In this thesis we study the chemical reactions and transport phenomena which occur in a microwave power assisted chemical vapour deposition (MPA-CVD) reactor which facilitates diamond growth. First we introduce a model of an underlying binary gas flow and its chemistry for a hydrogen gas mixture. This system is heated by incorporating a microwave frequency electric field, operating in a resonant mode in the CVD chamber. This heating facilitates the dissociation of hydrogen and the generation of a gas discharge plasma, a key component of carbon deposition in industrial diamond manufacture. We then proceed to summarise the discontinuous Galerkin (DG) finite element discretisation of the standard hyperbolic and elliptic partial differential operators which typically occur in conservation laws of continuum models. Additionally, we summarise the non-stabilised discontinuous Galerkin formulation of the time harmonic Maxwell operator. These schemes are then used as the basis for the discretisation method employed for the numerical approximation of the MPA-CVD model equations. The practical implementation of the resulting DG MPA-CVD model is an extremely challenging task, which is prone to human error. Thereby, we introduce a mathematical approach for the symbolic formulation and computation of the underlying finite element method, based on automatic code generation. We extend this idea further such that the DG finite element formulation is automatically computed following the user's specification of the convective and viscous flux terms of the underlying PDE system in this symbolic framework. We then devise a method for writing a library of automatically generated DG finite element formulations for a hierarchy of partial differential equations with automatic treatment of prescribed boundary conditions. This toolbox for automatically computing DG finite element solutions is then applied to the DG MPA-CVD model. In particular, we consider reactor designs inspired by the AIXTRON and LIMHP reactors which are analysed extensively in the literature.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:701216 |
| Date | January 2016 |
| Creators | Sime, Nathan |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/36227/ |
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