2.3 Basic equations governing the epitaxial reactor

2.3.1 Reactor geometry for calculations

As Fig. 2-1 shows, the pancake reactor has two symmetry planes: one including theou tlet and the other rotated 90 degrees from the outlet. The hatched region between
the two symmetry planes, which conlprises one-quarter of the entire reactor, is used
for the numerical calculations as the representative geometry. With this geometry,28Lhc lTIodel is sin1plified to reduce the calculation time.

Although the susceptor

is usually rotated dUrlng the epitaxial growth) this model cannot be applied to
calculate the effect of the susceptor rotation. The difference in gas motions between
the results with and without rotation was examined prior to a series of experimentsof the visualization. There was no significant change for the range of rotation rate
between 0 and 10 rpm; therfore) the results in this study are also applicable to thecase where the susceptor has small rotation rates.

2.3.2 Transport equations and boundary conditions

To exarnine the results from the visualization method) it is necessary to compare
the results of gas motions obtained experimentally with those obtained by the nu111Crical calculations of the transport phenomena in the reactor in a steady stateu, ing three-dimensional Cartesian coordinates. The governing equations for the gas
velocity are as follows.
Con ervation of mass:(2-1)
Conservabon of momentum:

8puu + 8pvu + 8pwu = _ 8p _ 8Txx _ 8Tyx _ 8Tzx
8x
8y
8z
8x
8x
8y
8z )

(2-2)

8puv

(

8pvv

8pwv

8p

8Txy

8Tyy

8Tzy

--a;: + 7fY + --a;- = - 8y - 8x - 8y - 8z )
8 puw

8 pvw

8 pww

8p

----a;- + ay + -----a;- = - 8z + pg -8Txz 8Tyz 8Tu
8x - 8y - 8z )

2-3)

()
2-4

where

28U _~ (8U + 8v + 8w)1 )Txx = -p, r
T.

yy

8x

3

8x

8y

8z

= _P, r28V _ ~ (8U + 8v + aw)l8y

Tzz = _p,

3

8x

8y

8z

r28W
_~3 (8U+ 8v + 8w)1
8z
8x 8y
8z

8U 8V)
Txy = Tyx = -p, ( 8y + 8x )
29

)

(2-5)
(2-6)
(2-7)

(2-8)

Tyz = T zy =-Tzx = Txz = -~ (~~ + ~;) ,(2-9)~ (~~ + ~~)(2-10)

In equations (2-1)- (2-10) p, p and I-L are the density pressure and viscosity of thgas and u, v and ware velocities in the x-, y- and z-directions r spectively. Th
gas velocities, u, v and w, are set to be zero on all surfaces of the solid walls asboundary conditions. The gas velocity and pressure at the inlet are 1.0 rn S- 1 and1.0133 X 10 5 Pa, respectively, which are consi tent with the actual observation.
The temperature, T, in the reactor is expressed by the following energy equation.
Conservation of energy:

apuCpT + apvCpT + apwCpT = _~ (A aT) + ~ (A ~T) + -f!- (A aT). (2-11)ax
ayaz
ax ax ay ay az az
In this equation, Cp is the heat capacity of the gas at constant pressure, and A is
the thermal conductivity of the gas.
The effect of radiation in the gas phase is of n1inor significancebecausemonoatomic and diatomic gases, such as hydrogen, helium and nitrogen, radiat
weakly, even at high temperature.

Radiation from the susceptor surface affectsgonly the temperature of the quartz chamber wall . According to the assumptions
mentioned above, the heat transfer by radiation is ignored in this study and thefollowing boundary conditions are imposed on equation (2-11). Th temperature of
the susceptor surface, Ts , is 1423 K. The temperature of the quartz wall surrounding
the entire gas stream is assumed to be 300 K . In fact, the ternperature at the outside
surface of the quartz chamber wall did not exceed 500 K even when the susceptor
was heated to 1473 K. Therefore the difference in the wall temperature between thecalculations and actual value should be within 200 K, and this difference is assum'dto be allowable in such an environment having a very large ternperature difference.
The gas density obeys the ideal gas law

pM
p= RT'

30(2-12)

where M is the 1110lecular weight of the gas aud R is the gas coustant.
'1'0 solve the transport equations described above, the calculation domain is divided

into a nonuniform mesh with 31 x 34 x 49 grid points (total 51646) in the X-, yand z-directions. Although the use of so-called boundary fitted coordinates (BFC)
has been very cornmon for several years to rnodel flows in complex geometries, thercctallgular griddillg on Cartesian coordinates are used in this study because theresults from these coordinates in various geometries are qualitatively correct 10 andthe calculatation time is shorter than that on BFC. To estimate the influence due
to rectangular gridding on Cartesian coordinates and the number of grid points, it
was found that the results frorn about half the grid points were essentially the sameas those in this paper. The gas is assun1ed to be composed of 100% hydrogen. The
gas properties of H2 , such as viscosity, heat capacity and therrllal conductivity, aretCtk ~n fronl the bterature 11 - 13 . Each physical constant is expressed as a function of
tenlperature.
bquution (2-1) - (2-12) for ga velocity and temperature are discretized into finite

clHf rence fonnulae and 'olved based on the SIMPLER algorithmlO. The calculations
ar p rformed on an Apple l\.'I acintosh IIcx personal computer with a Tektronix RP88
coprocessor board. The calculations in this work took over six months.

2.4 Results and discussion

2.4.1 Gas 1notion at rOO1n te1npeTatureI\s a prelill1illary strp, the gas flow visualizaUons and the calculations arc per[ornled at rOO1l1 tenlperature in order to evaluate the capability of the visualization
syst rn used, e pe ially its ability to allow observations for long periods of time.
Figure 2-3 shows the observed particle strearnlines at roorn temperature. Observations could be made frOll1 the start of the introduction of the tracer particles toth end of their generation, and even up to the state where they were present at31

very low concentrations. The entire process was carried out for more than 20 mil1-ute~ without any trouble. Gases including the small tracer particles of NH 4 Cl aretransported to the top of the quartz chamber. After reaching the top , the ga es flow
downward along the sidewall and approach to the center of the susceptor.

-

Fig.2-3 Gas motions observed in the pancake reactor at room temperature . Hyd roge nflow rate is 40 I/ min.

sus:ceptor
Fig .2-4 Vector diagrams of gas flow velocity at room temperature in the pancake reactor .
Hydrogen flow rate is 40 I/min .

32

These observed recirculating gas streams are compared with the calculated ones.
The calculateu gas strcarns are shown in Fig. 2-1, which are obtaincu in thc stcauy
state. The calculated gas motions also show large recirculation. Since the gases
spread throughout the entire quartz chamber, the gas velocity along the sl;lsceptor
is much lower than that near the top of the chamber. The gas motions in Figs. 2-3
and 2-4 show good qualitative agreement. It is therefore concluded that the gasesin the pancake reactor recirculate in the chamber.

2.4.2 Gas flow and heat transfer at epitaxial growth temperature

In this section, the gas rnotions in the pancake reactor at the ternperature for
epitaxial growth are discussed. As mentioned above, the observation is limited to
tbe vicini ty of the usceptor. Although the diruneter of the Si0 2 particles during theob crvation could not be measured the diameter measured after the observation was
found to be less than 20 {lm under an optical microscope. This value ind1cates thell1axilnuln diruneter because it was measured after many processes such as aggregation in the gas phase, sedimentation on the susceptor and sticking on the chamberwall. The diameter of particles observed in this study is assumed to be much lessthan 20 {lm and to be close to Il-lm which is easily recognized by the SUPER EYE.
In the reactor, near-steady-state motions of the gas flow are observed, as shown in
Fig. 2-5. The ga es flow from the outside toward the center of the susceptor, thenthese flow upward fron1 the inlet nozzle and downward along the sidewall of thereactor chrunber.
For a lnore precise discussion, numerical calculations are perfornled for this gas
flow ysteln. The calculated gas lnotions are shown in Fig. 2-6, which are the same
CLS the traccr n10Lions obscrv

d in Fig. 2-5. At the epitaxial growth temperature thegase near the usceptor flow parallel to the susceptor. Figure 2-6 shows that thegases along the susceptor have high velocity because of the expansion of gas volume
near the heated susceptor. These gases flow upward at the center of the susceptor
33and arc accelerated by the gases introduced frorn the inlet nozzle.

Fig.2-5 Gas motions observed around the susceptor in the pancake reactor . The temperature of susceptor is 1423 K and hydrogen flow rate is 40 Ij min .

outletFig .2-6 Calculated gas flow motions in two vertical slices of the pancake reactor . Slice
A is the plane enlightened by the laser light and slice B is that including the outlet . The
temperature of susceptor is 1423 K and hydrogen flow rate is 40ljmin .

34

Although the gas motions at the top of the reactor chamber cannot be observedin the visualization because of safety problems, the results of calculations show thatthe gas rDoUons are essentially similar to those at room temperature in the entire
reactor chanlber.

susceptor
Fig.2-7 Contour diagram of temperature in the pancake reactor. The temperature ofsusceptor is 1423 K and hydrogen flow rate is 401/min.

During these gas motions in the gas phase, the temperature near the center ofthe susceptor is higher than that at the outer edge of the susceptor and near thechanlber wall as hown in Fig. 2-7. The temperature profile in Fig. 2-7 tends toindue natural convection because the temperature near the susceptor is higher thanthat near the top of the chamber. However the gas motions are found to luaintain ahorizontal flow. The downstreaming of gases along the chaluber wall forces the gaseson the su ceptor to flow horizontally toward the center of the susceptor. The forced
horizontal gas flow is considered to suppress the generation of natural convection.
The luaximum gas velocity in the horizontal direction appears at a position about

O.03- 0.05IU above the susceptor, as shown in Fig. 2-6. When this distance is assumed35

as the typical length the Grashof and Rayleigh nurnbers near the susceptor are
estimated as about 300, which is much slnaller than the critical Rayleigh number

1tl.

The gas motions can hence be considered to be in a near-steady state, as observedin this study.
The pancake reactor is sometimes called the vertical reactor because it has beeD
speculated that this reactor provides uniform and vertical gas flow toward the 8U8ceptor 15 . However, the gases near the susceptor in this st.udy behave like those in asingle-wafer horizontal reactor according to the discussion above, and coin ide.' wi th
the re ults of Oh and co-workers 9 , 16. To confirm the gas Illotions obtained fr0111 theobservations and numerical calculations epitauxial silicon film is prepared using the
SiHCb-H2 system under the same conditions of gas flow rate and temperature as
discussed above. When gases flow over the substrate, the chemical reaction by whichsilicon film growth occurs results in consumption of the SiHC1 3 molecules, thus thedepletion of SiHCb leads to a higher growth rate at the upstream side and a lower
one at the downstream side. This growth rate profile is usually observed in a singlewafer horizontal reactorl. From the viewpoint of the gas flow direction, th actual
growth rate profile in Fig. 2-8 clearly shows that the upstream side correspond tothe outer edge of the susceptor and the downstream side corresponds to the centerof the susceptor. The trend of the observed epitaxial growth rate profile is in good
agreement wHh those predicted by observations and numerical calculations of gas
motions.
In this study, the three-dimensional calculations can also estirnate the effect of
the location of gas outlets because these calculations take into consideration theposition of the outlets in the reactor chamber. Figure 2-6 shows that the gas flow
motions above the susceptor are alrnost symmetrical around the inlet nozzle locatedat the ce~ter of the reactor chamber. The influence of the position of the outlet on
epitaxial growth is negligible in the pancake reactor.
In industrial applications, silicon epitaxial thin filrns with a very uniform thickness
profile are produced on the substrates. The results obtained in this study do not36

show th~ conditions required to obtain good un iforrnity. Thus nl0difying the gas
flow rate, the temperature profile on the susceptor and the design of the nozzle jet 8
is a suitable way to achieve good thickness uniformity. Increasing the diameter orheight of the reactor chamber rnay generate several vortices in addition to the large
recirculation strearn discussed in this study. In the pancake reactors discussed by Oh
and co-workers 9 , 16) the height of which was twice that in this study, the existence of
two recirculating flows in opposite direction was shown at higher fiow rates. In thissituation, gas streams in the pancake reactor become very complicated and unstable
and the variation of the growth rate on the substrate due to such gas streams may
he averaged to obtain a fiat profile of the thin film hy rotating the susceptor or by
unstably changing gas strearns.

1 .40 r - - - - - - - , - - - - - . - - - - , - - - - - , - - - ,Outer

Center

1.35

<-

--7

E
[

1.30

"-"

.y
Q)

1.25

~
~

~

1.20

o
CJ

1.15

~

1.100

20

40

60

80

100

Position from the inner edge of substrate (mm)Fig.2-8 Observed growth rate profile of silicon epitaxial film in the pancake reactor . The
temperature of susceptor is 1423 K and hydrogen flow rate is 40l j min including 0.7
mol% of SiHCI 3 .

2.5 Conclusions

The transport ph non lena in a pancake reactor for preparation of silicon epitauxial

37

thin filn1s have been discussed experimentally and nU111erically. The motions of tracers composed of low-densi ty materials) such as NHt! Cl or Si0 2 ) can be observed for avery long period using a high-sensitivity analogue canlera. The gas motions arc numerically calculated from the viewpoint of transport phenomena. These results are
consistent wi th those indicated by the growth rate profile. A large recirculating flowin the reactor charrlber exists at both room temperature and the epitau"Xial growthtemperature. It is concluded that the gases near the susceptor flow horizontally inthe pancake reactor under atrnospheric pressure for epitaxial silicon film growth.

38

Nomenclature
Cp : heat capadty at constant pressure(J kg- 1 K- 1)

y : acceleration due to gravity(m S-2)

M: 1110lecular weight of gas(kg mol-I)

p : pressure(Pa)

Ii : gas constant(J mol- 1 K-1 )T : tcrnperature(K)u : fluid velocity in x-directloll(m 8- 1)

'U : fluid velocity in y-direction(m S-1)

fluid veloci ty in z-di rection(m S-l)10 ::1: : coordinate in horizoutal direction(rn)y : coordinate in horizontal direction(m)'" . coordinate in vertical direction(m)(Wln - 1 K- 1)/\ : thennal conducti vi ty of gas
J-L : viscosity of ga'(Pa·s)

p : density of gas(kg m- 3 )39

References[1] Chapter 3 in this the is.
[2] M. Inoue, T. Shirai, T. Yoshida and T. Okada J. Visualization Soc. Jpn., 14,
34 (1994).
[3] E. Kamitsubo, Y. Ohashi and M. Kikuyarna, Protoplasnw, 152, 118 (1989).

[4] D. 1. F'otiadis and K. F. Jcn. en, J. Crystal Growth, 102, 743 (1990).
[5] L . Talbot, R. K. Cheng, R. '0/. Schaefer and D. R. Willis, J. Fluid Meeh. 101
737 (1980).

[6] F.C.Eversteyn, P.J.W.Severin C .II.J .v.d.Brckcl and H.L.Pcck, J.Eleclr·oehern.
Soc., 117, 925 (1970).
[7] E. P. Visser , C. R. Kleijn C. A. M. Gover ~, C. J. Hoogendoorn and L. J. Giling.

J. Crystal Growth, 94, 929 (1989).
[8] T. Suzuki, Y. Inoue, T. Aoyama and M . Maki, J. ElecLroehem. Soc., 132 , 14 0
(1985).
[9] 1.H.Oh, C.G.Takoudis and G.W.Neudeck J. Electrochem.Soc. 138 , 551 (1991).
1[10] S. V. Patankar ,Numerical Heat Transfer and Fluid Flow (McGraw-Hill New
York , 19DO).

[11] I(agaku Binran (Handbook of Chcmistry) (lwanall1i Tokyo 19 1) 3rd cd.)
1Chap. 6, p. 1I-39 [in Japanc c].

[12] I(agaku B,tnran (Handbook of Chelnisiry) (Twnnallll : Tokyo 1984) 3rd cd. )Chap. 6, p. II-71 [in Japanese].

[13] I(agaku Binrun (Handbook of Chcnlistry) (Twanmni) Tokyo, 1984) 3rd cd. ,Chap. 9, p. II-239 [in Japancse].
[14] C. P. Jackson and K. H. Winters, Int. J. Num. Methods Fluids , 4, 127 (1984).
[15] F. Shimura, Semiconductor Silicon Crystal Technology (Academic Press, San
Diego, 1989) Chap.5, p.204.

[16] 1. H. Oh and C. G. Takoudis, J. /lppl . Phys. , 69 , 8336 (1991) .

40

Chapter 3
Numerical Evaluation of Silicon Thin Film
Growth from SiHC1 3-H 2 Gas Mixture in aSingle-Wafer Horizontal Reactor

413.1 Introduction

The primary purpo e of this Chapter is to develop a l1un1erical rnodel which canpractically describe silicon epitaxial filnl growth fronl a SiHCb and Ih gas rnixturc
in a single-wafer horizontal reactor. To accurately analy7,c the transport of rea tantgases in a reactor with highly nonisothermal flow , a computational rnodel to predirt
gas flow, temperature and concentration fields is presented taking into account thechange in gas properties due to gas composition and temperature. The rate of asimplified surface reaction schen1e is evaluated to describe film preparation processes
since the elenlentary reaction schemes have not bcen fully clarified yet. The reaction
rate is estirnated using rneasured and predicted growth rates. The effccts of Sill C1 3
concentration and therrnal diffusion on the growth rate are also discussed.

3.2 Preparation of epitaxial silicon thin film

3.2.1 Reactor configuration and chemical reaction

Figure 3-1 shows the geometry of the reactor studied in this work. For our analysisof thin-film preparation on a heated substrate, we consider the preparation of silicon
epitaxial thin films by the thermal decomposition of SilfC1 3 with H2 gas . 1'h gas
mixture is introduced into the reactor and reacts at the surface of a substrate held
horizontally in the reactor (1 in Fig. 3-1). The susceptor is designed to prepar an
epitaxial layer on an 8-inch-diameter wafer. The suhstrate is heated to 1450 K using
infrared furnaces through the reactor walls consisting of quartz glass.
In order to evaluate the film growth rate in the case of the reactor with nonuniformly distributed temperature and gas flow fields, the mass, rIlornentum and energy
transport equations must be solved. The present model consists of transport equations and a chemical reaction at the surface of the substrate. Substrate rotation andheat of reaction are ignored in this Chapter. Crystalline defects due probably to42

flue particles formed by gas-phase reaction were not observed for the present reactor.
Consequently, effects of thermal non-equilibrium states induced by radiation by the
infrared furnaces, such as enhancement of gas-phase reaction, are considered to bevery small, thus these effects are also ignored in the analysis. We focus mainly on
the growth rate of a 8i-thin film at the center of the substrate and investigate thedependence of the growth rate on temperature and the concentration of 8iHCb.
gas in( SIHC~)('

IR furnace
~

300K

~L

quartz glass wall

730K - 770K

50mm ' - - - - - - .

substrate

~

o
o

C')

susceptor
1373K - 1453K

Fig. 3-1 Single-wafer horizontal reactor for preparation of silicon film .

in rnany previous theorebcal analyses of the filrn preparation processes surface
reactions are described usillg a phy~ical mechanism such as the mass flux by diffusion l - 9 or a collision Inodel. lO - 12 The e models nlay be appropriate when all elen1enLary reactions [or fUrn [onnation are understood. However, neither the elementary
reactions nor the rate-lin1iting process in the reactions have been determined for the
8i HC1 3-H 2 ~ysterll. In this case, using an Arrhenius-type expression for the chemical reaction and considering a sinlplified reaction schelne is a practical method
to nlOdel all the reactioll phellOlnena. We therefore consider the preparation of asiliC'on film on the ba is of th following overall reaction:
8iHCh + I-h -+ 8i + 3HCl.

(3-1)

In this Chapter, we determine the rate of chernical reaction of equation (3-1) by
Lh nUln rical Inodel de~cribed later. The activation energy, E) i assumed to be43

that proposed by Eversteyn 13 (E =: L38 X 10 5 J rnol- 1 ) for the react]oll-111nited
regime since tbe path of the chemkal reaction is assUlned to be the same over awide temperature range. The pre-exponential factor , which has not been reported
to date, is estimated in this Chapter..

