Run-To-Run control of the Czochralski process

Commercially, the Czochralski process plays a key role in production of monocrystalline silicon for semiconductor and solar cell applications. However, it is a highly complex batch process which requires careful control throughout the whole crystal production. In the present paper, an iterative method based on model predictive control (MPC) for calculating a new and improved trajectory from a growth run to the next is explored. The method uses the results of the previous growth run in combination with an underlying model which incorporates the complex dynamic effect of the heater temperature on the pulling rate. The motivation behind this choice of strategy is to enhance the quality of the fully grown ingot from one run to the next by applying the most recent estimates of the unknown parameters. The results show that combining MPC, estimation and Run-To-Run control has enabled simulation of effective control of the Czochralski crystallization process.