Перевод МММ / 3_%%%% 0648bacc A Study of Nonequilibrium Diffusion Modeling-

Abstract-A

new nonequilibrium diffusion model has been de-

to predict diffusion profiles. Earlier technologies could be

veloped aiming to study theinfluence of point

defectson dopant

simulated with steady-state diffusion models, which con-

redistribution, specially for transient

enhanced diffusion. The

sider macroscopic or phenomenological diffusivities [11.

coupled equations for point defects, substitutional impurities,

However, in order to obtain extremely shallow junctions

and impuritiedpoint defect pairs are solved under nonequilib-

riumcondition.

Charged

species are included and Poisson

needed in advanced MOS and bipolar technologies, strong

equation is solved. The characteristics and domain of validity

constraints arise for the thermal budget [2] and the influ-

of this model have been investigated. From the numerical point

ence of point defectsmust be explicitly included. Among

ofview,

it is found that a decoupled scheme solves efficiently

others, one of themost striking example is the anomalous

the system of equations, together with

an automatic time step

transientenhanceddiffusion

afterionimplantation[3].

selection. Moreover,indications are suggested to predict

the

conditions under which a steady-state model can be used. In

Suchbehaviorsaffectdrasticallyactualdeviceperfor-

thecase

of high-concentrationpredeposition,enhanced

dif-

mance [4]. This typical example demonstrates clearly the

fusion is observed and concave or exponential profiles are ob-

pointdefectsimportance,moreoverunderstrong

non-

tained for very short-time diffusion. These effects are amplified

equilibrium configuration. Generally speaking, the advent

by the nonequilibrium treatment. Applications are presented

of low thermal budget raises the question of the validity

for oxide diffusion sources,

in which insight is needed during

theearly

steps of diffusion. Moreover, the

generality of

the

of process models for these new conditions.

model is confirmed by long-time diffusion behavior and by the

From the modeling point of view, significant progress

influence of phosphorus diffusion on boron buried layer.

has been achieved in the last

few years about the under-

Anomalous effects observed during RTA steps after ion im-

standingofpointdefectsanddopantdiffusion[5].The

plantation are also well reproduced by the model, in terms of

duration of the transient diffusion and in terms of the amount

first simulation works including point defects focused on

of displacement, as a function of temperature. Successful com-

oxidation-enhanceddiffusionproblems

[6], [7]. Then,

parisons with experiments are reported for boron and for ac-

they were generalized, based on the concept of point de-

tual bipolar structures,with coupled arseniclboron diffusion in

fectimpuritypairs

[8]-[lo]. These latter models

rely on

a 0.5-pm Bi-CMOS process. Furnace and RTA are,also com-

physical principles and allow deep insight into the diffu-

pared forthese examples. The importanceof the initial amount

of point defects after ion implantation is discussed. Finally, the

sionmechanisms

[l I]. Equilibriumisassumedbetween

electrical influence of such problems is evaluated for a bipolar

point defects and impurities, and nonequilibrium is taken

technology. The effects of damage on two-dimensional diffusion

into account only for bulk recombination. These assump-

are alsoinvestigated.These

results have been obtained using

tions are valid as long as the concentrations of impurities

always the same values of the parameters, validating the gen-

are much greater than the species including interstitialsor

erality of the model.

vacancies [ 121. Althoughthisistheusualcase,itis

no

I. INTRODUCTION

more verified during the early stages

of diffusion follow-

ing ion implantation, since not only interstitials o r vacan-

HECONTINUOUSdecrease

in devicedimensions

cies but also impurityipointdefectpairsexceedtheim-

Tinduces new demands on process simulation, in order

purityconcentration. A completenonequilibrium formu-

Manuscript received March 22, 1991;revised June 20, 1991, Thereview

lation is thus required in this kind of situation.

