Model Reduction for a Tungsten Chemical Vapor Deposition

A model of a tungsten chemical vapor deposition (CVD) system is developed to study the CVD system thermal dynamics and wafer temperature nonuniformities during a processing cycle. We develop a model for heat transfer in the system’s wafer/susceptor/guard ring assembly and discretize the modeling equation with a multiple-grid, nonlinear collocation technique. This weighted residual method is based on the assumption that the system’s dynamics are governed by a small number of modes and that the remaining modes are slaved to these slow modes. Our numerical technique produces a model that is effectively reduced in its dynamical dimension, while retaining the resolution required for the wafer assembly model. The numerical technique is implemented with only moderately more effort than the traditional collocation or pseudospectral techniques. Furthermore, by formulating the technique in terms of a collocation procedure, the relationship between temperature measurements made on the wafer and the simulator results produced with the reduced-order model remain clear.