3.2.2 Basic equations governing the epitaxial reactor

The transport phenomena in the reactor in a steady state are so] ved using twodimensional Cartesian coordinates. The governing equations [or the gas velocity are
as follows:
Conservation of mass:: (pu) + : (pv) = O.
ux
'
uy

(3-2)

Conservation of momentum:

0 ( Ou)8881.1) + 8V) - ap.
-(pUlL)+ -(pVU)= -8 ( 2J-L-J-L- + -8 ( J-L8x
ay
8x
8J~
oy
oy
8y
8x
8x

(3-3)

8
8
8 ( 8V)a ( 8V) 0 ( 8U) 8p
ax (pUV) + 8y (pVV) = 8y 2pJoy + ox J-L ox + 8x IL 8y - oy + pg. (3-4)
In eqs. (3-2)- (3-4), 1.1 and v are horizontal and vertical velocities, p, p and J-L are thedensity, pressure and viscosity, respectively, of the mixLure of SiHCb, H2 and HClgas.
The gas density obeys the ideal gat:) law
pMav
p= RT '

(3-5)

where Mav it:) the local average molecullar weight of the gas and R is the gas constant.
The gas velocities, 'U and v, are set to be zero on all the surfaces of the solid walls
as boundary conditlons. The gas velocity and pressure at the inlet are 0.67 m 8- 1
and 1.01~3 x 10 5 Pa, respectively.
The temperature distribution, T, in the reactor is expressed by the following
energy equation:

44

COllHervation of energy:aaa (aT)a ( aT)
A~ + ~ A~ .
uX
uy
uy

~) ((JCpT'U) +~) ((JCpTv) = ~

(x

'1

(y

ux

(3-6)

In this equation, Cp is the heat capacity of the gas at constant pressure, and A thethermal conductivity of the gas.
The temperature of the substrate surface, T s , is varied between 1393 K and 1153 K.
This temperature is nlaintained constant by continuously monitoring the temperature and 'ontrolling the input power of the infrared furnaces. The temperature
at the inner surface of the walls imnlediately above and below the substrate (region 2 in Fig. 3-1) is higher than the temperature of the other walls. The outersurfaces of these quart~ walls are , however, cooled with a sufficiently large amountof cold air, so that it is reasonable to neglect absorption of radiation heat by thetransparent walls. Since the concentrations of SiHCl 3 and HCI are low, effects ofradiation heat on these gases are assumed to be negligible. According to the asSU111ptions mentioned above, we ignore heat transfer by radiation in equation (3-6)
and ilnpose the following boundary conditions on the equation. Since accurate measurenlent of the temperature in region 2 is extremely difficult, the temperature isestinlated ernpirically and assumed to vary linearly with the substrate temperaturein the range between 730 K and 770 K. The reactor wall illustrated by the hatchedregion in Fig. 3-1 is treated as a conducting wall with the thermal conductivity ofquartz glas . The outer surface of thi region (dotted lines in Fig. 3-1) is taken tobe t3urrounded by adiabatic walls. The temperature of the other reactor walls isregarded as 300 K since the walls are continuout3ly cooled with water.
Conservation of chemical species i (i = SiHCb, H2 and HCI) is described by thefollowing equation:
Cons rvation of pecies:

Tn this equation Wi is the mass fraction of species i. The diffusion coefficient, Di is45

assumed to be the binary diffusion coefficient of species i in Ib gas since the nlole
fraction (not mass fraction) of species other than J-h is small. The rnass transportphenomena driven by the temperature gradient (thermal diffu ion) are described. by
the terms relating to

Dr, the thermal diffusion coefficient. Dr is expressed as(3-8)

where Cti is the thermal diffusion factor of species i.
At the inlet of the reactor the composition of the SiHCl 3 and H2 gas mixture isexpressed in terms of the average molecular weight MW given by(3-9)
where Xi and Mi are the mole fraction and molecular weight of 'peci s z.

Theaverage molecular weight at the inlet ., MW, is varied b tween 2 x 10- 3 and 55 x
10-3kgmol-1, which corresponds to pure H2 and 39.7 rnol% (or 97.

wt%) SiB 13

in H2 , respectively.
At the surface of the substrate mass changes due to chemical reaction on th
surface are considered in the boundary conditions. Assuming that the reaction ofequation (3-1) is a second-order reaction, the mass rate of consumption or generationof species i at the surface is expressed as(3-10)
where k is the rate constant for the reaction expressed as k = A exp (-E / RT) andthe values of the molar stoichiometry coefficient, Vi, are - 1 for i = SiHCh and fb ,and 3 for i = HCl. The concentration of each species at the surface is governed bya balance between the rate of chernical reaction and the diffusion processes driven
by the concentration and temperature gradients. The boundary conditions on thesubstrate surface are therefore

R=' +. = - D.Bwi_DTo]nTJc

JT

P t oyiBy ,(3-11)

where jc and jT denote the diffusion fluxes driven by the concentration and temperature gradients.

46

The accurnulation of siljcon per unit tirne and area of the surface(3-12)

gives the growth rate of silicon film as(3-13)

where PSi is the density of Si, and the factor 6 x 107 is used for the unit conversionof n18- 1 to lim min-I.
To solve the transport equations described above, the calculation domain is divided
inLo <1 nonunjforrn mesh with 78 x 52 grid points in the x- and y-directions. Then theequations for gat; velocity, ternperature and rnass of chemical spedes are discretized
into fini Le difference forrnulae. In this Chapter, the computational fluid dynarnics
code FLUENT (ver. 3.03)14 is used as the solver.
The gas properties of H2 such as viscosity, heat capacity and therrnal conductivity
arc taken from the l1terature. 15- 17 The properties of SiRCl 3 and HCl are given by
Pollard and Newman. I8 Each physkal constant is expressed as a function of temperature using a polynomial fit.

The properties of the mixed gas are estimatedtheoretically. 14
The binary diffusIon coefficients of SiHCb and HCI in H2 are esLilnaLed wiLh Lhe
Inethod described in the literature. 19 Following Holstein,20 the thermal diffusion
coefficients of SiHCl 3 and HCI are obtained. Although the thermal diffusion coeffidents also vary with the local species concentration, the values of the coefficients inthis sirnulation are expressed only as a function of temperature at a representative
concentration because of a limitation on the format of physical constants in the
FL UENT code. The concentration at the center of the substrate surface is used as
the representative concentration .

47

3.3 Results and discussion

3.3.1 Estimation of the Tate of chemical Teaction fT07n the gTowth Tate

The solid line in Fig. 3-2 shows the calculaLed growth rate, Vc , as a function or
the temperature at the substrate surface, Ts , for an average n10lecular weight at the
inlet of MW=6.7 x 10- 3 kgmol- 1 . This figure shows that the growth rate increas 'IS
with Ts. In this calculation, the pre-exponential factor , A in the rate of chemica1
reaction, k, was fixed so that Vc calculated for Ts = 14.23 K agrees with the growthrate measured at that temperature when the substrate did not rotate (the solid
circle at the center). The rate of reaction is therefore estimated to be(3-14)

5.0 r - - - - r - - - - - - - r - - - - - - r - -- - - - - - ,
~ 4.8
E

E
::l

~ 4. 6

>
q)-

e4.4
..c

~

~ 4.2

4.0 ' - - - - - - - I I . - - - - _ - - - I_ _ _- l_ __ --.J
1380
1400
1420
1440
1460
SubstratE~ temperature, T s (K)Fig. 3-2 Comparison of calculated (solid line) and measured (solid circles) growth rat es.
The average molecular weight at the inlet , MW, is 6.7 X 10- 3 kg mol -I.

Figure 3-2 illustrates that the values of Vc obtained by the present nlodel withequation (3.1) agree well with those obtained experimentally in the temperature
range from 1393 K to 1453 K. Although the rate-limiting step for preparing silicon
film in the SiHC13-H 2 system is generally recognized to be mass transport, the48

dependence of growth rate on temperature in the temperature region considered hereis successfully described by the activation energy obtained under reaction-limited
conditions. It is also considered that the simplified reaction scheme, equation (3-1) ,in which only the concentrations of the source gases are taken into account, cancl scribe the filrn growth process. The rnechanisms of ehernical reaction contributing
to the filrn growth are hence considered to be unchanged irrespective o[ the ratelilniLing step.

6o~----~----------~----------~--~

4

6

8

3
Average molecular weight MW ( X 10- kg/mol)

Fig. 3-3 Comparison of calculated (solid line) and measured (solid circles) growth rates.
The substrate temperature, T s , is 1398 K.

Figure 3-3 shows the dependence of experimental and calculated growth rate upon
the average molecular weight of gas at the inlet , MW, for a substrate temperature of
T=1398 K. The calculated growth rates increase with the average molecular weight,

which corresponds to an increase in the concentration of SiHCh at the inlet. The
slight deviation between the calculated and measured values is considered to be due
to urface chemical processe which will be discussed in Chapter 5. Although the~lopc of the calculated line is sOlnewhat higher than t hat of the n1easured values

the present calculation d crib e t he experimental trends satisfactorily.

49

3.3.2 Transport phenomena in the reactor

As described in §3.2, the amount of reactant gas actually consumed on the substrate is affected by distributions in the gas velodty temperature and cone ntrationof each reactant gas. In this section, we present typical calculated gas velocity, telllperature and concentration fields in the reactor for the case of an average molecularweight MW = 6.7 X 10- 3 kgmol- 1 and a substrate temperatur Ts = 1423 K.

Fig . 3-4 Streamlines in the reactor . The average molecular we ight at the inlet, J\;[W, is3

6.7 X 10- kg mol - 1 and the substrate temperature , Ts , is 1423 K .

Figure 3-4 shows t he streamlines for the gas flow in the reactor, while Fig. 3-5 is a
contour plot of the gas velocity in the horizontal direction, u. Figure 3-1 shows thatthe streamlines above the substrate are almost parallel to the surface except theregion near the leading edge of the subRtrate, where the gaR stream from the inlet
divides into the strearns above and below the substrate. Flow induced by naturalconvection was not observed in the reactor. The gas flow above the centcr of thesubstrate is, as described in Fig. 3-5, found to have a paraboli c profi le, so that theflow is regarded to be nearly developed.

50

0.74

Fig. 3-5 Contour lines of gas velocity component in the x direction, u, in the reactor. The
average molecular weight at the inlet, MW, is 6.7 X 10- 3 kg mol- 1 and the substratetemperature, Ts , is 1423 K .

_ _..;;.80....
5_ _
918

___--1o30-----'"

t:==:=::tIJ~~~H~o1370~~· -~~-----1251140--~- ~ 1030---,.,.---....- - - -Fig. 3-6 Contour lines of temperature, T, in the reactor. The average molecular weightat the inlet, MW, is 6.7 X 10- 3 kg mol- 1 and the substrate temperature, T s , is 1423 K .

The contour plot for the gas temperature, Fig. 3-6, reveals that the gas temperature increases rapidly at the leading edge of the substrate. However , the contour
lineB near the center of the substrate are almost parallel, similar to those of the ga51

velocity.

.,.-0.50 0.41

1~

t::::===::;, ~~~~~~0~_. 32~~~40
0.24 0.15
---.

0.1 5

0.320.41_____ 0.50..;..._ _ _, . , . - -....

Fig. 3-7 Contour lines of mass fraction of SiHCI 3 . The average molecular weight at the
inlet, MW, is 6.7 X 10- 3 kg mol- 1 and the substrate temperature, Ts , is 1423 K.

Fig. 3-8 Contour lines of mass fraction of HC/. The average molecular weight at the
inlet, MW, is 6.7 X 10- 3 kg mol- 1 and the substrate temperature, Ts , is 1423 K.

The transport of reactant gas takes place in the environment described above.
Figures 3-7 and 3-8 show the contour diagrams for the concentrations of SiHCb and
HCI, respectively. The concentration of SiHCl 3 decreases as the substrate surface isapproached because of consumption by the chemical reaction contributing to silicon
film formation, while HCI concentration increases due to generation on the substrate52sirnul taneously.
12r--r------,-----~------~------~~

o~~------~----~------~----~~~

o

50

100

150

200

Position from the leading edge of substrate (mm)Fig. 3-9 Profile of calculated growth rate on substrate surface along x direction. The
average molecular weight at the inlet, MW, is 6.7 X 10- 3 kg mol- 1 and the substratetemperature, Ts, is 1423 K.

These figure' also indicate that the concentrations of SiHCh and HCI are notunifornl along the substrate surface.

This results in a non-uniform growth rate

profile along the gas flow direction as shown in Fig. 3-9. The growth rate is largest
at the leading edge of the substrate and decreases toward the trailing edge.

3.3.3 EJJect of SiHCl3 concentration on gas flow and temperature

Since the present model, which considers simultaneous transport phenomena anda chelnical reaction can explain the measured growth rates well, the effects of varying the SiB

b cone ntration on gas velocity and temperature field is investigatedfurther.
l-i'igure ~)-l 0 ,how the gas . velocity profile in the x-direction, u, above the center of1

the substrate for Ts = 1423 K and MW between 6.7 x 10- 3 and 55 x 10- 3 kgrnol- .
At a low av rage mole ular wight the gas velocity attains its maximum near thecentral position betwe n the sub trate (h s = 0111m) and the upper wall of the sub-53

strate (h s = 20 mm). When the MW increases, Le., the SiHCb concentration at the
inlet becomes larger, the position at which the velodty becomes maxirnum shifts
toward the substrate surface. Equation (3-1) indicates that the volume of gas increases by a volume of 1 mole of gas during formation of 1 mole of solid Si and 3moles of Hel gas. The gas volume increasing in a unit time was estimated frorn
the calculated growth rate of the silicon film.

By conlparing this volllrne withthe volumetric flow rate above the substrate where there was no chernical reaction (MW = 2 x 10- 3 kgmol- 1 in Fig. 3-10, the increase in the gas velodty with

MW, shown in Fig. 3-10 , was almost explained. Since Hel gas is generated onlyat the substrate surface, it is reasonable to ascribe the significant increase in gas
velocity near the substrate surface to production of Hel by the chemical reaction.

~ 1.0 r----~~::::------r----~--.__,

E
::J_

0.8

+-'

c(l)

c

& 0.6
E

o

u

:>,

+-'

0.4

'u
o

~ 0.2
~

C

2 0.0

.§
I

" " - - - - . L - -_ _--L_ _ _-L-_ _----l

0

5
10
15
20
Distance from substrate surface, h s (mm)Fig. 3-10 Calculated profile of velocity in the x direction, u, above the center of thesubstrate. The substrate temperature, Ts , is 1423 K.

The decrease in gas velocity near the reactor wall with increasing MH! is thought
to be caused by the change in the temperature field near the wall. Figure 3-11 shows
the change in temperature profile above the center of the substrate as MW lncreascs.
. . .,
At low average molecular weight, the temperature decreases almost linearly withthe distance from the substrate, hs . With increasing average rnolecular weight,54however, the ternperature between the substrate and reactor wall tends to decrease
more rapidly. One reason for this trend is considered to be that increase in gas
temperature by heat transported frorn the hot substrate is suppressed because of
the large heat capacity of gas of a large MW. The ternperature on the surfaces

or the walls facing the substrate rnight decrease accordingly. The temperature of
the wall surface is, however, fixed in the simulation because of the reason describedin §3.2 .2. Figures 3-10 and 3-11 indicate that an increase in the average rnolecularweight changes the flow and ternperature fields and that the gas flow is not fully
develop 'cl over the substrate when the COlH.:eIltration of SiTlCh is large.

1400

Q'
;

1200

~::J

~ 1000

~
E

~

800

600

o

5

10

15

20

Distance from substrate suriace , hs (mm)Fig. 3-11 Calculated profile of temperature , T, above the center of the substrate. The
substrate temperature, TSI is 1423 K.

If the average molecular weight is extrernely low, and thus the gas velocity andtemperature fields in the reactor are sufficiently close to those for pure H2 system,
a n10del that does not consider the effect of gas composition may be adequate forpredicting transport phenomena in the reactor. However, as demonstrated here, sucha model will fai 1 to predict the growth rate for large MW because the conlposi tionof gas has a considerable effect on the flow and ternperature fields.

55

3.3.4 Effect of SiJICl3 concentration and thermal diffusion on growth rate

Relatively high concentrations of reactant gas are often used in industrial prOCCf-lf-lCf-l
in order to achieve large growth rates. We therefore investigat d the effect of SiIICh
concentration on the growth rate further. The solid line in Pig. 3-12 shows the change
3

1

in growth rate with the average molecular weight [or MW up to 55 X 10- kg Inol- .
At low values of MW the slope of the graph is relatively large, but the slope becoD1cs
flatter as MW increases.
25~----~----~----'------'-----'~

.~

E

-

20

~

'-' 15

><.9
Q)-

~

10 -

..c

~

e 5

(!)

o~----~----~----~----~----~~

a

10

20

30

40

50
-3

-1

Average molecular weight, MW ( x 10 kg mol)Fig. 3-12 Calculated growth rate as a function of average molecular weight, MW. Solidline indicates the result obtained by considering thermal diffusion; the dashed line is thatwithout considering thermal diffusion.

It is recognized empirically that growth rate does not increase in proportion to thc
concentration of reactant gas. One possible reason for thc non-proportionality oft n
encountered in the actual film preparation process is thought to be etching of thr.
silicon film by Hel synthesized at the surface. As previously discussed, silicon fihn
preparation is governed by transport of the reactant gases and chelnical reaction toform the silicon film. Beside these mechanisms, the reaction(3-15)

56

is likely to occur and reduce the growth rate of silicon filrns. The contribution of thisreaction will be significant especially when the concentration of Hel above the silicon
film is high, that is, the consumption of reactant gas, SiHCb is high. Nevertheless,we have delTIonstrated the non-proportionality of the growth rate by the present('alculation without accoullting for the etching reaction by HCl. Consequently, thedependence of the growth rate on MW rnay be attributed to changes in the transportof reactant gases which arc caused by the changes in gas flow and temperature
distributions with MW as shown in the previous section.
The relationship between the growth rate of the silicon film and the flux of reactant
molecules is expressed by equation (3-11). This equation states that the growth of
the film is governed by the balance between reactant consumption due to reaction
at the surface of the substrate and diffusion of the reactants driven by concentrationand ternperature gradients. The concentration gradient in the reactant gas flux,

jc depends on the flow and temperature distributions which vary with the average
Inol cular weight MW. The flux due to therrnal diffusion, jT, depends on MW
because the flux is proportional to the ten1perature gradient above the substrate
which also varie ' with MVV. For these reasons, it is expected that the growth rate
will not increase linearly with the concentration of SiHCh·
The effect of thennal diffusion is investigated further by using the present numerical model. The flux driven by the telTIperature gradient, jT, depends on thethern1al diffusion coefficient , D!.
The value of D!
\. for SiHCl 3 in H2 increases withthe average molecular weight of gas mixture, May, as shown in Fig. 3-13. Although
the value of aSiHCl3 decrease slightly with increase in the SiHCh concentration,
the increase in the value of PWSiHCbwH2 causes

Dr to become large as shown in the

figure. The da hed line in Fig. 3-12 shows the growth rate predicted by neglecting
thennal di ffusion i. .,Dr being set to zero. Figure 3-14 shows the relative difference

betw ~en the dashed and solid lin

in Fig. 3-12, den10nstrating the effect of thern1al

diffusion on the gTowth rate. These figures illustrate that thermal diffusion of thereactant gas suppresses the growth rate as the average molecular weight increases.
57

The effect of a difference between the molecular weight of the carrier and reactant
gas has been discussed by Kleijn.21 To demonstrate the effect of thermal diffusion on
the concentration of SiHCh above the substrate, additional calculations were carriedout in which no surface reaction was assumed. Figure 3-15 shows that the SiIICh
concentration in the absence of thermal diffusion (dashed line) is aln10st uniform
between the substrate and wall surfaces. In contrast to the dashed line, the SiITCb
concentration including the effect of D'[ (solid line) becOlnes slnaller as the substra.tesurface is approached although no consumption at the surface is assumed. Because
the molecular weight of SiHCb is much larger than that of H 2, SiHC1 3 Inolecule
are transported away from the hotter region near the substrate toward the colder
mainstream and the growth rate is reduced. The present calculations indicate thatthe effect of thermal diffusion is not negligible in predicting the growth rate. A
calculation model that does not consider the effect of thermal diffusion will overestimate the growth rate especially when the SiHCb concentration, and thus thegrowth rate, is high.
"';- (J)

8

"';-

E
())
~

If

7

a

or-

x

6

"

f- ~

5

E<l>

'u

4

'+=

Q)
0

u

3

c

0

'w

:E

2

i5
~

E

I.-

<l>

L

f-

2

3

4

5

6

Average molecular weight M av (X10 3 kg/mol)

Fig. 3- 13 Thermal diffusion coefficient ,nT, for SiHCI 3 in H2 as a fun ctio n of the averagemolecular we ight of gas mixture , Mav.

58

12r------r------.-------r------.------~----~

~
t9

> 8
,~
<l>
U
C
<l>

a;

::::

is
<1>

>

'''::;

4

~

Q)

a:

o~----~------~------~------~------~----~

o

20

60

-3
Average molecular weight , MW (X10 kg/mol)

Fig . 3-14 Calculated change in growth rate due to the thermal diffusion as a functionof average molecular weight , MvV. The ordinate is the relative difference between thepredicted values of growth rates , solid and dashed lines in Fig . 3-12 .

Z 0.74
<")

U

I

U5

3

<")

072
•

U

I

i:I5
without D T'0§ 0.70'''::;

u

~

~

CI)
CI)

~

~ 0.68o15
10
5Distance from substrate surface, h s (mm)20

Fig. 3-15 Mass fraction profiles of SiHCI 3 calculated for the condition of no surface
reaction . The solid line indicates the result obtained by considering thermal diffusion;
the dashed line is that without considering thermal diffusion.

593.4 Conclusions

Preparation of epitaxial silicon thin films using the SiHC1 3-H 2 system has been
discussed using a numerical model. The model predicts gas velocity, temperature,
concentration of the gases and growth rate. Thermal diffusion and changes in thephysical properties of the gas with ternperature and composition are accounted for.
The dependence of the growth rate of the siHcon film on the substrate temperature and the concentration of SiHCb could be adequaLely lllodeled by assuming
an Arrhenius-type rate expression for chemical reaction on the substrate surface.
The apparent activation energy of the reaction was 1.38 x 10 5 J mol- 1 with the preexponential factor of 2.65 x 10 3 m 4 mol- 1 S-l. The nonlinear dependence of growthrate on the concentration of SiHCh was attributed to the change in the gas flow
and temperature fields in the reactor with the SiHC1 3 concentration. The effect ofthermal diffusion in the present system was found to result in a reduced growthrate. Thermal diffusion of SiHCh , which transports SiHCh molecules away fromthe hot substrate surface, had a considerable effect on growth rate especially when
the growth rate was high.

