## 4 Discussion  
Each individual spectrum for positive and negative ions has a prominent threshold region of reactive oxygen gas flow where we witnessed a nonlinear dependence. The signals recorded by both optical spectroscopy and ion mass spectrometry for the most representative species of aluminum and oxygen are compared in Figure 8. The optical data for O\({}^{+}\) ions were omitted because of their negligible intensity. Therefore, the comparative analysis can be made for the ion flux behavior of O\({}^{+}\) and Al\({}^{+}\) ions and spectral intensities of O (777.14 nm) and Al\({}^{+}\) (394.36 nm) emission lines. One might observe a clear similarity in the starting point of hysteresis loops for all the curves, being at an oxygen flow of about 0.9 sccm. With increasing oxygen flow, both particle and optical signals for aluminum demonstrate alike behavior. The resulting width of hysteresis loops is nearly the same for both types of diagnostic data. At the same time, in the 0-0.9 sccm flow rate range, intensity of the Al\({}^{+}\) emission line decreases in contrast to the Al\({}^{+}\) ion current, which is stable. The intensity of emission lines is governed by the complex set of reactions in plasma involving electrons and heavy species. The declining intensity of the selected Al\({}^{+}\) line might indicate the changes in electron energy distribution resulting in depletion of the electronic transitions responsible for the intensity of this particular emission line, even if the flux of Al\({}^{+}\) species remains constant. Another cause might be the change in Al\({}^{+}\) ions' energy. Testing the true cause requires additional energy-resolved measurements. For oxygen, both signals measured in the forward direction, i.e., with increasing oxygen flow, show good agreement in the curve shape. The reverse measurements, however, give contrasting pictures. The O\({}^{+}\) ion flux signal has a steady value when decreasing the oxygen flow from 4.2 to 3.0 sccm. At the same time, the optical O signal goes down along the forward trend but then has a shifted horizontal part. These are apparent differences in the hysteresis loop width between O\({}^{+}\) ion flux and O emission intensity. Figure 7: Optical emission intensities of plasma constituents vs. oxygen flow rate: (**a**) flow rate increasing; (**b**) flow rate decreasing. The observed discrepancy suggests that the O emission line intensity cannot be fully representative of the O\({}^{+}\) ion flux. Measured optical emission intensity should correlate with the concentration of excited O atoms, which, in turn, can be related to O\({}^{+}\) and O\({}^{-}\) concentrations by solving a set of equations for the relevant plasma-chemical reactions. The transition threshold at 1.2 sccm of the O\({}_{2}\) reactive gas supply can be explained by the joint construction of the reactive sputtering Berg model and the experimental results. Let us consider the basic steady-state Berg model comprising the following equations [51; 52]:  
\[0=dN_{\mathrm{t}}/dt=(2/Z)\alpha_{\mathrm{t}}F(1-\theta_{1})-(j/e) \gamma_{\mathrm{c}}\theta_{1}, \tag{1}\] \[\mathrm{[chemisorption]}\mathrm{[ sputtering]}\]  
\[0=dN_{\mathrm{s}}/dt=(2/Z)\alpha_{\mathrm{g}}F(1-\theta_{2})+(j/e)\gamma_{ \mathrm{c}}\theta_{1}(A_{\mathrm{t}}/A_{\mathrm{s}})(1-\theta_{2})-(j/e)\gamma _{\mathrm{m}}(1-\theta_{1})(A_{\mathrm{t}}/A_{\mathrm{s}})\theta_{2}, \tag{2}\] \[\mathrm{[chemisorption]}\mathrm{[oxide growth]}\mathrm{[ deposition of metal]}\]  
\[p_{\mathrm{atm}}q=(2/Z)\alpha_{\mathrm{t}}\varepsilon F(1-\theta_{1})A_{ \mathrm{t}}+(2/Z)\alpha_{\mathrm{g}}\varepsilon F(1-\theta_{2})A_{\mathrm{s}} +pS, \tag{3}\]  
Figure 8: Comparison of hysteresis curves in ion mass spectrometric (**a**,**b**) and optical emission spectroscopic (**c**,**d**) measurements: (**a**) ion flux signal of O\({}^{+}\) ions; (**b**) ion flux signal of Al\({}^{+}\) ions; (**c**) emission intensity of O line (\(\lambda\) = 777.14 nm); (**d**) emission intensity of Al\({}^{+}\) line (\(\lambda\) = 394.36 nm).