Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Through an inverse heat transfer method, this paper presents a finite difference formulation for determination of incident heat fluxes to achieve thermal uniformity in a 12-in silicon wafer during rapid thermal processing. A one-dimensional thermal model and temperature-dependent thermal properties of a silicon wafer are adopted in this study. Our results show that the thermal nonuniformity can he reduced considerably if the incident heat fluxes on the wafer are dynamically controlled according to the inverse-method results. An effect of successive temperature measurement errors on thermal uniformity is discussed. The resulting maximum temperature differences are only 0.618, 0.776, 0.981, and 0.326/spl deg/C for 4-, 6-, 8- and 12-in wafers, respectively. The required edge heating compensation ratio for thermal uniformity in 4-, 6-, 8and 12-in silicon wafers is also evaluated.