<title>Modeling and control of rapid thermal processing</title>

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.