## 4 Discussion
The chemical reaction of fluorine with Li, Nb and O atoms and the formation of volatile fluorides and oxyfluorides (NbF\({}_{5}\), NbOF\({}_{3}\), OF\({}_{2}\)) and non-volatile LiF. 5. Swelling of the near-surface layer due to the accumulation of volatile compounds [23]. Fluorine easily diffuses into the structure of LiNbO\({}_{3}\) because of the small positive ion radius (atomic radius of fluorine = 65 pm [35]); however, the out-diffusion of the reaction products is obstructed. At the stage of intense etching, a drastic increase in the etching rate occurs as a result of the rupture of the cavity with the reaction products, and a polycrystalline LiF film with a porous structure forms on the surface. Figure 7: Schematic of the ridge waveguide profile with microtrenches near the base of the waveguide. Based on the model described above, the received results may indicate that plasma-chemical etching with a dominant chemical component of plasma occurred during process #14 rather than during the RIE process. The sample surface was covered with a brown film-like layer after the etching process with recipe #14. The SEM-EDX analysis of the near-surface layer was carried out using an INCA X-act detector (Oxford Instruments). The analysis revealed the presence of the following elements: O:F:Nb = 18.56 wt%:36.56 wt%:44.88 wt%. Li was not detected with this tool. On the one hand, this analytic technique can be used only for elemental analysis, not for chemical compound identification. On the other hand, fluorine compounds are present on the surface and LiF is a non-volatile compound that forms in the LN etching process. This is why we suggest that the brown film-like layer included a LiF\({}_{\mathrm{x}}\) compound. After the etching process with recipe #13, fluorine was not found near the surface of the etched LiNbO\({}_{3}\). The sample after etching was transparent like the initial LiNbO\({}_{3}\) without any observed color changing. The surface of the etched sample in the near-waveguide region was mostly smooth (Figures 5 and 6). The only difference between recipes #13 and #14 was the process pressure (0.03 mbar and 0.007 mbar, respectively). The ICP-RIE system Ethna-100 allowed for separately controlling the process pressure, flow rates of the process gases, and ICP and TCP powers. The bias voltage was a derivative parameter and it may be controlled through the variation of the parameters described above. During the experiments, the influence of the process pressure on the bias voltage was revealed. The bias voltage defines the kinetic component of the plasma since it is directly related to the kinetic energy of the accelerated ions. Figure 8 shows the dependence of the bias voltage to the substrate stage on the pressure for W\({}_{\mathrm{ICP}}\) = 500 W and W\({}_{\mathrm{TCP}}\) = 100 W, as well as different ratios of plasma-forming gases. Normally, the bias voltage can be increased by reducing the chamber pressure. Its dependence on the pressure is related to the mean free path of the particles, which defines the average distance that the particle travels before a collision [36]. Theoretically, this law is satisfied for pressures of 0.05 mbar and higher. In practice, the dependence has an inflection point in the range from 0.05 to 0.03 mbar (Figure 8). For pressures lower than 0.03 mbar, the bias voltage drop was observed regardless of the ICP and TCP power and ratios of plasma-forming gases. In our work, the bias voltage during the etching was 186 V with recipe #13, and 141 V with recipe #14. We suppose that this difference in bias voltage caused a transition from  
Figure 8: Bias voltage versus pressure for different ratios of plasma-forming gases for W\({}_{\mathrm{ICP}}\) = 500 W and W\({}_{\mathrm{TCP}}\) = 100 W.  
reactive ion etching (in the case of recipe #13) to a radical chemical etching process (in the case of recipe #14). [PERSON] et al. [37] conducted a detailed study of ion energy distributions (IEDs) for ICP plasma sources with parameters similar to those used in our experiments.