60

N onlenclature(In1 rn 01- 1 s - 1)

A : pre-exponential factor of' raLe consLant(Jkg-1K- 1 )()p : heat capacity at constant pressuref)i : binary diffusion coefRcicnt of species 'i in

TIz

D; : thcrrnal diffusion coefficient of species i in Ih
E : activation energy of rate constant(m 2 S-I)(kg m- l S-I)

(J lTIol- 1)(m S-2)y : acceleration due to gravity

hs : distance frorn substrate surface(m)[i] : mole concentration of species i(mol m- 3 ).7 ' : cli[rusion flux driven by concelltraLion gradient(kgn1- 2 s- 1 ).J'l' : diffusioll flux driven by tClnperatul'c gradiellt(kg1n- 2 s- 1)(ln4 11101- 1 S-1)

k : Arrhenius-type rate constantl"'vlav : averagc molecular weight of gas Inixture(kg mol-I)

Alsi: lllolecular weight of 8i(kg Inol- l )lvI( lIlolecular weight of specie z(kg mol-I)

MW: average molecular weight of gas n1ixture at reactor inlet(kg mol-I)(Pa)

p : pressure(J mol- 1 K- l )R : gas constant~ : mass rate of change in species i by chemical reaction(kg m- 2 S-I)

RSi : rnass rate of change in 8i by chen1ical reaction(kg m- 2 S-I)

(K)

T : ten1pcrature?L : fluid velocity in x direction(m S-I)

fiuid velocity in y direction(1118- 1)'U :(p,mmin-l)

Vc : growth ratex : coordinate in horizontal direction(n1)

Xi : mole fraction of specics i(-)

y : coordinate in vertical direction(In)thermal diffusion factor of species i(-)

A : thermal conductivity of gas mixture(Wm- 1 K- l )

(Xi :

61

(Pa·s)/1, : viscosity of gas n1ixturc
Vi :molar stoichiometry coeffidcnL for species i in chernical reaction(-)

P : density of gas mixture(kg m- 3 )PSi : densi ty of 8i(kg m- 3 )Wi :mass fraction of species i

(-)

62

References[1] C. It Kleijn and C. J. l1oogendoorn, Chem. Eng. Sci. 46, 321 (1991).
[2] l.H.Oh, C.G.Takoudis and G.W .Neudeck, J. Eiectrochem. Soc.138, 554 (1991).
[3] 1. H. Oh and C. G. Takoudis, J. Appl. Phys. 69 , 8336 (1991).
[4] R. L. Mahajan and C. WeI, Trans. ASME, J. Heat Transfer 113 ,688 (1991).
[5] P. B. Chinoy, D. A. Karninski and S. K. Ghandhi, Numer. Heat Transfer, Part A
19 , 85 (1991).

[6] P. B. Chinoy, D. A. Kaminski and S. K. Ghandhi, J. Eiectrochem. Soc. 138, 1452
(1991).
[7] F. Langlais, C. Pl'cbcnde and J. r. Couderc, J. Cryst. Gruwth 113 , 606 (l991).

[8] C. R. Kl ijn, C. J. Hoogendoorn, A. Hasper J. Holleman and J. Middlehoek J.
liicclTuchC7TL. Soc. 138 ,509 (1991).
[9] A. 11. Dilawari and J . Szekely, J. Cryst. Growth 108 ,491 (1991).
[10] II. K. Nloffat and K. F. Jensen, J. Electrochem. Soc. 135 , 459 (1988).
[11] M. E. Coltrin R. J . Kee and J . A. Miller, J. Electrochern. Soc. 133 , 1206 (1986).
[12] M. Frenklach and H. Wang, Phys . Rev. B 43 , 1520 (1991).
[13] F. C. Eversteyn Philips Re . Rep. 29 45 (1974).
[14] FLUENT

ser's Manual, Vcr. 3.0 (Fluent Inc., Hanover, 1990).

[15] J(agaku Binran (Handbook of Chenustry) (Iwanami Tokyo, 1984) 3rd ed.,Chap. 6, p. 1I-39 [in Japane e].

[16] J(agaku B'inran (Handbook of Chenustry) (Iwanami, Tokyo, 1984) 3rd ed.
Chap. 6, p. II-71 [in Japane~e].

[17] Kagaku Binran (Handbook of Chenustry) (lwanami Tokyo, 1984) 3rd ed.
Chap. 9, p . II-239 [in J apanese].
[18] P. Pollard and J .

eWlnarl J. Electrochem. Soc. 127, 744 (1980).

[19] R .C.Reid , J .M. Prausni tz and B.E.Poling, The Properties of Gases and Liquids(McG raw-Hill New York 1987) 4th ed.
[20] W . L. Holstein , J. Electroche1n. Soc. 135 ,1 788 (1988).

63

[21] C. R. Klcijn, J. Electroche1n. Soc. 138, 2190 (1991).

64

Chapter 4
Modeling of Epitaxial Silicon Thin-Film Growth
on a Rotating Substrate in a Single-Wafer Horizontal Reactor

654.1 Introduction

In Chapter 3 the silicon epitnxial growth rate fronl a SiTlCl 3-11 2 gas lHixtUH'
in a single-wafer horizontal epitaxial reactor under atmospheric pressure was discussed experimentally and theoretically using numerical calculation based on twodimensional Cartesian coordinates. However the effect of substrate rotation cannot
be described by a two-dirnensional model because of the gas motion induced by therotation.
In this Chapter, calculations based on the three-dimen.sional coordinates including
the substrate rotation are therefore perforrned to evaluate and discuss the effect of
the rotation on the n1ass , lllomenturn, energy and chen1ical species transport a11d
silicon epitaxial growth rate in a single-wafer horizontal epitaxial reactor. The effectof the rotating motion of the substrate is discu ed under the condi Lions gi ving nearly
uniform film thickness profile. Since SiHCb i widely used for the epitaxial growthof silicon thin-films in industrial applications, the epitaxial growth in the SiHCb-f-b
system is discussed.

4.2 Silicon epitaxial thin-film growth process

4.2.1Reactor configuration for experiments and calculations

For obtaining epitaxial silicon thin-filIns experin1entally, the single-wafer horizontal reactor having the geometry shown in Fig. 4-1 is used, in which the sub. tratc
on the susceptor usually rotates. Gas n1ixture of sn 1C1 3 and 112 gas is i l1troduccd
into the reactor and reacts at the surface of an 8-inch-diarneter substrate held horizontally on the rotating susceptor in the reactor. The substrate is heated to ] 398 K
using infrared furnaces through the transparent quartz glass walls. The epitaxial
thin-films were grown for 60- 120 s, which thicknesses were measured using interference fringe in Fourier-transform infra-red spectra. As described above, calculations

66

iucluding the substrate rotation require the use of three-dimensional coordinates
because any symrnctric nature cannot be assumed throughout the entire space inthe reactor. Such three dimensional calculations need much computer memory andcomputation time, so that focusing only on the main gas flow reglon is very effective
for the cost of calculation. Following this reason, the simpler geometry shown in
Fig. 1-2 is assurned to describe the transport phenomena and epitaxial growth on
the substrate by calculaUon. Since the silicon deposition occurs on the susceptor
as well as on the substrate, the susceptor and the substrate are assumed to be one
large substrate.

IR furnace
~

300K

~L

50mm " - - - - - - .

quartz glass wall

.,

740K

x::
o
o

w~tr~

ro

susceptor
1398K

gas

(~1~~'3\~~~CI)

FigA- l Single-wafer horizontal reactor for preparation of epitaxial silicon thin-film.

67

!L

740K

300K

300K

left

100mm

Top face
Outlet( SiHCI3

Inlet(~~C~ )~~=30=O=K~~~~~s~s~~==74=O=K~~,~s~s~s~s~s~s~s~,~3=O=O=K~~ ~~I
~

z

LJ~

~

substrate
iSS

$

$

$

$

51

300K

susceptor
Side view

100mm

L

300K

Y

300K

300K

300K

300K

740K

300K

left

E 100mm
E

g

right

Bottom faceD~ heat conducting wall (quartz glass)~ with adiabatic outside boundary

constant temperature wallFig.4-2 Geometry and wall temperature conditions of single-wafer horizontal reactor withrotating substrate for the numerical calculations.

684.2.2 Basic equations Jor transport phenomena and chemical reaction

In order to evaluate the film growth rate in the case of the reactor with nonuniform
tCl11pcrature and gas flow fields, the mass, rnomenturn, energy and chemical species
transport equations are solved with a chemical reaction occurring at the surface ofthe substrate.
Since neither the elementary reactions nor the rate-limiting process in the reacbons
have been deterrnincd for the SiHCI3 -H 2 system, an Arrhenius-type expression forthe chernical reactions and a sirnplified reaction scheme were used to model thereaction phenOlnena. We therefore consider the preparation of a si licon filrn on thebasis of the overall reaction of equation (4-1).

SiHC1 3 + I-h ---t Si + 3HC1.

(1-1)

The transport phenomena in the reactor at a steady state are solved using Cartesian coordinates. The governing equations for the mass is as follows:
Conservation of mass:

8 pu + 8 pv + 8 p'W = 0
ox
oy
oz
'

(4-2)

where u, v and 'Ware velocities in x- y- and z-directions, respectively. The X - ,y- and z-directions are indicated in Figs. 4-1 and 4-2. The equations for the gas
veloci ties areConservation of momentun1:

yx

opuu

8pvu oP'Wu
8p 8Txx OT
OTzx++----a;- -----ay' ----a;- - 8x ox oy 0z '
opuv

8pvv

oP'Wv

8p

8Txy

OTzy

OTyy

----a;- + -----ay + ----a;- - -8y- -ox- -oy- -8z )zz
8z

8pu'W 8pv'W 8p'W'W
8Txz 8Tyz OT__+L.:.-- + - - = -8p- +pg - - - - - - - - - ,
8x

8y

8z

8z

ox

oy

( 4-3)

(4-4)
(4-5)

where

xx --

-

8u
- - -2 (ou- + -ov + -ow)l ,{,I 28x
3 8x
oy
oz

(4-6)

T

-

ov - -2 (ou
8v ow)l ){/, 2oy 3 -8x + -8y + -8 z

(4-7)

T

yy --

r
r

69

Txy

= Tyx = -~ (~~ + ~~) ,Tyz= T zy = -~ (~~ + ~;) ,Tn = Tn= -~ (~; + :~)(4-] 1)

In equations (4-2)- (4-11), p, p and f-l are the density, pressure and viscosity of thegas mixture. The gas velocities, u, v and w, on the surfaces of the solid walls are
set to be the same values as the solid wall have as the boundary conditions. Thatis, the velocitjes of u, v and w on the stationary walls are all set to be zero. The
method to set the velocity cornponent for the surface of the rotating substrate is
described later.
The gas velocity at the inlet section is unifornl and 0.1667 nl s-] which has been
estirnated in Chapter 3. where the same reactor was dealt with in calculation. The'epitaxial film is grown under the pressure of 1.0133 x 10 5 Pa atnlospheric pres urc.
1 he gas density obeys the ideal gas law(4-12)
where Mav is the local average molecular weight of the gas mixture and R is the ga 'constant.
The distribution of the tenlperature T , in the reactor is expressed by th following
energy equation:
Conservation of energy:

fJpuCpT fJpvCpT fJpwCpTfJ (fJT)OT)~++= A- + -fJ (OT)
A- + -D ( A(4 13)
ux
oy
fJz
fJx
ox
oy
fJy
oz
oz' In this equation, Cp is the heat capacity of the gas at constant pressure, and A thethermal conductivity of the gas.
The ternperature of the sllhstrate surface, T R , is 1398 K as shown in rig. ~-2. The
effect of heat transfer by radiation on the substrate temperature is ignored becaus
70

Llw substrate tClnpcraturc is cC)l)tinuously and precisely controlled by a sensing andheating system of the reactor. Since the concentrations of SiHCb and HCl are low,
the effects of radiation heat on these gases are also assun1ed to be negligible. Sinceac urate measurement of the temperature at the transparent wall of quartz glass
is extrerncly difficult, the side and upper walls near the substrate are empiricallyassurned to be 740 K, as shown in Fig. 4-2. The quartz walls around the substrateof bottom surface are assurned to be heat conducting walls. Heat of reaction at thegrowth surface is ignored in the present rnodel.
The transport of chemical species is governed by the following equation:
Conservation of species:

a

8
8
8 .
8.
8.
-;- (P 1LWi) + -D (fYUWi) + -D (PWWi) = - -a Jx - -8 Jy - 7).Jz,
ox
y
z
x
y
oz

(4-14 )

where
· _ _ D .()Wi _ D T DIn T
P t axi
8x '(4-15)· __ ]) . 8 Wi _]y P t 8y(4-16)]x -DT81nTi8y· = _ D .aWi _ D!8InT]z
P t OZtaz .

(4-17)In these equations, Wi l ' the nla s fraction of species i. The diffusion coefficient,

IJ i , is asslllned to be the binary diffusion coeffident of spedes i in H2 gas since themole fraction (not mass fraction) of species other than H2 is much smaller thanthe case where multi-colTIponent diffusion phenomena lTIUSt be considered. 1 The
assurnption of the binary coefficient is also considered to be reasonable since thetransport of reactants and reacLion products by diffusion is less irnportant thantbat by cOllvection ill single-wafer horizontal reactor and the diffusion coefficients
under atnlO pheric PI' ssun~ arc slllaller than those for low-pressure chemical vapor
u.epoj Lion (LP VD). 1 The llla" tran . . port phenon1ena dri ven by the ten1perature
gradient (th nnal diffu.'ion) are described by the terrns relating to

D; the thermal

difi'usion coefficient. Dr.t is expressed as(4-18)
71

where CYi is the thermal diffusion factor of species i.
At the inlet of the reactor the composition of the SiHCb and H2 gas rnixLure isexpressed in tenns of the average rnolecular weight MW given by(4-19)
where Xi and Mi are the 11101e fraction and n10lccular weighL o[ 'pecic. 1" The average'
1

molecular weight at the inlet, MW, is 6.7 X 10- 3 kgmol- , which corresponds Lo
3.5 mol% of SH-ICb or the mass fraction of 0.71.

At the surface of substrate, the increase or decrease ill the rnass of each species
by the ,chemical reaction on the surface is considered in tenns of Lhe boundary
conditions. Assuming that the reaction of equation (4-1) is a second-order reaction,
the mass rate of consumpLion or generation of species i at the surface is expre sed
as( 4-20)where k (m4 mol- 1 S-l) is the rate consLant [or the reactioll . The values of Lhe molar
stoichiornetry coefficient, [Ji, are - 1 for i = SiHCb and}h and 3 for i = HCl. The
concentration of each species at the surface is governed under a balance between
the rate of chemical reaction and the diffusional transport processes driven by tbe
concentration and temperature gradient. The boundary conditions on the substratesurface are therefore
D
It-j,

_.

.

OWi
t 8z

_

TO In T

-JC +JT - -pD·- - D · - t

uz '(4-2] )

where jc and jT denote the diffusion flux driven by the concentration and ternpcrature gradients, respectively.
The accumulation of silicon per unit time and area of the surface(1-22)

gives the growth rate of silicon film as(4-23)

72

where PSi is the density of Si, and the factor 6 x 10 7 is used for the unit conversion
of rn 8- 1 to I.L1D Inin-l. Since very smooth surface of the epitaxial filrns without any
hillocks are obtained in varion:::; growth conditions, only negligible arnount of siliconparticles are proclll(,(~ cl by the Chclllical ]'cacUon ill thc gas pha.se.
To solvc the above cquations for the rna."s, gas velocity, ternperature and chelnicalspecies, the 'c are discretizcd into fini te difference forrnulae. The calculation domain,
the entire reactor of ~ ig. 4-2, is divided into a nonuniforrn cornputational subdomain.
Prelilnillary calculations usillg different numbers of grid points showed that a meshwith It3 x 26 x 21 grid points in the X-, y- and z-directions is sufficient to obtainaccurate calculation results.

The discretized equations are solved based on the

SIMPLER algorithm.2

U

Computational celly~xw : angular velocity
IU I =Ixw ,u = -Usin ex atX
IV I = Iy w ,v = V cos 8y at Yo &-~--~~-------Fig.4-3 Velocity at the substrate surface given by the substrate rotation.

Figure 4-3 illustrates th concept of the lnethod for assigning velocity to the surfaceof the rotating substrat in the nUITleri cal calculation. The rectangular region in the
figur COlT sponds to any computational subdomain (cell) located on the surface ofthe substrate. The velocities, 'U and v, for the cell are defined at the positions X
73

and Y ,' respectively. The point 0 in the figure is the center of the substrate, i. e, thecenter of rotation. Defining the distance OX and OY as lx and ly, and using theangular velocity of the rotation, w, the moving velocities , U and V at the positions

X and Y in the figure , are expressed as lxw and lyw , respectively. Consequently,
u and v are derived frorn the components parallel to the x - and y - dir cUon asU= - U sin ex and v = V cos ey , where ex and ey are the angles shown in the figure.
To account for the dependence of the distribution of the chemical species, SiH 13

and HCI, on the gas velocity and temperature , the equations (4-2) - (4-23) ar coupled
and solved simultaneously.
The gas properties of H2 such as visco ity, heat capacity and thcrrnal conductivity
are taken from the literature. 3- 5 The properties of Si11Cb and HCl are given by
Pollard and Newman. 6 Each physical constant is expressed as a fUllction of tenlperature. The properties of the mixed gas are estimated theoretically. 7, 8 The binary
diffusion coefficients of SiHCb and HCI in H2 are estimated with the method d scribed in the literature. 9 Following Holstein 10 the thermal diffusion coefficients of
SiHCh and HCI are obtained using data of Lennard-Jones potential 9, 11, 12 and physical properties. 13 In a region with a very low species concentration such as that near
the substrate surface, the thermal diffusion coefficient.s of SiHC1 3 and He1 inrrea, ('with temperature and concentration.

4.3 Results and discussion

4.3.1 Silicon thin-film growth rate and thickness on the rotating substrate

In this section, the growth rate and the thickness of silicon thin-film on the rotating
substrate in the single-wafer horizontal reactor is discussed with the results of themeasured and calculated epitaxial growth rate.
Figure 4-4 shows the calculated distribution of SiHCh mass fraction in the innnediate vicinity of the substrate surface. At rotation rate of 0 rpn1, the SiH 13 fraction74

is very largc at the leading edge of the substrate and decreases as the trailing edge
is approachcd because of the consumption by the surface chemical reaction of equatiOl) (1-1). [n this case, the contour lines of SiHC1 3 on the substrate is symlnetricalwith rcspect to th . lTIid-plane of the reactor. At 20 rpm the contour lines of SiHChrnass fraction frorn the inlet to the leading edge of the substrate showed no significant differen 'e from that at 0 rpm, but on the substrate the contour lines are forced
to be bent by the rotating motion of the substrate. The rotating substrate transports the SiHCl 3 along its path of the rotation of the substrate. With increasing
rotation rate, the shape of the contour lines is deformed more and appears to bea..c;Yll1rnetric. It can be easily expected that this variation in the concentration will
gi ve a nonuniforrn profile of the film growth rate.

Left

E
ro

(l)
~

(;j

c

~

o

o

Fig.4-4 Contour lines of mass fraction of SiHCI 3 over the substrate in x-y plane
0.0175 mm above the substrate at rotation rate of 0, 20 , 50 and 100 rpm . The average molecular weight at the inlet, MW, is 6.7 X 10- 3 kg mol - 1 and the substratetemperature, Ts, is 1398 K.

Figur 1-5 shows t he alcul at d growth rate profiles on t he entire surface of t hesubstrate at various r'Jtation rates. Wi th increasing the rotation rate, the calculated

75

growth rate near the farther side in the figure (len) increase' whlle that at the closer
side (right) decreases, but the growth rate profiles do not become flat.

'2'E......

'2

5'E......
E

E

...;;

...;;
<.!)

>Q)

<.!)

4
left

~

.c

~

5

>Q)

-

4
left

~

.c

~

3

3

0
C)

....

0

(5

right

right
(b) 20 rpm(a) 0 rpm

'2

'2 5

<.!)

~

e

C)

4

..:;,

4
left

~
....

.c

<.!)

E

E

..:;,

>Q)

-

5

'E

'E

3

>Q)

left

~
....

.c

~

e
C)

3

Fig.4-5 Growth rate distribution over substrate surface at 0, 20, 35 and 50 rpm .

Figure 4-6 shows the profiles of t he calculated and measured filrn t hi cknes" growll
for uni t time along the mid-plane of the reactor. At the substrate rotatin g speedof 35 rpm , the calculated grow th rate i largest at the leading edge of the substratr
and decreases toward the trailing edge. Thi s is t he saIne tendency as di scussed at,

orpIn in Chapter 3. At 35 rpm , however , the Ineasured mIn t hi ckn ess profile is very
fl at on the substrate. To compare the calculated growth rate with t he measurCInent,t he continuous change in the position of the substrate due to the substrate rotationmust be taken into consideration. The film thickness at a given position on thesubstrate should be calculated by integrating the growth rat e over all the positions
which are the same distance away from t he substrate center. In other words, the film
thickness profile is obtained by integrating the growth rate distribution along 111any

76

cOllcentric cirde~ on the substrate. The dashed line in Fig. 4-6 is the integTated one

obtained for 35 rpm and agrees well with the measnrelnent.

