Thermal Model of Rapid Thermal Processing Systems

Continuously shrinking device parameters and the enlargement of wafer diameters in semiconductor industry require best temperature homogeneity in Rapid Thermal Processing (RTP). This together with the requirement of high ramp rates in the range of 200 °C s as advantageously used in ultra shallow junction processes [1] challenges temperature control in RTP technology. In order to design advanced control concepts, a mathematical model was developed, which consists of a set of non-linear differential equations and simulates the heat transport in the RTP chamber. The model incorporates the dominant heat transport mechanisms and takes into account the spectral and temperature dependent parameters of the heating lamps, the quartz ware and of silicon. Based on this model, advanced multi-zone control concepts can be investigated and the wafer temperature control can be optimised not only during steady state conditions but also during ramp phases of the thermal treatment. Moreover, the model can be applied as an observer in the control loop. Some modern RTP system concepts, e.g. AST EVOLUTIONTM [2] and AST 3000 of STEAG RTP Systems use wafer rotation in order to achieve a concentric temperature profile with maximal temperature uniformity. Therefore, the static description is extended in order to model system concepts including wafer rotation.