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Proceedings Paper

Contribution to optimal lamp design in rapid thermal processing
Author(s): Young Man Cho; Arogyaswami Paulraj; Stephen A. Norman; Guanghan Xu; Thomas Kailath
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Paper Abstract

Recent studies of wafer temperature control in rapid thermal processing systems have indicated that a multi-ring circularly symmetric lamp configuration with independent (multivariable) control of the power applied to each ring is likely to be more successful than the earlier lamp design approaches. An important issue in such multi-ring lamp systems is the optimal shaping of the output heat flux profile (HFP) of each ring, as measured at the wafer surface with a reference value of input power, to provide good controllability of the wafer temperature. In this paper we seek to optimize the ring HFPs via the lamp design parameters: ring positions and widths. We start by determining the heat loss profiles over the wafer surface for a variety of temperature setpoints and processing conditions. In order to maintain temperature uniformity across the wafer at a given setpoint, the lamp system should provide a compensating HFP. The total lamp HFP is the sum of the individual ring HFPs weighted by their respective applied powers. The HFPs are, in turn, functionally dependent on the lamp design parameters and this dependence can be measured through a calibration process. Therefore, the resulting optimization problem reduces to determining the lamp design parameters that result in a total lamp HFP which best approximates the collection of the wafer heat loss profiles. Our method provides a practical technique for determining the optimal lamp design parameters.

Paper Details

Date Published: 16 March 1993
PDF: 11 pages
Proc. SPIE 1804, Rapid Thermal and Laser Processing, (16 March 1993); doi: 10.1117/12.142091
Show Author Affiliations
Young Man Cho, Stanford Univ. (United States)
Arogyaswami Paulraj, Stanford Univ. (United States)
Stephen A. Norman, Stanford Univ. (United States)
Guanghan Xu, Stanford Univ. (United States)
Thomas Kailath, Stanford Univ. (United States)

Published in SPIE Proceedings Vol. 1804:
Rapid Thermal and Laser Processing
Dim-Lee Kwong; Heinrich G. Mueller, Editor(s)

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