54 Model of the epitaxial chemical vapor deposition reactor for design and performance optimization

ChemrcalEngrneenngSc~ence Vol 35,pp 429-436 Pergamon PressLtd ,1980, Pnntedm GreatBntam

54

*,lODEL OF

THE

EPITAXIAL

FOR

DESIGN

RoZnov,

n.o.,

:'Inst~tute

of

J.

RoZnov

Radh,,

Drocess

Academv

of

DEI'OSITION

REACTOR

OPTIYIZATION

Cermdk"*

nod

Chemical

Czechoslovak

VAPOR

I'ERFOR?IANCE

Jbza",

LJ.

ATesla

CHEMICAL

AND

Czechoslovakia

Fundamentals,

Science,

Prague,

Czechoslovakia

ABSTRACT "lode1

of

the

based

on

fundamental

geneous transnort

reactlon

nhenomena set

results

of

being

denosltlon

with

"ubllshed the

taken

occur

In

Into the

account

gas

The

for

above 1s

set

design

the

heterowith

denosltlon

solved

of

comnarlson

nrocess

develoved

of

slmultaneouslv

nhase

renresentative

1s

Kknetrcs

ecuatlons

models.

model

reactor

nrlnclqles.

dlfferentlal

compared

of

vanor

1s

which

Fartlal

orevlouslv

sultabllrty

chemical physlcochemlcal

denosltlon

Obtalned

with

epltaxlal

surface.

numerlcallv,

exoerlmental has

the

data

demonstrated

and the

nurnoses.

KEYWORDS Epltaxlal

reactor;

reactor

design;

phenomenologlcal

chemical

model;

vanor

deoosltlon;

thermodlffuslon.

INTRODUCTION Chemical mental CVD of

vapor

deposltlon

chemical

nrocesses

reactors

a

gaseous

monocrvstalllne

the

laver

At

of of

In

the

desired

the

the

reactant

slllcon

manufactured).

nroblem

nrocesses

mixture

(on

surface

which of

nronertles

modelllng

(CVD)

reDresent

nroductlon

streams

belnq

over

formed. an

the

funda-

heated

In

wafers

structures

reactions In

of

the

clrcults.

the

clrcult

chemical

zone

themselves

Integrated

inteqrated

wafers

denosltlon

of

take

nresented

erlitaxlal

are Dlace,

yaper

reactor

the

1s

solved. vonocrvstalllne (1300-1600 tlvelv.

enltaxlal K)

The

sIllcon

reduction

prlnclnal

SlC14

+2H2

SJ_H*

-

or

laver

nvrolvs1s

chemical _

1s

of

reactlons SJ_ +

4

formed

by

chlorosllanes

the and

hlqh

temperature

sllane

resnec-

are:

HCl

and

resoectlvelv. Hydrogen barrel

1s tvne

SX

BesIdes used 1s

as

+

2

S1C14 a

denlcted

carrier

H2 other

chlorosllanes

gas.

In

schematlcallv.

429

Fig.

1

are an

also

enitaxial

used

some

reactor

times. of

Electrochemrcal

430

Reactor Engmeenng

lb

GAS

Metallu~

-

Use of New Forms of Energy

I-54

INLET (H2 + SiCIk)

I--

FUSED

o--

SILICA NBE(+-Q2m)

RF HEATING GRAPHITE

COIL HEATER

SI WAFERS

Fig.

SchematIc

1.

nlcture

of

the

enltaxlal

reactor

THEORY The

problem

number

of

of

however

authors.

lImIted

anDllcabllltv the

Rundle

(1968)

hermal

lamlnar

rlcallv a

have

the

slug

nar

of and

boundarv assume

of

the

the

and

model

existence

as

more the

of

of

mass

dlffuslon

suitable.

laver

far their

and

In

a

All

controlling

In

Isot-

solve

lamlnar

nume-

flolr

Donaghev

(1977)

simultaneous While

channel

Andrews

Everstevn gas

the

system.

the

a

thennodlffuslon.

