A Computational Framework for Boundary-Value Problem Based Simulations

Abstract

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, distributed-parameter system models. Four industrially relevant examples taken from electronic materials and chemical processing applications are used to demonstrate the simulation approach developed.

Simulation and Model Reduction Methods for an RF Plasma Glow Discharge

“…These fluid type formulations have had great success in explaining the physics of the glow discharge, and the results can be comparable to those produced by Monte Carlo particle simulation techniques [16]. In this study, the model is equivalent to the modeling equations presented in [17,19] and the modifications according to [20,21] are adopted for this RF simulation and model reduction study. The single exception to the cited modifications is that a separate effective electric field meant to compensate for potential errors introduced by applying the diffusiondrift approximation to the ion species balance was not included in this study; under the conditions used for this simulation study, it was found that this effective electric field could be neglected because of the relatively small displacement of ions during an RF cycle.…”

Influence of gas composition on wafer temperature in a tungsten chemical vapor deposition reactor: Experimental measurements, model development, and parameter identification

“…The model accounts for gas flow across the wafer, the three-dimensional gas temperature field, heat conduction within the wafer, and heat transfer between the wafer, gas, and reactor chamber. The gas temperature field submodel is solved using a global discretization method, 17,18 resulting in a relatively low order and computationally efficient simulation procedure. This model was used in an iterative, optimization-based parameter estimation procedure to determine a subset of the heat transfer parameters, using experimental measurements of wafer temperature as a function of gas composition.…”