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 realtime 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.

Multivariable Optimal Learning Control of Wafer Temperatures in a Commercial RTP Equipment

“…For such systems, therefore, traditional model-based MIMO (Multi-Input Multi-Output) control techniques may show limited performance because of their strong model dependency. Such a problem is manifest from the previous studies (Breedijk et al, 1993;Cho et al, 1997;Dilhac et al, 1992;Gyugyi et al, 1992;Schaper et al, 1994;Stuber et al, 1994;Theodoropoulou., 1999).…”

Dynamics and control of thin film surface microstructure in a complex deposition process

“…Significant research efforts have been made on the feedback control of thin film deposition processes with emphasis on control of film spatial uniformity in rapid thermal processing (RTP) (Baker and Christofides, 1999;Theodoropoulou et al, 1999;Christofides, 2001) and plasmaenhanced chemical vapor deposition (PECVD) (Armaou and Christofides, 1999). In addition to achieving spatially uniform deposition of thin films, one would like to regulate film properties such as microstructure Christofides, 2003a, 2005a,b,c) and composition (Ni et al, 2004) that characterize film quality.…”

Low‐order optimal regulation of parabolic PDEs with time‐dependent domain

“…These modes, known as empirical eigenfunctions, can be adopted as the basis set of functions in the Galerkin's method to find a ROM. This approach is widely used in the derivation of accurate reduced‐order approximations of many distributed parameter systems, for example, diffusion‐reaction systems, sheet‐forming processes, molten carbonate fuel cell model, thermal microsystem models and ground‐water flow model …”