State of the art in the modelling of SiC sublimation growth

Materials Science and Engineering B61–62 (1999) 18–28

State of the art in the modelling of SiC sublimation growth

M. Pons a,*, M. Anikin b, K. Chourou b, J.M. Dedulle b, R. Madar b, E. Blanquet a,A. Pisch a, C. Bernard a, P. Grosse c, C. Faure c, G. Basset c, Y. Grange c

a Laboratoire de Thermodynamique et Physicochimie Metallurgiques, UMR CNRS/INPG/UJF 5614, Institut National Polytechnique de Grenoble,BP 75, 38402 Saint Martin D’Heres, France

b Laboratoire de Materiaux et de Genie Physique, UMR CNRS/INPG 5628-ENSPG, Institut National Polytechnique de Grenoble, BP 46,38402 Saint Martin D’Heres, France

c LETI-CEA Grenoble, Departement Optronique, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France

Abstract

Different computational tools have helped to provide additional information on the sublimation growth of SiC single crystalsby the modified-Lely method. The modelling work was motivated by the need of a better control of the local temperature fieldinside the crucible. Because there is an environment of strong thermal radiation in which the SiC boule growth process occurs,heat transfer must therefore be coupled with gaseous species transport and reactivity. This highly coupled model must take intoaccount all geometric modifications in crucibles which strongly influences the crystal growth process. Local thermochemicalequilibrium linked to heat and mass transfer is the model proposed in this paper to give the magnitude of the growth rate andthe shape of the crystal. This modelling field is still too young to propose a software package including all modelling aspects anda reliable material database. However, some parts of the modelling work have reached maturity like electromagnetic heating andthermal modelling coupled with simplified chemical models. We show in this paper selected examples in order to demonstrate thetypes of information which can be routinely available by simulation and how to approach defect formation from a macroscopicpoint of view. Minor geometric modifications of the holes for pyrometric measurements drastically change the magnitude ofthermal gradients in the crucible. Geometric modifications of the crucible change the computed crystal shapes. The calculatedresults complete the experimental knowledge by a quantification of the local macroscopic fields. © 1999 Elsevier Science S.A. Allrights reserved.

Keywords: Sublimation growth; Strong thermal radiation; Electromagnetic heating; Local macroscopic fields

1. Introduction

During the last 5 years, significant progress has beenmade on the modelling of sublimation growth of siliconcarbide single crystals [1–10]. The different computa-tional tools have helped to provide additional informa-tion to experimental knowledge. Such an effort wasprimarily motivated by the need of a better control ofthe local temperature field inside the crucible which isan environment of strong thermal radiation in whichthe SiC boule growth process occurs. The computedtemperature distribution can help to qualitatively ob-tain the growth history in relation to process parame-ters and geometry. Global heat transfer phenomena

were mainly studied and must include conduction, con-vection, radiation and induction heating as well as theheat of crystallisation and sublimation at the crystal–vapor and source–vapor interfaces [11]. As pointed outby Tsvetkov et al. [12], minor variations in crucibledesign can lead to different crystal shapes due to simul-taneous modifications in heat and mass transfer. It wasfound that local fluctuations of temperature and tem-perature gradients over the seed can be one of themultiple causes of defect formation [10]. High tempera-ture thermophysical data, principally emissivity andconductivity of SiC source powder, single and poly-crystalline SiC are under study [11,13]. Their accurateknowledge still remains a challenge but is essential forrealistic simulations. In addition, during the sublima-tion growth of crystals of significant length, the temper-ature distribution inside the crucible changes. This is

* Corresponding author. Tel.: +33-4-76826532; fax: +33-4-76826677.

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

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M. Pons et al. / Materials Science and Engineering B61–62 (1999) 18–28 19

because of the increase in crystal size, deposition oncrucible walls and modifications of the volume as wellas porosity and properties of the SiC powder.

