# Continuum and kinetic simulations of the neutral gas flow in an industrial physical vapor deposition reactor

Kirsten Bobzin, Ralf Peter Brinkmann, Thomas Mussenbrock, Nazlim Bagcivan, Ricardo Henrique Brugnara, Marcel Schäfer, Jan Trieschmann

Surface and Coatings Technology 237 (2013) 176-181

## 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.

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