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SILICON CARBIDE

ConsultingPVT Growth > Silicon Carbide

Silicon carbide is a promising semiconductor material for high-power and high-temperature electronics. The basic problem to be overcome in the production of commercial SiC substrates is poor quality of bulk SiC crystals of desired dimensions. The most widely used industrial technique of growing bulk SiC crystals is the sublimation method (Physical Vapor Transport, Modified Lely Method) which employs sublimation of the polycrystalline SiC powder and transport of the vaporized species containing Si and C atoms to the substrate where single SiC crystal growth occurs. The species transport from the source to the substrate is governed by the temperature gradient maintained in the growth system.

Heat Transfer Modeling

Since the crystal growth by PVT is governed by the temperature distribution in the growth system, the thermal control is of primary importance. The heat transfer modeling involves the consideration conductive and radiant heat transfer, as well as the calculation of the heat sources in the growth system.
To ensure the desired temperature field, RF heating is commonly employed in the sublimation growth systems. Modeling of the Joule heat sources due to inductive heating is carried out by solving the Maxwell equations in a large computational domain that includes the growth system, coil and the ambient.
Electric intensity distribution in a SiC growth system Temperature distribution in a SiC growth system

Figure 1. Left: Electric intensity distribution in a SiC growth system. Right: Temperature distribution in a typical SiC growth system

Radiation is the principal mechanism of heat exchange in the sublimation technique due to high growth temperatures of about 2000-2500C. Because of an extremely high non-linearity of the radiation emission, the everyday experience is of little use for designing crucible, modifying a heating system or even for a tentative understanding of the heat transfer in the crucible. So a detailed modeling of the heat transfer becomes an indispensable tool to predict and control the thermal field in the crucible.
One of the problems arising in modeling SiC sublimation growth is the lack of knowledge on the properties of the used materials, in particular, of the thermal insulation and SiC powder. The models used to describe the heat transfer through the powder source and porous graphite are described in the section Models.

Modeling of Species Transport in SiC Growth

The analysis of mass transport in the growth chamber addresses the following main issues of interest: (i) sufficiently high growth rates (0.3-1.0 mm/h) acceptable for the industrial fabrication of the bulk crystals; (ii) control of the crystal shape aimed at avoiding a polycentric crystallization on the growth surface and generation of parasitic polytypes which is crucial for the growth of a single SiC crystal [1]; (iii) control of the vapor composition, which prevents generation of secondary phase (graphite or liquid Si) inclusions on the growth surface. Simulation of the mass transport accounts for diffusion and convection. The latter cannot be neglected due to the relatively high crystal growth rate and, hence, a considerable Stefan flow [2].

Heterogeneous processes in SiC sublimation growth

In sublimation growth of SiC crystals, the Si-C vapor consists of Si, Si2C, and SiC2 which are diluted by an inert carrier gas, normally, Ar. The reactive species are produced by sublimation of the SiC powder charge and transported to the seed where they contribute to the SiC growth. Use of graphite as a crucible material leads to a chemical intercaction of the reactive species with the crucible walls, supplying additional material to the growing surface. The chemical model used to describe the heterogeneous processes involved in SiC growth is described in the section Models .
Si distribution in the growth chamber Ar distribution in the growth chamber
Si2C distribution in the growth chamber SiC2 distribution in the growth chamber

Figure 2. Species distribution in the growth cavity.

Secondary phase formation during the growth run

In bulk SiC growth, inclusions of the secondary phases (graphite or liquid silicon) can be captured by the growing crystal. These defects usually appear on the growth surface due to non-optimal vapor composition. Thus, a precise control of the vapor composition is required during the entire growth run in order to avoid the secondary phase formation on the surface. In a similar way, polycrystalline SiC can deposit on the graphite crucible walls (here, poly-SiC is considered as a secondary phase on a graphite surface). Usually, the poly-SiC deposits are formed near the seed in a relatively cold zone on the crucible lid [3]. Merging of the poly-SiC deposit and the single SiC crystal leads to a considerable defect density in the boule.
Secondary phase diagram for SiC sublimation growth Prediction of Poly-SiC deposition on the crucible lid

Figure 3. Left: secondary phase diagram for SiC sublimation growth. The vapor composition is changed by varying the Si content, with the SiC2 and Si2C partial pressures being constant. Right: prediction of Poly-SiC deposition on the crucible lid.

Crystal shape control during the growth

A key issue of the SiC growth is the control of the crystal shape. To grow a high quality large size boule, it is beneficial to maintain a slightly convex surface profile during the entire growth run. However, this is a complicated task because the growth rate distribution over the seed is controlled not only by the instantaneous thermal field in the crucible and the respective powder sublimation rate but also by the heterogeneous chemical processes occurring on the crucible walls.
Crystal Shape after the end of growth Experiment

Figure 4. Crystal Shape after the end of growth. Left: Modeling. Right: Experiment.

