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

Abstract

A reduced-order model describing a rapid thermal chemical vapor deposition (RTCVD) process is utilized for real-time model based control for temperature uniformity across the wafer. Feedback is based on temperature measurements at selected points on the wafer surface. The feedback controller is designed using the internal model control (IMC) structure, especially modified to handle systems described by ordinary differential and algebraic equations. The IMC controller is obtained using optimal control theory on singular arcs extended for multi-input systems. Its performance is also compared with one based on the Hirschorn inverse of the model. The proposed scheme is tested with extensive simulations where the full-order model is used to emulate the process. Several cases of significant uncertainty, including model parameter errors, process disturbances, actuator errors, and measurement noise are used to test the robustness of the controller to real life situations. Both controllers succeed in achieving temperature uniformity well within the desirable bounds, even in cases where several sources of uncertainty are simultaneously present with measurement noise.