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Proceedings Paper

Modeling and control of rapid thermal processing
Author(s): Charles D. Schaper; Young Man Cho; Poogyeon Park; Stephen A. Norman; Paul Gyugyi; G. Hoffmann; S. Balemi; Stephen P. Boyd; Gregory Franklin; Thomas Kailath; Krishna C. Saraswat
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Paper Abstract

A first-principles low-order model of rapid thermal processing ofsemiconductor wafers is derived. The nonlinear model describes the steady-state and transient thermal behavior of a wafer with approximate spatial temperature uniformity undergoing rapid heating and cooling in a multilamp RTP chamber. The model is verified experimentally for a range of operating temperatures from 400°C to 900°C and pressure of 1 torr in an inert N2 environment. Advantages of the low-order model over detailed models include ease of identification and implementation for real-time predictive applications in signal processing and temperature control. This physics-based model is used in the design of an advanced real-time multivariable control strategy. The strategy employed a feedforward mechanism to predict temperature transients and a feedback mechanism to correct for errors in the prediction. The controller is applied to achieve a ramp from 20°C to 900°C at a rate of 45°C/second in a one atmosphere environment with less than 15°C nonuniformity during the ramp and less than 1°C average nonuniformity during the hold as measured by three thermocouples.

Paper Details

Date Published: 1 February 1992
PDF: 16 pages
Proc. SPIE 1595, Rapid Thermal and Integrated Processing, (1 February 1992); doi: 10.1117/12.56658
Show Author Affiliations
Charles D. Schaper, Stanford Univ. (United States)
Young Man Cho, Stanford Univ. (United States)
Poogyeon Park, Stanford Univ. (United States)
Stephen A. Norman, Stanford Univ. (United States)
Paul Gyugyi, Stanford Univ. (United States)
G. Hoffmann, Stanford Univ. (United States)
S. Balemi, Stanford Univ. (United States)
Stephen P. Boyd, Stanford Univ. (United States)
Gregory Franklin, Stanford Univ. (United States)
Thomas Kailath, Stanford Univ. (United States)
Krishna C. Saraswat, Stanford Univ. (United States)


Published in SPIE Proceedings Vol. 1595:
Rapid Thermal and Integrated Processing
Mehrdad M. Moslehi; Rajendra Singh; Dim-Lee Kwong, Editor(s)

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