Study of the plasma pre-sheath in magnetron discharges dominated by Bohm diffusion of electrons

Abstract

This paper seeks to extend and improve upon an existing 1D isothermal model [1] for the cathode plasma boundary in magnetron discharges. Using an electron energy balance equation and treating the sheath as a source of electron heat flux, the plasma parameter profiles are solved in the pre-sheath, above the sputter trench. The cross-field transport of electrons is assumed to be dominated by Bohm diffusion (and mobility) in the mutually perpendicular electric and magnetic fields, while ions created by electron impact ionization fall directly to the cathode. Solutions show a fall in electron temperature with distance from the sheath-edge, with plasma densities rising by a factor of typically three or four from sheath-edge to plasma. This latter result is a departure from the normal prescription for Bohm sheath formation. Reasonable agreement between the model predictions and Langmuir probe measurements made in the region directly above the `race-track' sputter trench in a commercial magnetron show the usefulness of such simple models.