Optimal heating control conditions to unify temperature distribution in a wafer during rapid thermal processing with lamp heaters

To unify temperature distribution in a wafer during rapid thermal processing, we calculated the effect of the heating control conditions on the temperature distributions during heat-up and at steady state by using a program for analyzing three-dimensional radiative heat transfer. We calculated optimum monitoring positions on the wafer in order to minimize the temperature distribution in the wafer. The effect of the number of heating zones in an axisymmetric heating apparatus was also calculated. The minimum steady-state temperature distribution in the wafer at the optimum condition was calculated as ±0.1 K during 100 K/s heat-up and ±0.02 K at 1273 K steady state. We also developed two rapid computation techniques to find the optimum heating conditions: a parallel-computation technique to find the optimum conditions for the whole heating process; and a technique that uses a reduced number of calculation elements under the assumption of almost uniform temperature in the wafer. Computation time using the latter technique is reduced to 1/250 compared to that using conventional method.