Nonequilibriumdiffusionmodelinghasbeen

first pro-

of this paper was arranged by Associate Editor N.Kawamura

posed by Hu [131, in order to explain the anomalous dif-

B. Baccus was with the ULSI Research Center, Toshiba Corporation, 1.

KomukaiToshiba-cho,Saiwai-ku,Kawasaki

210, Japan.Heis now with

fusion of phosphorus. However, the feasibility andpoten-

ISEN, 59046 Lille Cedex, France.

tiality of thistype

of modelinghavebeendemonstrated

T. Wada, N. Shigyo, H . Nakajima, K. Inou, T. Iinurna. and H. Iwai are

onlyrecently by MulvaneyandRichardson.Phosphorus

withthe

ULSI ResearchCenter,ToshibaCorporation.

I , Komukai To-

shiba-cho, Saiwai-ku, Kawasaki 210, Japan,

diffusion has been studied [14]-[ 161 and it has been shown

M.NorishimaiswiththeSemiconductorDeviceEngineeringLabora-

that transient diffusiondue toion-implantation damage can

tory, Toshiba Corporation, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki

bealsoqualitativelyreproduced

[17]. A formulationin-

210, Japan.

IEEE Log Number 9105348.

cluding boron, interstitial, and

boron-interstitial

pair has

BACCUS er ol : STUDY OF NONEQUILIBRIUM DIFFUSION MODELING

655

diffusion from 5 s to 1 min. Such procedures were applied

lOI4 at/cm2 at 60 keV)atfour

differenttemperatures:

successfullyforothertemperatures.Theexactmecha-

8OO"C, 9OO0C, 95OoC,and 1000°C. One of the key pa-

nisms by whichpointdefects

areinjected

insiliconare

rametersforsuchsimulations

isthedescriptionofthe

not clear atpresent,butcouldbeexplained

by the very

damage induced by ion implantation, which is taken into

highconcentration of arsenic in theoxide,which might

account by

assuminghighconcentrationsofinterstitials

drag in silicon a significant amount of silicon atoms. This

and vacancies. As these vacancies and interstitial profiles

example is typical of the type of problems

that will have

were found to be almost identical [40], we use always the

to be modeled in the near future.

sameinitialdistributions

forthesetwospecies.More-

over, the amountof damage is assumed to be directlypro-

portional to the dose. These distributions can now be de-

IV. ANOMALOUSDIFFUSIONAFTERION IMPLANTATION

Ontheonehand,

they canbe

Investigating anomalous diffusion arising after ion im-

terminedintwoways.

obtainedfromMonteCarlosimulations(MC),andspe-

plantation is the most interesting application of the pres-

cially,Hoblerprovidedone-andtwo-dimensionaltabu-

entmodelbecausethisis

by natureacompletenonequi-

lations for the usual dopants [40]. Note that in these tab-

librium phenomenon. As reported in the Introduction, by

ulations,self-annealingduringionimplantationwasnot

usingnonequilibriummodeling,boron-transient-en-

takenintoaccount,thus

thecalculatedvaluesareover-

hanceddiffusion

at950°Cwasqualitatively

reproduced

estimated. On the other hand, a first-order modeling is to

[171, and

the temperature dependence thisof

transient

time

suppose that the concentrations of interstitials and vacan-

wasalsodeterminedforboronat1050°Cand1150°C

cies can be obtained by simply multiplying the implanted

[181. Concerninglow-temperature,arseniciphosphorus

dopant profile. Since these initial defect distributions

are

junctions have been studiedwith a local equilibrium model

at present not well determined (moreover, they might de-

[37]. General agreement could bc obtained, although this

pend on the exact ion-implantation conditions, such as the

approach is not strictly valid because some basic assump-

current) we have

usedbothmethodstostudytheirinflu-

tions are notverified,such

as equilibrium. In thisstudy

enceonthe

finaldopantprofile.Concerningthespecies

[37], only one temperature was investigated

(900°C). On

includingboron,

it hasbeenfoundexperimentallythat

the other hand, empirical modeling has been successfully

after ion implantation boron is mainly located on intersti-

reported in the past few years [38], in which thediffusion

tialsites [41],

so that (BZ)speciesdeterminestheinitial

coefficientstake

intoaccountthedamage

by

assuming

dopantprofile.

