Continuum and Kinetic Simulations of the Neutral Gas Flow in an Industrial Physical Vapor Deposition Reactor

TL;DR

This study compares fluid and kinetic models to simulate neutral gas flow in an industrial plasma reactor, revealing the fluid model's limitations in the transition Knudsen regime and emphasizing the importance of kinetic modeling for accuracy.

Contribution

The paper demonstrates the inadequacy of the fluid model in transition regimes and highlights the necessity of kinetic simulations for accurate gas flow analysis in plasma reactors.

Findings

Fluid model fails in transition regime due to non-local effects

Kinetic model accurately describes gas flow in the transition regime

Proper definition of the local Knudsen number is crucial for regime estimation

Abstract

Magnetron sputtering used for physical vapor deposition processes often requires gas pressures well below 1 Pa. Under these conditions the gas flow in the reactor is usually determined by a Knudsen number of about one, i.e., a transition regime between the hydrodynamic and the rarefied gas regime. In the first, the gas flow is well described by the Navier-Stokes equations, while in the second a kinetic approach via the Boltzmann equation is necessary. In this paper the neutral gas flow of argon and molecular nitrogen gas inside an industrial scale plasma reactor was simulated using both a fluid model and a fully kinetic Direct Simulation Monte Carlo model. By comparing both model results the validity of the fluid model was checked. Although in both models a Maxwell-Boltzmann energy distribution of the neutral particles is the natural outcome, the results of the gas flow differ significantly. The fluid model description breaks down, due to the inappropriate assumption of a fluid continuum. This is due to exclusion of non-local effects in the multi dimensional velocity space, as well as invalid gas/wall interactions. Only the kinetic model is able to provide an accurate physical description of the gas flow in the transition regime. Our analysis is completed with a brief investigation of different definitions of the local Knudsen number. We conclude that the most decisive parameter - the spatial length scale L - has to be very careful chosen in order to obtain a reasonable estimate of the gas flow regime.