(1972)

of

flow

so

transfer

solution

consider

stagnant

of

Manke

(19661,

(1970)

being

developed

lamlnar

Bradshaw

used

bv

ootlmlzatlon.

co-workers

fullv

nroflle

vroblem

Belvl

of

and

analvtlcal

mixture,

Kuznetzov

chase effect

with

subsenuentlv

nerformance

nroblem

temnerature

develoned

been and

the

In

dealt

have

gaseous

F~-I~L _

transfer

fully

solve

reactor In

svstem.

mass

been

attalnable

neglected

apnroxlmatlve

reactant

laver the

and

flow

In

authors

flow

(1969)

the

and

dlffuslon

linear

transfer

mentloned

design

has which

models

analytically

nroblem

transversal

mass

of

denosltlon, solves

obtained

and

the

assumed

the

modelllng

aparoxlmatlons

accuracy

for

have

of

reactor

Rough the

as

authors

Drocess

with

eDItaxIal

and

heat the

with

above laml-

co-workers

anpllcatlon

of

and

co-workers

adlacent

to

the

lamlnar (1970)

denosltlon

surface, The

alrn of

nrocesses

our which

descrlptlon

as

work

consists

occurr exact

In as

In

elaboration

reactor

deqosltlon

uosslble

Our

basic

of

more

zone model

nreclse using

model

therr

assumntlons

of

mathematical are

follo-

wing: 1)

lamlnar

of

reactant

2-dlmenslonal mixture

flow

dlffuslon

of

reactant

_nrofrle),

4)

thermodlffuslon

gaseous

nhase,

5)

of

(develonlng to

flnlte

reactant

mixture,

temnerature

and

devosltlon

rate

surface

owing

to

high

of

chemical

2)

(develonlng temnerature reaction

gradual

velocltv

3)

concentration gradients

on

temneratlon

nroflles),

the

In

denosltlon

I-54

surface,

6)

the

chlorosllane as

well

tor

effect

to

as

In

the

5).

reoresents

the

model

the

reactlon

nroducts

being

Assuming

the

blnarv can

qhenomena

In

gaseous

The

equation

of

nhase

contlnultv

the

equation

of

motion: =

of

"nabla

=

51

= =

=

p

1s

dlffuslon

conductlvlty

+

c

the

exnresslons

(Eqs

(1)

-

(4))

P

flow

-yr

neraendlcular

w1

1

for

chlorosllane, of

Llghtfoot,

2

for

transnort

1960).

vector are

dlfferentlal given

as

onerator

follows:

T

mass DT

sneclflc fluxes

exnresslng we

(5)

some

can

fraction thermal n

(Eas vector

and

the

reactant,

-

set

(7))

of

i!ilinear

coefflclent,

unit tensor, $ constant nressure.

eauatlon

the

brought

at

(5)

reasonable

be

of

dlfsuslon

nressure, heat

obtain

condltlons

Into (Ecr.

five

geometry

of

the

fIna

(pD

awl -1

+"

3)

as

two

martial

assumntlons

to

erruatlons

which reactor form

veloT

X

abso-

thermal Substltuof

change

scalar

ones

drfferentlal result

malnlv

denosltron (gas

flow

zone,

dlrectlon-

x>: awl -+uax

awl ”

a(pux)

>

=

ay

a ax

ax

DT aT (--> ax

T

(8)

ax

a (puy) +

ax

time.

(7)

masslc

eauatlons

P(Ux

of

(6)

tensor,

Introducing gas

DT31n

stress

flow),

set

mass

&cDT

for

and

(two-dlmenslonal

the

and

effect

ps 2

mass,

a

and

of

+

-

coefflclent,

tlng

the

pD3wl

+

volumetric

temperature,

eouatlons.

f

--X$T

D

lute

-

&

city,

the

0

pwlf

where

heat

and

if

pb W

momentum,

1.