Mass transport in the powder charge

The processes in the powder source affect significantly the boule growth. The latest publications on SiC sublimation growth [4], [5], offered a new insight into the powder evolution. It has been found that a considerable stratification of the powder is developed during the growth run. First, low-density graphite foam is usually formed in the hot zones due to complete silicon evaporation out of SiC granules resulting in their graphitization. The evaporated species penetrate into the powder bulk and then condensed on the granules in the cold zone near the powder top. The powder evolution was found to depend greatly on the mean size of SiC granules in the source.
Sublimation rate distribution Porosity distribution

Figure 5. Simulation of the Powder Evolution. Sublimation rate (left) and porosity (right) distribution after 5 hours of growth.

An advanced 2D model of the powder evolution and graphitization has been recently elaborated. The computations show that intensive powder sublimation occurs near the crucible walls, i.e. in the high-temperature zone. The reactive species are transported to the relatively cold regions (the bottom and top of the charge) where supersaturated vapor species condense on the granule surfaces. Here, the granule diameter rises and the porosity decreases.
It should be noted that the porosity evolution and granule graphitization change significantly the powder heat and electric effective conductivity. In turn, this may result in a considerable redistribution of the global thermal field in the crucible. The latter fact clearly shows that the mass transport and heat transfer are coupled processes in the sublimation technique, which has to be adequately accounted for by modeling.

Thermoelastic stress in a growing crystal

An issue of permanent interest is how the defect density level and distribution over the grown crystal are related to the growth conditions. Dislocations represent the basic type of defect in bulk wide-bandgap semiconductors. We distinguish between threading dislocations propagating along the growth direction and dislocations gliding in a certain slip plane. For hexagonal SiC crsytals, dislocations glide in the basal plane normal to the main growth direction. The origin of the dislocation motion, nucleation and multiplication is the thermoelastic stress produced by the temperature gradients in the growing crystal.
Dislocation density distribution in the growing crystal in the beginning of growth Dislocation density distribution in the crystal after the growth run

Figure 6. Dislocation density distribution in the growing crystal for two different growth stages.

Virtual Reactor (SiC)

Most processes occurring during sublimation growth are strongly coupled with each other. Simulation of the SiC growth requires a global model of the sublimation growth, accounting for all the factors mentioned above. Specialized software Virtual Reactor has been developed to treat this problem.

References

[1] E.N. Mokhov, M.G. Ramm, A.D.Roenkov, and Yu.A. Vodakov, Mat. Sci. Engin B 46 (1997) 317.
[2] S.Yu. Karpov, A.V. Kulik, M.S. Ramm, E.N. Mokhov, A.D. Roenkov, Yu.A. Vodakov, and Yu.N. Makarov, Mat. Sci. Forum 353-356 (2001) 779.
[3] M.S. Ramm, A.V. Kulik, I.A. Zhmakin, S.Yu. Karpov, O.V. Bord, S.E. Demina, and Yu.N. Makarov, Mat. Res. Soc. Symp. Proc. 616 (2000) 227.
[4] M. Pons, M. Anikin, K. Chourou, C.M. Dedulle, R. Madar, E. Blanquet, A. Pisch, C. Bernard, P. Grosse, C. Faure, G. Basset, and Y. Grange, Mat. Sci. Engin. B 61-62 (1999) 18.
[5] P.J. Wellmann, M. Bickermann, D. Hofmann, L. Kadinski, M. Selder, T.L. Straubinger, and A. Winnacker, J. Cryst. Growth 216 (2000) 263.

Publications

[1] Karpov S.Yu., Makarov Yu.N., Ramm M.S.
Analytical model of silicon carbide growth under free-molecular transport conditions.
Journal of Crystal Growth, Vol.169, p.491-495, (1996)

[2] Karpov S.Yu., Makarov Yu.N., Ramm M.S.
Theoretical consideration of Si-droplets and graphite inclusions formation during chemical vapor deposition of SiC epitaxial layers.
Institute of Physics Conference Series, N.142, Chapt.1, p.177-180, (1996)

[3] S.Yu. Karpov, Yu.N. Makarov, M.S. Ramm
Simulation of Sublimation Growth of SiC Single Crystal.
Physica Status Solidi (b), Vol.202, p.201-220, (1997)

[4] Karpov S.Yu., Makarov Yu.N., Mokhov E.N., Ramm M.G., Ramm M.S., Roenkov A.D., Talalaev R.A., Vodakov Yu.A.
Modelling of species transport and excess phases formation during sublimation growth of SiC in sandwich system.
Institute of Physics Conference Series, N 155, Chapt.9, p.655-658, (1997)

[5] Karpov S.Yu., Makarov Yu.N., Mokhov E.N., Ramm M.G., Ramm M.S., Roenkov A.D., Talalaev R.A., Vodakov Yu.A.
Analysis of silicon carbide growth by sublimation sandwich method.
Journal of Crystal Growth, Vol. 173, p.408-416, (1997)

[6] Karpov S.Yu., Makarov Yu.N., Ramm M.S., Talalaev R.A.
Control of SiC growth and graphitization in sublimation sandwich system.
Materials Science and Engineering, Vol.B46, p.340-344, (1997)

