Reduced order model for the CVD of epitaxial silicon from silane and chlorosilanes

Journal of Crystal Growth 230 (2001) 247–257

Reduced order model for the CVD of epitaxial siliconfrom silane and chlorosilanes

Gianluca Valente, Carlo Cavallotti, Maurizio Masi*, Sergio Carr"a

Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, via Mancinelli 7, 20131 Milan, Italy

Abstract

The epitaxial silicon deposition from silane and chlorosilanes diluted in hydrogen carrier was analyzed by means of amultiscale approach that links together models related to different aspects of the growth as the deposition rate profileand the morphology of the obtained crystal. The model hierarchy here developed considers (a) the reactor model, (b)

the terrace model (i.e., the description of the way the crystal grows and of the stability of the growth process) and (c) theelementary chemical kinetics. Each one of these models was solved in a 1D framework to obtain an overall picture ofthe deposition system without numerical complexities. Detailed kinetic mechanisms were proposed and comparisonswith experimental data obtained in horizontal reactors were performed. # 2001 Elsevier Science B.V. All rights

reserved.

PACS: 81.10.Aj; 82.20.�w; 85.40.�e; 81.10.Bk

Keywords: A1. Growth models; A1. Surface processes; A3. Chemical vapor deposition processes; A3. Chloride vapor phase epitaxy;

A3. Vapor phase epitaxy; B2. Semiconducting silicon

1. Introduction

A large segment of the whole microelectronicindustry is based on the availability of epitaxialsilicon wafers, where a thin single crystalline layerof silicon is deposited onto the polished siliconwafer by means of a high temperature chemicalvapor deposition process. A very stringent qualityrequirement is placed for these wafers, particularlyregarding the uniformity of film thickness andcomposition (i.e., dopant level) as well as to themorphology (i.e., film roughness) and the defectsdensity of the deposited crystal. Since these films

are grown in one-through cold wall batch reactors,the evolution of the gas composition within thereactor places some issues regarding the constancyof the crystal properties. Accordingly, besides thethickness and composition profiles of the epitaxiallayer, it is of key importance to understand thechemical and physical phenomena responsible forthe morphology evolution of the film.Current status of chemical vapor deposition

simulations is concerned mainly with the macro-scopic aspects related to the deposition (e.g.,growth rate) while the crystal morphology aspectsare still mostly empirically addressed. However, itis possible that the process conditions optimizingthe growth rate profile might not coincide withthose related to crystal quality. Therefore, thecurrent needs of the microelectronic industry

*Corresponding author. Tel.: +39-2-23993131; fax: +39-2-

23993180.

E-mail address: [email protected] (M. Masi).

0022-0248/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 3 4 9 - 5

require that all those aspects shall be consideredtogether during the definition of the optimalprocess parameters. For these reasons, our interestis devoted to assembling the problems above into aunified approach whose aim is to obtain acomplete picture of the growth systems by meansof a multi-scale approach [1], which links macro-scopic reactor models with mesoscopic and micro-scopic ones (i.e., related to film morphology and toformation of defects). Thus, the model hierarchyhere developed considers (a) the reactor model,whose main parameters are the chemical kineticsand the transport kinetics and (b) the terracemodel (i.e., the description of the way the crystalgrows and of the stability of the growth process).Furthermore, this approach should be completedwith the different models related to the defectsformation. It is easy to recognize that thementioned models refer to processes whose char-acteristic length scales are quite different, goingthrough the centimeters up to the nanometers. Toreduce the numerical complexities and to obtain aglobal model suitable to be used during the day byday operations to adapt process conditions to theclient needs, the models were here developed at thelowest scale as possible (i.e., 1D framework). Ofparamount importance is the availability of areliable deposition chemistry mechanism becausethe novel reactors types do not operate longer inmass transport limited regime. Thus, detailedchemical kinetics are needed with rate parametersestimated independently from transport ones.In the present work, a detailed mechanism for

