## 3 Results and Discussion
### Structural Characterization of the Ga\({}_{2}\)O\({}_{3}\)-Shell
As shown on Figure 4, the peak of GaN (11-20) is very sharp, indicating uniform crystal parameter of GaN synthesized by PA-MBE. By contrast, the Ga\({}_{2}\)O\({}_{3}\) (020) peak is quite broad and slightly shifted towards higher degrees. To explain these observations, we have to consider two phenomena: (1) due to the stress undergone from GaN and/or due to the possible presence of defects at the GaN/Ga\({}_{2}\)O\({}_{3}\) interface, the crystal parameters of Ga\({}_{2}\)O\({}_{3}\) are varied in whole oxide shell. The variation of crystal parameters leads to the variation of 2 ThetaChi, causing the wide peak in XRD spectrum. (2) If we finely \begin{table}
\begin{tabular}{c c c c c} \hline  & **Si (220) 1** & **GaN (11-20)** & **Ga\({}_{2}\)O\({}_{3}\) (020)** & **Ga\({}_{2}\)O\({}_{3}\) (403)** \\ \hline T = 900 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/1.3, Time = 7 & 47.3516\({}^{\circ}\) & 57.8236\({}^{\circ}\) & 61.0465\({}^{\circ}\) & 64.6155\({}^{\circ}\) \\ min, Shell thickness = 6.9 & & & & \\ T = 850 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/1.3, Time = 15 & 47.3277\({}^{\circ}\) & 57.8005\({}^{\circ}\) & 61.0825\({}^{\circ}\) & 64.0635\({}^{\circ}\) \\ min, Shell thickness = 6.5 & & & & \\ T = 850 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/0.8, Time = 15 & 47.3262\({}^{\circ}\) & 57.8005\({}^{\circ}\) & 61.0400\({}^{\circ}\) & 64.4000\({}^{\circ}\) \\ min, Shell thickness = 8.1 & & & & \\ Pure GaN NWs & 47.3211\({}^{\circ}\) & 57.7507\({}^{\circ}\) & & \\ Theory 2 ThetaChi & 47.3010\({}^{\circ}\) & 57.7742\({}^{\circ}\) & 60.8969\({}^{\circ}\) & 64.6319\({}^{\circ}\) \\ \hline \end{tabular}  
* Because the crystal parameters remain unchanged after oxidation process, the Si peak is considered to compare values of GaN and Ga\({}_{2}\)O\({}_{3}\) in the different samples.  
\end{table} 
Table 2: Peak positions for three different samples before and after dry oxidation. \begin{table}
\begin{tabular}{c c c c} \hline  & **a of Si** & **a of GaN** & **b of Ga\({}_{2}\)O\({}_{3}\)** \\ \hline T = 900 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/1.3, Time = 7 min, Shell thickness = 6.9 & 5.426 Å & 3.186 Å & 3.033 Å \\ T = 850 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/1.3, Time = 15 min, Shell thickness = 6.5 & 5.428 Å & 3.188 Å & 3.031 Å \\ T = 850 \({}^{\circ}\)C, N\({}_{2}\)/O\({}_{2}\) = 5/0.8, Time = 15 min, Shell thickness = 8.1 & 5.428 Å & 3.188 Å & 3.034 Å \\ Pure GaN NWs & 5.429 Å & 3.190 Å & \\ Theory parameter & 5.431 Å & 3.189 Å & 3.040 Å \\ \hline \end{tabular}  
* As shown on Figure 4, the peak of GaN (11-20) is very sharp, indicating uniform crystal parameter of GaN synthesized by PA-MBE. By contrast, the Ga\({}_{2}\)O\({}_{3}\) (020) peak is quite broad and slightly shifted towards higher degrees. To explain these observations, we have to consider two phenomena: (1) due to the stress undergone from GaN and/or due to the possible presence of defects at the GaN/Ga\({}_{2}\)O\({}_{3}\) interface, the crystal parameters of Ga\({}_{2}\)O\({}_{3}\) are varied in whole oxide shell. The variation of crystal parameters leads to the variation of 2 ThetaChi, causing the wide peak in XRD spectrum. (2) If we finely  
\end{table} 
Table 3: Parameters of crystals extracted from XRD measurements. analyze the reference XRD spectrum of \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) (Figure 4b), we can note the presence, very close to the Ga\({}_{2}\)O\({}_{3}\) (020) peak, of the Ga\({}_{2}\)O\({}_{3}\) (710) peak, with an estimated (from theoretical parameter) 2 ThetaChi of 62.6294\({}^{\circ}\). The widening of the Ga\({}_{2}\)O\({}_{3}\) (020) and Ga\({}_{2}\)O\({}_{3}\) (710) peaks due to the non-homogeneous crystallinity of the shell can lead to their overlap, then resulting in the appearance, on the XRD spectrum, of a unique Ga\({}_{2}\)O\({}_{3}\) (020) broad peak slightly shifted with respect to the peak theoretical position. XRD analyses evidence that the thermal treatment of MBE-grown GaN NWs leads to the formation of oxide-shell with \(\beta\)-Ga\({}_{2}\)O\({}_{3}\) crystalline phase.