[7] Egorov Yu.E., Galyukov A.O., Gurevich S.G., Makarov Yu.N., Mokhov E.N., Ramm M.G., Ramm M.S., Roenkov A.D., Segal A.S., Vodakov Yu.A., Vorob'ev A.N., Zhmakin A.I.
Virtual reactor as a new tool for modeling and optimization of SiC bulk crystal growth.
Materials Science Forum, Vol.264-268, p.61-64, (1998)

[8] Makarov Yu.N., Demina S.E., Karpov S.Yu., Kulik A.V., Mokhov E.N., Ramm M.G., Ramm M.S., Roenkov A.D., Vodakov Yu.A., Zhmakin A.I.
Specific features of sublimation growth of bulk SiC crystals in tantalum container.
International Conference on Silicon Carbide and Related Materials, Abstract N 247., (1999)

[9] Segal A.S., Vorob'ev A.N., Karpov S.Yu., Makarov Yu.N., Mokhov E.N., Ramm M.G. , Ramm M.S., Roenkov A.D., Vodakov Yu.A. , Zhmakin A.I.
Transport phenomena in sublimation growth of SiC bulk crystals.
Materials Science and Engineering, Vol.B61-62, p.40-43, (1999)

[10] Ramm M.S., Mokhov E.N., Demina S.E., Ramm M.G., Karpov S.Yu., Roenkov A.D , Vodakov Yu.A., Segal A.S., Vorob'ev A.N., Kulik A.V., Makarov Yu.N.
Optimization of sublimation growth of SiC bulk crystals using modeling.
Materials Science and Engineering, Vol.B61-62, p.107-112, (1999)

[11] Zhmakin I.A., Kulik A.V., Karpov S.Yu., Demina S.E., Ramm M.S., Makarov Yu.N.
Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide.
Diamond and Related Materials, Vol.9, p.446-451, (2000)

[12] Segal A.S., Vorob'ev A.N., Karpov S.Yu., Mokhov E.N., Ramm M.G., Ramm M.S., Roenkov A.D., Vodakov Yu.A., Makarov Yu.N.
Growth of silicon carbide by sublimation sandwich method in the atmosphere of inert gas.
Journal of Crystal Growth, Vol.208, p.431-441, (2000)

[13] Selder M., Kadinski L., Makarov Yu., Durst F., Wellmann P., Straubinger T., Hofmann D., Karpov S., Ramm M.
Global numerical simulation of heat and mass transfer for SiC bulk crystal growth by PVT.
Journal of Crystal Growth, Vol.211, p.333-338, (2000)

[14] Karpov S.Yu., Kulik A.V., Zhmakin I.A., Makarov Yu.N., E.N. Mokhov, Ramm M.G., Ramm M.S., Roenkov A.D., Vodakov Yu.A.
Analysis of sublimation growth of bulk SiC crystals in tantalum container.
Journal of Crystal Growth, Vol.211, p.347-351, (2000)

[15] Bogdanov M.V., Galyukov A.O., Karpov S.Yu., Kulik A.V., Kochuguev S.K., Ofengeim D.Kh., Tsirulnikov A.V., Ramm M.S., Zhmakin A.I., Makarov Yu.N.
Virtual reactor as a new tool for modeling and optimization of SiC bulk crystal growth.
Journal of Crystal Growth, Vol.225, p.307-311, (2001)

[16] Karpov D.S., Bord O.V., Ramm M.S., Karpov S.Yu., Zhmakin A.I., Makarov Yu.N.
Mass transport and powder source evolution in sublimation growth of SiC bulk crystals.
Materials Science Forum, Vol.353-356, p.37-40, (2001)

[17] Bogdanov M.V., Galyukov A.O., Karpov S.Yu., Kulik A.V., Kochuguev S.K., Ofengeim D.Kh., Tsirulnikov A.V., Zhmakin I.A., Komissarov A.E., Bord O.V., Ramm M.S., Zhmakin A.I., Makarov Yu.N.
Virtual reactor: a new tool for SiC bulk crystal growth study and optimization.
Materials Science Forum, Vol.353-356, p.57-60, (2001)

[18] Kulik A.V., Demina S.E., Kochuguev S.K., Ofengeim D.Kh., Karpov S.Yu., Vorob'ev A.N., M.V. Bogdanov, Ramm M.S., Zhmakin A.I., Alonso A.A., Gurevich S.G., Makarov Yu.N.
Inverse-computation design of a SiC bulk crystal growth system.
Materials Research Society Symposium Proceedings, Vol.640, p.H1.6.1-H1.6.6, (2001)

[19] Bogdanov M.V., Demina S.E., Karpov S.Yu., Kulik A.V., Ofengeim D.Kh., Ramm M.S., Mokhov E.N., Roenkov A.D., Vodakov Yu.A., Makarov Yu.N., Helava H.
Modeling analysis of free-spreading sublimation growth of SiC crystals.
Materials Research Society Symposium Proceedings, Vol.742, p.K1.3, (2003)

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