Model Reduction for a Tungsten Chemical Vapor Deposition System

Abstract

A model of a tungsten chemical vapor deposition (CVD) system isdeveloped to study the CVD system thermal dynamics and wafer temperaturenonuniformities during a processing cycle. We develop a model for heattransfer in the system's wafer/susceptor/guard ring assembly and discretizethe modeling equation with a multiple-grid, nonlinear collocation technique.This weighted residual method is based on the assumption that the system'sdynamics are governed by a small number of modes and that the remaining modesare slaved to these slow modes. Our numerical technique produces a model thatis effectively reduced in its dynamical dimension, while retaining theresolution required for the wafer assembly model. The numerical techniqueis implemented with only moderately more effort than the traditional collocationor pseudospectral techniques. Furthermore, by formulating the technique in termsof a collocation procedure, the relationship between temperature measurementsmade on the wafer and the simulator results produced with the reduced-ordermodel remain clear.