the silicon deposition from silane and chlorosi-lanes is proposed. The mechanism was testedagainst experimental data of surface science natureand of deposition rate. For the latter tests, thekinetic mechanism was embedded in a 1D reactormodel estimating the mass transport throughrelationships based on the boundary layer theory.The reactor model was then linked with amorphology model in order to describe the surfacequality of the deposited layer. While the macro-scopic part of the model was tested for all theprecursors, the morphological model was at thismoment applied only to silane, for which thesurface chemistry is well known. To be completed,these models should be linked together with

growth stability models, partially addressed inprevious works [2,3] and with models quantita-tively predicting defects formation. The latteraspect is still under exploration and it will beexamined in forthcoming papers.

2. Deposition chemistry

Silicon epitaxy is usually conducted adoptingsilane or chlorosilanes as gas phase precursors.Because of the quality issues risen in the introduc-tion, the knowledge of the detailed gas phase andsurface chemistry involved in the depositionprocess is of fundamental importance. Duringthe last years a great effort was devoted to thecomprehension of the reactions involved in silicondeposition [4–16,19–22]. The mechanism and theinvolved rate constants for the silicon growth fromsilane can be considered almost consolidated,while the same conclusion cannot be drawn forthe chlorinated ones. That is in contradiction withthe partitioning of the industrial epitaxial pro-cesses that are performed mainly by means ofchlorosilanes because of their lower cost.

2.1. Silane chemistry

Silane chemistry has been thoroughly investi-gated in the last years. The gas phase mechanismadopted here was mainly taken from Ho et al. [4]who summarized many years of experimental andtheoretical work. In the present work, trisilaneswere neglected because they are usually producedin extremely low concentrations and thus onlySiH4, SiH2, Si2H6, Si2H4 and HSiSiH3 wereconsidered as gas phase species. Silane decomposesto give SiH2 and hydrogen. SiH2 then can reactwith SiH4 to give Si2H6. Other disilanes can beformed: HSiSiH3 from SiH4 and Si2H6 and byelimination of hydrogen from Si2H6, while Si2H4can be formed by isomerization of HSiSiH3.Regarding the surface mechanism, four differentspecies were considered on the silicon surface:three silicon hydrides SiH*

3 ; SiH*2 ;SiH* and the

adsorbed hydrogen H*. Rate constants for SiH4and SiH2 dual-site type chemisorption weredetermined by Gates and coworkers as well asthose for the progressive dehydrogenation steps up

G. Valente et al. / Journal of Crystal Growth 230 (2001) 247–257248

to the incorporation into the film [5–8]. Because ofthe high incorporation rate, the loss of the lasthydrogen ðSiH* ! Si*þH* Þ and the adatomincorporation in the film ðSi* ! s þ SiðbÞÞ canbe lumped together ðSiH* ! H* þ s þ SiðbÞÞ:Furthermore, the hydrogen adsorption–desorptionequilibrium has to be included, being hydrogenadsorption competing with silane for free surfacesites. A more detailed discussion on the overallmechanism, including the rate constants alterationdue to the addition of dopant elements can also befound in Refs. [4,9]. The reactions and the rateconstant parameters are summarized in Table 1.The values reported did not consider the pressuredependence of rate constants because the epitaxialsilicon deposition is performed at nearly atmo-spheric conditions and thus out of the ‘‘fall off’’regime.

2.2. Chlorosilanes chemistry

Chlorosilanes chemistry has not yet been deeplyinvestigated since the industrial deposition pro-cesses were traditionally conducted in the diffusionlimited regime, where kinetics aspects are lessimportant. The new horizontal reactors designedfor handling large diameter wafers are insteadoperated in conditions where the process is still

affected by the deposition chemistry and thus thisgrowth chemistry cannot be neglected longer. Themost adopted chlorinated precursors are tetra-chlorosilane (SiCl4), trichlorosilane (SiHCl3) anddichlorosilane (SiH2Cl2). A peculiarity of all thoseprecursors is that their thermal dissociation leadsto the formation of SiCl2, which is a very stablespecies. Several authors investigated the growthchemistry of silicon from these precursors.A lumped gas phase mechanism was proposed

