for microlithography applications: Modeling, simulation and optimization of the crystal growth process

Optimization is the ultimate goal of numerical modeling of crystal growth processes. We present the most important physical phenomena to establish a numerical process model for an industrial vertical gradient freeze (VGF) process of barium fluoride ( BaF 2 ). After reviewing the governing equations we describe an adaptive finite element approach for a phase change problem with internal radiation. We describe an interface to a commercial software package for industrial crystal growth processes to define a numerical process model in a highly automatized way. In this way we can apply an external optimization algorithm to our process model. We use a modified quasi-Newton method to propose an improvement of an industrial VGF growth process of BaF 2 .