## 4 Discussion
where \(N_{t}\), \(N_{s}\)--numbers of oxygen atoms, which formed compounds with metal atoms at the target and substrate/wall, correspondingly (per unit area); \(\theta_{1}\)--fraction of the target surface area covered by the oxide compound (poisoned); \(\theta_{2}\)--compound fraction on the substrate/wall surfaces; \(j\)--ion current density; \(p\)--partial oxygen pressure; \(\gamma_{c}\)--puttering yield of the compound; \(\gamma_{m}\)--sputtering yield of the metal; \(\alpha_{t}\), \(\alpha_{s}\)--sticking coefficients of oxygen atoms to metallic parts of the target and substrate/wall surfaces, correspondingly; \(A_{t}\)--target surface area; \(A_{s}\)--substrate/wall surface area; \(e\)--elementary charge; \(F=p(2\pi\delta_{\mathrm{B}}Tm)^{-1/2}\)--relationship between flux \(F\) of neutral oxygen molecules and partial oxygen pressure \(p\) (\(k_{\mathrm{B}}\)--Boltzmann constant, \(T\)--gas temperature, \(m\)--molecular mass); \(p_{\mathrm{atm}}\)--atmospheric pressure; \(q\)--oxygen flow rate; \(\dot{k}=V_{M}p_{\mathrm{atm}}/N_{\mathrm{A}}\)--unit conversion factor (\(V_{M}\)--molar volume, \(N_{\mathrm{A}}\)--Avogadro constant); \(Z\)--stoichiometry factor of the compound (3/2 for Al\({}_{2}\)O\({}_{3}\)); and \(S\)--effective pumping speed. Equation (1) describes the oxidation state of the target surface. The substrate coverage with the oxide compound is determined by Equation (2). Equation (3) expresses the balance of reactive gas species supplied to the chamber. In the steady state, \(dN_{t}/dt=0\) and \(dN_{c}/dt=0\)[51; 52]. The system of Equations (1)-(3) was used to calculate the dependences of oxygen partial pressure \(p\) on oxygen flow rate \(q\) taking into account the processes of poisoning and sputtering. The overlay of the calculated results and experimental discharge parameters is shown in Figure 9.  
In the power regulation mode, both the voltage and current change when the reactive gas flow is varied. In Figure 8, several pressure-flow lines were built according to Berg model solutions corresponding to different voltages, at a constant power of 100 W. They were calculated for a fixed pair of experimentally observed voltage and current values (indicated in the legend). The circles correspond to the potential operation modes available for the given oxygen flow. To reconstruct the real oxygen pressure-flow curve, one should therefore combine the experimental evidence for the metallic-to-oxide transition (Figures 3, 4 and 8) and the calculated hysteresis curves (Figure 9). It was found that the experimental hysteresis trajectories observed when changing the supply of reactive gas are slightly different compared to the Berg model results, but the position of the transition point coincides with the calcula  
Figure 9: Hysteresis loop evaluation by simulation and experiment. Dashed line represents the “real” oxygen pressure–flow curve for a discharge operating in power regulation mode. plotted on the graph of the experimental results are marked with arrows, and the dashed line indicates the resulting path of the working point for various flow rates of reactive gas supply. The experimental result is confirmed when we see a sharp change in the partial pressure of the reactive gas during the transition from the metallic to the oxide regime.