The resultingevolutionduringannealing

transientmultiplyingfactors.This

is analternativesolu-

is almost the same as reported

in [ 171: a progressive de-

tiontotheusualdiffusionmodelsbecauseitisveryat-

crease ofI and V by diffusion and interactionswith dopant

tractive from the viewpoint of CPU time. However,

it is

species-B

and @I)-and

exchange in the relative levels

not based on physical principles and the extension to two

of B and ( B I ) .

dimensions is notstraightforward.

In any case, such em-

Simulations have been carried outin the following three

piricalsolutionhighlightsthecomplexity

of

simulating

cases for the initial defect distribution: 1)

4 times the im-

directly these phenomena.

planted dopant profile,

2) 20 times the dopant profile,

3)

In the following, it is shown that the present model can

deduced from MC simulations [40]. In case 3), the max-

explaintheanomalousdiffusionintherange

of 800°C-

imum value of

I and Vis about 200 times the maximum

1050"C, and the advantage of RTA over furnace anneal-

dopant concentration. As a function of temperature, Fig.

ingin

limitingtheamount

ofdisplacementisverified.

6 shows the evolution of saturation time which is defined

Moreover, the influence on diffusion of the choice of ini-

asfollows:

it isconsideredthatanomalousdiffusionis

tial point-defectsdistributionisdiscussed.

Thesesimu-

achieved once the amount of diffusion is compatible with

lationsare

firstpresentedforthecaseof

boron(from

the predictions of usual steady-state models without point

Michel

[3]), andforthecaseof

coupled

anenidboron

defects [l], [24]. It shouldbenotedthatresultsforcase

diffusion in a 0.5-pm Bi-CMOS process (from Norishima

2 lie between the ones for case1 and 3, and are not shown

[4], [39]). Finally, basic electrical characteristics are sim-

ulated for a bipolar n-p-n transistor and two-dimensional

hereforclarity.The

firstremarkisthataremarkable

agreement is found between experiments and simulation.

effects are presented.

To our knowledge, it is the first time that such agreement

A . Boron Diffusion: Michel

's Experiments

is obtained overa wide range of temperature: from800°C

to lOOO"C, where the saturation time evolves from around

Theanomalousdiffusionofboronafterlow-doseion

5 s to 30-40 min. The second conclusionis that the choice

implantation was studied as a function of annealing tem-

of initial defect distribution

does not change significantly

perature by Michel [ 31. Thedurationtime

oftransient-

the saturation time. This means that the activation energy

enhanced diffusion (or saturation time) was found tohave

andamount

ofsaturationtimereflectthebasicinterac-

an activation energy of more than 4.5 eV. This activation

tions between dopants and point defects, and depends on

energy is

significantly greater than the ones for

impurity

some combining factors such as the diffusivity of defects,

diffusion in silicon, thus

it cannot be explained only

by a

binding energies, and strength of the kinetic reactions.

large diffusivity

of boronhnterstitial pairs. We have sim-

Fig. 7 represents the amount of boron displacement at

ulatedtheprocessesreported

in [3] (boronimplant

2 X

the end of the anomalous diffusion time,

as a function of

656

IEEE TRANSACTIONS ON ELECTRON DEVICES,

VOL. 39. NO. 3 . MARCH 1992

temperaturerange.

In

fact,ourcalculationsdid

notin-

clude the

formation of

some clustersor precipitates, which

are not present at

1000°C but are obvious at 800°C [3].

It would reduce the amount

of displacement by reducing

theamount

of mobileboronspecies.Thisphenomenon

has been treated recently by Cowern using an equilibrium

model,and

itcan

be introducedinacompatible

wayin

the present model. Reaction between m substitutional bo-

ron atomsand n interstitialsmightform"Intermediate

Defect Configurations"[42]

* IDC.

mB + nl

(27)

In ordertoextendthepredictioncapabilities

of

our

model,this

kind offormulation

will beimplemented

in

the near future in our simulations.

