Numerical modelling of MPA-CVD reactors with the discontinuous Galerkin finite element method

Abstract

In this article we develop a fully self consistent mathematical model describing the formation of a hydrogen plasma in a microwave power assisted chemical vapour deposition (MPA-CVD) reactor employed for the manufacture of synthetic diamond. The underlying multi-physics model includes constituent equations for the background gas mass average velocity, gas temperature, electromagnetic field energy and plasma density. The proposed mathematical model is numerically approximated based on exploiting the discontinuous Galerkin finite element method. We demonstrate the practical performance of this computational approach on a variety of CVD reactor geometries for a range of operating conditions.

Automatic Symbolic Computation for Discontinuous Galerkin Finite Element Methods

“…Degrees of freedom discretisation of systems of multi-physics PDEs in a simple and concise manner; as an example, we have employed the software here for the DGFEM approximation of microwave power assisted chemical vapour deposition reactor employed for the manufacture of synthetic diamond; see [28,36]. Moreover, the code can easily be extended to other problems, and indeed other DGFEM schemes, so that users can tailor the software to their own applications.…”

“…Indeed, in the final two examples, we have included the DGFEM approximation of the indefinite Maxwell problem and a hyperelasticity problem, respectively. The exploitation of the software developed within this article allows the user to build up the DGFEM Degrees of freedom discretisation of systems of multi-physics PDEs in a simple and concise manner; as an example, we have employed the software here for the DGFEM approximation of microwave power assisted chemical vapour deposition reactor employed for the manufacture of synthetic diamond; see [28,36]. Moreover, the code can easily be extended to other problems, and indeed other DGFEM schemes, so that users can tailor the software to their own applications.…”

“…This is particularly the case when exploiting FEMs for the numerical approximation of systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist of power series or functionals of the solution variables, cf. [28].…”

“…This work was originally inspired by the need to numerically model the formation of a hydrogen plasma in a microwave power assisted chemical vapour deposition reactor employed for the manufacture of synthetic diamond; this includes constituent equations for the background gas mass average velocity, gas temperature, electromagnetic field energy and plasma density, cf. [28,36].…”

Effect of methane flow rate on gas-jet MPCVD diamond synthesis

“…In [11], the effect of separate injection of precursor gases on the synthesis of diamond is considered. Papers [12,13] are devoted to the development of numerical approaches to the analysis of processes in MPCVD synthesis of diamonds.…”