Optimal iterative learning control of wafer temperature uniformity in rapid thermal processing

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 the next and eventually converges 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 differences overcoming various disturbances