Modeling of silicon carbide crystal growth by physical vapor transport method

Wide-bandgap silicon carbide (SiC) substrates are needed for fabrication of electronic and optoelectronic devices and circuits that can function under high-temperature, high-power, high-frequency conditions. The bulk growth of SiC single crystal by physical vapor transport (PVT), modified Lely method involves sublimation of a SiC powder charge, mass transfer through an inert gas environment, and condensation on a seed. Temperature distribution in the growth system and growth rate profile on the crystal surface are critical to the quality and size of the grown SiC single crystal. Modeling of SiC growth is considered important for the design of efficient systems and reduction of defect density and micropipes in as-grown crystals. A comprehensive process model for SiC bulk growth has been developed that incorporates the calculations of radio frequency (RF) heating, heat and mass transfer and growth kinetics. The effects of current in the induction coil as well as that of coil position on thermal field and growth rate have been studied in detail. The growth rate has an Arrhenius-type dependence on deposition surface temperature and a linear dependence on the temperature gradient in the growth chamber.

Modeling of Heat Transfer and Kinetics of Physical Vapor Transport Growth of Silicon Carbide Crystals

Transient numerical investigation of induction heating during sublimation growth of silicon carbide single crystals

Kinetics and modeling of sublimation growth of silicon carbide bulk crystal

We present a transient mathematical model for the sublimation growth of silicon carbide (SiC) single crystals by the physical vapor transport (PVT) method. The model of the gas phase consists of balance equations for mass, momentum, and energy, as well as reaction-diffusion equations. Due to physical and chemical reactions, the gas phase is encompassed by free boundaries. Nonlinear heat transport equations are considered in the various solid components of the growth system. Discontinuous and nonlocal interface conditions are formulated to account for temperature steps between gas and solid as well as for diffuse-gray radiative heat transfer between cavity surfaces. An axisymmetric induction heating model is devised using a magnetic scalar potential. For a nonlinear evolution problem arising from the model, a finite volume scheme is stated, followed by a discrete existence and uniqueness result. We conclude by presenting and analyzing results of transient numerical experiments relevant to the physical growth process.

https://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=6&iss=3&rank=2

Modeling and simulation of sublimation growth of SiC bulk single crystals

Silicon carbide (SiC) substrates can be used to fabricate electronic devices and circuits which can function under extreme high-temperature, high-power, high-frequency conditions. The bulk growth of SiC single crystal by physical vapor transport (PVT) technique (modified Lely method) involves sublimation of a SiC powder charge, mass transfer through an inert gas environment, and condensation on a cold substrate seed. The SiC vapor deposits on the seed which has a lower temperature than the powder charge, and the SiC single crystal grows. Control of mass transfer and temperature distribution in the furnace with an extremely high temperature is critical to the quality of grown SiC single crystal. Modeling of the growth process is important for the design of efficient growth furnaces and reduction of micropipes and defect density in the grown crystal. A system model for SiC growth by PVT method is developed here that incorporates the radio frequency (RF) heating, and radiative and conductive heat transfer in the growth system. The generated heat power by RF heating of the graphite susceptor is calculated by solving the electromagnetic field. It is found that the radiation heat transfer plays a dominant role under high temperature and low pressure conditions.

H. Zhang

Papers

A system model for silicon carbide crystal growth by physical vapor transport method