Recursive solution of an inverse heat transfer problem in rapid thermal processing systems

Rapid thermal processing (RTP) is a new technique for performing various wa fer fabrication operations such as annealing, oxidation and chemical vapor deposition in a single chamber. The success of the RTP depends on the preci se control of wafer temperature by adjusting wall heat flux. In the present investigation, an efficient recursive method is developed to solve the inv erse heat transfer problem of estimating the wall heat flux on the wafer fr om the measurements of wafer temperature. The present recursive method is b ased on the Kalman filtering technique and the Karhunen-Loeve Galerkin proc edure. Although the direct implementation of the Kalman filter on heat cond uction equation is never feasible due to the tremendous requirement of comp uter time and memory, a practical method of recursive estimation is devised in the present investigation by reducing the partial differential equation to a minimal set of ordinary differential equations by means of the Karhun en-Loeve Galerkin procedure. (C) 2001 Elsevier Science Ltd. All rights rese rved.