Date of Award

Spring 2005

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Raja Nassar

Abstract

To fully investigate a pyrolytic Laser-induced chemical vapor deposition (LCVD) system for growing an axisymmetric rod, a novel integrated three-dimensional mathematical model was developed not only to describe the heat transport in the deposit and substrate, but also to simulate the gas-phase in the heated reaction zone and its effect on growth rate. The integrated model consists of three components: the substrate, rod, and gas-phase domains. Each component is a separate model and the three components are dynamically integrated into one model for simulating the iterative and complex process of rod deposition.

The gas-phase reaction is modeled by the gas-phase component, an adaptive domain attached on the top part of the rod. Its size and mesh decomposition is dynamically determined by the rod temperature distribution and the chosen threshold. The temperature and molar ratio are predicted and used to adjust the growth rate, by taking into account the diffusion limited growth regime, and to improve the simulation of entire deposition process. The substrate component describes the heat flow into the substrate, and the substrate surface temperature can be used to predict the initial rod growth which may affect the successive growth of the rod. The rod growth process is simulated using a layer-by-layer axisymmetric model. For each layer, the rod grows along the outward normal direction at each point on the rod surface. This simplified model makes the process more predictable and easier to control by specifying the height of the rod and the number of total iterations.

Finite difference schemes, iterative numerical methods, and parallel algorithms were developed for solving the model. The numerical computation is stable, convergent, and efficient. The model and numerical methods are implemented sequentially and in parallel using a standard C++ code and Message Passing Interface (MPI). The program can be easily installed and executed on different platforms, such as Unix and Windows XP. Computation in the gas-phase domain is encapsulated in a C++ class, and it is convenient for users to choose either the integrated or the kinetic model to perform simulation of rod growth. Parallel implementation improves the computational performance.

To demonstrate the capability of the integrated model, silane is chosen as the precursor to grow the axisymmetric rod with silicon as deposit and graphite as substrate. The integrated 3D LCVD model and the corresponding numerical methods are applied to simulate the gas-phase reaction process, and to predict heat transfer, molar ratio, initial and successive rod growths and growth time at each iteration. It is found that the diffusion-limited growth can affect the deposition process and must be taken into account when the temperature is higher than a certain threshold. The initial rod growth can affect the successive rod growth and its geometry. This modeling approach may provide a useful means for investigating the effect of different model parameters for optimizing the LCVD process.

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