A phenomenological equilibrium model applicable to high-power pulsed magnetron sputtering

Abstract

We present a phenomenological equilibrium model applicable to high-power pulsed dc magnetron sputtering with relatively long steady-state discharge regimes established during pulses. The model makes it possible to calculate the fraction of ionized sputtered atoms directed back to the target, σ, the degree of ionization of sputtered atoms in front of the target, β, the normalized rate coefficient, α (determining the deposition rate of films per target power density), and the ionized fraction of target material atoms in the flux onto the substrate, Θ, as functions of the magnetron voltage, Ud, and the fraction of target material ions in the total ion flux onto the target, mt (being related to an applied target power density). We used this model to clarify the large differences between the corresponding deposition characteristics (such as the deposition rate of films per average target power density in a period and the ionized fraction of target material atoms in the flux onto the substrate) of copper and titanium measured by us during high-power pulsed dc magnetron sputtering of the two materials. We investigated the effects of higher losses of the target material ions to the chamber walls and of reduced additional ionization in the plasma bulk in the magnetron system with a weaker magnetic confinement. For total self-sputtering of copper, when mt = 1, we obtained values of σ in the range from 0.54 at Ud = 600 V to 0.32 at Ud = 1000 V, in excellent agreement with the recent measurements of Andersson and Anders.