Particle modelling of low-pressure radio-frequency magnetron discharges including the effects of self-induced electromagnetic fields
Résumé
Modelling of radio-frequency (RF) magnetron discharges is performed using a particle-in-cell/Monte Carlo technique in the case of low-pressure argon gas at 4 mTorr and high external magnetic field in order to self-maintain the discharge and to generate an energetic quasi-ion beam required for cathode sputtering applications. An emphasis is made, for the first time in the literature in the case of low-pressure RF discharges, on the development of a particle model coupled with the full set of electromagnetic field equations. The aim is to analyse the effect on the RF plasma features of the plasma-induced magnetic field resulting from the coupling of the Maxwell–Ampere equation. We also analysed the effect of the electric field due to the time variation of magnetic field resulting from the coupling of the Maxwell–Faraday equation. For the present asymmetrical plasma reactor, the mean relative difference on, for instance, the ion density with and without the consideration of
plasma-induced magnetic and electric fields due to the time variation of the magnetic field can reach about 2.5% in the region of the plasma bulk and about 10% in the lateral sheath. The effects of these two induced electromagnetic fields are in fact higher in the regions where the radial magnetic field generated by the external magnets belonging to the magnetron configuration is low. These non-negligible relative differences clearly show the importance of rigorously taking into account, beyond the usual Poisson’s equation for the space charge electric field, the full set of electromagnetic Maxwell equations for a more accurate modelling of these low-pressure discharges, particularly when the total current density reaches a few mA cm−2 .