Verification of Numerical Models

The utility and benefits of modeling of crystal-growth processes depends strongly on the reliability of the simulation results. Therefore, the procedure for the development and validation of a global thermal model of a growth facility should ideally consist of the following steps, which are summarized in Fig. 5.9. 

The first step is to build the model based on an original, but simplified CAD drawing of the real growth equipment and on a set of reliable material data. The second step is to perform a systematic sensitivity analysis. The sensitivity analysis consists of pure numerical parametric studies. It has the objective to identify 

For vahdation, so-caUed model experiments have to be performed under well-defined and weU-documented conditions [5]. They are designed to provide quantitative data (e.g. temperatures) related to important phases of the growth process. They should come as close as possible to the real growth setup and growth conditions, but should not have the necessity to grow a high-quality crystal. 

A proper and frequently used concept of experimental vahdation is the use of thermocouples in dummy crystals or inside the melt and crystal that allows for an in-situ measurement of temperature distributions along certain positions (e.g. crystal/crucible axis) at various time steps of the growth process. However, 

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