$ 1s momentum flux tensor and 3 1s sf. Mass, momentum and energy fluxes El

nhase control

energv-

(S.Sw> where

mixture:

gas

reac-

0

q

of

eauatlon

for

of

8)

klnetlcs

descrlntlon

Stewart,

densltv

assumptions

reactlon

mathematical

comnonent

llmlts

Introduced

same

of

mixture

denendant,

the

(subscrlnt

for

conversron

reactlon

simultaneous

the

the

reactant

between

above

at

(Bird,

contlnultv

eouatlon

the

the

-

431

temoerature

denosltlon

mixture

with

the

'&$'

of of

on

denosltlon

the

considered

start

($_Z5,>

on

solution klnetlcs

reactant

we

and

based

numerical

qroblem,

and

region 3)

(HCl)

nronertles,

concentration

transltlon

transfer

hvdrogen)

product

transoort

(assumption The

chemical vapordeposltlon reactor

reaction 7)

rate

control

Cassumptlon

of

s111con,

reactlon

oneratIng

dlffuslon

from

epltaxml

Modelofthe

= av

0

(9)

FIectrochemzcal Reactor Engmeenng Metallurgy ~ Use of New Forms of Energy

432

au

aLI

y+u

P(Ux an

-

above

have

to

an -

-

(10)

ay

ax

(11) 3 (cnT)

+u

Y

ax

Introduced

esuatlons be

ax

a (CDT)

teal

au .--x)

=

0

P(Ux The

v

3X

=

ax

Y) ay

I-54

ecruatlons

(PDE)

find

=

as

In

five

functions

In

(12)

ax

renresent unknown

2)

tx

fax

ay

the

set

of

variables-ux,u

terms

of

x

and

five

nartlal

dlfferen-

,T,n

and

These

v satrsfvlng

y

wL. the

boundary

condltlons-

UV

V

=

Y

> 0;

0

x

=

u

U

odx)

= 0:

=

U

=

X

T

0

0

TO(x)

ux(v>

v

T

=

=

-

-uxw

T1(y)

=

x

x

=

H(y):

= 0

uY

T

= T2(v)

UX

=

PD

-

last

eauatlon

Ln

which

nrovldes

condltlon flux

on

the

denosltron

nreexnonentlal

factor

reactron

rate

Once

solution

the

eauatlons

the

been

for

and

the

H(v)

obtarned,

of

LS

of

can

along

of

set

Arrhenlus

of

boundary

and of

reactor

drffuslon

reactant,

A

enuatlon

for

channel.

nartlal

the

reactor

rate

fraction rn

wrdth

calculate

the

non-linear

reactron

mole

energv

Introduced we

slllcon

strongly

1s

the

Cl51

ax

dlfferentlal

dlstrrbutlon

denosltron

zone

of

the

according

to

relation: ElS, g(y)

e(y)

=

designates

does

not

the

eaual

yield

to

1

of

=

T

ax

the

owing

2HCl+S1

DT aT +---->

awl -

(pD hill p.S1

0

enualltv (x=0).x1

above

T

a

actrvatlon

(14)

DT aT +--_=O

awl

remresents the

E

and

of

rate

(14)

surface

constant

has

denosltlon

Eqs

C-E/RT)

0

ax

The

exP

A

(13)

0

ax

PT 1

n

aT .-

ax P

=

n

01

DT

awl ---

-D

=

5 > 0;

y

=w

w1

to S&12

ax

denosltlon the +

reaction.

formatlon H2

(16) y,x=o

of

Kx(T)

Uszng

SrC12 1

by

chlorosilanes a

fast

it

reactlon.

XSIC12 2

(17)

XHCl Gaseous vleld

.SLC~~ of

diffuses

denosltlon =

9

a-way

GSlCl*

l-

concentratLon

lated LS

then

from

the

given

aqnroxlmatlve

of mass by

the

derJosltlon

surface

and

reduces

the

8: _ %1C14

GS1C14 The

from

%C12

Prlmarv balance,

En.(l7)

analytIca

(18)

and

reactlon SlC12 the

solution

nroduct

HCl,

concentration mass of

flux GSlCl corresnondln$

xHcl
the can

can

deposltlon be

dlffuslon

obtained

be

calcusurface bv

eauatlon.

the

I-54

Model ofthe epltaxml chemicalvapor deposltlon reactor

433

RESULTS Program

for

numerlcal

solutron

using

method

elaborated, that

the

equations

calculations flow

of

out

the are

from

the

reactant

due

to

of

the

entrance

above

flnlte

narabollc

mixture

the

of of

At

non-llnearltv

of

set

makes

L>osslble

of

reaction

zone

each

sten

the

has

fact of

dlrectlon to

and

been

The

nrogress

have

enuatlons

PDE

1979).

