A Systematic Approach to Simulating Rapid Thermal Processing Systems

Abstract

We present a systematic approach to the modeling of rapid thermal processing systems. In this approach, a discretized version of a computer-aided design file of a rapid thermal processing system is incorporated into fundamental physically based models of the transport phenomena to aid in design and optimization of these reactors. These models include a detailed radiative-heat-transfer description which is used to compute radiative exchange factors involving both diffuse and specular surfaces. The radiative exchange factors are then incorporated into transient finite element fluid-flow and heat-transfer models to investigate effects of conductive and convective heat transfer on wafer temperature uniformity. This approach is illustrated in investigations of the effects of thermal guard rings and radiative properties of the chamber on wafer temperature uniformity. Comparisons are made with experiments, and reduced-complexity models are evaluated to identify their range of applicability.

Nonlinear Model Reduction Strategies for Rapid Thermal Processing Systems

“…The solid thermal properties, except for the thermal conductivity of the silicon wafer, are constant in the model. The boundary condition for (9) takes the following form [10], [11] (10)…”

“…This is balanced on the right hand side by conduction in the gas, energy input from the lamps, and energy transfer with other surfaces in the system. In (10), is the solid thermal conductivity, is the absorptance of the solid surface, is the radiation intensity of lamp is the Stefan-Boltzmann constant, is the percentage of radiation, in band leaving surface which is absorbed by surface (by direct viewing and all intervening reflections). The exchange factors, are assumed to be temperature independent based on the high temperature opaque silicon properties [10], [11].…”

“…A detailed, physical model of a generic twodimensional (2D) RTP system [10], [11] with features relevant to the next generation of RTP systems serves as the base case for the model reduction study. The modeling strategy used to generate this detailed model is similar to that used in previous simulations of RTP systems [10], [11]. It is based on a finite element (FEM) solution of the general equations representing conservation of mass, momentum and energy.…”

“…The boundary condition of the energy equation describes the radiation heat transfer, which separates the thermal radiation into multiple wavelength bands and includes the effect of multiple reflections. In the present case studies the velocity field is assumed to be constant through the RTP cycle, fixed at a steady state solution at the process hold conditions, a reasonable approximation at low pressures [10], [11]. At higher pressures transient flow effects must be included, but the general model reduction strategy will remain the same.…”

“…The modeling equations are solved by the Galerkin finite element method [10], [11]. In this method the unknown flow and temperature fields are approximated by expansions in piecewise, low order polynomials.…”