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# Investigation of Lightpipe Volumetric Radiation Effects in RTP Thermometry

[+] Author and Article Information
David J. Frankman, Brent W. Webb, Matthew R. Jones

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602-4201

J. Heat Transfer 128(2), 132-141 (Jul 28, 2005) (10 pages) doi:10.1115/1.2136917 History: Received November 18, 2004; Revised July 28, 2005

## Abstract

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.

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## Figures

Figure 1

Schematic of the computational domain modeled

Figure 2

Spectral absorption coefficient and index of refraction for sapphire (9)

Figure 3

Band model approximations to the spectral variation of sapphire absorption coefficient and index of refraction

Figure 4

Representative predicted wafer temperature profiles with and without the lightpipe for the 2mm separation distance, Gray, Finite Optical Thickness radiation model, κ=1000m−1

Figure 5

Predicted local wafer temperature depression using the three-, six-, and nine-band Spectral model for separation distances of (a) 2mm, (b) 4mm, and (c) 6mm

Figure 6

Predicted local wafer temperature depression using all radiation transfer models for separation distances of (a) 2mm, (b) 4mm, and (c) 6mm. Spectral model results are shown by closed symbols.

Figure 7

Predicted maximum wafer temperature depression as a function of gray absorption coefficient and separation distance. Predicted Spectral (nine-band) and Volumetrically Nonparticipating model results are shown on the right axis.

Figure 8

Predicted lightpipe centerline temperature profiles for all radiation transfer models for separation distances of (a) 2mm, (b) 4mm, and (c) 6mm. Spectral model results are shown by closed symbols.

Figure 9

Predicted local wafer temperature depression for a gray, non-absorbing (κ→0) lightpipe of non-unity index of refraction (n=1.7) with a separation distance of 2mm, and lightpipe removed but aperture open to the black environment at 300K

Figure 10

Predicted maximum wafer temperature depression as a function of refractive index and separation distance for the Gray, Finite Optical Thickness model, κ=60m−1

Figure 11

Predicted net radiation and total heat transfer through the various lightpipe surfaces (lightpipe tip, enclosure-exposed side, environment-exposed side, and bottom) expressed as a percentage of the total heat input to the wafer for all three separation distances. Arrows indicate the direction of heat transfer on each surface.

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