In the growth of ribbon by the EFG method, the geometry of the grown crystal is largely controlled by the meniscus height. The need to control meniscus height automatically during growth (in a closed-loop control system) has led us to a review of the possible control systems and a study of the dynamics of the process itself. The complete dynamic process has been broken down into two components: a heater-die thermal system, and the physics of the EFG process itself. A lumped parameter model has been developed for the thermal system, and the physics of the EFG process has been reviewed and extended so that it might be easily interpreted in the light of experimental data. Frequency response data has been obtained through the use of an instrumented crystal growth system which included an anamorphic optical-video system (enlarges in one direction more than in the other) and video tape recorder. Data have been obtained on the response of meniscus height, ribbon thickness, and die temperature to heater power level, as well as the response of meniscus height and ribbon thickness to pulling speed changes. In all cases, theory and experiment agreed well. To summarize, it has been found that the heater-die thermal system behaves as a second-order system; e.g., die temperature and heater power level are related by a second-order differential equation. Further, it has been found that the EFG system per se behaves as a second-order system. That is, meniscus height or ribbon thickness and pulling speed or die temperature are related by a second-order differential equation. In the case of ribbon thickness response, the terms involving pulling speed or die temperature involve only constants, while in the case of meniscus height response these terms involve first derivatives as well. The dynamic response is identical whether the input is pulling speed or die temperature. Finally, it has been found that the complete, composite system behaves as a fourth-order system; e.g., meniscus height or ribbon thickness is related to heater power level by a fourth-order differential equation. The implications of these results on the design of meniscus height measurement-based automatic control systems are discussed.
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