A contribution to optimal lamp design in rapid thermal processing

Recent studies of wafer temperature control in rapid thermal processing systems have indicated that a multiring circularly symmetric lamp configuration with independent (multivariable) control of the power applied to each ring is likely to be more successful than the earlier lamp design approaches. An important issue in such multiring lamp systems is the optimal shaping of the output heat flux profile (HFP) of each ring to provide maximum controllability of the wafer temperature. In this paper we seek to optimize the ring HFP's via the lamp design parameters: ring positions and widths. We start by determining the heat loss profiles over the wafer surface for a variety of temperature setpoints and processing conditions. In order to maintain temperature uniformity across the wafer at a given setpoint, the lamp system should provide a compensating HFP. The total lamp HFP is the sum of the individual ring HFPs weighted by their respective applied powers. The HFP's are, in turn, functionally dependent on the lamp design parameters and this dependence can be measured through a calibration process. Therefore, the resulting optimization problem reduces to determining the lamp design parameters that result in lamp HFP's which best approximates the collection of the wafer heat loss profiles. Our method provides a practical technique for determining the optimal lamp design parameters.>