IOOO/T I'KJ

3. Application to n-p-n Bipolar structures

Fig. 6. Evolution of saturationtime

as a function of temperature in the

case of boron diffusion after low-dose ion implantatlon. Measurements are

Theformationof

n-p-nbipolartransistorsundervar-

from [3]. The initial defects distributions are: case 1 , 4 times the implanted

ious conditions has been studied and has demonstrated in

boron profile; case 2.20 times the boron Implanted profile:case 3, deduced

fromMonte Carlo calculations.

a very clear manner the importance of damage introduced

by ion implantation [4], [39]. Arsenic was implanted at a

dose and energy of 5 X IO"

at/cm2 and 40 keV, respec-

tively. Boron was implanted at a dose and energy of 4 X

lOI 3 at/cm2 and 20 keV, respectively. In some cases, ar-

senic was not included in order to separate the effects due

to each species (this is also almost equivalent to assume

that arsenic would be diffused from polysilicon). Furnace

annealingwasperformedat

800"C, 850°C, and 900°C

500

for 30min. RTA was also used for 15 s, at temperatures

200

ranging from 850°C to 1050°C. From thesimulation point

of view, the exact thermal conditions were taken into ac-

100L

I

I

count(includingramp-up),andtheimplantedprofiles

08

0.9

wereadjustedto

SIMS measurements,whenneeded.

IOOO/T PKI

Comparisons between the present model and the standard

Fig. 7. Boron displacement as a function of temperature for the same con-

one-with

the meaning described

in Section 111-A-were

ditionsas

Fig. 6 .

also performed.

temperature. This boron displacement refers to thediffer-

Fig. 8 summarizes the resultsas a function of annealing

temperaturefor:a)theborondisplacementatthebase/

ence in boron profiles before and after diffusion, aatcon-

collector junction in the case where arsenic is not intro-

centration level of 1016at/cm3. Now, case 3 predicts too

duced, b)

theborondisplacementatthebaseicollector

when using the lowest initial distributions (case 1). Apart

the base width, and d) the enlitterjunction depth. We con-

fromtheuncertaintyabouttheinitialdefectprofiles,a

sider first the case of boron-only diffusion and the varia-

precisesimulationshouldtakeintoaccountthethermal

tion in boron displacement. Again, two cases were stud-

history of the wafer, e.g., ramp-up conditions. However,

ied: the initial I and V distributionsare 1 )

4 timesthe

in opposition to the results presentedin the following sec-

implanted dopant profile, or 2 ) deduced from

MC simu-

tion (IV-B), noinformationisavailable,and

as aresult,

lations [40]. Fig.8(a)showsthatthestandardmodel

more quantitative comparisons with the experiments can-

underestimates the boron diffusion. On the other hand, it

not be expected. Nevertheless, it can be remarked that a

wasfound that. whensimulatingpreciselythethermal

calculationneglectingion-implantationdamag?would

conditions,usingthedefectsdistributionsfrom

MC

predictonlysmalldisplacements:lessthan

50 A for all

slightly exaggerates boron diffusion, but good prediction

thermal conditions [3]. From our calculations, it was also

capabilitiesareobserved.Thusfromthesimulationsof

deduced that the most

important factor concerning the dis-boron diffusion [3], 141, 1391, it is concluded that reason-

placementisthemaximumlevelofdefectsand

not the

able results are obtained

by decreasing the defect profile

exact shapeof the initial profiles, because of the high dif-

predicted by Hobler's calculations, with an amplitude de-

fusivities of I and V. Finally, it can be seen in Fig. 7 that

termined from our empirical modelingof damage.

goodagreementcannot

be obtainedoverthecomplete

Thecaseofcoupled

diffusion is morecomplex.For

BACCUS pi a/.:STUDYMODELlKGOFDIFFUSIONNONbQlJlLIBRIUM

657

of RTA and justifies the use of high-temperature and short-

timeannealingtoobtainveryshallowjunctions.Thisis

associated with thepoint-defectremovalkineticssimu-

lated here.

c)Theseremarks

holdalso

forarsenic diffusion (Fig.

