Model reduction for a tungsten chemical vapor deposition system

Abstract

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract: 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.

A collocation/quadrature-based Sturm–Liouville problem solver

“…These and related functions can be obtained from http://www.ench.umd.edu/software/MWRtools. These methods primarily have been used for simulation of chemical vapor deposition reactors and other unit operations in semiconductor device fabrication [18] and model reduction studies [19,20]. In the latter, the eigenfunction expansion methods are instrumental for identifying optimized trial functions for reduced-basis discretizations as well as in the implementation of nonlinear Galerkin methods [21] for the reducing the dynamic degrees of freedom in discretized boundary-value problems.…”