Thermal modeling of a wafer in a rapid thermal processor

A model, using geometric optics, has been developed to calculate the illumination of a wafer inside a rapid thermal processor. The main parameters of the model are: the processing chamber geometry, the lamp number and location, the reflector characteristics, and the wafer temperature. Each incident light component, i.e., direct or reflected, is identified, its contribution to the illumination of the wafer is calculated through a 3D analytical model, and the corresponding contour maps are depicted. Then, the heat diffusion equation is numerically solved in two dimensions, and thermal maps of a Si wafer are given versus various experimental conditions, such as the effect of patterning the reflectors, of individually adjusting the electrical power applied to each lamp, and the impact of rotating the wafer or using crossed lamp banks. The latter method, while being easy to implement, is shown to give excellent thermal uniformity