by Narusawa [10] who considered two gas phasereactions: the reaction between SiCl4 and H2 toSiHCl3 and HCl, and the decomposition of SiHCl3to SiCl2 and HCl. The surface reactions werecompletely neglected and the rate constant para-meters were fitted on growth rate data byassuming SiCl2 the growth precursor. A moredetailed mechanism was proposed by Hierlemannet al. [11] who considered the gas phase andthe surface decomposition pathways for SiH2Cl2,upgrading the original mechanism of Coonet al. [12] with the addition of the reactionbetween adsorbed chlorine and gaseous hydrogen.This reaction was first proposed by Oshita et al.[13], who estimated an activation energy of 40–50 kcal/mol fitting experimental growth rate dataand 110 kcal/mol from quantum chemical calcula-tions. Trichlorosilane decomposition kinetics was

Table 1

Gas phase and surface reaction mechanism for silicon deposition from silane. Units in terms of mol, cm, s, cal and K and rate constants

expressed as k ¼ ATae�E=RT: Surface reactions written as irreversible while rates are in mol/cm2 s. Gas phase reaction rates are inmol/cm3 s and subscripts f and b stand for forward and backward reaction, respectively. Otherwise backward reaction parameters

estimated through equilibrium consistency. c=estimated through collisional theory [17,18]. *=adsorbed species, s=free surface site

Reaction Log10A a E Ref.

G-1 SiH4 $ SiH2 þH2 9.49 1.70 54710 [4]

G-2 Si2H6 $ SiH4 þ SiH2 10.26 1.70 50200 [4]

G-3f HSiSiH3 þ SiH4 $ Si2H6 þ SiH2 14.24 0.40 8900 [4]

G-4 Si2H6 $ H2 þHSiSiH3 9.96 1.80 54200 [4]

G-5 HSiSiH3 $ H2SiSiH2 13.40 �0.20 5380 [4]

G-6f HSiSiH3 þH2 $ SiH2 þ SiH4 13.97 0.00 4092 [4]

A-1 SiH4 þ 2s ! SiH*3 þH* 19.06 0.5 3000 [5–8]

A-2 SiH3 þ s ! SiH*2 þH* 17.64 } 27000 [5–8]

A-3 2SiH*2 ! 2SiH* þH2 24.38 } 45000 [5–8]

A-4 SiH2 þ s ! SiH*2 11.76 0.5 0 [17,18]

A-5 SiH* ! SiðsÞ þ 12H2 þ s 11.90 } 47000 [5–8]

A-6 2H*!H2+2s 22.11 } 43000 [5–8]

A-7 H2+2s! 2H* 11.36 0.5 17250 [36]

G. Valente et al. / Journal of Crystal Growth 230 (2001) 247–257 249

compiled by Ho et al. [14] who pointed out thatSiCl2 has a high desorption rate and thus assumedSiHCl3 as the most important precursor. There, mostof the rate parameters were taken from the literature,while the HCl desorption parameters were fitted oversome experimental results. The above kinetic modelwas then adopted for 1D and 2D simulations ofsingle wafer horizontal reactors operating in condi-tions nearly diffusion limited obtaining fairly goodagreements with growth rate data.As it can be evidenced from the considerations

above, at this stage, there are still some uncertain-ties on the chlorosilanes chemistry. In particularthe kinetics of the HCl and SiCl2 adsorption anddesorption is not clear and our contribution isdevoted to try to fill this gap. The overallmechanism comprehends all the three majorprecursors and their fragments in gas and inadsorbed phase and it is summarized in Table 2.Most of the gas phase reactions were already