6.0

As calculated
Measured,_----.0----

Upstream
3.0
-0.1

-0.05

Downstream

0.0

0.05

0.1

Position from the center of substrate (m)Fig.4-6 Measured (circle) and calculated (solid line) local growth rate at substrate rotation rate of 35 rpm. Dashed line is film thickness grown for unit time obtained byintegrating the growth rate along concentric circles on the rotating substrate.

Here, the rate constant, k , for the reaction of equation (4-1) is 0.038m 4 mol- 1 S-l
at 1398 K, which is estimated so that the calculated growth rate at the center ofthe substrate coincides with that of the lneasured growth rate at 0 rpm. This value
differs a little fronl 0.01 rn 4 mol- 1 S-l which was obtained in Chapter 3. thus thedifference in the growth rates obtained by both rate constants was only about 10 %.
It can be concluded that the epitaxial growth is limited by the transport of SiHCh
molecules.
Figure 4-7 shows the thickness variation of the film as a function of the rotation
rate. Here, the thickness variation, tv (%), is defined as

tv = (t max - t min ) / (t max + tmin) x 100,
77

(4-24)

where t max and tmin denote the maximurn and rninilTIUlTI film thicknesses on Lhesubstrate, respectively. The circles show the measured value and the solid line isthe calculated results. Although the calculated tv for 0 rprl1 is sOlTIewhat slnallcr
than the measured one, both the measured and the calculated tv show the same
behavior. The thickness variation is large at 0 rpn1 , but it drasticall y decreascs evcn
at sInal l rotation rate and shows very slnall change with the rotation rate as long as
the substrate rotates.

30 ~----~----~--~----~--~oCalculated

MeasuredO~----~----~--~-----L--~

o

10

30

20

40

50

Rotation rate (rpm)FigA-7 Calculated (solid line) and measured (dashed line) film thickness variation tv atthe substrate rotation rate of 0 to 45 rpm.

The results nlentioned above clearly indicate that the good uniformity in filln
thickness is a result of the averaging effect by integrating lo cal growth rate overdifferent positions, which is caused by the rotating motion.

4.3.2 Transport phenomena induced by rotating substrate

In this section, the effects of substrate rotation on the distribution in gas velocity,78

telllperature and chernical species concentration are discussed.
'rhe velocity of gases coming from the inlet changes its profile under an effectof viscosity. Figure 1-8 shows the calculated gas velocity vectors at the x-y plane
0.0175 mm above the substrate for the rotation rate of 0,20, 50 and 100 rpm. Whenthe substrate does not rotate, the gas in the vicinity of the non-moving wall has
v ry small velocity as shown in Fig. 4-8(a). At 20 rpm, the gas near the substrate
has llluch higher velocity than in the rest of the reactor as shown in Fig. 4-8(b). At
50 and 100 rprn , the gas velocity ncar the substrate further increases . The gas in thevicini ty of the rotating substrate shows large velocity but in the rest the gas Illotionis hardly affected by the substrate.
Left

E

_

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

I~· ·
::)

E
ctS

.:.:.:::.:: •.. :. ~i- - . ...... .... . . .

Right

0

o

E

E
~ a; : : :::.

ctS

• ....

· .~~-~-c . . . .. .
CJ)-

c.

• ' :::1 C..... -

·0::
o
o

::)

Right

(a)O rpm

Q)(b)20 rpm

Left

E

E
ctS ...

ctS
...

(1)

~~CJ)-

Q)

~

Sen
o ~
o
o

C.
::)

(c)50 rpm(d)100 rpm

Fig.4-8 Gas flow velocity distribution in x-y plane 0.0175 mm above the substrate at
rotation rate of 0, 20, 50 and 100 rpm .

Figure 4-9 shows the contour lines of tenlperature of the gases in an x -y plane
near the substrat . Temperature of the ga introduced from the reactor inlet stays
at ahnost 300 K until the gas COll1es close to the substrate, and it increases rapidly
at its leading edge. The stairway form of the temperature contour lines aroundth substrate re 'ults fronl the contouring procedure, ince rectangular gridding ofth clonlain doe' not exactly nlatch the round shape of the substrate. In contrast

79

to the gas velocity distribution, the rotation rate has very slnall influence on thetemperature distribution from 0 through 100 rpm.

This is because thth :>rnlcd

conduction from the heated substrate to the gases is very rapid.
Left

Left

-+50
E
ro

-+50

E
ro

C')

~

Ci5

~-+
C/)

c

~
0

0.
:::)

0

E
ro

C')

E
ro

~

Ci5

~-+

c
~
o

C/)

0.
:::)

o

-+

-+
(a) 0 rpm

Right(b)100 rpm

Right

Fig.4-9 Contour lines of temperature in x-y plane of 0.0175 mm above the substrate at
rotation rate of a and 100 rpm.

During the epitaxial growth, the species consumption by the surface ch rnieal
reaction of equation (4-1) causes the concentration gradient of chemical species aswell as the thermal diffusion, but the species distribution, at the same time tend tobe homogenized by the diffusion. To extract the effect of the substrate rotation on
the species distribution from these complicated phenomena, which is composed ofthe mass, momentum, energy, chemical species transport and the chemical reaction,
addi tional calculations were performed where the chemical reaction is intentionallyignored.

To estimate the effect of the rotation on the species distribution, thecomposition of the species at the reactor inlet is purposely set to be nonunHorrn
as found in Fig. 4-10 at the reactor inlet. In the calculations, the mass fraction of
SiHCl 3 is 0.4 near the center of the inlet and those near the right and left side walls
are 0.71.
The concentration nonuniformity iInposed at the inlet becomes smaller as the gas
approaches to the substrate because of the diffusion in the horizontal direction. Th
temperature gradient is very large at the leading edge of the substrate, where the80therrnal diffusion strongly affects on the distribution of the chemical species. The
thermal diffusion transports SiHC1 3 gas away from the hot substrate surface, and it
generates a large region having relatively lower SiHCb concentration near the leading
edgc of the substrate as shown in the figure. With increasing the rotation rate, theshape of the contour lines of mass fraction is deformed more but the variation inth SiHCh concentration on the substrate tends to become smaller, as indicated by
the increasing area on the substrate with the mass fraction between 0.45 and 0.5.

Left(a) 0 rpm

Left

Right

(b) 20 rpm

Left

Right

Left

Fig.4-10 Contour lines of mass fraction of SiHCb ignoring the chemical reaction in x-yplane 0.25 mm from the substrate at rotation rate of 0, 20, 50 and 100 rpm .

The contribution of thermal diffusion in the silicon thin-film growth has been
discussed in Chapter 3. where the calculation neglecting the thermal diffusion overestimated the growth rate. To evaluate the role of thermal diffusion on the reaction
with the rotating substrate in detail, calculations are performed additionally ignoring the transport by the thermal diffusion and the chemical reaction.
Figure 4-11 shows the Inass fraction distribution of SiHCh over an x-y plane
O.251nm above the substrate, where nonuniform SiHCb concentration at the inlet
is again assumed. In case the thermal diffusion is ignored, the region having low

81concentration do not appear near the leading edge of the substrate. The rotationof substrate distorts the contour lines on the substrate and generates a large region
having almost uniform concentration with increasing rotation rate. The difference
between the contour lines in Figs. 4-10 and 1-11 indjcates that SiHCb gas, under theconditions for the epitCL-xia:l growth, distributes inhon1ogeneously due to the thermal
diffusion even at high rotation rates.

~

~0.6

Left

~~11-~ 0.6-+~(b) 20 rpm(c) 50 rpm
Fig.4-11 Contour lines of mass fraction of SiHCI 3 ignoring the chemical reaction and~hermal diffusion in x - y plane 0.25 mm from the substrate at rotation rate of 0, 20 ,50 and '100 rpm.

According to the discussion above, the thermal diffusion lessens the SiHC1 3 conce ntration at the leading edge of the substrate, whereas t he chemical reaction rnakes thedepletion of SiHC1 3 toward the trailing edge of the substrate. These two phenom na
induce the opposite gradient of SiHCb concentration which compensate each oth r ,forming moderate gradient of SiHCb concentration and thus assisting the formationof fiat profile of the film thickness.

However, the distribution in the grown film

thickness on the rotating substrate is basically explained as the averaging effect byintegrating local growth rate over eoncentrjc circles which , at the same time , is aided
by the change of the SiHC1 3 distribution by the rotating motion. This mechanism

82

leading to relativcly uniforn1 filrn thickness is fundarnentally different from that ina vertical reactor with very higb rotation rate of substrate,14 which is designed tohave very simple gas stream and a rather homogeneous species distribution.

11.3.3 Method to improve fiLm thickness uniformity

Th discussion in this chapter shows that the silicon epitaxial film is forrned byintegrating the growth rate along concentric circles on the substrate surface. Although the large growth rates at the front side of the substrate and the small onesat the rear side can compensate each other to form uniform thickness profile, thethicknesses at the substrate edges are still larger than that at the center of the substrate. This profile is due to higher growth rates at the substrate edges, especiallyat the right and the left edges, than those at the inner region of the substrate.
Therefore the growth rates at the right and the left sides cannot compensate eachother. This indicates that the uniform temperature at the substrate surface and theuniform source gas concentration at the reactor inlet cannot result in the completely
uniform epitaxial filn1 thickness profile. To improve the filrn thickness uniformity
I110rC two methods are possible fron1 the view point of adjusting the growth rate.
One method is to set nOlluniforrn telnperature within the substrate; the other is toset nonuniform concentration profile of the source gas, SiHCb at the reactor inlet.
Since the nonuniforn1 ternperature wi thin a substrate often causes the crystal defectof slip due to thermal stress, the former method is not appropriate. A large-diameter
wafer is very sensitive to the ten1perature distribution within itself.I5
The latter method is considered to be effective since Fig. 4-10 shows that thetendency of the nonulliforrn concentration of SiHCb set at the reactor inlet can be
kept on the rotating substrate. 1t should be tried for achieving very high thickness
uniforn1ity to set the nonuniforn1 SiHCl 3 concentration between the right and left
sides of th reactor inlet which cause the nonuniform growth rate profile to be
cOlnpcnlsated betwc n the right alld the left edge of the substrate.
834.4 Conclusions

Preparation of sill con thin-film on a large rotating substrate with SiHC1 3 -H 2 system in a single-wafer horizontal reactor has been discussed using a nunlerical calculation model. The effect of a substrate rotation in a single-wafer horizontal reactor
is quite different frorn that in a vertical reactor. Although nearly unifornl fihn thickness is achieved by the rotating substrate, the concentration of SiHCh itself is not
uniform on the substrate even at very high rotation rates. The good uniforrrli ty infilm thickness is achieved by the continuous change in the substrate surface position
due to rotation, which causes averaging effect of the nonuniform growth rate alongconcentric circles on the substrate surface . The change in the transport phenomena
induced by the rotating motion also contributes to the thickness uniformity.

84

Nomenclature

A : pre-exponential factor of rate constant

Cp : heat capacity at constant pressure(n14 mol- 1 S-I)
(Jkg- 1 K- 1 )Di : binary diffusion coeffic1cnt of species 'i in H2

D; : thermal diffusion coefficient of SpCc1CS i in H2
E : activation encrgy of ratc constant(m 2 S-I)(kgm- 1 S-I)
(J mol-I)(m S-2)g : acceleration due to gravity

hs : distance fronl substrate surfacc(m)['i] : Inole concentration of spec1e. i(mol m- 3 )jc : diffusion flux drivcn by conccntration gradient(kgrn- 2 S-I)

JT : diffusion fiux drivcn hy tClnpcrature gTC1dicnt(kgrn- 2 s- 1 ).'lx : diffusion fllL'<. dri VCll by concentration and tClllperatnre gradient ill x directiOll

Jy : diffusion flux driven by concentration and tcrnperature gradient in y direc(kgm- 2 s- 1 )tion

Jz : diffusion flux dri ven by concentration and tenlperature gradient in z direc(kgm- 2 S-l)tion

(m 4 mol- 1 S-I)

k : Arrhenius-type rate constantlx: distance OX(m)ly: distance OY(m)Mav: average n101 cular weight of gas nnxture(kg mol-I)

MSi : molecular weight of Si(kg mol-I)

M i : n10lecular weight of pecies i(kg n10l- 1 )MW: averagc lnolccular weight of gas 11lixturc at reactor inlct(kg mol-l )(Pa)

p : PI' ssure

R : gas constant(Jmol- 1 K- 1 )Ri : mass rate of change in specie' i by ch n1ical reaction(kgn1- 2 S-l)

R Si : mass rate of change in Si by chemical reaction(kgm- 2 S-I)

(K)

T : temperature85Ts : substrate temperature(K)t max : maximum value of the fUrn thickness(j1m)tmin : minimum value of the film thickness

(j1m)

(%)

tv : thickness variationu : fluid velocity in x direcbon(nls- I)v : fluid velocity in y direction(nls- I)

(j1111 min-I)

VG : growth rate

(1n S- I)

w : fluid velocity in z direction(m)x : coordinate in horizontal direction
Xi : mole fraction of species i(-)

y : coordinate in horizontal direction(nl)z : coordinate in vertical direction(ill)ai : thermal diffusion factor of species i(-)

ex: angle shown in the Fig.4-3(rad)ey : angle shown in the Fig .4-3

(rad)(\\1 111- 1 K- I )A : therrnal conductivity of gas rnixtllrr
j1 : viscosity of gas mixture
Vi :(Pa ·s)molar stoichiometry coefficient for species i in che1nic[\'1 reaction(-)

P : density of gas mixture(kg m- 3 )PSi: density of Si(kg m- 3 )W :angular velocity of the rotation

Wi :rnass fraction of species i(rad s- t )(-)

86

References[1] K. J. Kuijlaars, C. R. Keijn and H. E. A. van den Akker, Chem. Eng. J., 57, 127(1995).

[2] S.V.Patankar,Nurncrtcal heaL Lransfer and fiuid flow (McGraw-Hill, New York,1980) .

[3] J(agaku Binran (Handbook of Chenustry) (Iwanami, Tokyo, 1984) 3rd ed.,Chap. 6, p. II-39 [in Japanese].

[4] Kagaku Binran (Handbook of Chenlistry) (Iwanami, Tokyo, 1984) 3rd ed.,Chap. 6, p. II-71 [in Japanese].

[5] I(agaku Binran (Handbook of Chenlistry) (Iwanami, Tokyo, 1984) 3rd ed.,Chap. 9, p. II-239 [in Japanese].
[6] P. Pollard and J. Newman, J. Electrochem. Soc., 127, 744 (1980).
[7] C. R. Wilke , J. Chem. Phys., 18 , 517 (1950).
[8] I.H.Oh , C.G.Takoudis and G.\i\1.Neudeck, J. Electrochem. Soc. , 138 ,554 (1991).
[9] R.C.Reid , J .M. Prausnitz and B.E.Poling, The Properties of Gases and Liquids(McGraw-Hill, New York , 1987) 4th ed.
[10] W. L. Holstein, J. Electrochem. Soc., 135, 1788 (1988).
[11] P. D. Neufeld, A. R. Janzen and R. A. Aziz, J. Chem. Phys., 57, 1100 (1972).
[12] L. W. Flynn and G. Thodos, A. I. Ch. E. Journal, 8 , 362 (1962).
[13] M. A. Drews, W. L. Schenck , Jr., J. D. Smith, J. Walker and C. L. Yaws, Solid

State Technology, p. 39 (Jan. 1973) .
[14] Y. Sato, T. Tamura and T. Ohmine, Extended Abstracts 1992 Int. ConI Solid

State Devices and .A1aterials, 20 (1992).
[15] F. Shimura, Semiconductor Silicon Crystal Technology (Academic Press, San
Diego, 1989) Chap.7 , p.285.

87

Chapter 5
Model on TraIlsport Pllenomena and Silicon
Epitaxial Growth of Thin-Film in SiHCl 3-H 2
System under Atmospheric Pressure

895.1 Introduction

In thi chapter\ the elemental surface proce, s ill a SillCl :3-1T 2 SystC'Hl is cliscuss( clquantitatively in conjunction with an entire analysis of the transport pbenOlnena i1)
a single-wafer horizontal reactor for the condition ' applicable to indu trial pitaxial
growth, since the Si HCh-H2 ystern have not yet rwcn discussed sufRdentl y. The
rate processes discussed in this Chapter include che1ni sorpt ion of Sil I Ch and dccornposition o f the chemisori)('d ,pecics. The raie COl1stanL of all overall rcaction is
obtained froJ11 the experi n1en tal growth rate data and. disCllSS('d t () cVR luate t h(' 1'(1 t ('constant, of the chernisorption and the decOlnpo"jboll. The 111odr1 drveloped in this
Chapter de, crib es the silicon epitc.1..'{ial growth over a wi de tCll1p crat ure range fl'01ll
the reaction limited region to the t ran 'por t li1nited region for \ arious concentrationsof SiHCI 3 ·5. 2 P reparation of silicon epitaxial Thin-films

Figure 5-1 shows the geometry of the reactor studied in this study. For the an alysisof t hin-film preparation on a heated ub trate ,ve prepare ili con epitaxial Thinfilm s on sili coll (100) substrates by SiIIC1 3 and H2 ga ' 8, . The ep iL axia l thin-Rhn
t hickn esses were n1easurcd using interferellce frillge in the Fourier-transform infr(1 red pectra.

The gas rnixture is introduced into t h e reactor under at ll1 0sphrricpressure a nd rcacts at the surface of the sub.'iralc ll cld horj7,ont all y 011 a susccptOl'in the reactor.

Tn this Chapter , the susceptor is no t rotated.

The susceptor isdesigned to prepare a epitaxial layer on an 8-inch-diameter sili on substrate. Th
substrate is heated to 1073 , 1223 and 1398 K using infrared furnaces through thereactor walls consisting of quartz glass. The temperatur is maintained constant bymonitoring the temperature and controlling the input power of the infrared furn aces
continuously. The outer surfaces of the quartz walls ar e cooled v.dth a suffici ntly
la rge arno unt of cold air , so that it is reasonable to neglect a n ahsorption of ra di aL ion

90h'1:lt by the transparent walls. Since the conccntratiol1s of 8i 11 Cb and lf C] ar~ low ,effects of radiatioll heat on these gases are assurned to be negligible.

gas

t

300K

ii

~~CI3 )

IR furnacequartz glasswalll~~J~~·=: =: = ~~:::::~: =: ~za=~22L::-Z• .T.r...r.""..t:7.7.T~ I~

susceptor
1073K -1398K

r1

y

Lx l:=:===:=:=:=:t7_:::~Z::i::::1I
adiabatic~Lgas out(~~CI3) ~

T"-

50mm

HCI

Fig.5-1 Single-wafer horizontal reactor for preparation of silicon epitaxial film.

5.3 Basic equations governing the epitaxial reactor

In order to evaluate the fihn growth rate in nonuniforn1ly distributed tenlperature
alld gets How fields the lllclSS I110lnentum energ) alld species transport equatiolls
lllUSLbe solved sinlultaneously. The present 111odf'1 also includes chenlical reactions

011 the substrate surface.

Vie focus n1ainly on the growth rate of a film at the center of the substrate.
1['he transport phenomena in the reactor in a steady state are solved using two-

dilllensional Cartesian coordinates. The governing equations for the gas velocity are
as follows:
COllservation of Inass:

a

a

x

uy

-8 (pu) + ~ (pv) = o.
91

(5-1 )

Conservation of 1110rnentUln:

ov ) - oxap 'axa (pULL,)+ aya (pvu) = axa (2p, auax ) + oya ( p,au
By ) + oyD (/I,ax(5-2)

av ) + ox0 ( P, oxav ) + ax0 (Iiau
op + pg. (S-3)
axa (puv) + Bya (pvv) = aya (2p,oyoy ) - !Jy
In equabons (5-1 )- (5-3), x and yare the coordinates in the horizontal and verticaldirections, u and v arc the velocities in x- and y-dir('( lions , p, p and {i A.rc t 11('density, pressure and viscosity, respectively, of t he mixture of 8i HCh , [[ 2 and He }gas .
The gas density obeys the ideal gas law(5-1 )
where Mav is the local average molecular weight of the gas and R is the gao constallt.
The gas velocities, u and v, are set to be zero on all the surfaces of the solid wall. as boundary conditions. The gas velocity and pressure at the inlet are 0.67 m S-I
and 1. 0 133 x 10 5 Pa, resp ectively.
The temperature distribution T , in the reactor is expressed by the following
energy equation:
Conservabon of energy:a (pCp Tu ) + ~a (pCp T v) = -aa (A--;:)aT ) + ~8 ( A--:-)aT) .
-;:;ox

(JY

.T

(J.T

(}Y

( Y

(5-5)

In this equation, Cp is the heat capacity of the gas at constant pressure, and A Lhet hennal conductivity of the gas .
Heat of reaction at the substrate surface is ignored in t he present model because
the heat capacity of the susceptor, the temperature of which is well controlled,
is so much larger than that of the gas mixture that the temperature change by
the heat due to the reaction is negligible. VI./e ignore heat transfer by radiation inequation (5-5) as mentioned, and impose the following boundary conditions on theequation. Since accurate measurement of the temperature of the transparent quartz
glass walls is extremely difficult, their temperatures are estimated empirically and92

HSSUlllCcl to vary linearly wiU} the substrate tCIllperature ill the range between 610 K

and 740 K. The reactor wall illustrated by the hatched region in Fig. 5-1 is treatedas a heat conducting wall with the thermal conductivity of quartz glass. The outersurface of this regioll (dotted lines ill Fig. 5-1) is taken to be surrounded by adiabaticwalls. Tbe tenlperature of the other reactor walls is regarded as 300 K since the walls
arc continuously cooled with water.
Con 'crva.tion of chernical species i (i = SiHCI 3 , H2 and HCI) is described by thefollowing equation:(\)11s('l'vaLioll of species:

()

()

D(

T) + -.a ( pD auJ~ + JJ Tuln T)

UW~-. (plLWt) + -, (PUuJi) = - . p!Ji -,- + JJ Talni -():l.'
cJ y
rJx
rJr
cJx

c)y

i -.--

cJy

_i -.

cJy

.

