Dual Loop Feedforward Control for Czochralski Silicon Single Crystal Growth

摘要

A control system of Czochralski silicon single crystal growth based on lumped parameter model is designed in this paper. The control system includes a lumped parameter model that involving the hydrodynamics-geometry and thermodynamic systems. The lumped parameter model is established by the equilibrium equation of the solid-liquid interface of the thermodynamic subsystem, and including the modeling of crystal radius, slope angle and meniscus shape. The pulling speed feedforward control determines the growth rate of the reference and reduces the influence of the meniscus shape on system parameters. The feedforward control of the heater improves the calculation accuracy of the main process parameter and, combined with the feedback control, ensures high quality of the most important variables such as the diameter and the growth rate. In addition, the dependence of the growth rate and crystal shape on the feedforward control of the heater is analyzed.