studied in the literature. SiHCl3 decomposition

was studied by Lavruschenko et al. [15], whoobserved the formation of SiCl2 and HCl (reactionF-1) while the SiH2Cl2 decomposition can giveeither SiCl2 and H2 (reaction F-2) or SiHCl andHCl (reaction F-3) [16]. SiHCl3 on the contrarydecomposes through the formation of SiCl3 and Cl(reaction F-4), successively SiCl3 can react with H2to give SiHCl3 (reaction F-5), and finally SiHCl3can decompose into SiCl2 and HCl. It is importantto note that the direct SiCl4 decomposition toSiCl2 was excluded because the activation energyof this reaction is about 8 kcal/mol higher than theactivation energy of reaction (F-4). RegardingHCl, two other reactions were taken into account:the HCl decomposition (reaction F-6) and theformation of HCl through the reaction between H2and the radical Cl (reaction F-7).About the surface chemistry, three adsorbed

species were considered: H*, Cl* and SiCl* that inour mechanism represents the growth precursor.All reported reactions are chemisorption or

Table 2

Gas phase and surface reaction mechanism for silicon deposition from chlorosilanes. Units in terms of mol, cm, s, cal and K and rate

constants expressed as k ¼ ATae�E=RT: Surface reactions written as irreversible while rates are in mol/cm2 s. Gas phase reaction ratesare in mol/cm3 s and backward reaction parameters estimated through equilibrium consistency. c=estimated through collisional

theory [17,18]. *=adsorbed species, s=free surface site. (a)=estimated through transition state theorya

Reaction Log10A a E Ref.

F-1 SiHCl3$SiCl2+HCl 14.69 0.0 73700 [16]

F-2 SiH2Cl2$ SiCl2+H2 13.92 0.0 77400 [16]

F-3 SiH2Cl2$HSiCl+HCl 14.84 0.0 75800 [16]

F-4 SiCl4$Cl+SiCl3 15.68 0.0 111160 (a)

F-5 SiHCl3+H$ SiCl3+H2 12.39 0.0 2500 [37]

F-6 HCl$H+Cl 13.64 0.0 81700 [38]

F-7 Cl+H2$HCl+H 13.68 0.0 5258 [39]

B-1 SiHCl3+4s! SiCl*+H*+2Cl* 8.05 0.5 �3800 [14]

B-2 SiH2Cl2+4s!SiCl*+2H*+Cl* 8.58 0.5 �3800 [14]

B-3 SiCl4+4s!SiCl*+3Cl* 9.84 0.5 �672 [21]

B-4 H2+2s! 2H* 11.36 0.5 17250 [36]

B-5 HCl+2s!H*+Cl* 10.73 0.5 0. [19] (a)

B-6 SiCl2+2s!SiCl*+Cl* 10.51 0.5 0. (b)

B-7 2SiCl*! SiCl2+Cl*+Si(b)+s 24.20 0.0 67000 [21]

B-8 2Cl*+Sib!SiCl2+2s 24.20 0.0 67000 [21]

B-9 SiCl*+Cl*!SiCl2+2s 24.20 0.0 67000 [21]

B-10 2H*!H2+2s 22.15 0.0 43000 [20]

B-11 H* ! 12H2 þ s 15.30 0.0 57100 [20]

B-12 H*+Cl*!HCl+2s 25.85 0.0 60300 (c)

B-13 H*+SiCl*!HCl+2s+Sib 25.85 0.0 60300 (c)

aNote: (a) collisional theory with sticking coefficient 0.1, from Ref. [19]; (b) collisional theory with sticking coefficient 0.1, assumed;

(c) fitted.


