Linear parameter-varying approach for modeling rapid thermal processes

In the present paper, a new approach is presented to model rapid thermal processing (RTP) systems. Within 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 all the nonlinearities within the system. The model is then discretized into a high-order affine LPV system; 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. Finally, simulations demonstrate that the low-order LPV model, which is in a form suitable for controller design purposes, retains the properties of the original full-order model.