BaF2for microlithography applications: Modeling, simulation and optimization of the crystal growth process

Authors:
Rainer Backofen;Angel Ribalta;Axel Voigt;Dirk Wulff-Molder
Affiliations:
Crystal Growth Group, Research Center Caesar, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany;Crystal Growth Group, Research Center Caesar, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany;Crystal Growth Group, Research Center Caesar, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany;Korth Kristalle GmbH, Am Jägersberg 3, 24161 Altenholz (Kiel), Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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.