desorption reactions. All gaseous species (i.e.,SiCl4, SiHCl3 and SiH2Cl2) adsorb dissociativelyon the surface leading to the formation ofadsorbed hydrogen, chlorine and SiCl* throughreactions (B-1), (B-2) and (B-3), respectively.Hydrogen and HCl adsorption are describedthrough reactions (B-4) and (B-5), respectively.Regarding HCl adsorption, the sticking coefficientdependence on the temperature is not known inliterature. Then, kinetic constant reported in Table2 was obtained from collisional theory [17,18]assuming a sticking coefficient equal to 0.1 asexperimentally evaluated by Mendicino and See-bauer [19] at 300K. Reaction (B-6) corresponds tothe SiCl2 adsorption, whose rate parameters wereagain evaluated by collisional theory adopting asticking coefficient of 0.1. The surface mechanismwas then completed with three desorption reac-tions corresponding to H2, HCl and SiCl2 deso-rption. Hydrogen desorption occurs either with afirst order mechanism or with a second ordermechanism, as reported by Flowers et al. [20], whoused Temperature Programmed Desorption todetermine the kinetic constants for reactions (B-10) and (B-11). The SiCl2 desorption pathway canproceed through three reactions: (B-7), (B-8) and(B-9).It is important to note that reaction (B-7)

contributes directly to the growth of the epitaxialsilicon film while reaction (B-8) is an etchingreaction. The kinetic parameters of the threereactions reported above are supposed to be equalto the SiCl2 desorption kinetic parameters esti-mated by Gupta et al. [21] through TPD studies.Similar to SiCl2 desorption, HCl desorption canproceed through two reactions: (B-12) and (B-13).Simulations confirm that reaction (B-13) re-

sulted to be the most important growth reactionand it was found in competition with the etchingreaction (B-9). Rate parameters of reaction (B-13)were evaluated through TPD studies using TiCl4and SiH4 as gas phase precursors [19]. Thereaction exhibits a second order desorptionkinetics with an activation energy of 71.3 kcal/mol for chlorine coverage higher then 0.14% and afirst order kinetics with an activation energy of48.4 kcal/mol for chlorine coverage lower than0.14%. Since in our simulations of industrially

deposition conditions a chlorine coverage higherthan 0.14% was always evidenced, only the secondorder reaction was considered in the kineticscheme reported in Table 2. However, simulationsperformed adopting the kinetic constants pro-posed by Mendicino and Seebauer in Ref. [19]showed that at low temperatures the siliconsurface is completely covered by chlorine, whichinhibits the silicon growth in disagreement withexperimental data. Since HCl desorption is thefastest pathway through which Cl can be removedfrom the surface, its desorption kinetic constantwas fitted over growth rate data reported byAngermeier et al. [22]. The kinetic parametersreported for this reaction correspond to a pre-exponential factor of 1025.85 cm2/mol s and activa-tion energy equal to 60.3 kcal/mol.To test the feasibility of the kinetic parameters

so determined quantum chemistry calculationswere performed. Our approach to estimate gasphase and surface rate constants through quantumchemical calculation consisted in a standardizedprocedure that analyses the most relevant reac-tions of the kinetic scheme initially throughsemiempirical methods (e.g., PM3). The energeticsof the reactions is then refined by means of morerigorous methods (i.e. DFT). The value of the rateparameters is determined by means of TransitionState Theory [23]. In particular the HCl desorptionwas studied with the semi-empirical PM3 Hamil-tonian [24,25], using the Gaussian 98 programsuite. The calculated activation energy was41.9 kcal/mol, thus a value below that estimatedby fitting the experimental data (e.g., 60 kcal/mol)and that measured by TPD (e.g., 71 kcal/mol).Thus it appears that some work both experimentaland theoretical is needed in order to understandthis key point. In particular we are performingDFT calculations to test the validity of semi-empirical results.

3. Reactor and film morphology models

The reactor model here adopted was a 1Dboundary-layer based model. This model is able todescribe the evolution of the system along thereactor main coordinate, provided that proper


relationships to describe the precursors masstransport towards the susceptor are adopted.The model equations can be derived directly

from the complete set of transport equations. Dueto the decoupling of the velocity field, which canthus be determined ‘‘a priori’’, the reactor modelreduces to mass and energy conservation equa-tions [1,26].The proper boundary layer relationship to be