The simple simulation of heat transfer does not di-rectly allow the determination of the growth rate andthe shape of the crystal. However, this first step hasproved its efficiency for the optimization of the localtemperature field and to insure predominant materialtransport to the seed by suppressing deposit formationon the walls [4]. Mass transfer which is the drivingphenomena for the growth certainly depends on thetemperature distribution but also on the diffusion ofgaseous species, convection and chemical reactivity.

We focus our attention on the seeded method (theso-called modified-Lely method [14]) where a seed isplaced in a crucible containing a powder charge ofSiC, with graphite walls and operating temperatures inthe 2400–2800 K range within the gas phase. Thetemperature range was calculated from heat transferand controlled by pyrometric temperature measure-ments.

Related growth processes involving tantalum con-tainers or short distance between source powder andseed are also used. The effect of a tantalum containeron the growth process is not completely understood.The published results are based on the assumptionthat metastable tantalum disilicide is formed on thewall of the tantalum container during sublimationgrowth [4]. The sublimation sandwich method (SSM),for growing epitaxial SiC films with low density ofdefects is out of the scope of this paper. In this lastsystem, mass transport is arranged between two SiCwafers being maintained at different temperatures.Both wafers are placed in a closed container. Vodakovet al. [15] have reviewed this subject involving graphiteor tantalum containers.

In this contribution, a description of models andsimulations for the modified-Lely method will be pre-sented, the thermodynamic ones in Section 2 and theprocess ones in Section 3. Some advanced examplesand their technological involvement will be developedin Section 3. Tentative relations between process simu-lation and defect appearance will be shown in Section4. Experimental results of our recent SiC bulk growthprocess development will complete the presentationand are included all along in order to verify experi-mentally the validity of the models.

2. Thermodynamic modelling

A classical thermodynamic analysis of the Si–C–Arsystem can provide the equilibrium composition in thegas phase above silicon carbide during its sublimationin the temperature range 2300–3000 K. The thermo-

dynamic data came from the recent work of P. Ro-cabois et al. [16]. They generated a self-consistent setof data for the gaseous molecules Sin and SixCy, froma literature review, measurements and their own heatcapacity and entropy calculations using recent resultson molecular structures, vibrational frequencies andelectronic spectra.

From their conclusions, nine gaseous species in ad-dition to argon (Si1, Si2, Si3, C1, C2, C3, SiC, Si2C,SiC2) and three condensed phases (the stable form ofSiC, Si and C (graphite)) were considered.

The thermodynamic calculations were carried out bydirect minimization of the total free energy of thesystem. The parameters introduced in the calculationswere the temperature (2300–3000 K), the volume ofthe crucible (V=0.051) and the initial quantities ofargon and solid silicon carbide for the source. Theresults confirmed that the free sublimation of SiC isnot congruent (enrichment of the condensed phase incarbon) and that the gas phase is essentially composedof Si1(g), SiC2(g) and Si2C(g). Earlier mass spectromet-ric data [17] and recent results [18] agree with theseconclusions. One can also calculate the temperaturedependence of the silicon to carbon ratio in the gasphase. Using these data in an appropriate transportmodel, a satisfactory agreement is found between hightemperature features of the powder (graphitization andsublimation) and the thermochemistry.

This approach is the first step of the modellingstrategy. It does not give the actual state of the pro-cess because of the dynamic nature of the crystalgrowth. However, by linking this approach with heatand mass transfer, the resulting crystal shapes, theoccurrence of some defects and modifications of thepowder can be discussed (Sections 3 and 4).

3. Process modelling: macroscopic features of crystalgrowth

The sublimation growth process involves multicom-ponent fluid transport, gas–surface chemistry and heattransfer by radiation, conduction, convection and in-duction heating. Chemical and thermal databases com-plete the description of the problem.

3.1. Multicomponent fluid transport

The fluid transport model is based on the low pres-sure kinetic theory of gases. Transport coefficientssuch as viscosity, conductivity, specific heat, diffusivityand thermodiffusion coefficient are calculated as localfunctions of temperature, pressure and composition.The Stefan–Maxwell formulation for diffusive trans-

M. Pons et al. / Materials Science and Engineering B61–62 (1999) 18–2820

port ensures complete mass conservation of all speciesin the system.

