Return of target material ions leads to a reduced hysteresis in reactive high power impulse magnetron sputtering: Model

A tendency to disappearing hysteresis in reactive High Power Impulse Magnetron Sputtering (HiPIMS) has been reported previously without full physical explanation. An analytical model of reactive pulsed sputtering including HiPIMS is presented. The model combines a Berg-type model of reactive sputtering with the global HiPIMS model of Christie-Vlček. Both time and area averaging is used to describe the macroscopic steady state, especially the reactive gas balance in the reactor. The most important effect in the presented model is covering of reacted parts of target by the returning ionized metal, effectively lowering the target coverage by reaction product at a given partial pressure. The return probability of ionized sputtered metal has been selected as a parameter to quantify the degree of HiPIMS effects. The model explains the reasons for reduced hysteresis in HiPIMS. The critical pumping speed was up to a factor of 7 lower in reactive HiPIMS compared to the mid-frequency magnetron sputtering. The model predicts reduced hysteresis in HiPIMS due to less negative slope of metal flux to substrates and of reactive gas sorption as functions of reactive gas partial pressure. Higher deposition rate of reactive HiPIMS compared to standard reactive sputtering is predicted for some parameter combinations. Comparison of the model with experiment exhibits good qualitative and quantitative agreement for three material combinations, namely, Ti-O₂, Al-O₂, and Ti-N₂.