This paper presents a systematic way of developing low order nonlinear models from physically- based, large scale finite element models of rapid thermal processing (RTP) systems. The low order model is extracted from transient results of the finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are used as basis functions in spectral Galerkin expansions of partial differential equations solved by the finite element model to generate the reduced models. Simulation results demonstrate good agreement with steady state and transient data generated from the finite element model.

We present simulation and experimental results for determining the distribution of radiation throughout an RTP system and evaluating the design of optical temperature sensors. The simulations are performed with a general purpose, three dimensional Monte Carlo method. The simulation models internal reflection, absorption, and transmission within participating media explicitly, and includes wavelength, temperature, and material dependent properties. Simulation results are compared to measurements of the lamp intensity profile within the lamphouse and at possible sensor locations. Simulations are used to examine the effect of several optical probe designs. The predicted responses of potential sensor designs resulting from these studies are presented.

We present a general purpose Monte Carlo method for the simulation of radiation heat transfer in rapid thermal processing (RTP) chambers. Three-dimensional mesh generation software is used to discretize the surfaces within the system, allowing the simulation of realistic chamber and reflector designs. An adaptive subdivision of the chamber geometry reduces the number of raysurface intersections which must be computed. The method models internal reflection, absorption, and transmission within participating media, and includes wavelength, temperature, and material dependent optical properties. Radiation heat transfer simulations are used to examine a reflector assembly, and to test the assumptions of optical wafer temperature measurement techniques.