3.2. Gas and surface chemistry

A comprehensive capability must be available tosimulate multi-step gas and surface chemistry. Largesets of multi-step reactions or thermodynamic equi-librium must be handled in the code. The surfacechemistry is treated by doing a complete reaction–dif-fusion balance at the surface to obtain the surfaceconcentration of species. The heat release from thegas–surface reactions are included in the model.

3.3. Thermal radiation, induction heating

Electromagnetodynamics must be coupled with heattransfer, especially radiative heat transfer within thegrowth cavity. In our code, the radiation model istightly coupled to the fluid transport, conjugate heattransfer and chemistry models to ensure energyconservation.

3.4. Material database

It must include the electrical and the thermal conduc-tivity of crucible and insulation material, the source andthe boule material properties, the gas species and asso-ciated reactivity data, the induction frequency and thecurrent density.

The complete model is complex because of the pres-ence of coupled phenomena as well as the lack ofknowledge of materials data. Nilsson et al. [13] haveperformed an impressive work to measure and calculatehigh temperature thermophysical data.

The sublimation growth process occurs in a semi-closed system. The configuration used is schematicallyshown in Fig. 1. For the modified-Lely method withgraphite crucible, within the range of investigated ex-perimental parameters, we have verified that the naturalconvective transport of heat and of chemical speciescan be neglected when compared to diffusive transportand conductive heat [2]. The recent work of Hofmannet al. [1] gave the same conclusions. Intensive sublima-tion of material in the source generates a macroscopic

Fig. 1. Schematic representation of the experimental set-up used for the crystal growth.


Fig. 2. Schematic representation of the right-half part of a generic reactor with the equations to be solved [2].

flow (Stefan flow) from source to seed which is modeledusing momentum conservation equations coupled withmass conservation equations [7]. The velocities of themacroscopic flow from source to seed could be as highas 1 m s−1 at low pressure (100 Pa) at about 2200 K[7].

In the results presented in this paper, Stephan flow isnot taken into account. Heat transfer in the crucible ismainly driven by heat conduction and radiation andtransport by mass diffusion [2,10].

The schematic representation of the axisymmetricgeometry, used to illustrate the modelling work, isshown on Fig. 2. More details about the equations tobe solved can be found in [2,10].

The temperature and concentration distributions inthe crucible and on the surface of the growing crystalare among the key parameters determining the growthrate distribution and therefore the shape of the crystal-lization front. In situ observations and measurementsof the growth process are extremely difficult particu-larly at the level of determining specific reaction mecha-nisms and pathways with spatially resolvedtemperatures and compositions. Hofmann et al. [6]investigated the dynamic growth rate evolution of thecrystal by nitrogen injection. Valuable informationabout the growth process has been obtained from exsitu examination of deposited films by correlating themorphology of the crystalline material and the defectsincorporated in the material with the growthconditions.

The global computation is complex. The question is:what qualitative information can be derived andquantified from heat and mass transfer analyses whilekeeping in mind the assumptions which underlie thecomputations? The five examples presented below givesome answers.

3.5. Heat transfer: general o6er6iew

A temperature field is established inside the reactor(Fig. 3). In our experiments, a thermal gradient of lessthan 100 K.cm−1 is typical (see inset of Fig. 3). Thevalue of the growth rate is determined by the growthtemperature, the total pressure in the system, the tem-perature difference between the surfaces of source andseed and the seed-source distance.

3.6. Heat transfer: minor geometric modifications

Here, it is important to note that the challenge is tocontrol small temperature differences (less than 100 K)in the gas cavity, as compared to the total temperaturedifference. Fig. 4 illustrates that a small geometricmodification of the graphite lid affects drastically, atthe seed–gas interface, the thermal gradient field. Ther-mal gradient is higher when the hole is deeper in thegraphite lid. Thermal gradients contribute to the shapeof the growing crystal. A correlation between the tem-perature gradient at the back of the seed and macrode-fect distribution will be discussed in Section 4.


