Dynamics and Control of a Rapid Thermal Multiprocessor
C. Schaper, Y. Cho, P. Gyugyi, G. Hoffmann, S. Norman, P. Park, S. Boyd, G. Franklin, T. Kailath and K. Saraswat
Proceedings SPIE Conference on Rapid Thermal and Integrated Processing, 1595(1):2-17, 1992
A first-principles low-order model of rapid thermal processing of semiconductor 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 400C to 900C and pressure of 1 torr in an inter 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 20C to 900C at a rate of 45deg/second in a one atmosphere environment with less than 15deg nonuniformity during the ramp and less than 1deg average nonuniformity during the hold as measured by three thermocouples.