(5-6)
III thL equation, Wi is the Illass fraction of species i. The diffusion coefficient D i , isa' 'uIlled to be the binary diffusion coefficient of specie i in Ih gas since the 1110le
era tion (not ma

fraction) of species other than H2 is small. The mass transportphenonl na driven by the teInperature gradient (thermal diffusion) are described by
the ternlS relating to

Dr, the thermal diffusion coefficient. Dr is expressed as(5-7)

where ni is th thernlal diffu ion factor of specie i.
At the inlet of the reactor the C0111pO .. ition of the SiHCh and H2 ga Inixture icxpres 'ed in tenns of the average Inolecular weight, J\I{V. J\;fW is given by(5-8)
wh re Xi and J\1i ar the Inole fraction and molecular weight of species i. J\1W isvaried between 2.7 x 10- 3 and 11 x 10- 3 kgmol- 1 .

At an initial step, we consider the preparation of a silicon film on the basis of thefollowing overall reaction.
SiHCh + Th -* Si + 3ITCl

93

(5-9)

'l ass changes due to the chelnical reaction of equation (5-9) on the surface arC'
considered in the boundary conditions at the surface of the substrate. A. sUlning
i haL the reaction of equaUon (5-9) i

a second-order reaction

the rate of lllassconsurnption or generatioll of species i at the surface is expressed as(5-10)
where k is the rate constant for the reaction expressed as k = A exp (- E / RT), andthe values of the molar stoichiometry coefficient, Vi are - 1 for i = SiHCl 3 and IJ 2
and 3 for i = HC1. The concentration of each speci

at lhe urfac e is governed by abalance between the consumption by the chemi al reaction and the diffu ion fluxes
driven by the concentration and temperature gradi nts. The boundary condition.
on the substrate surface are..

OWij(.1, = 7(' +]T = -pl) 1·-, 8,J'[UIll ra- f) 1,. - - 1
Yl/(:>-1 1)

where jc and jT denote the molecular and thennal diffu ion flux('s.
The accumulation of silicon per unit time and area of the surface(5-12)
gives the growth rate of silicon film as

VG = 6 X 10 7 Rsj PSi(J.1m min -1),

(5-13)

where PSi is the density of silicoll, and the factor 6 x 10 7 is used for the unit
conversion of m S-1 to J.1m min -1.
To solve the transport equations described above, the calculation dOll1ain is divided
into a nonuniform mesh with 78 x 52 grid points in the x- and y-directions. Thell theequations for gas velocity, temperature and mass of chemical species are discretized
into finite difference formulae. In this Chapter, the computational fluid dynamic.'code FLUENT (ver. 3.03)1 is used as the solver.
The gas properties of Ib such as viscosity, heat capacity and thennal conductivity
are taken from the literature. 2 - 4 The properties of SiHC1 3 and HCI are given by Pol5

lard and Newrnan. Each physical constant is expressed as a function of temperature94

using a polynomial fit. The properties of the mixed gas are estimated theoretically. 1
The binary diffusion coefficients of SiHCb and HCl in H2 are estimated with thel1lCthod described in the literature. 6 Following Holstein,7 the thermal diffusion coefficjcnts of Si HCh and HeI are obtained.
III tbis Chapter, the overall rate constant, k, and the concentration of SiHCb

at the substrate surface are obtained at the initial step so that calculated growth
rates agree with the growth rates measured at various temperatures. At the next
st p dependence of the overall rate constant on the 8iHC1 3 surface concentration is
discuss d to clarify surface processes including the epitaxial growth.

5.4 Mathematical model of the rate process

In this section, epitaxial growth processes in the transport and epitaxy Inodel is
di Cll sed after a brief description of the behavior of chemical species in the gas
phase and at the silicon surface.

5.1.1 Che'mical species in the gas phase

The intenl1ediate species in the gas phase for the silicon epita.xy from 8i-H-Cl sysLern have been discussed in l1lany papers. 8 - 13 At a telnperature higher than 1400 K,
8iCl 2 11101 cules are suggested as a major intermediate gas species for an Si-H-Cl
system. 10, 11, 13, 14 The overall reaction of equation (5-9) is discussed by Sirtl et al., 11
who stated that Si Clz existed in the gas phase and at the surface. It is also shownby the calculations assulning in an equilibrium state ll - 13 that 8iCb concentration ishigher than 8iHCh above 1300 Kundel' atnl0spheric pressure. However the entire
state in the reactor cannot be in an equilibrium state8 because the crystal growth{,(UlllOt be achi v d wi th no free energy change. The entire sLate in a cold wall reacLor wi tll a, high growth rate can b in a steady state but should be strictly recognized

as a non quilibriulll state.

95

Among 111any experinlental studies to identify the chernical species in the gas
phase,8, 9,15-17 Aoyama et al. 8 demonstrated that ch mical species of Si 14 SiITCh
8iJbCb and SiCb existed in the gas phase of SiC1 4 -1b sy't('nl in a cold wall reactor
and that all of th('rn contrihuted to th(' epitaxial gTowth at high grew, th LCll1P< 1'(1,ture. However, the concentration of SiCh wa' found to be 111uch lower than thai or
8iC1 4 and SiHCh even at 1473 K. This uggc t that in the SilICh-Ih syst 111 8i rrCb
molecules are transported to the sub trate surfac to playa Inajor rol in the ilicon
epi taxial growth.
Chemical reactions in the gas phase can al 0 be e timated cxperimentally frorn
the surface morphology of the epitaxial film. Particle generation in the gas phasesometimes consume much reactant species to decrease the film growth rate. 18 If alarge amount of particles are generated near the sub'trate surfacc, some portion of
the particles will attach to the surface to form hillocks. However) th fihn grownin thi study had a very slnooth urface without any hillock.

Therefore it ran

be a sunled that there is no particle generation to reducc the growth rate for theexperi nlcntal coneii bons of this tudy.
Consequently, chemical reaction which cause thermal deCOlTIpO ition of SiHCh or
particle generation in the gas phase can he assumed to be ignored. Only SiBC1 3 istherefore considered to calculate the growth rate.

5.4.2 Chemical species and adsorption at substrate surface

Behavior of chemical species at the substrate surface is noted briefly here. Abov

50 or 873 K, no hydrogen atom is present at silicon (100) surface. 19-21 Oxygen atOlns
are removed rapidly from the substrate surface as SiO molecules above 1000 K.22 Th'
surfacc is terminated hy Cl atoms as SiC} bonds during the low tcmpQ.raturc molccular bcarn epitaxy (MBE),23 but Cl atoms arc desorbccl ahove 623 K.21 IIirva andPakkanen25

showed that SiHC1 3 molecules were chernisorbed at the silicon surfac

accompanying HCl formation. Photoemission rneasurerncnts also show that most or96

CI adhering to silicon surfaces rClnain on the surface up to 873- ] 073 K. At higher
tempcrature, they are desorbed as 8iC1 2 rnolecu1cs. 26 From this discussion , there isno hydrogen and oxygen atoins on the surface above 1000 K. However, C1 atorns and3iCb rno1ecu1es IllUSt be taken into account.
Adsorption is classified into physisorption and chen1isorption. Physisorption is theweakest [onn of adsorptioll to a solid surface and is characterized by tbe lack of atrue cheinical bond bctween the adsorbate and the substrate. 27 Physisorbed species
111igrate toward reactive sites and react to be chemisorbed there. 28
Wher 'as SiH

h is valence saturated species which can only be physisorbed at

the surfc1cc , 8iCb is valence unsaturated and can be chemisorbed at the surface. 2D
Th epitaxial growth on (100) surface has the predon1inant nlechanisrn [or stable
CliIn'l' opening. 30 In the iniLial stage) the physisorbed species) 8iHC1 3, n1igrates tothe renlaining dangling bonds of the dimer and decompose to 8iCl x (x= 1,2 ,3) which
are hCIni orbed. 31 ,32 This generates a C1 ternlinated surface, which reacts with H2lllOlcculc in the gas phase to desorb as H C1 n101ecu1es .30\iVr as 'lUll that cherni orbed 8iCb (*8iCb) is the dominant species for the epi-

la-xlal growth rate.

5.1.3 Che1nicaL 7'eactions and rate process at the sU'ljace

1'11 ' purpose of this Chapter i to build a cornpact model for an epitaxial growth
in 1uding both the transport phenonlena and the surface processes which is basedon E1ey and Rideal 33 and Langnluir. 34 To obtain the transport and epitaxy model)
th followings are assuined.
(i) Th sub trate surface has a fixed number of reactive sites.

(ij) Ea h reacti ve site can hold one chenlisorbed rnolecule.
Oii) The chenlisorption is re Lricted to a nlonolayer.
(lv) At the epitau'{ial gro\ th teinperatur and pressure) a fraction) 8, of the reactive
siLes is occupied by chenusorbed Inolecules and a fraction, 1-8, is not occupied.
97

(v) There is no interaction between chemisorbed n101eculcs.
(vi) The hC(tt, clue to t he physisorption or chen1isorption is ignored.
(vii) Si ITCh Inoleculcs do not dccOlnposc in the gas phase.
(viii) H2 Inolecules are not adsorbed at the substrate urface.
By using equation (5-10), the overall rate constant k for th overall reaction of'equation (5-9) is estimated. To discuss the surface reaction proces, t he OVCl'-

al1 reactlon of equation (5-9) is assumed to be decOlnpo cd of ev ral elCll1entary
react ions.
Main Stream>

SiHCI3
Gas phase

HCI

SiHCI3

SiCln

CI

CI

"Si : *SICI2.
/ ,Fig.5-2 Transport and epitaxy processes during silicon epitaxial growth from chemical
reactions of SiHCI 3 , H2 and HCI molecules at substrate surface.

The entire processes of the silicon epitaxial growth on a (100) sili con surfa e anbe illustrated as Fig. 5-2. The reactant, an SiHC13 rnolecule, is transportcd frolnt he gas phase to the vicinity of the substrate (process (a)) and is captured loosely
at the substrate (process (b) : physisorption).

Then , the reactant migrates ordiff'uses to an unoccupied reacti ve site (process (c)). At the unoccupied reacti ve

98site, SiHCb decornposes into *SiCh and BCI. The substrate crystal of silicon has
chenlical bonds with the *SiC1 2 (process (d)), where Cl atorns are directed to thegas strcalll.

Ther fore this surface is regarded as a silicon crystal covered with

Cl atcnns. Such a chclnisorbed surface reacts with Ih rnolecules in the gas phase(process (e)) to produce silicon atorns releasing the by-product, HCl molecules. Afterthese processes, the occupied reacUon site rcturns to be an unoccupied site , and thesurface undergoes thc next growth process. At the same time, side reacbons takeplace. Chclnisorbed *SiCh call recLct with IICI in the gas phase to produce SiHCh
which is <lesorbed frmTl the substrate surface (process ([)). I1Cllllolecules in the gas
phas call atLack the substrate surface to etch the surface and produce SiCln which
is tntl1sported away [1'0111 the surface (process (g)).
'T hrough these processes silicon epitaxial films are grown. The key processes intbese are described by equations (5-14)- (5-17).
Chenlisorption of SiH Cb (process (d) ):SiHCb -4 *SiCb + HCl.

(5-14)De 'orptioll of SiHCh (process (f)):*SiC1 2 + HCl -4 SiHC1 3 .

(5-15)

DecOlllposition of *SiCh (production of silicon fihn' process (e)):(5-16)
Etching (process (g)):
Si + nHCl -4 SiCl n + (n/2) H 2 .

(5-17)The rate of reactions (5-14)- (5-17) at the ubstrate surface are described according
to the rate process theory as follows.
Hale of SiIlC1 3 ('helnisorption:

Vad = k~cta(l - 8) [SillC1 3 ] = kad(1- 8) [SiIlC1 3],99(5-18)

where Vad denotes the chemisorption rate of SiIICh, k~d is the cherrusorption rate
constant for a reactive site, a is the density of reactive sites and k,u\ is "<tel x a.
[SiHCb] lS the mole concentration of SlHCb at the substrate surface.
Rate of SiIlCh desorptioll:(0- H»)
where Vde denotes the desorption rate of SiHCb, k~e i the desorption rate constantfor a reactive site, kde lS k~e x a, and [HCl] i the Inole concentration of Hel at thesubstrate surface.
Rate of decomposition:(5-20)
where Vr denotes the decompo iLion rate to produce i k~ i the decOlnposition rat
con tant for a reactive site, and kr is k~ x a. [Ih] is the nlole concentration of IT:2
at the suhstrate surface.
Rate of etching:(5-21 )
where Ve denotes the rate of etching the silicon surface,k: is the etching rate COllstallt

for a reactive site, n is the order of etching reactioll allJ kc is k: x a.
Under the reaction condition for obtaining a very large growth rate, the rate of
SiHCb desorption should be much s111aller than that of Si lIC1 3 chemisorptioll .15 The
desorption of SiHCb is hence ignored in tbis study.
The fraction of occupied reactive sites, 8, is ohtained at a steaJy state fron1
equations (5-18) and (5-20).

8-8 a8 = Va~ - Yr. = 0,f,

8 =kad[SiHCb]
kad [SiHC1 3 ] + kr [H 2 ] .
100(5-22)(5-23)

Thc lnolc growth ratc of sHkoll epitaxial fihn V, is described using equaUons (5-20),(5-21) and (5-2.1).
(5-24)(5-25)As described ill cCJ,uaLioll (5-12)(5-26)
b~quations (5-25) and (.5-26) givek = k . kad - ke[HClf I[SillCh]Ikad [Si 11Ch] + kr [1 h].

(5-27)

or(5-28)For the epitCL'(ial growth Ih lllolecules cOlnprize generally more thall 95% of theiolt'l] gas lllO]CCllleS alld t]m ' UIC (,Ollccutration is assumecl as constant o,t cadl tcrn-(5-29)\\']}('n the gro\\'t11 rate is \'('1'y large the cOlltributioll of ctching proces' call oe
ignored in conlpal'isOll \\'ith the cOlltribution of jljcon fonnation.
(5-30)
Finally, the following equation is obtained.
(5-31 )
] ~JqUo,tiOll (5<31) shows that 1I k 'lnd [SiHCh] have a linear relaUonship. Herc, kr

and "'ad arc obtained b . t he slope of 1I k "'ith respect to [SiHCh] and the intercept
to the ilk axis respectively. The growth rate is cxprc scd uSlng equations (5-26)
and (5-31).

(5-32)

101

When the concentration of SiHCb at the substrate surface is very snlall , equation (532) is simplified to equation (5-33).

v = kad[SiIICb].
Equation (5-33) gives the growth rate when the rate i.' linlitcd hy t he chcnlisorptiol1of SiHCb. On the contrary, in the case that the surface concentration of 8i1 1C1 3 isvery high , t he growth rate is expressed as(5-34)
Clearly, this film growth rate does not depend on t he SiIICh concentration. Equation (5-34) is, in other words , the growth rate whcn the rate is lin1ited by t h e
decomposition of *SiCh.

5.5 Results and discussion

In this section, the validity of the transport and epitCL'<y 11lodel proposed above is
examined by analyzing rneasured growth rates.

5.5.1 Sili con epitaxial growth rate and grown film quality

The measured epitaxial growth rates are shown in Fig. 5-3. At every ternperature ,the growth rate increases with increasing the average D101ecu1ar weight, MH!, when

MW is srnall. However , its slope decreases gradually, aud finally the growt h rate
saturates with MW. This behavior is obvious at ] 073 an d 1223 K.
The quality of grown silicon fUrns was evaluated prior to discussion of the growtb
rate and the surface phenomena. Over the entire tenlperature r ange, th e grown £111ns
were characterized as single crystal by using the electron bearn di (fraction nlethod .
The gate oxide integrity (G01)36 was also evaluated throughout the surfaces of
epitaxial wafers. According to the results of the GOr measurements, the epitaxial
filrns were in the group of C mode faHure.
102

This evaluation shows that the filrn

prepared here with the SiIlCb-II2 system under atmospheric pressure has sufficientquali ty for fabricating rnicroelectronic devices.

This coincides with Sedgwick et

al. ,37, 38 who howed possibility of growing films of good quality under atrnosphericpressure down to 873 K using an Si lI 2Ch-fh systern. Consequently, the growth rates
obtained in this study arc co])sidered to be reli able for the analysis of thc epitaxial
growth.

10.----,r---~----~----~----~o----o 1223K-: calculated

6 0 0 : measured

o

1073K

o
o

0.01

~

2

__

- - I_ _---L_ _---'-_ _- - ' -_ _.....J

4

6

8

10
12
-3
Average molecular weight MW (X 10 kg/mol)

Fig.5-3 Epitaxial growth rates calculated (solid lines) and measured at 1073, 1223 and1398 K (circles, squares and triangles, respectively).

5.5 .2 Transport phen07nena in the ingl e-wafer horizontal reactor

Pr ior to di scussing th surface processes, the t ransport of rnornent ulIl , heat andChclllical species in t he 'ingle-wafer horiLjontal reactor incorporating chelnical react ions at '1 ubst rat surface ill '1 steady state are lllent ioned briefly since it is essentiall y t he S(1l11C a ' those in Chapter ~3 . whi ch di cussed t he t rallsport phenOl11ena fort he pi taxial sili con thin-fihll growth in det ail.
103

Streamlines in the reactor were essentially the same over the ternperature and
SiHCh concentration range of this study; the streanlllnes above the substrate were
almost parallel to its surface, and flow induced by natural convection was not observed in the reactor.

The gas temperature decreased almost llnearly with the

distance fronl the substrate due to a cold-wall environnlent. At 1398 K, SiB C1 3 concentration at the substrate surface were calculated to be Inuch lnwcr than that at the
inlet of the reactor because of the consurnption by the surface chenlical reactions,the diffusion and the thernlal diffusion as discussed ill Chaptcr 3. This diiTercllcc
of SiHC1 3 concentration became smaller with decreasing the substrate temperature
mainly due to depressing the the surface chemical reaction rates.
Over the epitaxial growth conditions in this Chapter, the gas flow, the ternperature profile and the chemical species distribution kept sinlilar patterns as thoseat 1423 K (Chapter 3) although the values of velocities, temperatures and species
concentrations varied with the substrate temperature and J\1W.

5.5.3 8v,rjace rate process

As mentioned, equations (5-1) - (5-13) are solved nUlnerically to obtain the overall
rate constant, k, and the surface mole concentration of SiHCI 3 , [SiHCbJ, so thatthe·calculated growth rates agree with the measured growth rates. Figure 5-1 showsthat 11k r:hangcs linearly with [SiHC1 3 ] as predicted by equation (5-31). A linear
relationship between [SiHCb] and 1I k holds over a wide temperature range. This
relationship also clearly indicates that the species and the clelTIental processes of theepit8u'Cial growth do not change in the wide temperature range.
The rate constants, kr and kad, are obtained by the slope and the intercept respectively in Fig. 5-4 from equation (5-31). Figure 5-5 shows kr and kad as a function ofliT. The rate constants, kr and kad' obey the Arrhenius law and are described asfollows:

kad = 2.72 x 10 6exp(-1.72 x 10 5 IRT),
104(5-35)

kr = 5. G3 x 10~1CXp ( - 1.80 X 10 5 1RT ).

(5-36 )

1::~ 1
o

0.02

0.04

0.06

0.08

0.1

~

~ 1000
(J)

"0

g

~

600
200

~

O----~----~--~----~--~

0.1

60000
40000

0.2

1073K

20000~

o

0.2

0.4

0.6

3
Surface concentration of SiHCb [SiHCbj ( mol / m )Fig .5-4 Change in 11k with SiHCI 3 concentration at 1073, 1223 and 1398 K .

10
10

1
0

......... 10- 1(J)~ 10-2~~ 10-3
"'0

ro

~

10

-4

10-5
10- 6
0.70

0.80
0.90
1 / T X 103 UK)

1.00

Fig.5-5 Rate constants of chemisorption, kad' and decomposition of *SiCI 2 , kr, as afunction of reciprocal temperature.