3.7. Heat transfer: geometric modification of thegrowth area

It is advantageous for the growth of SiC crystals toprevent formation of SiC deposits on the crucible walland around the seed. To achieve this, it is necessary toestablish a temperature on the surface of the crucible

which is everywhere higher than the temperature ofcrystallisation. This results in material transport pre-dominantly to the seed. A flat deflector [19] allowsgrowth of the crystal while avoiding poly-SiC growth.Fig. 5 compares the thermal fields for two cruciblegeometry. They are not identical principally in theregion near the seed. For these configurations, the

Fig. 3. General representation of the potential vector (x radius) in Wb, the Joule losses (W m−3) and temperature (K) fields (current density:1.6×107 W m−2; frequency: 125 kHz).

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Fig. 4. Local thermal gradients for two configurations, (a) and (b) of the graphite lid and associated macrodefect distribution on wafers.


Fig. 5. Comparison of the thermal fields (a) without and (b) with screen for the same experimental parameters. All other part of the geometryare unchanged.

crucible geometry is evolving when the crystal grows toa length of about 10 mm. This is because the source–seed distance is 15 mm. For the configuration withoutscreen, the evolving geometry leads to a decrease of theaxial thermal gradient and consequently to a decreaseof the growth rate. For the configuration with screen,the evolving geometry causes modifications of the crys-tal shape. These experimental observations are going tobe quantified.

3.8. Heat and mass transfer: trends in crystal shapes

Mass transfer analysis linked with local thermo-chemical equilibrium (LTCE) [2] allows the computa-tion of fluxes of carbon- and silicon-containing gaseousspecies and subsequent growth rate and crystal shape.Careful attention must be paid to the deposited flux asthe geometry is evolving due to crystal growth. Calcu-lated temperature fields during growth showed that thetemperature gradient decreases and subsequently thegrowth rate. Results of the initial crystal shapes (about1 mm growth) are first presented. Because of the differ-ent geometric configurations near the seed and associ-ated thermal distributions, the deposited fluxes aredifferent showing the importance of coupled diffusionand temperature activated reactivity (Fig. 6). The calcu-lated shape is almost flat for configuration (a) andconvex for configuration (b). For both configurations,the deposited fluxes correspond to the experimentalshape. For the configuration with a flat screen, masstransport modelling confirms that no deposition occurson the screen. The crystal grows freely.

The modeling provides a good understanding of theenlargement of the crystal [20–22] based on the radialgradient and associated fluxes along the growth surface.Due to this radial thermal gradient, ingot diameterincreases with an increase in length if the growth ofpolycrystalline SiC on graphite lid follows the ingotgrowth (configuration (a) in Fig. 6). An increase in thethermal radial gradient would increase the lateralgrowth rate [22]. If the distance between the ingot andthe polycrystal increases, resublimation of the ingotleads to a decrease in diameter with increasing crystallength. In the same way, using the flat screen configura-tion (configuration (b) in Fig. 6), mass transport model-ing shows that, after an initial enlargement, the ingotdiameter progressively decreases. The screen becomestoo far from the growing interface to ensure the samegrowth conditions. (Fig. 7). This geometry seems inade-quate to ensure a long-lasting enlargement due tochanges in the thermal and flux fields during growth. Itmust be noticed that the shape evolution presented canbe modified by changing temperature and pressure.

