Modeling and control of rapid thermal processing

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

doi:10.1117/12.56658

1 February 1992 Modeling and control of rapid thermal processing

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

Author Affiliations +

Proceedings Volume 1595, Rapid Thermal and Integrated Processing; (1992) https://doi.org/10.1117/12.56658
Event: Microelectronic Processing Integration, 1991, San Jose, CA, United States

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.

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Charles D. Schaper, Young Man Cho, Poogyeon Park, Stephen A. Norman, Paul Gyugyi, G. Hoffmann, S. Balemi, Stephen P. Boyd, Gregory Franklin, Thomas Kailath, and Krishna C. Saraswat "Modeling and control of rapid thermal processing", Proc. SPIE 1595, Rapid Thermal and Integrated Processing, (1 February 1992); https://doi.org/10.1117/12.56658

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