0

8(d)).However,theanomalousdisplacementis

not so

u

large as for boron, but still, it is always greater than pre-

dicted by the standard model.

d) Experimentally, a significant reduction in basewidth

wasobservedbetweenthe1000°Cand

1050°C RTA

cases, due to

the arsenicdiffusion. This is also reproduced

by the simulations. It is interesting to notice that a similar

result was obtained when forming emitterby doping from

ANNEALINGTEMPERATURE (%I

polysilicon [4], [39]. This is duetotheevolution

of the

diffusivities D(As- v) and D,,,- ,)

with temperature.

e)Exactinclusionoframp-upconditionsisneeded,

otherwise the types of behavior as

a function of temper-

ature cannot be reproduced, specially in the case of fur-

naceannealing(forexample,whenneglectingramp-up,

more boron diffusion would be predicted at800°C than at

900"C, contrary to the experimental results. Actually, the

900°Cannealing

firstincludesaramp-upstartingat

800"C, thusthe

anomalous diffusion is

mainlydeter-

mined by thedurationofthisramp-up,andnot

by the

900"C, 30-mindiffusion).It

is

wellknownexperimen-

tally that ramp-up is very important to control dopant dif-

fusion.This

isexplainedhere

by

thepoint-defectski-

PC1

netic.

ANNEALINGTEMPERATURE

f ) Finally, it is concluded that the usual standard model

Fig. 8 . Study of bipolar devices withRTA

or furnaceannealing.The

ex-

fails completely to describe the experimental results. This

periments are from [4],[39]. (a) Boron displaccmcnt as a function of tem-

isparticularlytrueforborondiffusionanditsimpacton

perature(borononly case). Theinitial

defects distributlonsare: case

l.4

the base width,

for furnace annealing.

times thc implanted boron profile; case

2, deduced from Monte Carlo

cal-

culations.For the resultsfromcoupledarseniclborondiffusion,theinitial

These results are illustrated

in another manner in Fig.

point-defectsdistribution is definedasthe

rnaxlrnurn of the implanted ar-

9(a) and (b), which represent the arsenicand boron-sim-

senic profile and o f 4 times the boron implanted profile. (b) Boron displace-

ment as a function of temperature (coupled diffusion casc). ( c ) Base width

ulated profiles afterthe 900°C furnace annealing,by using

as a function of temperature. (d) Emitterjunctiondepth

X,, as a function

the standard and new model, respectively. In thefirst case

of temperaturc.

(Fig. 9(a)), the boron profile is almost unchanged

by the

diffusion step,

but

usingthenewmodelaremarkable

high-doseionimplantation,

the

siliconbecomesamor-

agreementisobtained(Fig.9(b)).There

isonlyaslight

difference forarsenicdiffusion.Fig.

10 shows,forthis

phous and the modeling of damage

used here may

reach

900°C furnace diffusion case, the dopant

profiles as well

its limits. Possible extensions of this work

to describe, in

as the species involving defects. In additionto the Poisson

a more precise manner, the physical mechanisms will be

equation, 7 coupled equations are solved, and due to the

discussedbrieflyintheConclusions.However,itisim-

portant to investigate the possibilities of the present work. assumptionofequilibriumbetweenchargedandneutral

In any case, compared to the

boron-only situation,

as the

species, 14 species are actually deduced from these types

of calculations. Only some of them are representedin Fig.

amountofdamageisenhanced

by thearsenicimplanta-

10. This illustrates the complexityof the calculations and

tion,muchmoreborondisplacementisobtained,as

Our simula-

the need for sophisticated models when aiming to repro-

clearlyseenexperimentally(Fig.8(a),(b)).

duce the experimental behavior

in a consistent manner.

tions revealed that a good description of the experimental

In order to perform a comprehensive study, the electri-

features can be reproduced by simply choosing the initial

calbehaviorofthesedeviceswassimulated.Thetrian-

I and V profiles to be equal to the implanted arsenic dis-

gularmeshdevicesimulator

TRIMEDES [43] wasused

tribution. This condition was used for all the sirnularions

in the way described in [44]: three one-dimensional sim-

reported hereafter in the

case of

coupled arsenic/boron dif-

fusion.Fig.8(a)-(d)shows

very interestingresults:

ulationswereperformedfortheintrinsicbipolardevice

(the results Dresented above). the linked base, and the ex-

a) Borondisplacement

is

greater whenusingfurnace

trinsic base regions. Since for this technology under study

annealing, in comparison with RTA.

the results are mainly determined by the profile in the in-

b) This displacement is drastically reduced in the case

trinsicregion,

thisapproach

issufficient

(441. Thede-