Inverse model-based real-time control for temperature uniformity of RTCVD

A reduced-order model describing a rapid thermal chemical vapor deposition (RTCVD) process is utilized for real-time model based control for temperatu re uniformity across the wafer. Feedback is based on temperature measuremen ts at selected points on the wafer surface, The feedback controller is desi gned using the internal model control (IMC) structure, especially modified to handle systems described by ordinary differential and algebraic equation s, The IMC controller is obtained using optimal control theory on singular arcs extended for multi-input systems. Its performance is also compared wit h one based on the Hirschorn inverse of the model. The proposed scheme is t ested with extensive simulations where the full-order model is used to emul ate the process. Several cases of significant uncertainty, including model parameter errors, process disturbances, actuator errors, and measurement no ise are used to test the robustness of the controller to real life situatio ns. Both controllers succeed in achieving temperature uniformity well withi n the desirable bounds, even in cases where several sources of uncertainty are simultaneously present with measurement noise.