Optimizing the temperature profile during sublimation growth of SiC single crystals: Control of heating power, frequency, and coil position
- Meyer, Christian
- Philip, Peter
2010 Mathematics Subject Classification
- 80M50 80A20 65Z05 65K10 49-04
2008 Physics and Astronomy Classification Scheme
- 81.10.Bk 02.60.Pn 02.60.Cb 44.05.+e 84.32.Hh
- Numerical simulation. Sublimation growth. Physical vapor transport. Modified Lely method. SiC single crystal. Nelder-Mead method.Optimization. RF heating.
We use a numerical optimization method to determine the control parameters frequency, power, and coil position for the radio frequency (RF) induction heating of the growth apparatus during sublimation growth of SiC single crystals via physical vapo transport (PVT) (also called the modified Lely method). The control parameters are determined to minimize a functional, tuning the radial temperature gradient on the single crystal surface as well as the vertical temperature gradient between SiC source and seed, both being crucial for high-quality growth. The optimization is subject to constraints with respect to a required temperature difference between source and seed, a required temperature range at the seed, and an upper bound for the temperature in the entire apparatus. The numerical computations use a stationary mathematical model for the heat transport, including heat conduction, radiation, and RF heating to solve the forward problem, and a Nelder-Mead method for optimization. A minimal radial temperature gradient is found to coincide with a minimal temperature at the single crystal surface, and a maximal temperature gradient between source and seed is found to coincide with a low coil position.
- Crystal Growth & Design, 5 (2005), 1145 - 1156.