Gas rarefaction in high power impulse magnetron sputtering: comparison of a particle simulation and volume-averaged models

We calculate the rarefaction of Ar background gas in front of a magnetron caused by sputtered target material atoms (so called 'sputtering wind effect') during pulsed sputtering. For a detailed analysis, we use a three-dimensional particle simulation using the direct simulation Monte Carlo (DSMC) method. We compare the results with those of two volume-averaged (V-A) models describing the same problem but with significantly lower computational demands. The comparison is made for three values of flux of sputtered atoms (expressed as 'sputtering current' in the units of amperes) and for three target materials (Zr, Al and C) sputtered from a circular target of 5 cm diameter placed in a chamber with realistic geometry. Ar rarefaction is more pronounced for target atoms with higher mass, but the difference between the three target materials is surprisingly small. The region where Ar is significantly rarefied extends much further from the target than a typical extent of the high-density plasma confined by the magnetic field. The V-A models provide good approximation of the time evolution of the target material density in front of the target compared to the DSMC simulation. However, the presented V-A models underestimate (in all but one case) the magnitude of Ar rarefaction during the pulse-on time and also predict faster return to equilibrium during the pulse-off time comared to the DSMC simulation.