Nonlinear control of rapid thermal chemical vapor deposition under uncertainty

Abstract

This article focuses on nonlinear control of a rapid thermal chemical vapor deposition (RTCV'D) process in the presence of significant model uncertainty and disturbances. Initially, a detailed mathematical model of the RTCVD process is presented consisting of a nonlinear parabolic partial differential equation (PDE) which describes the time evolution of the wafer temperature across the radius of the wafer, coupled with a set of nonlinear ordinary differential equations (ODEs), which describe the time evolution of the concentrations of the various species. Then, the synthesis of a nonlinearoutput feedback controller based on the RTCVD process model by following a control methodology for nonlinear parabolic PDE systems introduced in ( Baker and Christofides, 1998) is discussed. The controller uses measurements of wafer temperature at four locations to manipulate the power of the top lamps in order to achieve uniform temperature, and thus, uniform deposition of the thin film on the wafer over the entire process cycle. The nonlinearoutput feedback controller is successfully implemented through computer simulations and is shown to attenuate significant model uncertainty end disturbances and to outperform a proportional integral (PI) control scheme.