Linear Parameter-varying Approach for Modeling and Control of Rapid Thermal Processes

In the present paper, a new approach is presented to model and control single wafer rapid thermal processing (RTP) systems. In the past decade, RTP has achieved acceptance as the mainstream technology for semiconductor manufacturing. Thermal processing is one of the most efficient ways to control the phase-structure properties. Moreover, the time duration of RTP systems reduces the so-called thermal budget significantly compared to the traditional methods. RTP implementation is based on the use of light from heating lamps to provide a heat flux. This process is highly nonlinear due to the radiative heat transfer and material properties. By invoking the first principles-based models, we develop in this paper a linear parameter-varying (LPV) model to directly account for the nonlinearities within the system. The model is then discretized into a high-order LPV model; thereafter, principal component analysis (PCA) method is utilized to reduce the number of LPV model's scheduling variables, followed by the use of proper orthogonal decomposition (POD) for model order reduction. Using the reduced order model, we then design a gain-scheduled controller to satisfy an induced L-2 gain performance for tracking of a temperature profile and show improvement over other controller design methods suggested in the literature.