As di ' cuss Old in the previous section, the surface during the epitaxial growth is t er-

105

minated with chlorine atonlS or bonded with SiCb or SiCl. 39 The activation energyof the surface reaction leading to silicon formation is calculated to be 1.8 x lOs J In101
as shown in equation (5-36), which is close to 2.2 x lOs J Ilnol reported by Ohshita
and Hosoi. 4o The desorption of SiCb and HCI rnay take place silllultaneously since
the surface reactions in SiHC1 3-H2 and SiH 2Cb-I-b systeln are considered to be thesarne after the chemisorption of SiCb.
The calculated growth rates using equations (5-35) and (5-36) in two dirnensiona]coordinates are shown in Fig. 5-3 by the solid lines. Furtherrnore, the three din1ensional calculations are additionally performed by introducing the equations (532) ,(5-35) and (5-36) into the calculation model discussed in Chapter 4. The growth
rates obtained by the three dimensional calculations are found to be overlapped withthose measured and by the two dimensional calculations as shown in Fig. 5-3. The
measured growth rates are explained well by the calculated growth rates. It follows that the transport and epitaxy model developed here can describe the surface
reaction processes incorporating the transport phenomena in the reactor.

5.5.~

Evaluation of Hel etching effect on silicon cpita.T'ial growth ralc

The by-product produced by the decomposition of SiHC1 3 and SiCJ 2, HClrnolecules, can etch the silicon surface as 12

Si + 2HCl -+ SiCb + H2.

(5-37)In an SiC14-Ih system, the epitaxial growth rate have its rnaximurn with respect
to temperature and SiHC1 3 concentration. This phenomenon is attributed to theetching reaction by the HCI by-product.41 The SiHC1 3-H2 systern also has the maximum epitaxial growth rate 42 ,43 in a temperature range above 1193 K or 1500 K. Tbis
phenornena is thought to be caused by decrease in the total arnount of chernisorbcd
SiBCb at that temperature range. 43 These pheno111ena arc found above 1173 K, butsuch a high temperature is not used in recent silicon epitaxial growth processes. Dis106

cu.-sion in Chapter 3 showed that a growth rate calculation ignoring etching by HCl
could reproduce the Ineasured growth rate qualitatively. It has been clearly shownin Fig. 5-1 that there is a lillcar relationship between 11k and [SiIICb], which Ineansthat c4uation (5-30) it) sufficient to describe the growth in the SiHCb-H2 system.
The etching of silicon surfacc by lICI can therefore be ignored in the calculation of
epitaxial growth rate under the conditions of this study.

5.h .5 Stale of surface during epitaxial growth

The -taLc of the surface during the epitaxial growth is discussed further. The disC1L 'sion in this Chapter has shown tbat the non-linear dependence of the growth rate
011 th 1 readant concentration can be described by considering both the cherrusorpLiOll and clecOlllposition.

....--.. 1.0
I

'-'"
If)

2 0.8
'Vi
Q)

>

'p

u
~ 0.6
~

"'0
Q)

'6..

B
0.4
u

o
~

o

§ 0.2

'p

u

ro
u.
~

0.0

2

4

6

8

10 X10·3

Average molecular weight MW(kg/mol)

Fig.5-6 Fraction of occupied reaction sites, 8 , at substrate surface at 1073, 1223 and1398 K.

107

The s,ubstrate surface is covered with the chemisol'bed species, *SiCb. The fra Lionof occupied reactive sites, 8, is obtained from equation (5-23) using equations (f>-35) and (5-36). Figure 5-6 shows the state of the chemisorbed , urface during theepitaxial growth. At 1073 K, nearly all reactive sites are occupied by *SiCh ,veIl
at a very low average molecular weight of rnixed gase', MW. With increa ing th 'growth tClnperature, 8 tends to decrease, but over 80% of th reactive site' at thsubstrate surface are covered with *SiCl 2 even at 139 K and AIW of 6.7. Thi,'
n1ean that large portion of the reactive sites i chenli orbed by *Sj

h under boththe transport and reaction lirnited conditions u ed in industrial pro e, sC ' .

Decomposition-limited 1073K

1398K

Chemisorption-lim ited
0 . 1~----~------~------~------L-----~

o

2

4

6

8

1Ox1 0-3

Surface mole fraction of SiHCI 3 (-)

Fig.5-7 Growth rate limiting factor , F sp , at substrate surface during epitaxial growth .

It is also interesting to identify the rate limiting process at the substrate surface.
By considering a balance between the growth rates limited by the chernisorption(equation (5-33)) and the that by the decomposition (equation (5-34)), the surface
process lirniting factor) F sp , is defined here as follows:Pc_ kn.d [SiJICb]

SF -kr[fb]
108(5-3R)

F.sp is larger than one wbell the clecOlllposition is the rate lirnitillg process) while iti. srnallcr than one when the chernisorption is the rate limiting process. Figure 5-7
show~ the variatioll of the growth rate limiting factor, F sp , as a [unction of thesurface lllole fraction of SiIICI J . With increasing the growth ternperatul'c, Fsp tends
to decrease, that is, the growth rate is lilnited rnore oy the chernisorption.
Although the physisorption process does not appear in the description of theepitaxial growth rate, the physisorption is thought to be important for the quality of
the film because physisorbed reactants migrate and diffuse on the substrate surface.
Since tll chelnisorbcd species can hardly migrate on the surface, the physisorbed
reactant species should l11igrGtte to appropriate sites where silicon atoms should be
illC'orporat d. It is considered that tbis phenOlnenon makes it possible to obtain
good quality fUrns even uncler the reaction limited condition.

5. ').6 Non-linear increase in epitaxial growth ratelIere it is agalll considered why the silicon epitaxial growth rate changes nonlinearly with the increase in the MvV. As mentioned in Chapter 3, the transportphenomena are important.

Especially, all physical constants, for example, heat

capacity viscosity, diHusivity and thennal diffusivity, change with the tempratureand the NIW in ga, phase. The reactor for silicon epitaxial growth usually employs
tClllperature nvironnlent of cold wall where the substrate and the susceptor have thehighe t telnperature, thus, the gas temperature decreases with the distance from thesubstrate and sus epto!' urface. As shown in Fig. 5-8, the increase in the MW causes
the increase in heat capacity of gas 11lixture and thennal diffusivity. Since larger heat
capacity requires Inore heat to raise the ternperature of gases, the gas temperature
decreases with increasing the J\JvV. This leads to the increase in the tenlperatutegradient in ga phas , since the tenlperature of the substrate surface is controlled
to keep constant by using the heating and the tenlperature-monitoring system of
the epitaxial r actor. Furthel'nlOre, diffusivity and ITlany other physical constants109

of gas 111ixture dectrea. e due to low gas ternperatul'e. Although the decr ase in
the gas temperature lower the thermal difusivity, totally, the flux due to thcnnal
diffusion increase. The changes in transport phenOlnena are a part of the llon-]illc(1,rchange in the epitaxial growth rate, however, these arc not ufficient as descri bed ill
Chapter 3. The most important reason should be ascribed to the surface coverage' by
the source species at the substrate. When the substrate surface is covered completelyby the source species as discussed in this Chapter, the reaction rate at the, urfacc ,that is, the epitaxial growth rate, saturates and callnnot incr a e any more. Thi.
behavior is observed e pecially at the low sub trate telnperature.

As di cussed

above, the mechanisn1 of the non-linear increase in the ilicon epitaxial growth rCtLe
is cornposed of the change in transport phenornena and in surface chernical process.
Here, the former is minor and the latter is major.

I

Increase in MW

1

,

'*

'f

Increasein DT

Increase in Cp
of gas mixture,\

Increase insurface coverage
by source species

Decrease in T
in gas phase'*

Saturationof reaction rate
at substrate surface

Decreasein DT

Increase in 'J In T
in gas phase'¥

Decrease in 0 i

,

l

~

..

~

i'

~

,II

Increase in thermal diffusion
JT= - DT'Jln T
from substrate surface
to gas phase

Decrease in diffusionfrom gas phaseto substrate surface

t

~

W

'*

Non-linear increase in growth rate

1

Fig.5-8 Mechanism for non-linear dependence of epitaxial growth rate on source species
concentration in SiHCI 3 -H 2 system.

] 10

5.6 Sunlmary

The transport alld epitaxy lllodel in the SiHC1 3 -H 2 systen1 have been developedand evaluated experimentally and theoretically. The growth rate influenced by thetransport phenomena in the reactor and chemical reactions at the surface has been
described following the Eley-Rideal lTIode1. The entire processes of the silicon epitaxial growth in the SiHCh-H2 system have been assumed to be composed 'of fiveprocesses in the model, that is , (a) transport, (b) physisorption, (c) migration or diffusion, (d) chernisorpbon, (e) decornposition of chernisorbed species and desorptionof by-products. The surface reaction processes deternlining the growth rate consistof the ehelnisorptioll of Si HCh and the decornposition of the chernisorbed species,*SiCb, which reacts with H2 in the gas phase to produce silicon aton1S and HCI
IllO]CCllIcH. l3 y Llsi Ilg the raLe prOCCHS Llleory, Lhe LrallsporL auJ epi taxy lllOJel has

be n vcrHled to be an effective rnethod which can estilnatc the rate constants of the
Chcll1isorption and decornposition accounting for the transport phenomena in thereactor. The physisorption is also hnportant for the film quality because it enables*SiCh to rnjgrate appropriately on the surface, which results in excellent epitaxial filrns under industrial epita.,'(ial growth conditions. Since the epitaxial growthof silicon filn1s are usually performed below 1473 K, the etching effect due to theby-product, HCI, on the growth rate can be neglected.

111

N olnenclature(n101 n) - 2)

a : densi ty of reactive sites(.1 kg- I K - I)

Cp : heat capacity at constant pressure(1112 . - I)

Vi : binary diffusion coefficient of species i in lh(kgnl- l S- I)

D'[ : thermal diffusion coefficient of species i in 1[2(-)

Fsp : surface process limiting factor(m S-2)

9 : acceleration due to gravity(In)

hs : distance from substrate surface(mol m- 3 )[i] : mole concentration of species i at substrate surface
Jc : diffusion flux driven by concentration gradient(kg nl- 2 S-I)

JT : diffusion flux dri ven by temperature gradient(kgm- 2 s- l )(n14 m 0 }-1

k : overall rate constant

- 1)

k~d

chernisorption rate constant per ullit 11101e concentration of reactivesite(m 3 Inol- 1 -1)

kad :

k~e

k~d x adesorpUon(m S-I)
rate constant per uni L Inole concentration of reacLi ve(m 3 mo}-1 S-l)sitekde'. k'de x a(m .S,-I)

k: : etching rate constant per unit rnole concentration of reactive site
ke : k: x a

(111

3n

nlol-n ,-1)

(111 317,-2 nlol 1-n S-I)k~ : reaction rate constant per unit rnole concentration of reactive site(rn 3 nl0l- 1 ,-1)

kr : k~ x a(IllS - I)

Mav: average nl0lecular weight of gas mixture(kgmo]-I)

Msi : molecular weight of 8i(kg mol- I)

M( molecular weight of species i(kg lDOl- l )MW: average molecular weight of gas mixture at reactor inlet(kg mol-I)n : an order of etching reaction(-)

p : pressure(P8,)

U : gas constant(J nlol - I K - I )1J2

Ri : lnass rate of change in species i by chenlical reaction(kgm- 2 s- 1 )rnass rate of change in 8i by chernical reaction(kgm- 2 s- 1)

RSi :T : ternperature(K)

fluid velociLy in x-JirecLioll(In S-l)v : fluid velocity ill y-dirccLioll(nls- 1)1l :V : growLh raLe
V:\d :(n101 1n- 2 S-I)

chemisorption rate of 8iHC1 3(mol m- 2 S-l)

Vde : desorption rate of 8iIICh(mol m- 2 S-l)

\Ie : etching rate of 8i surface(mol m- 2 S-l)

Vc : growLh rate

(J-Lln min - 1)~, : decon1position rate to produce 8i(mol Ill- 2 S-l)x : coordinaLe in horizonLal direction(m)

X i : 1110le fraction of species i(-)

y : coordinate in vertical direction(m)Lhennal diffusion factor of species 'i(-)

A : therrnal conductivity of ga nlixLure(Wm- 1 K- 1)

0i :J-L : viscosity of gas rnixLure
Vi :(Pa·s)

Inolar stoichiOlnetry coefficient for species i in chelnical reaction

8 : fraction of reaction sites by adsorbed molecules

densi ty of 8i

Wi :mass fraction of species i(-)(kgm- 3 )P : densi ty of gas mixL ure
PSi :

(-)

(kgm- 3 )(-)* : chen1isorbcd staLe.

113

References[1] FLUENT U er s Manual, Ver. 3.0 (FluenL Inc. Hanov r , 1990).
[2] Kagaku Binran (Handbook of ChelnisLry) (lwallal)}i , Tokyo , 1081) 3rd cd.
Chap. 6, p. II-39 [in Japanese].

[3] Kagaku Binran (Handbook of Chenlistry) (Iwanan1i Tokyo, 1981) 3rd cd. ,Chap. 6, p. II-71 [in Japanese].

[4] Kagaku Binran (I-JandlJook of Chcll1i .. try) (Iwanall1i , Tokyo , 19 ~) 3rd ('d. ,Chap. 9, p . TI-239 [in Japancse].
[5] P. Pollard and J. Newlnan: J. Elect7'ochc7n. Soc. 127,711 (19 0).

[6] R.C.Reid, J.M.Prausnitz and B.E.Poling: Thc PropeTiies oj Gases and Liquids(McGraw-Hill, New York 1987) 1th cd.
[7] W. L. HolsLein: J. Electrochem. Soc., 135, 17

(] 9

).

[8] T. Aoyarna Y. Inoue and T. Suzuki J. Elecirochc7n. Soc. 130 2103 (1983) .
[9] J. Nishizawa and H. Nihira, J. Crystal Growth, 45 , 2 (1978).
[10] A. A. Chernov and M. P. Rusaikin, J. Cryst. Growth 45 , 73 (197 ).
[11] E. Sirtl, L. P. Hunt and D. H. Sawyer J. ElcctToche71L. Soc. 121,919 (1971).
[12] P. van der PuLtc , L. J. Giling and J. Bloc111 J. CrysL. Growth 41 ]33 (1977) .
[13] R. F. Lever, IBM J. Res. Dev. , 8 , t160 (1961).
[14] M. Nakagawa, Kogyo Kagaku Zasshi ) 62 177 (1959).
[15] J. Nishizawa and M. Saito, J. Cryst. Growth 52 213 (1981).
[16] V. S. Ban and S. L. Gilbert, J. ELectTochcrn. Soc. 122 , 1382 (1975).
[1 7] V. S. Ban, J. Electroche'm. Soc., 122 ,1389 (1975).

[J 8] Y. SaLo, T. 'l'alllura and T. Oll111111c: R~r{,cndcd 11 bsL'l'Ucls 1992 Int. Conf. Solid
State Devices and Materials, 20 (1992).
[19] M. Copel and R. M. Tromp, Phys. Rev. Lett., 72 , 1236 (1994).
[20] Y. J. Chabal and K. Raghavchari, Phys. Rev. LeU., 53 ,282 (19 4).
[21] F. Hirose, M. Suemitsu and N. Mi:yarnoto, Jpn. J. Appl. Phys., 29 , L1881 (1990).
[22] M. P. I) 'CVC1Yll, M. M. Nelsoll alld T. I ~~llgcl, S'l.l7j. Sci., 186, 7G (1~)~7).

114

[23J T. Urisu, J. Takahashi, Y. Utsullli, T. Akutsu and K. Kuchitsu, J. Electrochern.

Soc., 141, 1562 (1994).
[211] Y. Takahashi and T.

risu, Jpn. 1. Appl. Phys., 30, L209 (1991).

[2S] l). Il il'v(1 alld T. 1\. l\tkkallCll, S-u:rI Sci., 220, 1~37 (IU~D).
[26] L. J. WhiLlnan, S. 1\. Joyce, J. A. Yarrnofi', F . R. McFrecly, and L. J. Ternlinello,

SU'lj. Sci., 232, 297 (1990).
[27] A. Zangwill, Physics at Surfaces (Carnbridge Univ . Press, Cambridge, 1988)
Chap.8, pI88.
[2 J A. Sasaki, 1. Jpn. Assoc . CrysL. Growth, 20 ,321 (1993).
[29] W. A. Ti 1lcr, The Science of CTystalLizaLion: Microscopic interfacial phcn01ncna(Calnbridge University Press, CalTIbridge, 1991) Chap.5, p209 .
[30] W. A. Tiller, The Science of Crystallization:Microscopic interfacial phen01nena(Calllbridge[31]

niversity Press , Cambridge, 1991) Chap.5, p191.

Q. Gao, Z. Dohnalek, C. C. Cheng, \"'1. J. Choyke and J. T. Yates, Jr., Surf. Sci.,
30 2 1 (1994).

[32] A. C. Dillon, rI. L. ' Vi e, M. B. Robinson and S. M . George, 1. Vac. Sci . Technol.,A 13 , 1 (1995) .
[33] D. D. Eley and E. K. Rideal, Proc. Roy. Soc. (London), A178 , 429 (1941).
[31] I. Langlnuir, Trans. Faraday Soc . 17,621 (1921) .
[35] M. Kato J. :t\1urota and S. Ono 1. Crystal Growth, 115, 117 (1991).
[36] KYan1abc and KTaniguchi, IEEE Tran .Electron Devices, ED-32 , 423 (1985).
[37] T.O.Sedgwick, M.Bcrkcnbl1t and T .S.Kuan, Appl.Phys.LetL., 54 2689 (1989).
[3 ] T. O. Scdgwi k, P. D. Agnello NI. Berkenlit and T. S. Kuan 1. Electroche'm. Soc.,
138 3042 (1991),[39] Y. Ohshita, A. Ishitalli and T. Takada, 1. Crystal Growth, 108 , 499 (1991).
[4 0] Y . Ohshi ta and N. Rosoi, J. Cryst. Growth, 131 , 495 (1993).
[41] W . A. T iller , The Science of Crystallization:Microscopic interfacial phenornena(Carnbridge University Press, Cambridge, 1991) Chap .5, p202.
[42] S. E. Bradshaw, Int. J. Electron'ics, 21 , 205 (1966).
115

[13] J. M. Charig and 13. A. Joyce 1. ElecLrochC7n. Soc., 109 ,957 (1962).

11 G

Chapter 6
Effect of Transport Phenomena on Boron Concentration Profiles in Silicon Epitaxial Wafers

1176.1 Introduction

In this chapter the boron concentration profile ill silicon epitaxial ,\Taftr.' grov,]lunder atmospheric pressure in a single-wafer horiL',onLal r actor and a pall ake reactor i

Ludied, since boron is the mo t ill1portant dopant for YlOS device .. Pronl

the discussion of solid-state diffusion and the relation. hip between autodoping andmain gao stream in the reactor, it is shown that the lrug recir ulatioll of ga" in theepitaxial reactor greatly enhances autociopillg.

6.2 B asic equations for solid-state diffusion

(b)

(a)

OutletttOutletFig.6-1 Pancake reactor for preparation of silicon film . (a) , (b) and (c) show the heights
of horizontal planes of 20, 70 and 130 mm , respectively, from the susceptor and th e
substrates , where gas flow motion is visualized under a sh eet of laser light from the nea r
to the far side of the reactor chamber.

To improve the accuracy of evaluation of solid-state di (1'118ion in an epitaxial wnJcr ,118

t11e diHusivity of borOll atOllls ill p-type (100) silicon single crystals is evaluated[ronl boron concentration profiles fonned due to out-diffusion through heating in ahydrogen aJnuient at 1] 73, 1273 or 1373 K for 60 rnin in the pancake reactor shown
in Fjg. 6-1. Using the boron diffusivity obtained, the boron concentration profiles
in the epitaxial wafers arc calculated.
Equation and boundary conditions used for calculations of solid-state diffusion are
shown schernatically in Fig. 6-2. Conservation of boron atorns is described by thefollowing eC{uation:ac_~ = ~ (

at

ac)

ax D ax '(6-1)

where C is boron concentration (rn- 3 ) and D is the diffusivity (m 2 /s) of boron atorns
ill a silicon crystal. III lhc calculation or ouL-diffused uoron conceIltration profile,the following boundary conditions are irnposed on the substrate surface using anevaporation coefficient h (nl/s) as shown in Fig. 6-2 (a),

D

(~~)

=

h(Cs - Cg ),(6-2)

surfacewhere Cs and C g are the concentrations of boron atoms (m- 3 ) on the substratesurface and in the gas phase, respectively. Additionally, a boundary condition is
irrlposed wherein the boron concentration at an infinite depth from the surface attime t, Coo,t=t, keeps its initial value.

(6-3)
For the calculation of boron concentration in the epitaxial wafer, the boron concentration at a position in the epitaxial filnl sufficiently far from the interface between
the epitaxial film and the substrate at time t, C-oo,t=t) is fixed to the value measured
by secondary ion n1ass spectron1etry (SIMS), Cobs) as shown in Fig. 6-2 (b).
C-oo,t=L = Cobs

119

(6-4)

(l)
C/)

co

C/)

.c

8

0.

. ~

()

.0

<3

O'l

Ih (Cs - Cg)=D (-f- )I

epitaxial film

substrate(b)(a)

Fig.6-2 Equation and boundary conditions for calculations of solid-state diffusion. (a) isfor a heat treatment and a prebaking process ; (b) is for an epitaxial growth process .

