Temperature non-uniformity from combined conduction and radiation heat transfer within a doped wafer

Abstract

It has been proposed that the volumetric radiation heat absorption/emission inside the wafer should be considered in the rapid thermal processing to account for the temperature distribution. In this study, the combined conduction and radiation heat transfer inside the wafer was solved by using a commercial computational fluid dynamics and heat transfer software tool. Since the precise information of the thermal transport and optical properties of doped and undoped silicon are not known, transport properties were parametrically varied to examine their effects on the computed temperature distribution across the wafer and between the top and bottom sides. The study found that the temperature distribution across the wafer was sufficiently different when the radiation heat transfer was considered in the overall energy balance. It was also found that the variation of conductivity has a smaller effect on the temperature difference. Increased surface emissivity lead to slightly higher cross-wafer temperature difference but much larger mean temperature of the wafer. It confirms the important role of surface radiative property in the thermal energy control. The work has shown that volumetric radiation heat transfer needs to be considered and becomes even more important in the next generation milliseconds annealing processes