System Dynamics and Automatic Diameter Control

Abstract

In order to control the process effectively, the stability of crystal pulling against fluctuations in environmental conditions such as heater power, pull-rate etc. must be evaluated, i.e. we need to measure the dynamical response of the system to such perturbations. In the language of the electronic control engineer, the transfer function of the process must be determined. Specifically we need to know whether or not the process is stable, i.e. that, if we perturb it slightly, whether it will decay back to its original state. If the process is not stable then a servo-control system will be needed in order to maintain the desired growth conditions. In particular we will wish to grow a cylindrical crystal i.e. to ensure that the crystal radius remains constant. The response of the overall system has to be investigated but the crucial part of the process is the dynamics of the meniscus region and this is considered in the next section.