Investigation of Lightpipe Volumetric Radiation Effects in RTP Thermometry

A major obstacle to the widespread implementation of rapid thermal processing (RTP) is the challenge of wafer temperature measurement. Frequently, lightpipe radiation thermometers are used to measure wafer temperatures in RTP reactors. While the lightpipe distorts the wafer temperature profile less than temperature measurement techniques which require physical contact, the presence of the lightpipe influences the wafer temperature profile. This paper presents the results of a theoretical study exploring that influence for an idealized RTP reactor in which the wafer is treated as a nonconducting, opaque, constant-heat-flux surface imaged by the lightpipe. The coupled radiation/conduction transport in the lightpipe measurement enclosure is solved numerically. Radiation transfer in the system is modeled with varying levels of rigor, ranging from a simple volumetrically nonparticipating treatment to a full spectral solution of the radiative transfer equation. The results reveal a rather significant effect of the lightpipe on the wafer temperature, which depends on the separation between the lightpipe tip and the wafer. The study illustrates clearly the need to model the lightpipe as a volumetrically participating, semitransparent medium, and further, the importance of accounting for spectral variation of the lightpipe properties in the prediction of the radiative transfer. Finally, two primary mechanisms are identified by which the lightpipe affects the wafer temperature distribution.