Industrial & Engineering Chemistry Research, Vol.38, No.10, 3964-3975, 1999
Optimal control of rapid thermal processing systems by empirical reduction of modes
In rapid thermal processing (RTP) of semiconductor wafers precise control of wafer temperature is required throughout the process cycle to minimize dopant redistribution as well as wafer warpage. A low-dimensional dynamic model of RTP of semiconductor wafers is derived by using the Karhunen-Loeve-Galerkin procedure (Park, H. M.; Cho, D. H. Chem. Eng. Sci. 1996, 51, 81) to implement efficiently the optimal control scheme which ensures the transient temperature uniformity in RTP systems. The optimal control scheme employing the low-dimensional dynamic model is compared with the conventional method using the original partial differential equation and is found to be very efficient without losing accuracy.