Modeling and Control of Thin Film Growth in a Chemical Vapor Deposition Reactor

Abstract

This work describes the development of a mathematical model of ahigh-pressure chemical vapor deposition (HPCVD) reactor and nonlinearfeedback methodologies for control of the growth of thin films in thisreactor. Precise control of the film thickness and composition is highlydesirable, making real-time control of the deposition process veryimportant. The source vapor species transport is modeled by the standardgas dynamics partial differential equations, with species decomposition reactions, reduced down to a small number of ordinary differential equationsthrough use of the proper orthogonal decomposition technique. This systemis coupled with a reduced order model of the reactions on the surfaceinvolved in the source vapor decomposition and film deposition on thesubstrate wafer. Also modeled is the real-time observation technique usedto obtain a partial measurement of the deposition process. The utilization of reduced order models greatly simplifies the mathematical formulation of the physical process so it can be solved quickly enough to beused for real-time model-based feedback control. This control problem isfairly complicated, however, because the surface reactions render the modelnonlinear. Several control methodologies for nonlinear systems are studiedin this work to determine which performs best on test examples similar tothe HPCVD problem. One chosen method is extended to a tracking control toforce certain film growth properties to follow desired trajectories. Thenonlinear control method is used also in the development of a stateestimator which uses the nonlinear partial observation of the nonlinearsystem to create an estimate of the actual state, which the feedback controlformula then can use to guide the HPCVD system. The nonlinear trackingcontrol and estimator techniques are implemented on the HPCVD model and theresults analyzed as to the effectiveness of the reduced order model andnonlinear control.