In

lteratlons

differential

of

(Jdza,

type

(v=O)

(y).

Introduced

differences

of

be

carried

boundarv

con-

dltlons. The

binary

mixture

tant

mixture

nort

pro?ertres

nressure of

was

and

of

grid

theorv

Stewart,

values

for

E

narameters

the the

Grogram

surface

and

state

(In

In

dIrectIon

series

reactor

of

design

for

ments

(15

(Jbza, zone

the

barrel

total)

The

was

accuracy

described

are

the

each

deviation plotted

4

at data

nredlcted

on

Box

denosltlon and out-

nroflles

denosrtlon

the

on

can

high

If zone

average

capacltv

multlfactor

(Box,

two

efflclent

(y,T

along

factors

denosltlon

zone

characterized

rate

was

calculated

according

tvnlcal dlstrlbution

with

total)

agreement of

all

15

to

can

be

denosltlon

In

seen

rate

the

denosltlon mixture

the

and

StatIsrelative

exmerlments

exnerlmental results

of

uov.

bv

of

in

exnerr-

u 1' oy*x1) deoosltlon

reactant

conditions

comparison

the

namelv:

lnnut

the

nolnts

The

ldentrflcatlon

rate

of be

1957).

variables

In

lndustrlal

exnerlmental

Hunter,

three

entrance

The

at

1979)

program

the

For

90 A

the

denosltlon

obtained

model.

8%.

the

concentration the

needs

lndenendent

denending

exnerlment,

on

for

of

S1C14

deposltlon

value the

In

or=1.3%.

theoretlcal In

as Tl,

velocLtv of

of

deslgned

model

devlatlon

dlstrlbutlon

to

out

exploration

drstributlon

measured

linear

standard

dard

were

temperature

mean

Points

according

the

the

control-

velocltv7

velocity

along

A

estimated

(Jdza,

zone.

and

of

txme.

carrred

surface

from

geometrv,

denosltlon

run

heat

values

exnerlments

been

mixture

rate

orogram

comouter

was

tyme

response

One

tyne

zone

concentration denosltlon

The

data

reactant of

values

literature

from

has

exnerlmental

entrance

of

flow(v).

370

nolvnomlnal

g(v)

tlcal

gas

IBV

1979).

surface

the

temnerature,

exnerlments

In

emplrlcal

at

nolnt

1250K-klnetlcs

(annrox

trans-

from

The

evaluated

obtained

demosltlon

each

Sneclflc

(1971).

Kx(T)-Ea.(l7)

with

from

1974).

were

as

of

In

1954).

reac-

temnerature,

Hlrschfelder

over

tables

1979)

enter:

by

of

of

out

Bird,

Ec.(l4)

temneratures,

dlstrlbutlon

an

of

there wall

to

of

of

model

carried

taken

JANAF

constant

calculation

functions

Snegova,

rate

(Jdza,

The

derived

were

relation

behavlour

as

was

Sladkov, from

state

law.

Curtlss,

denosltlon

the

values

the

minutes A

Inputs

addltlon

requlred)

of

reactor

variables

nuts

of

Eculllbrlum

comnarlson

gas

(p,X,D,DT)

relatrons

taken

Arrhenlus

The

lteratlons

1960;

temperatures

denosltlon).

from As

In

Ideal

parameters

were

denendance low

all to

notentlal

gas

the

(Hlrschfelder,

Llghtfoot,

ideal

relatively led

In

gases

consldered.

mrxture

according

of

Lennard-Jones

temnerature

by

reactant

comnosltlon

(Bird,

and

was

described of

difference

krnetlc

H2+SlC14

the

the

above

data

(6

relative rn as

Fig.

stan2.

obtalned

There

Fig. from

the

tal

The

2.

the

condltlons

region).

