Comprehensive study on control system design for a rapid thermal processing (RTP) equipment has been conducted with the purpose to obtain maximum temperature uniformity across the wafer surface, while precisely tracking a given reference trajectory. The study covers from model development, identification, optimum multivariable iterative learning control (ILC), to reduced-order controller design. The highlight of the study is the ILC technique on the basis of a semi-empirical dynamic radiation model named as 4 -model. It was shown that the 4 -model-based ILC technique can remarkably improve the performance of RTP control compared with the ordinary linear model-based ILC. In addition, reduced-order control methods and the associated optimum sensor location have been addressed. The proposed techniques have been evaluated in an RTP equipment fabricating 8-in wafers.Index Terms-Iterative learning control (ILC), linear quadratic Gaussian (LQG), rapid thermal processing (RTP) control, RTP modeling.
An optimal iterative learning control (ILC) technique based on a quadratic optimal criterion has been implemented and evaluated in an experimental rapid thermal processing (RTP) system fabricating 8-inch silicon wafers. The control technique is based on a time-varying linear state space model which approximates a nonlinear system along a reference trajectory. Also the control technique is able to make improvements in the control performance from one run to next and eventually converge to a minimum achievable tracking error despite model error. Through a series of experiments with wafers on which thermocouples are glued, it was observed that the wafer temperatures are steered to the reference trajectory reducing the diyerences overcoming various disturbances.
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