Three-dimensional asymmetrical modeling of rapid thermal annealing of silicon wafers

We have developed an analytical tool to predict temperature variations occurring both across the wafer and down the thermal cycles, based on very simple 3-dimensional physical models depicting the heat transfer processes taking place during a typical rapid thermal processing (RTP) step. This model takes into account the convective and the radiative heat losses along with the thermal conduction within the wafer. An hybrid control volume formulation has been used to solve the heat conduction equation to yield numerical solutions of temperature variation, both on and within the wafer. The effect of ambient gas flow direction and the related asymmetric convective heat loss on the temperature non-uniformity across the wafer at different stages of the thermal cycle is well analyzed. Finally, the temperature non-uniformity across a wafer patterned with oxide is examined.