## 3 Results and Discussion
### Structural Characterization of the Ga\({}_{2}\)O\({}_{3}\)-Shell  
To study the composition and the crystal structure of the Ga\({}_{2}\)O\({}_{3}\) oxide shell, samples have been characterized by combining XRD, STEM and EDX analyses. Figure 4 shows typical spectra of GaN NWs before oxidation and GaN/Ga\({}_{2}\)O\({}_{3}\) NWs after oxidation, analyzed by XRD using in-plane Phi/2 ThetaChi scan configuration. The spectra performed on as-grown GaN NWs (Figure 4a) shows only two peaks located at 47.3\({}^{\circ}\) and at 57.8\({}^{\circ}\) corresponding respectively to the signals of Si (220) and hexagonal GaN (11-20). By contrast, the spectra of NWs after oxidation (Figure 4c) presents two additional peaks, located at 61.1\({}^{\circ}\) and 64.4\({}^{\circ}\), suggesting the signatures of oxide. According to reports [51; 52], monoclinic \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) phase, the most stable one, appears after similar oxidation processes of GaN. By comparing with the reference XRD spectra of \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) shown in Figure 4b [62], the peak at 61.1\({}^{\circ}\) is attributed to the signal of \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) (020), as confirmed by STEM analyses (presented later), while the one around 64\({}^{\circ}\) is assigned to the signal of \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) (403). Figure 4: XRD analyses using in-plane Phi/2 ThetaChi scan configuration. (**a**) XRD spectra of as-grown GaN NWs before thermal oxidation; (**b**) Reference XRD spectrum of the \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) in report [62] (Used with permission from JCPDS—International Centre for Diffraction Data); (**c**) XRD spectra of GaN/Ga\({}_{2}\)O\({}_{3}\) NWs after oxidation at 900 \({}^{\circ}\)C during 7 min under dry atmosphere with N\({}_{2}\) and O\({}_{2}\) fluxes of 5 sccm and 1.3 sccm, respectively. We note here that only the GaN (11-20) peak appears on Figure 4a,c. The peak of GaN (10-10) at 32.3903\({}^{\circ}\) does not appear, despite it is perpendicular to the sample surface and thus can give signal in XRD in-plane scanning configuration. However, in XRD phi/2 thetachi scanning mode, to observe several signatures in the same spectrum, the planes must be parallel to each other. The (11-20) plane cannot be parallel to the (10-10) one in same NWs as the 1D-nanostructures grown by PA-MBE are monocrystalline with a unique orientation. The missing of GaN (10-10) peak in Figure 4 confirms that NWs are preferentially oriented, as previously demonstrated [46]. The detailed positions of peaks for three different samples before and after dry oxidation are showed in the Table 2. The theoretical values of 2 ThetaChi have been calculated by using theoretical parameters of crystal. The mismatch existing between GaN and Ga\({}_{2}\)O\({}_{3}\) at the core-shell interface induces internal strain and thus affects their parameters as well as values of 2 ThetaChi in XRD spectrum. Due to the specific volume of GaN and Ga\({}_{2}\)O\({}_{3}\), from a theoretical point of view, Ga\({}_{2}\)O\({}_{3}\) should induce stretching in the GaN, and reciprocally, GaN should induce compression on Ga\({}_{2}\)O\({}_{3}\). This strain equilibrium depends on the thickness ratio between the core and the shell. By regarding the thickness of the GaN-core (diameter \(\sim\)40 nm) and of the oxide shell (for thickness \(<\) 10 nm), the main stress expressed in the heterostructure is localized in the shell, as demonstrated by the material crystal parameters extracted from XRD measurements, summarized in the Table 3. The average parameter of GaN-core does not changed while the increase of 2 ThetaChi of Ga\({}_{2}\)O\({}_{3}\) (020) in the Table 2 and the decrease of its parameter b, in Table 3, indicate the presence of a compressive Ga\({}_{2}\)O\({}_{3}\) shell. For the specific case of thick Ga\({}_{2}\)O\({}_{3}\) shell (thickness \(>\) 10 nm), the compressive strain starts to be relaxed. In consequences, this partially relaxed shell induces tensile strain on the GaN-core.