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In production processes of micro-electronics, optical and mechanical coatings and solar cells, high-purity materials in the form of a powder or a thin film are significant importance. The deposition of thin films on irregularly shaped surfaces can be done by chemical vapor deposition (CVD). Computer simulations are widely used to design CVD reactors and to optimize the process itself. The core of a computer simulation is a mathematical model of the gasflow and all chemical processes within the CVD reactor. A lot of (commercial) computer software has been written for CVD simulation. The emphasis has always been on modeling and validation. For the 'old' CVD processes this approach was sufficient. However, with the deposited films getting thinner and thinner, process times are reduced and transient times become more important. Further, the technology is moving towards inherent transient CVD processes (such as atomic layer deposition) making instationary simulations indispensable. Computing the time-dependent solution of the underlying mathematical equations is hard, because the involved chemistry makes these equations hard to solve. Commercial CFD software packages have often great problems to compute these solutions. Solutions computed by various codes have been reported to differ a lot and the computational times needed to find solutions are generally excessive. In this thesis a rigorous mathematical approach has been applied to these problems, with the aim to reduce computational times for simulations of CVD and related applications. The numerical techniques proposed in this thesis enables us to perform instationary, multi-dimensional gas flow simulations with multi-species, multi-reaction CVD chemistry in a computationally efficient way., Electrical Engineering, Mathematics and Computer Science

Electrical Engineering, Mathematics and Computer Science

Electrical Engineering, Mathematics and Computer Science

In this study various numerical schemes for simulating 2D laminar reacting gas flows, as typically found in Chemical Vapor Deposition (CVD) reactors, are proposed and compared. These CVD systems are generally modeled by means of many stiffly coupled elementary gas phase reactions between a large number of reactants and intermediate species. The purpose of this study is to develop robust and efficient solvers for the stiff heat-reaction system, whereby the velocities are assumed to be given. For non-stationary CVD simulation, an optimal combination in terms of efficiency and robustness between time integration, nonlinear solvers and linear solvers has to be found. Besides stability, which is important due to the stiffness of the problem, the preservation of non-negativity of the species is crucial. It appears that this extra condition on time integration methods is much more restrictive towards the time-step than stability. For a set of suitable time integration methods necessary conditions are represented. We conclude with a comparison of the workload between the selected time integration methods. This comparison has been done for a 2D test problem. The test problem does not represent a practical process, but represents only the computational problems.

In this study various numerical schemes for simulating 2D laminar reacting gas flows, as typically found in Chemical Vapor Deposition (CVD) reactors, are proposed and compared. These systems are generally modeled by means of many stiffly coupled elementary gas phase reactions between a large number of reactants and intermediate species. The purpose of this study is to develop robust and efficient solvers for the stiff heat-reaction system, whereby the velocities are assumed to be given. For non-stationary CVD simulation, an optimal combination in terms of efficiency and robustness between time integration, nonlinear solvers and linear solvers has to be found. Besides stability, which is important due to the stiffness of the problem, the preservation of non-negativity of the species is crucial. It appears that this extra condition on time integration methods is much more restrictive towards the time-step than stability. For a set of suitable time integration methods necessary conditions are represented. We conclude with a comparison of the workload between the selected time integration methods. This comparison has been done for a 2D test problem. The test problem does not represent a practical process, but represents only the computational problems., Electrical Engineering, Mathematics and Computer Science

In this study various numerical schemes for transient simulations of 2D laminar reacting gas flows, as typically found in Chemical Vapor Deposition (CVD) reactors, are proposed and compared. These systems are generally modeled by means of many stiffly coupled elementary gas phase reactions between a large number of reactants and intermediate species. The purpose of this study is to develop robust and efficient solvers for the stiff reaction system, where as a first approach the velocity and temperature fields are assumed to be given. Furhtermore, we neglect thermal diffusion (Soret effect). In this paper we mainly focus on the performance of different time integration methods, and their properties to successfully solve the transient problem. Besides stability, which is important due to the stiffness of the problem, the preservation of on-negativity of the species is crucial. It appears that this extra condition on time integration methods is much more restrictive towards the time-step than stability., Electrical Engineering, Mathematics and Computer Science