3.9. Heat and mass transfers: features of source powder

During sublimation growth of bulk SiC crystals ofsignificant length, graphitization or sublimation of thepowder source changes the thermal conductivity andradiative properties of the powder. These powder fea-tures can be explained on the basis of uncoupled ther-modynamic and heat transfer modelling (Fig. 8). Thesublimation of the SiC powder is not congruent andgraphitization is expected. Thermodynamic modelling


Fig. 6. Deposited carbon flux for two different configurations ((a) and (b) in Fig. 5). For better clarity, they are only presented in the vicinity ofthe original seed to depict the initial crystal shape.

showed that, when the temperature increases thegaseous Si–C ratio decreases. Experimentally, duringthe growth of SiC ingots, the source material (thepowder) partially carbonizes and recrystallizes. Someexperiments leading to higher temperatures in the pow-der have shown that, in accordance to thermodynamics,the graphitization is replaced by a local congruentsublimation of the powder when the gaseous Si–C ratiois close to one. We have focused our attention on therelationship between the thermal field obtained in thefirst stage of the growth process and the features of thepowder after five hours of processing. It clearly appears(Fig. 8) that in case (a), the periphery of the powder iscarbonized. In case (b), empty cavities are formed inthe powder. The associated thermal fields show that,with increasing temperature, the Si–C ratio decreasesleading to the occurrence of congruent sublimation ofthe powder. These results allow prediction of the mainfeatures of the powder and validation of some aspectsof our software and thermal database. This qualitativeinformation helps to demonstrate that the proposedmodel, although incomplete, depicts the experimentalreality.

We have illustrated the potential of heat and reactivemulticomponent mass transfer modelling by showinglocal temperature and fluxes fields rather than globalvalues as classically shown in previous papers. It clearlyappears that minor geometric modifications, even ifthey slightly change the thermal field, drastically affectthe thermal gradient field and the associated depositionfluxes. So, the crystal shape could be managed by thegeometry of the crucible set-up. Obviously, all theresults are to be taken with a care because they are only

valid for the different geometries presented and cannotbe extrapolated for lower pressures and/or tempera-tures, higher dimensions of the cavity etc. However,they can be used to learn about the simultaneousphenomena which drive the growth process. They com-plement and sometimes rationalize the experimentalability by picturing the local phenomena and dissociat-ing the different locally driving forces and flux. Thisanalysis can also provide guidelines for defect forma-tion and appearance as shown in Section 4.

4. Defects—macroscopic modelling relations

Now, we will address the complex domain of defectformation and localization from a macroscopic point ofview.

Fig. 7. Computed shapes of the crystal grown with a flat screenduring time (conditions of Fig. 5). The shape becomes more and moreconvex when the crystal grows.


Fig. 8. Cross-sections of the powder with associated thermal field (a) lower temperature than (b).

Macrodefects and micropipes are classified as hollowdefects [20]. Macrodefects are large vertical holes withhorizontal enlargement at their end. They may start atthe holder–seed interface and penetrate deep into thegrowing crystal. The formation of these defects hasbeen explained by secondary local sublimation of theseed and the growing ingot and not as a result ofinstabilities at the growth interface. High temperaturesand large temperature gradients between the seed andgraphite holder lead to a local sublimation at thebackside of the seed at the beginning of growth andthen to macrodefect formation. These macrodefects canbe eliminated using a specific design of the seed-holderattachment which determines the local gradient at theinterface between the seed and the holder. They canalso be partly eliminated by increasing the thermalradial gradient. Their growth angle increases and theyare blocked at the single-crystal polycrystal interface.They can also be eliminated by reducing the growthtemperature, by changing the composition of the pow-der and so, the composition of the gas phase.

Since the macrodefect formation involves a back-side sublimation from the seed, both the temperatureand the temperature gradient are important keyparameters to control the occurrence of the macrode-fects in SiC boules. We have investigated variouscrucible designs, growth chamber geometries and seedattachment techniques in relation with the macrode-fect distributions. Fig. 4 shows that the temperaturegradient profile and the corresponding SiC wafers fortwo different configurations. There is a strong corre-lation between the temperature gradient at the backof the seed and the macrodefect distribution. In case(a), the maximum concentration of macrodefects isreached where the temperature gradient is maximum,at the periphery of the seed. In case (b), the tempera-ture gradient is higher at the graphite–seed interface.The macrodefects are observed in the totality of thewafer. Even if the macrodefect appearance involvescomplex phenomena, local thermal gradient fields andtheir absolute values give some guidelines to their dis-tribution.