Although equation (6-1) can be analytically solved for evaporation and difTll iOllfrom the ubstrate to the epitau-xial layer individually, the epitaxial growth InusL
be performed immediately after the prebaking proc s. in which remove a naUve
oxide film of the substrate surface. Since boron atom ar evaporated during theprebaking process, the initial boron concentration profile for the epitaxial growthshows rather a gradual shape. Diffusion equation with, uch an initial condHion
can be solved only numericaly, therefore, equation (6-1 ) is discretized into finite
difference formulae. The calculation domain is divided into 300 nonuni forn1 lnc. he.
for the evaluation of diffusivity and 500 nonuniforrn Ineshes for the calculation ofboron concentration profile in the epitaxial wafers. The lnesh widths are less than1 x 10-8 rn.
The difIusivity of boron in a silicon wafer is as urned to be independ nt of boron
concentration since the diffusivity is essentially constant at low boron concentrations «10 25 m- 3 ).1 The diffusivity of boron, D, and the evaporation coeffici ent, h,
are deterrnined so that the calculated boron concentration profiles agree wi tb themeasured ones.

120

6.3 Preparation of epitaxial silicon thin-film

To cornpare the effects of various transport phenomena in an epitaxial reactor on
the dopant profiles , two kinds of epitaxial reactors were used to prepare epitaxial
sjljcon thin-films.
Epitaxial silkon thin-filrns were grown in the single-wafer horizontal reactor shownin Fig. 6-3, which transport phenomena and reaction chemistry were discussed in
Chapter 3 and Chapter 5. This reactor has streamlines that are parallel to thesubsLrate withouL forrnation of a vortex above the substrate. A mixture of SiHCb
and 112 is introduced into the reactor for reaction at the surface of a boron-doped(100)-illch-diallleter substrate held horizontally in the reactor at 1073, 1273 or

1373 K for 120- 1200 s after prebaked in a hydrogen ambient at 1463 K for 90 s forrernovillg a native oxide film of the substrate surface.

gas . (SiHCI3)
In

~

~

.1

IR furnace

NVVWVVWVVV\ quartz glass wall.~'---~----~~~-----.~~----'\'\
substrate
susceptor

y

Lx

~L

I,~_------------~
-

-

'\

IVWVVVWWW\~ 50mmIR furnace

Fig.6-3 Single-wafer horizontal reactor for preparation of silicon film and for numericalcalculations of transport phenomena.

Using the pancake reactor in Fig. 6-1, epitaxial silicon thin-films were also grownon boron-doped (l00) 4-inch-diameter substrates. The epitaxial films were grown
at J 273 and 1398 K for 300- 480 s after prebaked in a hydrogen ambient at 1273 K('or 210 sand 1398 K for 60 s, respectively.
121

A nlixturc of SiHCh and Jh was introduced fron1 the inlet nozzle located at thecenter of the susceptor to four horizontal directi()ns of the r actor ehaInber.
Boron concentration in the substrate ,vas 4- 6 x 10 24 III -3, and their back surfaces
were covered with 500 nm-thick Si0 2 film since this effectively suppresse autodoping. 2 - 4 Thicknesses of the epitau'eially grown filrns were measured using interference
fringes in Fourier-transform infrared spectra. The concentration profiles of horon
atoms were measured by SIMS u ing CAMECA 1110de1 I IS-4f. Th" influence of
autodoping was evaluated from the difference between the boron cone ntration profiles measured by SI IS and those calculated by equation (6-1),(6-3) and (6-1) of
the solid-state diffusion.

6.4 Analysis of gas flow

To study the transport phenomena, the gas flow patterns in the single-wafer horizontal reactor in Fig. 6-3 and the pancake reactor in Fig. 6-1 were analyzed. SincE'
the quartz chamber of the single-wafer horizontal reactor i cornpletely surrounded
by a heating lamp module, no visualization techniqueS could be applied. Therefore,
the gas flow pattern analysis was performed by calculating transport equation -, "HIlappropriate boundary conditions. In the pancake reactor, the numerical calculation required 111uch computation time due to the three-dimensional nature of thetran~port phenornena.

Fortunately the reactor chaTIlber of the pancake rcu,C'toI' isequipped with a window at its side wall, thus the gas flow visualization teC'hniqu( ()could be applied in this case. Therefore, gas flow at roorn temp rature was visualizedusing small NH 4 Cl particles which trace the motion of gas mixtures of SiHCl 3 -Tl 2
at epitaxial growth temperatures. Motion of the tracer particles was illuminatedunder a horizontally spread sheet of Ar+ (4 W) laser light in the horizontal planes
at distances of (a) 20, (b) 70 and (c) 130 mm from the susceptor shown in Fig.6-1.

122

G. [) Results and discussion

6.5.1 BOTon DiJJusivity

Ii igure 6-4 shows boron concentration profiles measured by SIMS as a function ofd pth [rom the surface after heating in a hydrogen ambient for 60 min. Triangles,.. quares and ircles denote the measured profiles at temperatures of 1173, 1273 and1373 K, respectively. Although boron atom concentrations do not change at infini ted pths, they exponentially decrea e with decreasing depth from the ubstratesurface. The boroll aLOIn concentratioll near the surface decreases wi th increasing
trl nprr(1 tur "

Q)
()
C1:S

t:

::J
(f)

1022~--~----~--~~--~__~

0.0

0.2

0.4

1.0

Oepth( ~m)Fig.6-4 Boron concentration profiles after heating in a hydrogen ambient for 60 min .
Triangles, squares and circles denote measured profiles at temperatures of 1173, 1273
and 1373 K, respectively. Solid lines represent calculated boron concentrations under thesame conditions of temperature .

To valuat b oron diflu ivHy, equation (6-1) is solved nurneri cally using the boundary condi tions of equa tions (6-2) and (6-3). The di ffusivity is detern1ined so that123the calculated boron concentration profile near the sub trate surface agre s with themeasured one. The solid lines in Fig. 6-4 show the calculated boron concentration
profile. which agree well with the Inca. un d profiles. Frotn these calculations horon
difTusivity in a p-type . ilicon single crystal isD = 1. 22 x 10-5-3.65 X 10
21
T
rn s
4

exp

(6-f»)as shown in Fig. 6-5 a a function of reciprocal temperature (solid line). The diffusivity from equation (6-5) agrees well with the boron intrinsic diffusivity.l, 7-10 This
also indicates that the anomalous diffusion 11 due to crystal imperfection can be ignored in the substrates used in this study. The evaporation coefficient, h, affected
the boron concentration profile slightly only at po ition near the ur[ace; thu. forevery temperature h was assumed to be 0.1 rnls, which was comparable to 0.31n/s
obtained by Grove et al. 12 The effect of ga phase turbulence on the evaporation
coefficent can be ignored since the ga flows in both reactor are lan1inar a. cliseu, .'cellater.

o10-20 ..............-~---J'---.L._--L-_--L...-_L----I
7.2
8.0
7.6
8.4
1
4
10 /T(K- )Fig.6-5 Boron diffusivity in p-type silicon single crystal as a function of reciprocal temperature .

124

1\ Hhough the calculated profiles arc slightly different fronl the n1easured ones near
the substrate surface, the depths of boron diffusion under the heating temperatures
ar obtained accurately.

6.5.2 Boron concentration profiles in epitaxial wafers

1301'011

concentration profiles are calculated using equations (6-1)-(6-3) for the

prcbaking process and using equations (6-1), (6-3) and (6-4) for the epitaxial growthpro('('s .. '1 he evaporatiol1 of boron at0111S at the substrate surface, equation (6-2)
is igllored sillce the pitaxial growth is rnuch faster than the diffusion of boron insilicoll.

-0.6

-0.4

-0.2

o

0.2

0.4

Depth (flm)

Fig .6-6 Measured and calculated boron concentration profil,es around the interface between the substrate and the epitaxial film . Epitaxial films were grown in the single-wafer
horizontal reactor at 1073 K for 1200 s, and at 1273 and 1373 K for 120 s.

Figure 6-6 hows boron concentration profiles around the interface bebveen thesubsLrate and epitaxial filn1s '~Thich were grown in the single-wafer horizontal reacLor aL 1073 K [or 1200 s and at 1273 and 1373 K for 120 s. The change in boron
cOllcentration ].' gradua l with increasing epitaxial growth ten1perature. Although125the boron concentration profile changes at depths of -0.4 to O/-Lm at the growthtemperature of 1373 K, those grown at 1273 and 1073 K change at depth of -0.1 too/-LIn.
The solicllines in Fig. 6-6 are calculat. d horo11 concclltratiOl1 profiles b;.)'su l 011 Lh<:solid-state diffusion of equation (6-1) using the boundary conditions of equations (G3) and (6-4) and the diffusivity of equation (6-5) and show IniniIl1Unl changE' in theboron concentration profile due to the ~pit~-xial growth proces,. The calculated
profile for growth at 1373 K has a slight difference from the lueasured profile whjch
is a.'3cribed to autodoping. For growth at 1273 and 1073 K the calculated boron
concentration profiles agree well with the measured ones. For epitaxial wafers grownin the single-wafer horizontal reactor at temperatures lower than 1273 K, the boron
concentration profile is concluded to be due entirely to solid-state diffu ion, andautodoping is negli gible.

Fig.6-7 Calculated streamlines at 1373 K in the single-wafer horizontal reactor .

An analysis of the transport phenomena in the single-wafer horizontal reactor
discussed in Chapter 3 shows that the laminar streamlines near and above the su bstrate are parallel to the substrate and show no vortex, as depicted in F ig. 6-7. In
this figure, the calculated streamlines at 1373 K using the transport equations were
the same as those calculated at 1273 and 1073 K. This gas stream transports boron
126

alOlllS vap0l'i:t,ed frmn the substrUL(\ Lo the ouLlet. III this C'llviroJllJlClll, lhe 1l1ll1l1)('I'o r auto doped boron atOlYlS in the epitaxial [ihn is negligihle. Sinc( vaporization ofhoron aLorns frOIn the substrate is suppressed wi Lh decreasing ('pi Laxial gro\\Tth t {,lIlperature autodopillg sho\\'8 a negligible effect on Lhe boron conceni ration profile atl(\lllPcraturcs lower than 1273 K in the single-wafer horizontal J'('(lctor.

- --.....................................

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

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

Fig.6-8 Visualized gas stream coming out of the inlet in the pancake reactor at room
temperature in the horizontal plane at (a) 20 , (b) 70 and (c) 130 mm from the substrate.
Left half is a photograph of visualized gas flow and right half depicts gas motion uSing
arrows . Dotted lines show the configuration of the pancake reactor.

To di s('uss t he relationship betweell th boroll cone llt ratioll profile and the transport ph CllOll1Cll <1, th ~ gas flow visualization t 'chl1 ique 6 was applied to the pancakc]'(\aclor ill j ~ ig. 6-1, by \\ hich epita.'{ial filnls were also grown. Figure 6- show' the127gas strealn out of the inlet in the pancake reactor at roo111 tonperature. Gas motion
is observed in the horizontal cross-sectional images at heights of 20, 70 and 130 Hnn
from the. ubstrate . The left half of Fig.6-8 is a photograph taken frorn th visualization and the right half depicts the gas flow patterns using arrows. Although
gas nlotion at 130 mn1 is not clear , those at 20 and 70 mm how recirculating flows.
Gases coming out of the small holes of the inlet tube flow directly to the harnber
wall and return to the inlet at the center of the reactor to form the redrculatingflows. These gas motions are not turbulent and are the same as those in a Inall pancake reactor observed by Suzuki et al. 13 Since the forced recirculation are dominant,it can be assumed that the gas flow pattern at the epitaxial growth temperatur s iessentially the same as that at room temperature. Although the recirculating gas
motion at the near side of the reactor is easily recognized as shown in Fig.6- ) the
motion. of the far side are not clearly hown because of the la er light illteD. ity
being weakened due to scattering by the tracer particles in the reactor.

c?' 10 24

5s::::~.... 10 23e~ 10 22

s::::

o
u

(0

1021

1019~--~--~~--~--~~--~--~

-3.0

-2.0

-1.0

0

1.0

2.0

3.0

Oepth( flm)

Fig.6-9 Measured and calculated boron concentration profiles around the interface between the substrate and the epitaxial film. Epitaxial films were grown in the pancake
epitaxial reactor. Circles: prebaked at 1398 K for 60 s and grown at 1398 K for 300 s;
squares: prebaked at 1273 K for 2405 and grown at 1273 K for 480 s.
128Thc large mnount of recirculation above the ~mbstratcs transports hoth SiHChrnolecules and the vaporized boron dopant to the substrate surface. The differencein the gas strearn between the two types of epitaxial reactors is considered to affectthe boron concentration profiles in the epitaxial wafers. The epitaxial films weregrown in the pancake reactor at 1273 or 1398 K, and the boron concentration profiles around the interface of the substrate and the epitaxial film were measured by
Sf

S and are represented by squares (1273 K) and circles (1398 K) in Fig. 6-9. The

soUd lines are the boron concentration profiles at 1273 and 1398 K obtained by thenUlnerical calculations of the solid-state diffusion. Although the difference between
the Inca 'ured and the calculated boron concentration profiles obtained at 1273 K in
the 'ingle-wafer horizontal reactor i. very small, that at the same ternperature inth pancake reactor is very large and can oe ascribed to autodoping.

Fig.6-10 Schematinc view of the transport of boron atoms In gas phase. (a) is forthe single-wafer horizontal epitaxial reactor without recirculation; (b) is for the pancake
epitaxial reactor having large amounts of recirculation of gas.

A large amount of boron aton1S is vaporized from the substrate at temperatures
abovc 1273 K, the rnajority of which possibly come from the back surface of the
slloSLrate through the silicon oxide filn1. Although the vaporized boron atOllls aretransported frorn th'uostrate to the outlet in the single-wafer horizontal reactor,the.)' arC' transported back to the substrate via the recirculating gas tream in the
pancake reactor, aUOll pronl

ch Inatically shown in Fig. 6-10. An abrupt boron concentra-

can b fornled in the pita.--xial growth environlnent without the large
129recirculating flows near and above the substraLe because of the short gas residcnce
time. 14 , 15 The numerical calculation of the relationship between autodoping and therecirculation of gas is believed to be theoretically possihle , whf're the calculation
mu t be pcrfonned thref'-dimensionally in llon-. teady-state. Sine surll a calculation requires enormou ly long calculation tinle the boroll cOllcenLraLion profile due
to auLodoping is not calculated ill this study.

In the single-\vafer horizontal reactor the substrate is u. ually rotated to ohtainan uniforrn epitaxial filn1 thicknes. ; ho\~ ever the rotatioll rate is usually less than
50 rpm and is considered to induce recirculating flow which is limited to the area inclose proximity to the substrate. Therefore the effect of autodoping is till minor
in the single-wafer horizontal reactor using substrate rotatioll.

6.6 Conclusions

Boron concentration profile in ilicon epitaxial wafer. were mea. ured and . Ludied
with consideration of the transport phenornena in epitaxial reactors.
Epitaxial growth at ] 073- ] 273 K u. ing a singlc-wafer horizontal reactor lead.' toan abrupt boron concenLration profile at the interface between the epitaxial film andthe substrate, the back of which is covered with an 8i0 2 fibn. ]n the single-wafer
horizontal reactor, the boron concentration profile is formed predominantly by solidstate diffusion at ternperatures lower than 1273 K even under aLrnospheric pressure
because of negligible auto doping due to little or 110 recirculation of gas flow llenr andabove the substrate. In a pancake reactor which has very large recirculating flows
in its chamber, a gradual change in the boron concentration profile is observed due
to autodoping. To obtain an abrupt boron concentraUon profile , large amount. ofrecirculation of gas in the epitaxial reactor should be avoided.

]30

References[1] R. B. Fair, J. ELecirocherrL. Soc., 122 ,800 (1975).
[2] B .A.Joyce , J.e.Weaver and D.J.Maule , J.El ectrochem.Soc ., 112 , 1100 (1965).
[3] G. Skelley and A. C. Adarrls, J. Electrochem. Soc., 120 , 116 (1973).
[~] VV. II. Shepherd, J. Electrochem. Soc., 115 ,652 (1968).

[5] W. J. Yang, JJandbook oj Flow Visualization (Hernisphere, New York, 1989).

[G] Chapter 2 in this thesis.
[7] lfika Nenpyo (ChronoLogical Scientific Tables), National Astronomical Observatory (ed.), lVlaruzen Co., Ltd. , Tokyo, (1995) p. 150.

[H] K . Osacia, Y. Zaitsu, S rvlatsUlllOLo, M. Yoshida , r~. Al'ai and T . Abc ,J. JlJleclrochc7n. Soc., 142 ,202 (1995).
[9] A. D. Kurtz and R. Vee, J. Appl. Phys., 31 ,303 (1960).
riO] C. S. Fuller and J. A. Ditzcnbcrger, J. Appl. Phys., 27 , .544 (1956).

[11] D.Kahng, C.O.ThOlnas and R.C.Manz, J.Electroche7n.Soc., 109 ,1106 (1962).
[12] A. S. Grove, A . Roder and T. Sah, J. Appl. Phys. , 36 , 802 (1965).
[13] T. Suzuki, Y. Inoue , T. Aoyama and Nt ~VIaki, J. Electrochem. Soc., 132 , 1480
(1985).
[I~]

C. A. " Tang, S. H. Groves, S. C. Palmateer, D. \N. Weyburne and R. A. Brown, J.

Crystal Gr'owth, 77 , 136 (1986) .
[15] D.I.Fotiadis , AJvLKrerner D.R.1vlcKenna and K.F.Jensen, J. Crystal Growth,
85 , 154 (1987).

131

Chapter 7
Roughness of Silicon Surface Heated in Hydrogen Ambient1337.1 Introduction

Native oxide film at the silicon ubstrate surface n1ust be rerl10ved without surfa croughening before the epitauxial growth proce s which is u. ually performed at hightemperatures in an hydrogen arnbicnt. To reaIiz~ a desirable heat treatlnent processroughening of the silicon surface during the relnoval or the native' oxide RInl at thetemperatures lower than 1000°C should be studied.

1oreover, surface roughellingunder atrno 'pheric pressure rnu 't be investigat d because aLrllospheric-pre.· urc epitaxy can be applied to improve cost perfonnance in rnicroelcctric device fabrication.
In spite of the importance of such research, the Inechani 111 of urface roughening is
still unfortunately unknown .
In this chapter, surface roughness under atmospheri c pressure is discussed froIn
the viewpoint of the etch rates of silicon and silicon dioxide by hydrogen gas, for the
first time . It is shown that the competitive etching reactions of ili con and silicon
dioxide. with hydrogen gas play key role' in the forrnation of the pits on th sili collurface.

7.2 Experimental

Sample used were mainly 100-rnrn-dialneter polished sili con wafers of p-type 0.01
0.02 ncm (100) which were cleaned by the RCA pro cess . 1 Thickness of the nativeoxide films on the polished wafer surfaces was measured to be 1.0- 1.5 nm using an
ellipsometer (Ll15 B, Gaertner Scientific Corp.). To avoid incorporation of trace impurities of water or oxygen during heat treatment, a pancake-type epitaxial reactor(AEC-1620, Shimada Rika) and hydrogen gas with less than 1 ppm water content
under atrnospheric pressure were used because t hi s com bi nation can produc

pitax-

ial wafers of excellent quality. The three heat treatrnent processes shown in I"ig. 7-lwere adopted. In pro cess (a), the wafers were heated at 900, ] 000 an d 1100 °C ror
1- 100 min. In process (b) , the wafers were exposed to air for 24 h after the growth134

of Ct 10p,ln silicon epitaxial film at 1125 DC) and were finally heated at 900) 1000 and1100 0e for 30min. Tn process (c) the wafers were heated at 1100°C for lOmin
and werc additionally heated at 900°C for 30 min without exposure to any ambient
othcr than hydrogen. After these heat treatment processes) all wafers were cooled toh low 350 ()in hydrogcn ambient to obtain a silicon surface terrninated by hydro-gell <1t0111S. 2 1 hickness of the n<1tivc oxide film was measured with the ellipso111cLcr
to c. ti1nate the removal of the nati ve oxide films. Employing the same process, thect h rate of silicon dioxide film was estimated using native oxide films and thermaloxid fihns of about 30 nm thick. Roughness of each wafer surface was evaluatedby a light scattering method (LS-6030, Hitachi Electronic Engineering). Surfaces of.. on1e wafers were further evaluated by atomic force microscopy (AFM) (Nanoscope
IT Digital InsLrun1ents) Lo identify the surface roughness lTIorphology.

Si epitaxial
growth(10 !-Am)
1100 0
Q)
~

:J

~

e

1000 0 e
goo oe1125 ° e
Q)

~

~

:J

::J

~

~

Q5
c.
E
Q)

~

Q)

c.
E
Q)

~

Q)

c.
E

r-

r-

1100 0 e
10 min .