used to estimate the mass transport coefficient isdependent on the geometry considered. Forexample, if a horizontal reactor is considered, theSherwood number (Sh ¼ kciH=Di) can be calcu-lated as a function of the Graetz numberðGz ¼ ReScdeq=xÞ : Sh ¼ Sh1 þ 0:0668 Gz=ð1þ0:04 Gzð Þ0:66Þ; where Sh1 is the limiting Sherwoodvalue for fully developed flow and Re, Sc, deq, xare the Reynolds ðrudeq=mÞ and the Schmidt ðm=rDÞ numbers, the equivalent diameter of the ductand the axial coordinate, respectively [27,28]. Thelimiting Sherwood number can be calculated as afunction of the height/width aspect ratio asreported by Luikov [26,29]. The transport coeffi-cients for the energy balance equation can beestimated from the mass transfer ones by means oflaminar fluid dynamics similarities [26,30].About the mesoscale model (e.g., characteristic

length of about 100 nm), the atomic mechanismsinvolved in the silicon growth developed wasdescribed through the Terrace-Step-Kink model,which is able to describe properly the layer bylayer growth mode typical of epitaxial growth [31].In this framework, the conservation of the adsorbedsilicon species (adatoms) is determined by thecompetition between their production throughsurface reactions and their diffusion perpendicu-larly to the step edge. The migrating adatoms canalso coalesce together to form clusters during thistime-period. As cluster mobility over the terrace isalmost negligible, only the surface diffusion ofadatoms is considered. Accordingly, the terracegrowth model considers a terrace of length L andthe adatoms are nucleated by surface chemicalreactions. Then, the so-formed adatoms migrateover the terrace surface up to be incorporated intoa terrace kink or into a cluster. A s-cluster isformed by the incorporation of a migratingadatom in a (s�1)-cluster and disappears incor-

porating a further adatom. Accordingly, in a 1Dapproach, the steady state material balances foradatoms and s-mers on the terrace are [2,3]:

R1ðosÞ �N1XSmax

s¼1

ksNs þDsq2N1qz2

¼ 0; i ¼ 1; ð1Þ

k1ffiffiffiffiffiffiffiffiffiffiffis� 1

pNs�1N1 ¼ k1

ffiffis

pNsN1; s ¼ 2; Smax;

ð2Þ

where R1ðoÞ indicates the adatom nucleation bysurface chemical reactions, the second termindicates the consumption of adatoms by clusterformation, and the last term indicates the diffusionof adatoms over the terrace. Eq. (2) indicates thebalance for the cluster containing s atoms, and itcontains only the generation terms because theyare assumed to be non-migrating over the surface.Moreover, Smax, Ds, k1 and ks are the maximumcluster size over the terrace, the surface diffusioncoefficient of adatoms and the rate constant of theadatom coalescence with adatoms and s-clusters,respectively. The balance equations for the s-mers(2) have been written here assuming a disc shapedcluster, and then the rate constant for theincorporation into a s-cluster becomes ks ¼ k1

ffiffis

p

[1]. The other parameters such as the surfacediffusivity and the incorporation constant can beestimated by the kinetic theory as reported in Refs.[1–3], as a function of lattice parameter ða0 ¼0:408 nmÞ and of the silicon vibration frequencyðn ¼ 7:521013 s�1Þ: The adopted activation en-ergies for the adatom diffusion and coalescencewere 22 and 19 kcal/mol, respectively. The bound-ary conditions for Eq. (1) are the symmetry andthe equivalence of the adatom flux to the kinkincorporation rate [2,3]. The incorporation con-stant of adatoms into the step kinks was againestimated by means of the kinetic theory as kk ¼0:25 n a0 expð�Ek=RT Þ: A first approximationfor the activation energy of this process is Ek �E1=2: A more detailed analysis about the bound-ary conditions removes the symmetry condition byintroducing a different insertion rate at upper andlower step kinks (Schoebel effect); this discussioncan be found in Refs. [32,33]. Due to the simplifiednature of our analysis this latter aspect was notanalyzed further.