A major problem in the growth of SiC is the presenceof other defects, called pinholes or micropipes [23–25].The origin of the formation processes of micropipes inSiC is complex. Most of the are based on the Frank’stheory proposing that a micropipe is the hollow core ofa screw dislocation with a large Burgers vector (severaltime the unit cell) and with the diameter of the coredirectly related to the magnitude of the Burgers vector[20,26,27]. Generally, in our experiments, a higher con-centration of micropipes have been observed in theregions of lower growth rate indicating the importanceof the crystal shape. The simulation of flat crystalshapes and associated geometric configuration and ex-perimental parameters could be of interest and couldcomplete the experimental work.

There is no doubt that the enlargement of the crystalis the main cause of the high stress level in the periph-ery region as shown by our recent results using syn-chrotron radiation and polarized light opticalmicroscopy [20,21]. We think also that the initiation ofmicropipes is partly due to small grains detached fromthe crucible wall or coming from the powder and liquidsilicon droplets. The grains can move against gravity tothe growing crystal showing the importance of theStefan flow [4,7]. Liquid silicon droplet condensation isa rather physico-chemical effect [3] which has to bequantify.

The macroscopic approach is able to qualitativelycontribute to explain some of the phenomena leading tothe appearance of certain types of defects and to theirspatial distribution. The remaining problem is to evalu-ate the relative importance of technological problemsand mechanical, transport and physico-chemical phe-nomena and so to propose a microscopic model linkingmacroscopic data, particularly local fields to defectinitiation on nanometric scale.

5. Conclusions

A software package must include advanced models tosimulate multi-component fluid flow, gas–surfacechemistry, conjugate heat transfer in arbitrarily geome-try. In addition, for the configurations shown in Section3, the geometry of the crucible is evolving duringgrowth, due to the relatively large crystal (10 mm) insmall cavities (10–20 mm).

To improve the accuracy of the predictions, an intri-cate mixture between experimental and simulated re-sults must be carried out because, on one hand thedirect measurement and monitoring of temperature andgrowth rate in the crucible is not feasible and, on theother hand the computational approaches have to bevalidated.

Models involving different levels of complexity canbe computed. Some simplified approaches have reached

maturity like electromagnetic and thermal modellingcoupled with simplified chemical models. Heat andmass transfers coupled with local thermochemical equi-librium (LTCE) have proved their efficiency for theprediction of crystal shapes. They are useful for obtain-ing the design trends and to obtain pictures of theactual fields. We have shown that minor geometricmodifications can lead to drastic changes in crystalgrowth, like the crystal shape and the defect formation.The modelling approach completes the experimentalability.

A detailed knowledge of the specific surface reactionsthat control crystallographic texture, microstructureand defect/impurity incorporation is still needed. All ofthese issues are critical for controlling crystal propertiesand processing. The remaining problem is characteriz-ing the different phenomena leading to the appearanceof defects. Some of them result from chemical phenom-ena like the so-called macro-defects and liquid silicondroplets, others from technological reasons and/ortransport phenomena like the incorporation of finepowders in the growing crystal. Simple thermo-mechan-ics concepts allow the determination of the importanceof thermal gradients during growth and cooling. Thisapproach is not sufficient to track micropipe generationwhich results from highly coupled phenomena not yetcompletely understood. Synchrotron radiation measure-ments can help to provide spatial distribution of defectsand to give the guidelines for a new modelling research.

References

[1] D. Hofmann, M. Heinze, A. Winnacker, et al., J. CrystalGrowth 146 (1995) 214.

[2] M. Pons, E. Blanquet, J.M. Dedulle, I. Garcon, R. Madar, C.Bernard, J. Electrochem. Soc. 143 (1996) 3727.

