On three different ways to quantify the degree of ionization in sputtering magnetrons

Quantification and control of the fraction of ionization of the sputtered species are crucial in magnetron sputtering, and in particular in high-power impulse magnetron sputtering (HiPIMS), yet proper definitions of the various concepts of ionization are still lacking. In this contribution, we distinguish between three approaches to describe the degree (or fraction) of ionization: the ionized flux fraction F-flux, the ionized density fraction F-density, and the fraction a of the sputtered metal atoms that become ionized in the plasma (sometimes referred to as probability of ionization). By studying a reference HiPIMS discharge with a Ti target, we show how to extract absolute values of these three parameters and how they vary with peak discharge current. Using a simple model, we also identify the physical mechanisms that determine F-flux, F-density, and a as well as how these three concepts of ionization are related. This analysis finally explains why a high ionization probability does not necessarily lead to an equally high ionized flux fraction or ionized density fraction.