The adatom nucleation rate R1 was determinedby the surface reactions that generate the singlesilicon atom over the surface. For example, insilane driven growth, the adatom nucleation ratecan be identified with the production rate of thespecies SiH* as determined by the reactor model.That condition establishes also the link among themorphology and the reactor models. The implicitunknown is the maximum cluster size Smax thattogether with the cluster density/terrace widthratio is directly linked with the film roughness.Eqs. (1) and (2) can be solved numerically bymeans of any method suitable for second orderdifferential equations. The reliability of this modelwas already tested in previous works [2,3].

4. Results and discussion

The reactor model was adopted to simulate thegrowth rate profile within horizontal reactors fedwith silane [34], trichlorosilane [22] and silicontetrachloride [35]. In the case of silane, the reactormodel was linked with the terrace model, thusobtaining information on crystal quality also.It is important to highlight that the surface

kinetics is critical in the determination of thegrowth rate and film quality, thus the model is

mostly sensitive to the kinetic parameters relatedto the growth: in particular to the HCl and SiCl2adsorption and desorption kinetic constants.In Fig. 1, the comparison between calculated

and experimental growth rate profile is illustratedfor two different process conditions [34]. Theagreement found between model and experimentaldata was good, particularly when considering thatno adjustment of the model parameters wasperformed. The corresponding predicted maxi-mum cluster size and adatom concentration alongthe reactor coordinate are sketched in Fig. 2. It isinteresting to note that with the present operatingconditions the maximum cluster size results to becomprised between 15 and 25 atoms (i.e., lowenough to think that the film grown is epitaxial).Moreover, it is important to note that the clustersize increases with the growth rate decrease,indicating a decrement of the film quality alongthe reactor coordinate.The trichlorosilane chemistry was checked

against data reporting the growth rate dependencefrom temperature obtained in a horizontal reactor[22]. The considered example evidences very wellthe process sensitivity to chemical kinetics. Inparticular, for chlorosilanes, because of the ex-istence of the ‘‘etching’’ reaction, the growth rate isobtained as the difference between the rate of

Fig. 1. Calculated (}) and experimental (&) growth rate data for epitaxial silicon growth from silane at atmospheric pressure [32].

Horizontal reactor, with rectangular section (2.2 cm high 4 cm width). Left: inlet gas velocity v0=17.5 cm/s, susceptor temperature10508C, inlet silane mole fraction y0=0.001, untilted susceptor. Right: inlet gas velocity v0=34 cm/s, susceptor temperature 10808C,inlet silane mole fraction y0=0.000639, susceptor tilt angle 2.78.


reactions (B-13) and (B-8). In the operatingconditions here examined (e.g., susceptor tempera-ture 10008C and 15%mol of inlet trichlorosilane)at a 20 cm distance from the leading depositionedge, the calculated rates for the deposition andetching reactions are 3.5 and 2.8 mmol/cm2 s,respectively. The resulting net deposition rate isthen equal to 0.7 mmol/cm2 s (i.e., one order ofmagnitude lower than deposition or etching rate).This result shows that in the conditions typical ofthe growth of Si from chlorosilanes, the growthrate is strongly dependent from competing ele-mentary processes with also competing influenceon film morphological evolution.Despite the effort placed in the rate estimation

through computational quantum chemistry, toreproduce the experimental data it was necessaryto fit the activation energy of the most importantsurface reaction (i.e. the HCl desorption reactionB-13) over growth rate data. The best-fittedactivation energy was 60.3 kcal/mol. This energyvalue is intermediate between that measuredthrough TPD analysis [19] and that estimated herethrough computational quantum chemistry. Asalready pointed out, it is our opinion that furtherinvestigations (experimental or theoretical) areneeded in order to determine the HCl desorptionkinetics.The comparison between calculated and experi-

mental deposition rate is illustrated in Fig. 3. To

highlight the importance of the etching reaction(B-8) in the epitaxial silicon deposition fromchlorosilanes, it is interesting to observe that if atemperature dependence of the HCl adsorptionrate is assumed, the decrease in the growth rate athigh temperature can also be simulated. Inparticular, in Fig. 3 a set of simulations are

Fig. 2. Estimated film morphology of the film for epitaxial silicon growth from silane at atmospheric pressure. Conditions as indicated

in Fig. 1. Maximum cluster size (&) is expressed in number of atoms, the adatom mean coverage (*) is expressed in mole fraction withrespect to the total number of surface sites (6.8 1014 at/cm2).