In

the

same

1s

nrogram).

HCl

on

addltlon C.

assumntlon

the of

of

The

and

3

Figs-

a

and

and

respectively program In

as

Figs

3a,b,c

well

as

referred

In

rather

as

(see

1s

r7revlouslv

of

was In

exnerlmodel

reactlon

nro-

neqlected.

In

calculation

of

slmnllflcatlons also

that

denosltlon

nubllshed

our

curves

own

the

introduced

(wl=O

rartlcularlv

the

reactzon nubllshed

and

klnetlcs

are

models)

by

and

whack

describe

experlmental

represent

(1972)

co-workers

models

model

E,F,G

obtalned

most

of 4

Fig. Manke

the

oractl-

and

the

data

is

predlctzons

Manke

correspondzng

(see

does

require

G)

one

bv

aLffu-

grven

In

Rundle

Donaghey"s

modlflcatrons

curves

a

sultable F)

that

the

the

for

a malnframe

dlstrlbutlon

model pocket for

rate the

(1977)

In

our

of

of

5

for

Rundle

of can

This

be

The model,

Fig

models

own

g(v)

there FLgs

Tl

(see

Fig.

and

'see

and

described

however,

1s

1s

efforts

Donaghey's

calculator

3a,c data

3b)

comgutatlonal

classlfled

at

J_S given

exnerlmental

K

model

rate

4

factor

with

the

programmable

a mlnlcomnuter. computer.

the

Yanke

calculator. a

on

Tl=1473

view

denosltlon In

agreement

work

no1n-t

of

temperatures.

deposltlon

Donaghey-s

for 1s

the

surface

Illustrate and

suitable

model

given

average

From

simple

curves

1s

deposltlon

accldental.

being

[see

Ea.(17)

concluded

of

modlflcatlons

effect

former

exnerlmen-

centre slmnllfvlng

neglected

the

the

the

some

the

denosztlon

of

them

of

B

was

be

corresnondang to

reactlon

can

I-54

nodel.

~revzousl~r

there

different dependance

the

It

the

corresnondlng

curve

besides

Energy

agaIn).

three the

(as

D

and

with

The

4.

FuJ~~

(19681,

denosJ_tlon

by

of

controlled

the of

case

curve

and

effect

thermodlffuslon

omitting

channel

the

obtalned

of

surface).

coirqarlson In

(as

dlffuslon

InvalIdates

slon

figure

thermodlffuslon

slgnlflcant

A)

of

assumptions.

corresnondlng

the

of

Use of New Forms

-

mc,del

(curve

In

of

case

denosltlon

effects

tally

vleld

effect

In

model

illustrated

the

the

the

some

for

orlglnal

curve

of

described

assumntlons

duct

effect

(both

In

Metallurgy

Engnaeenng

above

data

mental

at

Reactor

Electrochemrcd

434

curves

as E)

model FUJII-s In

the

this only

work one

Modelofthe

I-54

t 52 c E

I

a12m1

4J_.

\’ i,‘\

y-OQB

d.Ym

+mspl-

\ ’

2’ i

435

*-usoK

“\

51

epltaxnlchemmalvapordeposltlon reactor

‘;‘-.

‘\

\

ra

,,.“-----_____

-_

E

_-___----

\

t

0

a,

0

-44

O-2

d-*oop-bn=-

Fig,

1J-----J

Comparison with

az

0.1

0

dr(oncr

3.

1 t

RO 3b

t

of

daq

J

--rR

2-z

’

0

dl

*sta-ca

zun

&Qadual

different

exnerrmental

ho

theoretlcal

02

mow apaHi-

--rm

zonm

models

data.

-. a12md x,-a007 9

+.xpnn-

*ah

;

__

__.--

--

--

--

m-

dqJLlsltcm

Fig.

