Experimental application of a quadratic optimal iterative learning control method for control of wafer temperature uniformity in rapid thermal processing

Abstract

A quadratic-optimal iterative learning control (ILC) method has been designed and implemented on an experimental rapid thermal processing system used for fabricating 8-in silicon wafers. The controller was designed to control the wafer temperatures at three separate locations by manipulating the power inputs to three groups of tungsten-halogen lamps. The controller design was done based on a time-varying linear state-space model, which was identified using experimental input-output data obtained at two different temperatures. When initialized with the input profiles produced by multiloop PI controllers, the ILC controller was seen to be capable of improving the control performance significantly with repeating runs. In a series of experiments with wafers on which thermocouples are glued, the ILC controller, over the course of ten runs, gradually steered the wafer temperatures very close to the respective reference trajectories despite significant disturbances and model errors.