Numerical Modeling and Control of the Dynamic Single Silicon Crystal Growth Process

A new control strategy combing the Finite Element Method (FEM) with the control method is proposed to study the control of crystal growth process in this article. In the proposed control strategy, the crystal diameter control loop and the crystal temperature control loop are designed respectively to meet the requirements on crystal diameter and crystal temperature distribution. In the crystal diameter control loop, a bio-heuristic model based PID controller is designed to control crystal diameter. In the crystal temperature control loop, considering the undetectable characteristic of temperature distribution inside crystal, the control of crystal temperature distribution is transformed into the control of a key monitoring point in crystal and the constraint of crystal temperature gradient, and a model reference adaptive temperature controller is designed to achieve the control of the monitoring point temperature. Simulation results show that the crystal diameter and the temperature of the monitoring point are controlled well. Furthermore, the internal temperature distribution inside crystal is constrained within a reasonable range, avoiding the excessive thermal stress and dislocation defects. The proposed control strategy solves the problem of the traditional crystal growth system which cannot control crystal temperature, providing a new way for growing high-quality single silicon crystal.