Modelling of diamond deposition microwave cavity generated plasmas

Abstract

Some aspects of the numerical modelling of diamond deposition plasmas generated using microwave cavity systems are discussed. The paper mainly focuses on those models that allow (i) designing microwave cavities in order to optimize the power deposition in the discharge and (ii) estimating the detailed plasma composition in the vicinity of the substrate surface. The development of hydrogen plasma models that may be used for the self-consistent simulation of microwave cavity discharge is first discussed. The use of these models for determining the plasma configuration, composition and temperature is illustrated. Examples showing how to use these models in order to optimize the cavity structure and to obtain stable process operations are also given. A transport model for the highly reactive H2/CH4 moderate pressure discharges is then presented. This model makes possible the determination of the time variation of plasma composition and temperature on a one-dimensional domain located on the plasma axis. The use of this model to analyse the transport phenomena and the chemical process in diamond deposition plasmas is illustrated. The model is also utilized to analyse pulsed mode discharges and the benefit they can bring as far as diamond growth rate and quality enhancement are concerned. We, in particular, show how the model can be employed to optimize the pulse waveform in order to improve the deposition process. Illustrations on how the model can give estimates of the species density at the growing substrate surface over a wide domain of deposition conditions are also given. This brings us to discuss the implication of the model prediction in terms of diamond growth rate and quality.

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

“…This requires approximation of the electron thermal conductivity, as well as the rate coefficients of ionisation. The electrons would then be heated primarily by the applied microwave field; we refer again to [9] for a review of these models. In this work, we make the simplifying assumption that the electron temperature is strongly influenced by the time averaged magnitude of the applied electric field and the number density of the background gas of neutrals remains roughly constant such that…”

“…The primary peak in the electric field indicates that plasma ignition will occur as desired above the substrate surface, however, increasing the input power in the electric field does lead to a second plasma ball being generated at the top of the quartz bell jar. The first generation LIMHP reactor is known to exhibit this double plasma ball phenomenon [9].…”

“…A key mathematical issue is to balance the number of chemical species to be modelled, while ensuring an accurate description of the underlying CVD diamond synthesis process. Hassouni et al [9] present an excellent in depth review of hydrogen CVD plasma modelling; here, a model for the chemical species comprising hydrogen dissociation in CVD reactors is derived. This work highlights the complexity of plasma modelling due to the large number of chemical species involved in the many reactions.…”

“…The complexity of more detailed methane plasma modelling is further discussed in [11]. However, we stress that the incorporation of complex flow phenomena in a given microwave power assisted (MPA-) CVD reactor model has not previously been taken into account; for example, [9] neglects the natural convection arising due to the Soret effect from strong thermal gradients, though it is stressed that these thermo-convective flow conditions may strongly affect the microwave field coupling configuration.…”

“…Stimulated by the work undertaken in [9], in this article we present a fully self consistent model for a hydrogen plasma, with simplified chemistry, within a MPA-CVD reactor. We point out that, as noted in [12,13], for example, the difference in the shape, position and optimal microwave power absorbed in a hydrogen plasma CVD reactor is not significantly different to the case when small quantities of methane are present.…”