## 4 Data Analysis and Discussion  
Considering the intensity and reproducibility of the features on the \(I\)-\(V\) curves of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) JJs, one can suggest the involvement of the collective modes in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) in their formation. It makes sense to compare the features on the \(I\)-\(V\) curves of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) JJs with the results of far-infrared reflection experiments on bulk YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) crystals. The intensity and position of some features in \(I\)-\(V\) curves changed after annealing; therefore, one should find the reference spectra for bulk samples YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) with different oxygen contents \(x\). Table 1 summarizes the averaged values of the central frequencies \(f_{k}\) of the observed features on the \(I\)-\(V\) curves of bicrystal YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) JJs (the first column) and compares these frequencies with the peak positions in the optical conductivity \(\sigma\)(\(f\)) of bulk crystals YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) with different oxygen content, from O\({}_{6.0}\) (the second column) to O\({}_{6.95}\) (the sixth column). Data on optical conductivities \(\sigma\)(\(f\)) are from far-infrared reflection experiments [26; 27; 28; 29; 30] for two polarizations of the electric field \(E\) of incoming radiation: along the \(c\)-axis (\(E\mid\mid c\)) and along the \(a\)-axis (\(E\mid\mid a\)) of the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) crystals. If the \(f_{k}\)-values changed after annealing in atomic oxygen, two values \(f_{k}\)(b) and \(f_{k}\)(a) connected with the horizontal arrow. The vertical arrows \(\uparrow\downarrow\) indicate the increase (\(\uparrow\)) or decrease (\(\downarrow\)) of the intensities of the features after annealing. Figure 6: Differential conductances d\(I\)/d\(V\) vs. voltage \(V\) (bottom scale) and Josephson frequency \(f_{j}\) = 2\(eV\)/h (top scale) for four JJs junctions of different widths on the same 2 \(\times\) 11.3\({}^{\circ}\) bicrystal NdGaO\({}_{3}\) substrate with a 10 nm thick SrTiO\({}_{3}\) buffer layer. Sample yd705101_N, where N is the junction number on the substrate. The width values, in \(\upmu\)m, are 6, 3, 2, and 1 for JJs, with numbers N of 1, 2, 5 and 4, correspondingly. The letter b means that the sample was measured before annealing, and the letter a means that the sample was measured after low-temperature annealing in atomic oxygen. \(T\) = 4.2 K.  
The most intensive feature on the \(I\)-\(V\) curves of JJs is observed at \({f_{\rm k}}^{\rm(b)}=4.59\) THz. It shifts to a higher frequency of \({f_{\rm k}}^{\rm(a)}=4.62\) THz after annealing in oxygen with the intensity increase (\(\uparrow\)). These frequency values are close to the corresponding values for the intensive collective modes observed in the reflection spectra of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\) and YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\)[26] when the electric field \(E\) of radiation is parallel to the \(c\)-axis of the crystals. The highly doped YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\) material contains an intensive optical phonon mode at 4.65 THz (the sixth column), which splits into two modes at 4.59 THz and 4.41 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\) with reduced oxygen content (the fifth column). The 4.59 THz mode is more intensive than the mode at 4.41 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\), but with further oxygen reduction, the 4.41 THz mode dominates in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.7}\) (the fourth column), and additional splitting appears at 4.08 THz. Thus, the observed frequency shift (4.59 THz to 4.62 THz) in the feature on the \(I\)-\(V\) curve after annealing can be ascribed to the transformation of some parts of the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) material near the bicrystal boundary from YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\) to near YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\).