Validation of a Rapid Thermal Processing model in steady-state

Rapid Thermal Processing (RTP) is widely used in advanced semiconductor manufacturing. The present work deals with the heat transfer from infrared lamps to the silicon wafer in a commercial RTP equipment. Both numerical and experimental approaches are considered. For numerical purposes, the RTP system is modelled in two (2D) and three dimensions (3D). Calculations are performed in steady-state. The computational fluid dynamics method (CFD) is used for solving the mass and heat conservation equations. The radiative heat transfer equation is solved with the Monte Carlo method. In order to validate these models, measurements of the wafer temperature are realized for five electric power values supplied to the infrared lamps. The experimental wafer temperature profiles are in good agreement with the numerically calculated ones. Moreover, a confrontation between the experimental temperature of the infrared lamp filaments evaluated from the Ohm law and the one used in the numerical calculations shows a good agreement with the 3D model. The slight difference observed with the 2D model is explained. So the numerical simulations are fully validated. Two relations are established in order to predict the power which has to be applied to infrared lamps to obtain the required wafer temperature.