Control of rapid thermal processing: a system theoretic approach

In this paper, a framework is given for achieving the tight control of the wafer temperature essential in rapid thermal processing (RTP) of semiconductor wafers. Of the various techniques for controlling wafer temperature in RTP systems, we focus on model-based control since it has the greatest potential for attaining the best performance. First, the identification of a state-space model, based on the subspace-fitting technique, results in an empirical model. Then, convex optimization is used to obtain an approximation to the desired trajectory, close enough to allow high gain feedback controllers to 1) reduce temperature nonuniformity and 2) accommodate actuator constraints. Subsequently, a feedback linear quadratic Gaussian (LQG) controller is designed based on the identified model. The benefits of convex optimization together with LQG feedback control are demonstrated by experimental results from an RTP system at Stanford University, CA.