4.

Temperature

denendance

drfferent so

far

the

which

case

owing

to

of the

can the

w-r,

of

w

deposltlon

rate

for

models.

describe

adeauatelv

remalnrng

stronglv

1.mp.rut~

mentroned

slmplrfyrng

the

phvsrcal

models

one

assum?tlons

realltv. can

(Neither

expect

better

In

results

Introduced)

CONCLUSIONS The

comnarlson

necessltv

of

formulating about

the

with

the

The

red

emplrlcal

theoretical

renresentatlve

of

consrderable

model

the

theoretical

comnlexltv

rements. with

a

lntroduclnq

model obtalned

set

model model

model

Ideas of

of

anv can

be

the

reactor.

this

In

surtablv

however

hrgh

Its In

confirms

the

exactness

Thr_s

with

theoretlcal

consists

aoplled

data

sufflclent

together of

tyne,

experlmental

of

a CVD

obtarned

advantage

of

when

brrngs

computer model,

generality the

desrqn

recul-

when

comnaThe

of

a

new

Electrochemrcal Reactor Enganeenng Metallurgy -

436

reactor

or

when

solving

Sensltlvlty

reactor. geometrical)

renresents LIST

A C

OF

Arrhenius masslc

13

some

dlffuslon

of

another

of

the

the

oatlmlzatlon

effect

of

Interesting

of

different

area

of

an

existing

factors

Its

(e.g.

aonllcatlon.

SYMBOLS

preexponentlal speclflc

D

nroblems

analysis

I-54

Use of New Forms of Energy

factor

T

heat

coefflclent

DT

thermal

E

actlvatlon

dlffuslon energv

4

deposltlon

rate

G

mass

H

width

of

heat

flux

absolute

temnerature

U

linear

W

mass

fraction

mole

fraction

coefflclent

velocltv

xi

JW

flux reactor

equlllbrrum molar

p

pressure

transverse

Y

longltudlal

0

yield

x

thermal

conductlvlty

v

dvnamlc

vlscosltv

P

volumetric

T

stress

4

momentum

channel

constant

KX

M

X

mass

coordinate coordinate

mass

flux

REFERENCES Andrews,

R.

W.,

Technol., Bird,

3.

R.,

W

Phenomena, Box,

G

D.

M.

61-66, E.

P

and

New

, and

J.

E.

G.

Wright

(1969).

Solid

State

10.

Stewart,

WlleY,

E.

Rvnne,

No.

and

E.

N.

LIghtfoot

(1960).

Transoort

York. Hunter

S.

(1957).

Ann.

Math.

Statlstlcs,

28,

195-241. Bradshaw,

S.

Eversteyn, (1970). FuJ~~,

J.

E.,

@.‘

C.,

W.

J.

Electronrcs,

Severln, Sot.,

Nakamura,

J.

O.,

Gasses

JANAF

Thermochemical

Jbza,

J

C.

117,

K.

Haruna,

C.

and

F.

Curtlss,

Llqulds,

Tables

(1979).

Kuznetsov,

Int.

J.

205-227.

2,

H.

J.

Brekel,

and

H.

L.

Peek

925-931. and

Y,

Koga

(1972).

J.

Electrochem.

1106-1113.

119, of

P.

Electrochem.

H.

Hlrschfelder, Theorv

(1966).

E.

F.

Ph.

D.

F.

A.,

and

W.,

and

L_

(1971).

Thesis,

V.

I.

and

Wiley,

R.

B.

New

NBS,

(1970).

(1954).

Molecular

Washington.

Czechoslov.

Belvl

Bird

York.

Acad. J.

SCL.,

Prague.

Electrochem.

Sot.,

117,

785-788.

Manke,

C.

F.

Donaghey

(1977).

J.

Electrochem.

SOC.,

124

561-569. Rundle, Sladkov,

P. I.

C, B.,

(1968). and

Int. V.

V.

J.

Electronics,

Snegova

(1974).

24, Zhur

405-413. FXZ.

Khlm.,

48,

1867.