Numerical modelling of microwave plasma-assisted chemical vapour deposition reactors for diamond synthesis

Marsh, Jonathan (2020) Numerical modelling of microwave plasma-assisted chemical vapour deposition reactors for diamond synthesis. PhD thesis, University of Nottingham.

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Abstract

This thesis studies the numerical modelling of microwave plasma-assisted chemical vapour deposition (MPA-CVD) reactors for synthetic diamond synthesis. Specifically we model the formation of a plasma within these reactors, which is responsible for enabling the deposition of carbon onto a substrate for diamond growth. This involves first introducing a chemically reacting binary gas flow model for a hydrogen gas mixture, which in turn is coupled to an applied electric field operating at resonance. This electric field acts as the energy source for the ionising collisions that characterise plasma formation.

Following this, we introduce numerical schemes for general hyperbolic and elliptic operators based on employing the discontinuous Galerkin finite element method (DGFEM). Notably, in the case of Maxwell's equations, we employ a non-stabilised formulation of the symmetric interior penalty method. These schemes form the basis of the underlying numerical approximation of the MPA-CVD model.

A large portion of this thesis is dedicated to improving the predictive capabilities of the existing MPA-CVD model. Noteworthy changes include a more physically-accurate description of ionisation processes, the introduction of a secondary heat transfer mechanism, namely, enthalpic diffusion, and the use of an electron energy conservation equation to better approximate the average electron temperature. Additionally, the success of the model is demonstrated by its application to three existing MPA-CVD reactor geometries.

The majority of MPA-CVD reactors are largely axisymmetric, and thus, the majority of MPA-CVD simulation in the literature is performed in 2D. This disregards the possibility of non-axisymmetric perturbations to the plasma distribution. Here, we perform a 3D Maxwell eigenvalue analysis of two MPA-CVD reactor geometries to investigate the possibility of the electric field distribution being polluted by neighbouring non-axisymmetric resonant modes that operate close to the applied frequency. Additionally, we uncover a curious occurrence whereby a spurious eigenvalue spectrum is obtained when employing a higher order boundary representation in conjunction with a standard DGFEM for Maxwell's equations; as far as we are aware, this is not covered in the literature, but was overcome by application of a Piola covariant transformation.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Houston, Paul
Keywords: MPA-CVD, Diamond synthesis
Subjects: T Technology > TP Chemical technology > TP 785 Clay industries. Ceramics. Glass
T Technology > TS Manufactures
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 60919
Depositing User: Marsh, Jonathan
Date Deposited: 25 Aug 2020 13:20
Last Modified: 25 Aug 2020 13:37
URI: http://eprints.nottingham.ac.uk/id/eprint/60919

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