A Distributed-Parameter Approach for the Surface Temperature Estimation of an LED Heated Silicon Wafer

A variety of processes in the semiconductor industry require heating of the silicon wafer to the desired temperature. This process is widely referred to as rapid thermal processing. However, the contactless measurement of the surface temperature of the wafer is still a major challenge, especially in the case of rotating wafers. Measurements using infrared cameras are not suitable due to the fact that silicon is transparent in this wavelength range. Special sensors based on the principle of pyrometry are available, but such sensors can only measure the surface temperature at one single point. This paper presents an observer approach that estimates the wafer's surface temperature by using the temperature measurement of only one pyrometer. The approach is based on a mathematical model capturing the dynamical behavior of the wafer's temperature. It relies mainly on the quasi-linear heat equation. Real world experiments demonstrate the achieved accuracy of the proposed approach.