Optical and thermal modeling of a rapid thermal processor

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Abstract
During rapid thermal processing, temperature non-uniformities are likely to occur because of increased thermal radiation from the wafer edges, or inappropriate illumination of the wafer. Up to now, despite the fact that the optical conditions of the wafer play a dominant role in temperature non-uniformity, little work about the effect of heating lamps and reflector arrangement on wafer illumination distribution has been published, if one compares with other topics related to Rapid Thermal Processing (RTP). Simulation software, using geometric optics, has therefore been developed to calculate the illumination of a wafer inside a RTP processing chamber. The main parameters of the analytical model are: (1) the processing chamber geometry, (2) the lamp number and location, and (3) the reflector characteristics. Each incident light component, i.e. direct or reflected, is identified, its contribution to the illumination of the wafer is calculated, and the corresponding contour maps depicted. Then, the heat diffusion equations is numerically solved in two dimensions, and 2D thermal maps of a 4' Si wafer are given vs. various experimental conditions, such as the effect of individually adjusting the electrical power applied to each lamp, and the impact of rotating the wafer.

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