Iterative identification of temperature dynamics in single wafer rapid thermal processing

As the standard size of silicon wafers grows and performance specifications of integrated circuits become more demanding, a better control system to improve the processing time, uniformity and repeatability in rapid thermal processing (RTP) is needed. Identification and control are complicated because of nonlinearity, drift and the time-varying nature of the wafer dynamics. Various physical models for RTP are available. For control system design they can be approximated by diagonal nonlinear first order dynamics with multivariable static gains. However, these model structures of RTP have not been exploited for identification and control. Here, an identification method that iteratively updates the multivariable static gains is proposed. It simplifies the identification procedure and improves the accuracy of the identified model, especially the static gains, whose accurate identification is very important for better control.