Modeling of transport processes and kinetics of silicon carbide bulk growth

The diameter of silicon carbide (SiC) single crystal grown by the physical vapor transport method has increased significantly in recent years. Process modeling has played an important role in designing and developing the larg e diameter SIC growth systems. The numerical algorithm incorporates the cal culations of radio-frequency, time-harmonic magnetic field by induction hea ting, radiation and conduction heat transfer in the system, as well as the growth kinetics. The generated power density in the graphite susceptor is o btained by solving the magnetic vector potential equations, and radiative h eat transfer is calculated from the integrated equations for radiation. Che mical reactions and transport of gaseous species, Si2C, SiC2, SiC and Si, a re also considered. A growth kinetics model is proposed for the first time, which uses the Hertz-Knudsen equation to relate the growth rate to the sup ersaturation of a rate-determining vapor species, the driving force for the deposition. The theoretical predictions compare reasonably with the publis hed experimental data. The growth rate curves are obtained as a function of growth temperature and system pressure. The growth kinetics is greatly inf luenced by the inert gas pressure, temperature and temperature gradient. Si nce the vapor pressure is an ascending function of the temperature, for low temperature growth, a larger temperature gradient is needed in order to ac hieve the desired level of supersaturation (or growth rate). A low temperat ure growth is usually associated with small diameter systems, which maintai n larger temperature differences. At a high growth temperature, since the v apor pressure is high, only a small temperature difference is required to a chieve the same level of supersaturation. Desirable growth temperature and growth rate profiles can be obtained across the seed surface by optimizing the furnace components, such as the graphite susceptor, induction coil, and insulation materials. (C) 2001 Elsevier Science B.V. All rights reserved.