M.S. Ramm

Global numerical simulation of heat and mass transfer for SiC bulk crystal growth by PVT

Abstract A modeling approach for the numerical simulation of heat and mass transfer during SiC sublimation growth in inductively heated physical vapor transport (PVT) reactors is introduced. The physical model is based on the two-dimensional solution of the coupled differential equations describing mass conservation, momentum conservation, conjugate heat transfer including surface to surface radiation, multicomponent chemical species mass transfer and advective flow. The model also includes the Joule volume heat sources induced by the electromagnetic field. The evolution of the temperature profiles inside the crucible and of the crystallization front is studied. The radial temperature gradient at the crystal/gas interface causes strong radial non-uniformity of the growth rate and, in turn, influences the shape of the growing crystal. Results of calculations are compared to experimental observations to analyse the validity of the modeling approach. Both the computed growth rates, their temporal evolution and the shape of the growing crystal agree with experimental data.

Analysis of sublimation growth of bulk SiC crystals in tantalum container

Abstract Sublimation growth of SiC bulk crystals in tantalum container is studied both experimentally and theoretically. The model of heterogeneous processes occurred on the side wall of the tantalum container proposed recently in Ramm et al. (Mat. Sci. Eng. B 61–62 (1999) 107) is extended to take into account the process of carbon gettering by the container side wall. We formulate a quasi-steady approach for modeling of the bulk crystal growth. Using this concept we predict evolution of the crystal shape and study processes which govern SiC bulk crystal growth. We apply anisotropic thermal elastic analysis to predict stress distribution in the growing crystal. For the first time a model of dislocation formation is applied for SiC bulk growth to compute dislocation density field in highly stressed areas of the growing crystal.

Simulation of Sublimation Growth of SiC Single Crystals

Modelling of sublimation growth of SiC is discussed with the goal to describe the mathematical models necessary to optimize the process and design of the growth system. An analysis of the mechanisms of growth of bulk silicon carbide crystals is performed. Growth conditions which provide stable growth of single SiC crystals without formation of secondary phases are considered. The phase diagram of the formation of extra phases during the sublimation growth of SiC is presented. Modelling of the growth of bulk SiC crystals is considered. Results of modelling the temperature distribution inside the inductively heated system for the growth of bulk SiC crystals are shown. A mechanism of material transport inside the closed Ta container in the absence of an inert gas atmosphere is proposed which is different from that of diffusive or free-molecular transport. First results of the model analysis of chemical processes inside the volume of SiC powder during the sublimation growth are demonstrated. It is shown that the sublimation and re-crystallization of the SiC source is sensitive to the temperature distribution in the source.

Growth of silicon carbide by sublimation sandwich method in the atmosphere of inert gas

Silicon carbide growth by sublimation sandwich method in the atmosphere of an inert gas is studied both experimentally and theoretically. An analytical description of diffusion transport of gaseous reactive species, coupled with quasi-equilibrium heterogeneous reactions at the source-wafer and substrate surfaces is derived. The species transport inside the sandwich cell is shown to be essentially determined by conditions in the ambience. The growth rate is studied as a function of process parameters (substrate temperature, temperature difference between the source-wafer and the substrate, and others). The developed approach is extended to the transient from the diffusion to the collisionless regime of the species transport. The theoretical results are in good agreement with the experimental data obtained.

Virtual reactor as a new tool for modeling and optimization of SiC bulk crystal growth

We propose a new approach to optimization of SiC bulk crystal growth based on modeling. The idea is to employ a special software tool ‘‘virtual reactor’’ (VR) operated by the user of the code as an actual crystal growth system. The software tool includes the models necessary to simulate global heat transfer in the whole growth system and inside the crucible including radiative transport through the semi-transparent SiC crystal. It is known that accurate material properties are crucial for thermal modeling of SiC growth. A database with material properties of SiC crystal and powder, graphites and insulation is included into the VR-software. An advanced model of species transport during sublimation growth of SiC crystals is developed. The model includes convective and diffusive species transport, surface kinetics based on the Hertz–Knudsen equations and chemical models for all solid surfaces (SiC crystal, SiC source, graphite wall). A model to predict type of parasitic deposit and the corresponding deposition rate is combined with the mass transport model available in the VR-software. In this paper, we show the results of simulation of a large-size SiC bulk crystal growth using the VR-software tool with the focus on poly-SiC deposit formation on the graphite crucible lid around the crystal. # 2001 Elsevier Science B.V. All rights reserved.

Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide

Abstract The evolution of crystallization front and growth conditions during sublimation growth of SiC bulk crystal is studied using a coupled heat and mass transport two-dimensional model. It is shown, in particular, that movement of the inductor coil used for heating of the growth crucible modifies the temperature profile at the growth surface but can have no remarkable effect on the growth rate. Anisotropic elasticity theory and a semi-empirical model of dislocation generation are applied for a detailed analysis of thermoelastic strain and dislocation density evolution during SiC bulk crystal growth. An important effect of a method of SiC seed attachment to the holder is revealed by modeling. It is shown that under optimal attachment, the maximum dislocation density is concentrated near the crystallization front at the periphery of the crystal. The region of high dislocation density expands with enlargement of the crystal.

Optimization of sublimation growth of SiC bulk crystals using modeling

Analysis of factors determining growth rate and shape of the crystallization front during sublimation growth of bulk SiC crystals is presented. For this purpose, mass transport of species in the graphite crucible coupled with global heat transfer in a sublimation growth system is studied. Specific features of the growth process in a tantalum container are discussed.

Heat transfer through source powder in sublimation growth of SiC crystal

A problem of heat transport in a source powder is very important for sublimation crystal growth technique. This paper is devoted to the development and implementation of a model of powder heat transfer. As an example temperature field calculation in a growth chamber containing a SiC-powder layer is performed.

Analysis of silicon carbide growth by sublimation sandwich method

Abstract Basic mechanisms of growth of silicon carbide crystals using the sublimation sandwich method with reactive SiC C or SiC Si environment are studied both theoretically and experimentally. Dependence of the growth rate on the process parameters (substrate temperature, temperature difference between the source and the substrate, and temperature of the environment) is calculated using an advanced thermodynamic model. The effect of the environment on 6H SiC growth is studied in detail. The theoretical results are compared to the experimental data.

Transport phenomena in sublimation growth of SiC bulk crystals

Abstract Sublimation growth of SiC bulk crystals in the atmosphere of concentrated multi-component vapor is studied using a specially developed model of transport processes coupled with heterogeneous reactions at the source and the seed surfaces. The convective and multi-component diffusion mechanisms of the gas phase transport, dependence of the pressure level inside the growth chamber on the growth conditions, and kinetic jumps of the species partial pressures at the Knudsen layers on the reactive surfaces are taken into account in the model. The latter effect is described by introduction of novel boundary conditions representing extension of the Hertz–Knudsen relationship for the case of multi-component vapor. The results of calculations are shown to be in a good agreement with the available experimental data.