## 3 Results and Discussion
### Ga\({}_{2}\)O\({}_{3}\)-Shell Thickness Evolution and Formation
As the oxidation duration is important, as the oxide thickness increases. This process is also temperature dependent, as experimentally observed (Figure 2c). The increase of the oxidation rate with the temperature results from the increase of the O\({}_{2}\) sticking probability attributed to a higher activation energy for O\({}_{2}\) dissociation [54; 58]. In an oxidation diffusion-controlled regime, the oxidation process is controlled by the reagent transport through the growing gallium oxide layer. The oxidation kinetic can thus be described by a parabolic  
Figure 2: (a) Gaussian distribution of the NW diameter before and after oxidation, during 10 min and 15 min under a dry atmosphere at 850 \({}^{\circ}\)C for 1.3 sccm of O\({}_{2}\) and 5 sccm of N\({}_{2}\). The diameter expansion is schematized with dashed lines; (b) Schematization of the NW expansion; (c) NW diameter expansion as a function of the oxidation time for 1.3 sccm of O\({}_{2}\) and 5 sccm of N\({}_{2}\), for different temperatures and atmospheres; (d) NW diameter expansion as a function of the O\({}_{2}\) flux for a fixed temperature of 850 \({}^{\circ}\)C, a N\({}_{2}\) flux of 5 sccm, an oxidation time of 15 min and under dry atmosphere. model [57]. Although this regime is note observed for oxidation at 900 \({}^{\circ}\)C (green curve), we can assume an under-linear thickening of the shell for higher oxidation times. Figure 2c also presents the diameter expansion as a function of the time for the same oxidation conditions (T = 900 \({}^{\circ}\)C, O\({}_{2}\) = 1.3 sccm, N\({}_{2}\) = 5 sccm), but for different atmospheres, i.e., under dry (green curve) and wet (orange curve) thermal oxidation conditions. We can clearly show that the diameter expansion of oxidized NWs is more important under wet atmosphere. In other words, under wet atmosphere, the oxidation rate is much pronounced in comparison with the one occurring under dry atmosphere. This result points to the importance of the oxidation atmosphere composition on the GaN oxidation process. To understand the mechanisms in play, we need to take into account the different physical and chemical processes occurring during the oxidation step. In this experiment (Figure 2c), the oxidation being carried out at the same temperature of 900 \({}^{\circ}\)C and with equivalent oxygen flow, we can assume that the gas diffusion rate in the gas phase and at the gas/oxide interface are constant and do not influence the GaN oxidation. However, by regarding the atmosphere composition, the surface processes (chemisorption, decomposition and diffusion through the oxide layer) are not equivalent. Once chemisorbed at the NW surface, the reactive species are decomposed with the following equations:  
\[\text{Under dry environment: 4 GaN}_{(8)}+3\text{O}_{2(8)}\to 2\text{ Ga}_{2}\text{O}_{3(8)}+4\text{N}_{2(8)} \tag{1}\]  
\[\text{Under wet environment: 2 GaN}_{(8)}+3\text{H}_{2}\text{O}_{(8)}\to 2\text{ Ga}_{2}\text{O}_{3(8)}+2\text{N}_{2(8)}+3\text{H}_{2(8)} \tag{2}\]  
The species migrating at the surface, at the metal-oxide interface, and through the oxide layer are ionic species. Under a dry environment, the chemisorbed oxygen is dissociated to an ionic O\({}^{2-}\). Under wet environment, the oxygen coming from the chemisorbed H\({}_{2}\)O is dissociated to an ionic form of OH\({}^{-}\). After the formation of the first oxide layer covering the GaN-core NW (Figure 3a,c), the active species must to diffuse through the oxide film in order to form the Ga\({}_{2}\)O\({}_{3}\). The diffusion rate of O\({}^{2-}\) and OH\({}^{-}\) through the oxide layer being more efficient that the one of metallic ionic species (Ga\({}^{2+}\)) [54; 57; 59], the diffusion process is controlled by the oxygen-based active species. Thus, the O\({}^{2-}\) and OH\({}^{-}\) are diffusing through the oxide layer and are combined with the Ga\({}^{2+}\) species diffusing at the metal-oxide interface to form the Ga\({}_{2}\)O\({}_{3}\)-shell (Figure 3b,d).