Q)

r-

Time

Time
(a)

(b)

(c)

Fig. 7- 1 Heat treatment of silicon wafer in hydrogen ambient: (a) heated at 900 , 1000
and 1100 °C for 1-100 min, (b) kept in air for 24 h after 10 p,m silicon epitaxial film
growth , and heated at 900 °C, 1000 °C and 1100 °C for 30 min, (c) heated at 1100 °C
for 10 min and 900 °C for 30 min .
The etch rate of 'ilic011 urfac~ .. due to their chen1ical reaction with hydrogengas w ~rc

'tirnat'd u.'ing thc proc s' shown in Fig. 7-2.

Silicon wafer surfaces

were oxidiz,cd in oxyg n alllbient containing v·,later vapor at 11 00 °C to produce.'ili c011 di oxi d fil n1s of 500 11]11 thick. Some portion of the sili con dioxide film on the135wafer was removed using the patterning process. 3 Next, these wafers were heatedin hydrogen ambient for 60 min. After these heat treatment processes, the silicon
dioxide films were rernoved using HF aqueous solution, and finally a step apP(,fLredat the boundary between the area etched by hydrogen gas and that covered wi thsilicon'dioxide film. The step height was n1easured mechanically (a-step, TENCO H
Instruments) .

8i02 film

8i02 film. . . - - - - . . . , Oxidation ~8-i----------~1 open~ndOW
8i wafer~

Heat in H2 ambient\ Step8i02 film Remove 8i02 film

~Si~--~I--~I

~

I

8i

-;;7'

8i

Fig.7-2 Process to estimate the etch rates of silicon surface by hydrogen gas.

7.3 Results and discussion

First, thickness of t he native oxide film after heating in hydrogen ambient i n1easured as shown in Fig. 7-3 , as a function of heating time to recognize the surface
situation quickly. The conditions of the heating time at 1000 and 1100 °C in Fig. 7-3
were chosen empirically considering the minimum prebaking tirne to obtain good surfaces of epitaxial fHrns in the epitaxial growth process. At 1100 °C, the native oxide
film was easily removed within 1 min. At lower temperatures, removal of the nativeoxide film became more difficult; they were removed within 4 min at 1000 °e, hutremoval took more than 10 min at 900 °C. The measured oxide t hi ckness in Fig. 7-;~
not being reduced to zero after heating long time is attributable to a rneaSUreHlCrl t
error.
After heat treatment in hydrogen ambient, the native oxkle fi1m s recovered their
origjnal thickness when left to stand in air for about 2 weeks.
136

Senne of the wafer surfaces show an intense haze after heating in hydrogen ambi-

ent. Figure 7-4 shows haze intensity of the silicon surface as a function of heating
temperature in hydrogen ambient, the values of which were measured at a photoInulLip1c threshold vc'lltage (PMTHV) of 450 V. Haze of the silicon surfaces heated[01' 60 lllill intensifies with decreasing heating ternperature, as shown by the triangles

in I~ ig. 7-1 (a). To confirrn this trend, haze intensity after heated at 800°C for 30 rnin
was a.ddi Lionally observed to be ncar 200 bit.

2

E
c

en
en
Q)
c

~

()

£
Q)

"0

'x

0

c
0

0

10
Heating time (min)100

Fig.7-3 T hickness of native oxide film after heating in hydrogen ambient . The wafers areheated at 900 °C (circles), 1000 °C (squares) and 1100 °C (triangles) under atmosphericpressure .

The relationship between haze generation and oxygen atoms incorporated in thesilicon cry tal 4 is examined experin1entally using process (b) in Fig. 7- 1. The circles
in Fig. 7-1(b) sho,\' haze intensity behavior of the epitaxial silicon film surface. Hazeof the epitaxial fi lms also intensifies with decreasing heating temperature, the sarne
as in th:l srunples grown by the Czochralski (CZ) method in Fig. 7-4(a) . This resultclearly shows that t his haze intensity behavior does not depend on the oxygen atoIns
illcorporated in the silicon crystal, because t he epitaxial filn1 has a rnarkedly lower
oxygen conten t conlpared to CZ crystal. T he haze intensity behavior is assurned tobe due to native oxide film of even as thin as 0.4 nrn whi ch is expected to be formed137

on the hydrogen-terminated silicon surface after a 24-h exposure to air. 5 ,6 To verify
this assumption, the haze intensity of the silicon surface obtained using process (c) in
Fig. 7-1 is measured, where the native oxide film is completely removed after haLing
at 1100°C for 10 min prior to the heat process at 900°C. The haze intensity after
process (c) is very low as shown by the square in Fig. 7-4. Hence it is concluded LhaL
the native oxide film, even though quite thin, plays a key role in increasing surfa(,(,roughness dudng the heat treatrnent process in hydrogen C1rnbient.

c200

£
~
'ecn
Q)

~ 100
Q)

N

~

I

o

~~

900

__________ ______________
~

1000

~

1100

Temperature (oC)Fig. 7-4 Haze intensity of the silicon surface measured by the light scattering method after
heating in hydrogen ambient under atmospheric pressure: (a) polished wafer heated at900-1100 °C for 60 min (tri angles) , (b) epitaxial wafer kept in air for 24 h and heated at900-1100 °C for 60 min (circles), (c) polished wafer heated at 1100 °C for 10 min and
900 °C for 30 min (square).

To investigate the behavior of surface roughening , surfaces heated in hydrogenambient are observed using AFM since the relationship between the haze and thesurface roughness measured by AFM have b een well discussed experimentally 7 andt heoretically.8 Figure 7-5 shows AFM images of the (100) silicon surface after heat
treatment in hydrogen ambient at (a) 1000°C for 4 min and (b) 1100 °C for 1 min.
A nonheated polished wafer is shown in (c) as a reference.

Although the AFM

image in Fig. 7- 5 (b) shows a surface as smooth as that in Fig. 7- 5 (c), that in138

Fig. 7-5 (a) has slightly sLc(~pcr hills and valleys than Lhose ill Figs. 7-5 (h) and(c).

The rnorphology shown in Fig. 7-5 agrees with the haze intensity behavior

in Fig. 7-1. Figure 7-6 also shows AFM inlages of the (100) silicon surfaces afLer
h at LrcaLlnent in hydrogen mnbient at 900°C for (a) 31nin, (b) 10 min and (c)30111ill under atmospheric pressure. As shown in Fig. 7-6 (a), many small pits are[orn1Cd even after 3 rnin of heat treatment. As the heatlng time is increased, Lhe pit
size becomes larger, as shown in Figs. 7-6 (b) and (c). However, both peak-to-valley(P- V) and root-mean-square (RM S) pit depths determined by AFM remain nearly
constant after 10 min as a major behavior, as shown in Fig. 7-7.

139

50
0
0

40

P-v
0

E30

c
.r:.

0.
(])
020

RMS

40
80
60
Heating time (min)100

Fig.7-7 Measured pit depth at (100) surface after heat treatment at 900°C in hydrogenambient as a function of heating time under atmospheric pressure. The circles andthe squares show the peak-to-valley (P - V) and root-mean-square (RM S) values,
respectively.

Figure 7-8 shows the AFM in1ages of the silicon surface of the (a) (100) planeand (b) (111) plane having small pits due to heat treatment in hydrogen ambient at
900°C for 3 min under atmospheric pressure. The pit shape is square for the (100)plane and triangular for the (111) plane. This dependence of the pit shape on the
crystal plane is the same as in various other surface etching methods. 9
These results from AFM show that the formation of srnal1 pits is responsible forhaze on the surface, and that the pits are formed by son1e etch reactions on thesurface, where the native oxide film, the silicon surface and hydrogen gas play key
roles.
The most probable mechanism is the etching of silicon or native oxide by hydrogen .
The measured etch rates of silicon and silicon dioxide fHrn by hydrogen gas after the142heat treatlnent process in Figs. 7-1 (a) and 7-2 under atrnospheric pressure are shown
ill Fig. 7-9. The etch rA-te of j li coll by hydrogen gas is slower than that obtained by

Gallois ct al. 10, but is cOlllparablc to that by Langer and Uoldstdn. II

...

•

•

•

••• •
•

#-

• • ••.•. • ••

o.
_1.,.,.. -. .,;

-

•

,. .

•

. ,.• •••t. .'- ,
,

•

o

I

5000

I

nm

Fig.7-8 Silicon surface of (a) (100) plane and (b) (111) plane observed by AFM after
3 min of heat treatment in hydrogen ambient at 900 °C under atmospheric pressure.

The etch rate of sili con shown in Fig. 7-9 should be considered as the minimum
cstilnation , b cause the step height rneasurelnent in this study detects t he depth orheight at only the highest hill in contact with the probe, diamet r of 5 11n1. The

143

etch rate of i1ico11 by hydrogen gas changes gradually throughout the nleasur 'cl
temperature range of 900- 1100 °C, as shown in Fig. 7-9. Since the etching reaction
ja heterogeneou one, the etch rate of silicon by hydrogen ga.s is governed bytransport phenomena of reactants and products as discussed in this thesis; therefor
it is governed by the reactor configuration, the desorption of iIi con hydrides ,10and the temperature field, such as hot wall or cold wall. The weak dependence ofthe etch rate of silicon on heating temperatur ITlay b attributed io tIl transportphenomena in the reactor. Additionally, silicon redeposition frOln sili con hydrid~s
produced during the etching reaction n1ay occur

2
10

1100

ilnu1tan~ou 1y.

Temperature (oC)
1000
900

~--~------.--------.----~

Q)

Cti
~

i3 10

-1

ill
10

-2

7

9

Fig .7-9 Etch rates of silicon (circles) and silicon dioxide (triangles) by hydrogen gas underatmospheric pressure as a function of reciprocal temperature.

Unlike the case of silicon, the etch rate of the native oxide filrn decreases significantly with decreasing the temperature, as shown in Fig.7-9.
At a higher temperature of 1100 °C, the native oxide film is quickly and cornpletely
removed , thus etching by hydrogen gas begins at approximately the sarne time over144

all elltire ~i li coll Burface, Bhown on the left side of Fig. 7-10. Here the silicon surface

etched by hydrogen gas is very smooth.

Si02

Si

I

Si02 film is removed quickly.

F: ~4

Si02 islands still remain.

~

r:::

~

Si02
Si: ' 1~Pit Si02 Pit

rv si V1

Si

Pit

Si

~

Pit

rv-....,S~i VJ

Fig.7-10 The pit formation model at the silicon surface heat ed in hydrogen ambient.

At a lower temperature of 900 °C, because the etch rate of the native oxide film
much slower t han that of the Bicon surface, the removal of the native oxide film
is expected to be very slow and incomplete. This relationship leads to the model ofslnall pit [ornlatioll shown on the right side of Fig. 7-10. At small areas where thenative oxide is relTIoved earlier than the rest of the wafer , the bare silicon surfaces
are etched faster by hydrogen gas than the remaining native oxide film; thus manypi ts are ultimately formed.
The native oxide film appears as continuing hills and valleys, because the silicon145

urface i oxidized 1l0nunifonnly and the native oxide film appears as islands hapes.
12-14 1 he oxide islands are 30- 70 nm in diameter 14 which corresponds to 1 x 10 11 2x 10 10 cm- 2 of the density of the islands or valleys.

Furtherrnore, it has beenreported 15- 20 that decolllposition due to cherrucal reaction between silicon dioxideand silicon leads to evaporation of silicon monoxide and finally to void formation in
the native oxide film. The void density is on the order of 10 9 cnl- 2.17 Densities of
the native oxide islands and the voids are cOIllparllblc to 3- 4 X 10 8 Cl11- 2 in this study
and 4x 10 9 cm- 2 of Yanase et al.,21 which are les than that of the oxide islands andvalleys. At the valleys the voids tend to be formed ea i1y because the void d "'\l1S1 Ly
increases with decreasing native oxide thickness. 16 Based on this finding, the densityof the native oxide islands and valleys can be a . ulned to be the rna"'dmum d 118ityof the surface pits.

It is considered that the valleys and the voids do not affect the native oxide film
thickness measurement by the ellipsometer, for example the thickness after heatedat 900 0

e for 10 min in Fig. 7-3.

This pit formation rnodel in Fig. 7-10 indicates that the pit depth does not changr
after the native oxide filrn on the surface is removed conlpletely.

This hehavior

agrees with both F - V and Rl'vf 8 shown in Fig. 7-7.
The pit depth is calculated following the pit fornlation model in Fig. 7-10. Since
the bare silicon surface begins to react with hydrogen gas after the renloval of thenative oxide from it, the tirne at which silicon etching begins at each site depends
on the local thickness of the native oxide film.

Therefore, the pit depth can b

calculated from the time required to remove the native oxide of thickness .6. whichis the P - V of native oxide film.

Pit depth (nm) =ht:,. f s.o x Etch rate of Si
Etc rate 0] 2

Figure 7-11 shows the calculated pit depths at 900,1000 and 1100 0of .6. using the etch rates in Fig. 7-9.

(7-1)

e as a function

The calculated pit depth increases withdecreasing heating temperature, consistent with the experirnental results of this146

study. Considcring that 6. is lcss than thc thickness of the native oxide [i11n, 1.0
1.5111n, and that the etch rate of silicon by hydrogen gas in Fig. 7-9 is a lninimurn
estill1CLtioll, e - V in Fig. 7-7 is consistently larger than the pit dcpth estirnatcd
using the etch rate in Fig. 7-9 and that calculated in Fig. 7-11.

!60~

Q50~
8'
900

0

~ 40
::l
CJ)

.§ 30
'(j)

§ 20
.c

15.

~ 10

o

0.5

1.0

1.5

2.0

Valley depth of native oxide film,!J. (nm)Fig.7-11 Calculated pit depth, P - V, on silicon surface at 900, 1000 and 1100 °C as afunction of valley depth of native oxide film.

The chclnical reactions for hydrogen-silicon 10 and hydrogen-silicon dioxide 22 canbe a'slllned as

(7-2)

(7-3)
(7-4)

where 8i 11.1 , 8ilh and 8iO are con idered to be the volatile products of the etchingrcacLi )llS.

'fIle et 11 rates of silicon and silicon dioxide are estin1ated as

(7-5)
(7-6)

147

where [H2] denote the lTIolar concentration of hydrogen in gas pha.'e, and k 1 , k2 andk3 are the etch rate constants of equations (7-2), (7-3) and (7-1), respectively.

sIngequations (7-1) (7-5) and (7-6), the pit depth is obtained from equation (7-7).
kdH k32J + k2
Pit depth (nm) = ~ x(7-7)
According to this model the pit depth frOITI equation (7-7) is reduced with decreasinghydrogen pressure. To examinc this model qualitatively silicon wafers coverccl wi Lhnative oxide films were heated in hydrogen ambient under reduced pres ure of 90 torr
at 900, 1000 and 1100°C following process (a) in Fig. 7-1. At 900°C, more tha1l
30 min was necessary to remove the native oxide £1ln1. The haze intensity of thesilicon surface was measured at P 1THV of 700 \' to det ct the difference in ha~eintensity more sensitively. When the heating temperature was lowered fron1 1100 °C
to 900°C, the increment of the haze intensity was within 10 bit which was mucb
smaller than that under atmospheric pressure. This haze inten ity behavior withhydrogen pressure agrees with results of Ohkura et a1. 23
From the discussion in this Chapter, the validity of the pit formation model is clear.
The slightly steeper hills and valleys at 900°C in Fig. 7-5 (a) can be also considered
to be due to an uneven oxide thickness and voids formation.

Additionally, theminor behavior of P - V and RA1S reaching their peak at 10 min in Fig. 7-7 can beconsidered that the pits having initially very sharp edge shape are rounded due tothe etching by hydrogen gas. It is noted here that the result for surface roughness
at 800 0

e does not agree with that reported by Yanase et a1. 21 who showed llO

surface roughening. The reason for this discrepancy is believed to be that their heat
treatment of 10 rnin is too short to generate surface pits, since the etch rate of silicon
dioxide by hydrogen gas at 800°C is expected to be extrernely slow compared tothat at 900°C. In some other cases, it may be possible that the etch rate of siliconis enhanced by thermal etching 24 or the effects of moisture and oxygen 25 which are
not dominant in this study.

1~8

7.4 Conclusion

The change of the surface roughness of silicon wafer after heating in hydrogencU11bicnt at 800- 1100 °C under atmospheric pressure was studied. The AFM images
show that the rough surface after heating at 900°C consists of srnall pits whose shapedepends on the crystal plane. These pits are formed primarily due to the chemicalr action of silicon with hydrogen gas, since the bare silicon surface is etched fasterthall the native oxide islands. The pit depth on the silicon surface after heating inhydrogen arnbient is described as a function of P - V depth of native oxide film.
The ("Olnpctitive etch reactiolls of silicon and native oxide with hydrogen gas arc thedriving force in the formation of the many small pits on the silicon surface heated at
low te111pcrature, with the help of the incornplete removal of the native oxide films
and the void fornlation.

149

References[1] "'>/'. Kern and D. A. Puot inen , RCA Rev. 31 , 187 (1970) .
[2] Y. J. Chabal and K. Raghavachari , Phys. Rev. LeU. , 53 , 282 (1984).
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151Summary and Conclusions

153

The tranRport phenon1ena in epita.xial reactor for preparation of epitaxial siliconthin-films have been discussed experimentally and theoretically. Additionally, somequalities of a ilicon cpitaxial wafer affectrd by thc growth condition hav hcrn
di cussed in this thesis.

The gases near the sub tratc and the usceptor flo\\' horizontally in bot 11 th('pancake reactor and the single-\vafer hori,mntal reactor at the epitaxial growi hItelnperatures under atrnospheric pressure. These motion' are consistent with tbosr
indicated by the growth rate profile.
For preparation of silicon thin-films in a SiHCI 3 -H 2 system, the nonlinear dependence of growth rate on the concentration of SiHCb was partly attributed to thechange in the gas flow and temperature fields in the reactor \\lith the SiHCb concentration. The effect of thermal diffusion in the present system was found to resultin a reduced growth rate. A substrate rotation in a single-wafer horizontal reactor
causes averaging effect of the nonuniform growth rate along concentric circles 011 thesubstrate, urface to achieve the good uniformit) in fihn thickness. Although nearly
uniform filrn thickness is achieved by the rotating substrate the concentration of
SiHCl 3 itself is not uniform on the substrate even at very high rotation rate. Frorn
the view point of the rate theory, the entire processes of the silicon epitaxial growthin the SiHCb-H2 system have been assumed to be mainly composed of chemisorption and decomposition of chemisorbed species which rate constant can be estimate
accounting for the transport phenomena in the reactor. rrhe chemical reactions at
the surface following the Eley-Rideal model can describe the nonlinear behavior of
the epitaxial growth rate.

As a quality of silicon epitaxial wafer, boron concentration profiles in silicon epita.xial wafers by two types of the epitaxial reactors are studied witl) cOIl!:5ideration of
the transport phenomena in epitaxial reactors. Large arnounts of fE_circulation of gas
in the epitaxial reactor should be avoided for obtaining a sharp dopant concentration154

profilc .
The cha1lge of the surface roug1111css of si1icon wafer after heati1lg in hydrogencunhient at 800 - 1100 °C under atrnospheric pressure lS observed. Snlall pits areformed primarily at low ternperatures due to the competitlve etch reactions of silicon
and native oxide with hydrogen gas with the help of the incornplete removal of thenative oxide films and the void forrnation.

155

~2~

H. Habuka, M. Mayusumi , N. Tate and M. Katayama, "Gas Flowand Heat Transfer in a Pancake Chemical Vapor Deposition
Reactor" , J. Cryst. Growth, 1 5 1, 375 (1995). 1995.$.6 ~ ~fr~3~

H. Habuka, M. Katayama, M. Shimada and K. Okuyama,"Numerical Evaluation of Silicon-Thin Film Growth from SiHCI3H2 Gas Mixture in a Horizontal Chemical Vapor Deposition
Reactor" , Jpn. J. Appl. Phys., 33 , 1977 (1994). 1994.$.4~~1=r~4~

H. Habuka, T . Nagoya, M. Katayama, M. Shimada and K.
Okuyama, "Modeling of Epitaxial Silicon Thin-Film Growth on a
Rotating Substrate in a Horizontal Single-Wafer Reactor", J.
Electrochem. Soc., 1 42, 4272 (1995) . 1995.$.12 ~ ~1=r

~5~

H. Habuka, T. Nagoya, M. Mayusumi , M. Katayama, M. Shimada
and K. Okuyama, "Model on Transport Phenomena and Epitaxial
Growth of Silicon Thin Film in SiHCI3-H2 System underAtmospheric Pressure" , J. Crystal Growth (~nJli)~t:p). 1996.$.~1=r
.:y~

~5~

~~~~ , JtLlJ lE12t, ~EE~ , ~LlJ g~~, "~$m~t~ffijJXJit~~Ji L, t.:SiHCI3-H2*SiI [:::°9::t- ~ -\7 )l"px~O) - ;,x~~f@m*JT" ,a **5~px~~~~, 23(1), 2 (1996). 1996.$.3 ~ ~1=r

~6~

H. Habuka, M. Mayusumi , H. Tsunoda and M. Katayama, "Effectof Transport Phenomena on Boron Concentration Profiles in
Silicon Epitaxial Wafers", J. Electrochem. Soc., 143,677 (1996).
1996.$.2 ~ ~1=r

~7~

H. Habuka, H. Tsunoda, M. Mayusumi, N. Tate and M. Katayama,"Roughness of Silicon Surface Heated in Hydrogen Ambient", J.
Electrochem . Soc. , 142, 3092 (1995). 1995.$.9F.J~1=r