Validation, verification, and benchmarking of crystal growth simulations

The variety of physical phenomena in crystal growth processes requires diverse software tools for the numerical simulations. Both, dedicated 2D or 3D ready-to-use software for coupled simulations of a crystallization furnace and general-purpose 3D simulation packages have been used in the literature. This work proposes a general strategy for model development: validation of the physical model using model experiments; verification of the numerical model using analytical or high-accuracy solutions; testing of the computational efficiency using complex benchmark cases. The application of these steps is demonstrated for various models in directional solidification of silicon showing the capabilities of various open source or commercial software packages.