Control of wafer temperature uniformity in rapid thermal processing using an optimal iterative learning control technique

An iterative learning control (ILC) technique based on a quadratic optimal criterion is proposed for temperature uniformity control of a wafer under r apid thermal processing (RTP). The proposed technique is based on a time-va rying linear state space model which approximates a nonlinear system along a reference trajectory. For effective use of feedback measurements, it empl oys a periodically time-varying Kalman filter which is based on an augmente d model capable of describing the transition behaviors from one run to next , as well as those from one sample time to another. By retaining the releva nt information from previous runs in the Kalman state, the control techniqu e is able to make improvements in the control performance from one run to t he next and eventually to converge to a minimum-achievable tracking error d espite model error. A simple but effective method for identifying a time-va rying linear state space model for the RTP system is also proposed. The per formance of the proposed technique is evaluated through a simulation study involving the RTP model processing 8-in. silicon wafers.