Two-dimensional fluid approach to the dc magnetron discharge

Abstract

A two-dimensional (r, z) time-dependent fluid model was developed and used to describe a dc planar magnetron discharge with cylindrical symmetry. The transport description of the charged species uses the corresponding first three moments of the Boltzmann equation: continuity, momentum transfer and mean energy transfer (the last one only for electrons), coupled with the Poisson equation. An original method is proposed to treat the transport equations. Electron and ion momentum transport equations are reduced to the classical drift-diffusion expression for the fluxes since the presence of the magnetic field is introduced as an additional part in the electron flux, while for ions an effective electric field was considered. Thus, both continuity and mean energy transfer equations are solved in a classical manner. Numerical simulations were performed considering argon as a buffer gas, with a neutral pressure varying between 5 and 30 mTorr, for different voltages applied on the cathode. Results obtained for densities of the charged particle, fluxes and plasma potential are in good agreement with those obtained in previous studies.