Model Identification for Control System Design of a Commercial 12-inch Rapid Thermal Processor

This paper describes a model identification method that has been applied to a commercial 12-inch RTP (rapid thermal processing) equipment with an ultimate aim to develop a high-performance advanced controller. Seven thermocouples are attached on the wafer surface and twelve tungsten-halogen lamp groups are used to heat up the wafer. To obtain a MIMO balanced state space model, multiple SIMO (single-input multiple-output) identification with high order ARX models have been conducted and the resulting models have been combined, transformed and reduced to a MIMO balanced state space model through a balanced truncation technique. The identification experiments were designed to minimize the wafer warpage and an output linearization block has been proposed for compensation of the nonlinearity from the radiation-dominant heat transfer. As a result from the identification at around 600, 700, and 800 degrees C, respectively, it was found that y=T(K)(2) and the state dimension of 80-100 are most desirable. With this choice the root mean-square value of the one-step-ahead temperature prediction error was found to be in the range of 0.125-0.135 K.