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 diffe rence formulation for determination of incident heat fluxes to achieve ther mal 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 the rmal nonuniformity ran be reduced considerably if the incident heat fluxes on the wafer are dynamically controlled according to the inverse-method res ults, An effect of successive temperature measurement errors on thermal uni formity is discussed. The resulting maximum temperature differences are onl y 0.618, 0.776, 0.981, and 0.326 degreesC for 4-, 6-, 8- and 12-in wafers, respectively, The required edge heating compensation ratio for thermal unif ormity in 4-, 6-, 8- and 12-in silicon wafers is also evaluated.