Fig. 3. Comparison between calculated and experimental (&)

growth rate for epitaxial silicon growth from trichlorosilane as

a function of substrate temperature. Data taken from Ref. [20].

Cold wall horizontal reactor 50 cm long, 7.0 cm high and

19.0 cm width. SiHCl3 inlet mole fraction y0=0.137, inlet gas

velocity v0=0.63 cm/s, no tilting. (- - -) Calculated with constant

HCl adsorption rate. (}) Calculated with temperature depen-

dent HCl adsorption rate.


reported by supposing an activation energy of10 kcal/mol and a frequency factor of 1012.54 cm3/mol s for the HCl adsorption. That values appearto be reasonable if compared with the adsorptionactivation energy of H2, which was experimentallyfound to be 17 kcal/mol. With this assumption theetching reaction is favored at high temperatureleading to a deposition rate decrease similar to thatexperimentally observed.A further confirmation of the reactor model and

of the growth chemistry for silicon depositionfrom chlorosilanes was obtained analyzing theprocess conditions of Aoyama et al. [35], wheresilicon tetrachloride was adopted as precursor. Theinformation about the wall temperature is missingand thus in our simulation that temperature wasassumed 300K lower than that of the susceptor.The comparison between predicted and experi-mental growth rate data along the main reactorcoordinate is illustrated in Fig. 4. The samecomparison referred to the gas phase compositiontaken in the bulk (i.e., 1.6 cm to surface) and incorrespondence of the surface (i.e., 0.4 cm tosurface) is illustrated in Fig. 5, where the twospecies considered are SiCl4 and HCl. The agree-ment for HCl is excellent, while a lesser one is

observed for the ‘‘surface’’ value of SiCl4. In thiscase it is important to note that SiCl4 diffusestowards the surface and its concentration profiledrops very sharply near the surface. But, in a 1Dframework it is not possible to obtain compositiondata profiles but only bulk and surface values. Onthe contrary, HCl is produced at the surface anddiffuses towards the bulk and thus originates amore flat profile across the boundary layer.

5. Conclusions

The simulations performed in this work demon-strate the feasibility of a multiscale approach tosimulate the epitaxial silicon deposition both fromthe macroscale point of view (e.g., deposition rateprofile) and mesoscale one (e.g., crystal morphol-ogy). Since at this stage it was of interest to test themodel physics and to obtain a reduced ordermodel to be used in the day by day operations theequations were developed in a 1D framework. Inthis analysis the most important parameters arefound to be the kinetic parameters that nowadaysneed to be estimated independently from reactordata. For this reason computational quantum

Fig. 4. Comparison between calculated (}) and experimental [35] (&) growth rate axial profile for epitaxial silicon deposition from

silicon tetrachloride. Inlet gas velocity v0=34 cm/s, susceptor temperature 12008C, inlet mole fraction y0=0.0078, tilt angle 1.38.


chemistry was adopted to study at the atomic scalethe most important reactions involved in thedeposition mechanism. The development of thisapproach consists in considering also the forma-tion of the main defects affecting crystal quality, asslip lines, stacking faults, voids, vacancies andintersticials. This work is still under progress.

Acknowledgements

The authors are grateful to the Italian ResearchCouncil (CNR), ‘‘Progetto Finalizzato Materiali eDispositivi Elettronici Speciali}MADESS II’’ forthe financial support.

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Reduced order model for the CVD of epitaxial silicon from silane and chlorosilanes