Model-Based Temperature Control in Thermal Processing of Silicon Wafers

Abstract

The paper proposes a model-based control approach for thermal processing of silicon wafers such as rapid thermal processing. Heating of the wafer is achieved with a large number of high-power LEDs which enable targeted heating over the entire spatial domain. Taking advantage of this feature, a distributed PI controller is first designed assuming an idealized distributed input. This control signal is then approximated by the actual control that enters the system through shape functions using an optimization procedure. A formal analysis of the input-to-state stability with respect to the actuator error, extension with an anti-windup scheme and an experimental validation of the proposed approach are presented.