Recursive solution of an inverse heat transfer problem in rapid thermal processing systems
نویسندگان
چکیده
Rapid thermal processing (RTP) is a new technique for performing various wafer fabrication operations such as annealing, oxidation and chemical vapor deposition in a single chamber. The success of the RTP depends on the precise control of wafer temperature by adjusting wall heat ̄ux. In the present investigation, an ecient recursive method is developed to solve the inverse heat transfer problem of estimating the wall heat ̄ux on the wafer from the measurements of wafer temperature. The present recursive method is based on the Kalman ®ltering technique and the Karhunen±Lo eve Galerkin procedure. Although the direct implementation of the Kalman ®lter on heat conduction equation is never feasible due to the tremendous requirement of computer time and memory, a practical method of recursive estimation is devised in the present investigation by reducing the partial dierential equation to a minimal set of ordinary dierential equations by means of the Karhunen±Lo eve Galerkin procedure. Ó 2001 Elsevier Science Ltd. All rights reserved.
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