[3] R.C. Glass, D. Henshall, V.F. Tsvetkov, C.H. Carter, MRS Bull.3 (1997) 30.

[4] S. Yu. Karpov, Yu N. Makarov, M.S. Ram, Phys. Stat. Sol. (b)202 (1997) 201.

[5] P. Raback, R. Nieminen, R. Yakimova, M. Tuominen, E.Janzen, Mater. Sci. Forum 264–268 (1998) 65.

[6] R. Eckstein, D. Hofmann, Y. Makarov, St.G. Muller, G. Pensl,Mater. Res. Symp. Proc 423 (1996) 215.

[7] Yu E. Egorov, A.O. Galyukov, S.G. Gurevich, et al., Mater. Sci.Forum 264–268 (1998) 61.

[8] D. Hofmann, R. Eckstein, M. Kolbl, et al., J. Crystal Growth174 (1997) 669.

[9] SiC–Sim, Cape Simulations, Inc., Newton, MA 02181, USA,1997.

[10] M. Pons, M. Anikin, J.M. Dedulle, R. Madar, K. Chourou, E.Blanquet, C. Bernard, Surf. Coat. Technol. 94–95 (1997) 279.

[11] St.G. Muller, R. Eckstein, J. Fricke, D. Hofmann, R. Hofmann,R. Horn, H. Mehling, O. Nilsson, Mater. Sci. Forum 264–268(1998) 623.

[12] V. Tsvetkov, R. Glass, D. Henshall, D. Asbury, C.H. Carter Jr.,Mater. Sci. Forum 264/268 (1998) 3.

[13] O. Nilsson, H. Mehling, R. Horn, J. Fricke, R. Hofmann, St.G.Muller, R. Eckstein, D. Hofmann, High Press High Temp. 29(1997) 73.


[14] Yu M. Tairov, V.F. Tsvetkov, J. Cryst. Growth 43 (1978) 209.[15] Yu A. Vodakov, A.D. Roenkov, M.G. Ramm, E.N. Mokhov,

Yu N. Makarov, Phy. Stat. Sol. (b) 202 (1997) 177.[16] P. Rocabois, C. Chatillon, C. Bernard, F. Genet, High Temp.

High Press 27–28 (1995) 25.[17] J. Drowart, G. De Maria, M.G. Inghram, J. Phys. Chem. 29

(1958) 1015–1023.[18] R.C. Glass, D. Henshall, V.F. Tsvetkov, C.H. Carter, Phys. Stat.

Sol. (b) 202 (1997) 149.[19] Japanese patent 8-295595 (1996), Monocrystal growth device for

producing semiconductor devices.[20] R. Madar, M. Anikin, K. Chourou, et al., Diamond and related

materials 6 (10) (1997) 1249–1261.

[21] S. Milita, R. Madar, J. Baruchel, A. Mazuelas, Mater. Sci.Forum 264/268 (1998) 29.

[22] M. Anikin, M. Pons, K. Chourou, O. Chaix, J.M. Bluet, V.Lauer, R. Madar, Mater. Sci. Forum 264–268 (1998) 45.

[23] M. Sasaki, Y. Nishio, S. Nishido, S. Nakashima, H. Harima,Mater. Sci. Forum 264/268 (1998) 41.

[24] J. Heindl, H.P. Strunk, V.D. Heydemann, G. Pensl, Phys. Stat.Sol. 162 (1997) 251.

[25] W. Si, M. Dudley, R. Glass, V. Tsvethov, C.H. Carter Jr.,Mater. Sci. Forum 264/268 (1998) 429.

[26] J. Heindl, W. Dorsch, R. Eckstein, D. Hofmann, T. Marek,St.G. Muller, H.P. Strunk, A. Winnacker, Diamond Rel. Mater.6 (1997) 1269.

[27] R.A. Stein, Phisica B 185 (1993) 211.

.

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State of the art in the modelling of SiC sublimation growth