# Influence of Contacts and Applied Voltage on a Structure of a Single GaN Nanowire
## 4 Discussion  
To analyze the bending effect of the GaN NWs, a model of such bending was developed based on our pervious results (see Ref. [22]). A scheme of the intensity distribution in reciprocal space is shown in Figure 7a. It explains relation between the bending angle \(\theta=\arctan(q/|\mathbf{H}_{1010}|)\) of the NW and the elongation \(q\) of the gap between two star-like Bragg peaks with the known length of the scattering vector \(\mathbf{H}_{1010}\). To relate this bending angle with the split of the Bragg peak observed in the experiment and caused by this bending, we performed finite element method (FEM) simulations [25]. The lattice constants were considered to be \(a_{GaN}=3.189\) A, \(c_{GaN}=5.178\) A for the wurzite GaN crystal [26]. Since the GaN has a transversely isotropic structure of the unit cell, the full stiffness matrix is given by five independent components. The elasticity constants \(C_{ij}\) of the GaN used in the model were the following: \(C_{11}\)=374 GPa, \(C_{12}=138\) GPa, \(C_{13}=101\) GPa, \(C_{33}=395\) GPa, \(C_{44}=98\) GPa [27]. The equilibrium shape of the NW used in FEM simulations is shown in Figure 7b. The incident Gaussian beam profile with one micrometer full width at half maximum (FWHM) and 3D displacement field from the FEM model were used to simulate the intensity distribution in reciprocal space, which was compared with the experimental one. Varying displacement field in the model, the best correspondence between the angular distance of the Bragg peaks in the model simulations and experimental data were determined. For the free-lying NW with the diameter of 200 nm, an average bending angle of 0.45 degrees was calculated from the distance \(q\) between two peaks in reciprocal space (see Figure 4c,d) that, according to FEM modelling, corresponds to the maximum tensile strength in the NW of about \(3.4\times 10^{8}\) Pa. The bending angle of the contacted 350 nm GaN NWs was found to be 0.28 degrees and corresponds to \(2\times 10^{8}\) Pa tensile strength obtained from the FEM model. In our  
Figure 7: **(a)** Scheme of reciprocal space X-ray intensity distribution formation. **(b)** 3D FEM model of the bent GaN NW. The color scale bar gives values of the tensile strength obtained in this model. **(c)** Bending angle \(\theta\) of the NW with the size of 350 nm as a function of the applied voltage bias. **(d)** Maximum tensile strength in the NW under voltage bias. The stress in the NW is increased from \(2\times 10^{8}\) Pa up to the ultimate tensile strength of \(6\times 10^{8}\) Pa, at which the NW was broken. previous experiment, the GaN NW was bent to 0.4 degrees after the Au contacts deposition with the tensile strength of 3 \(\times\) 10\({}^{8}\) Pa, which supports the current findings. For the second type of Au contacts shown in Figure 5c we determined the angle of 0.29 degrees that corresponds to the tensile strength of \(2.1\times 10^{8}\) Pa. Dependence of the bending angle \(\theta\) between the two peaks of the 10\(\bar{1}\)0 GaN Bragg reflection for the GaN NW under operando conditions is given in Figure 7c as a function of the voltage bias. From the FEM simulations, the maximum tensile strength value of the most top part of the nanowire was obtained for different bending angles measured in the experiment. Dependence of this tensile strength as a function of applied voltage bias is presented in Figure 7d. The strain in the GaN NW increased from \(2\times 10^{8}\) Pa up to \(6\times 10^{8}\) Pa, at which the nanostructure was broken. In general, the strain values are in a good agreement with the dependence observed in our previous study, but the voltage values corresponding to the same bending angles are five times smaller. We attribute this discrepancy to the different geometric parameters of the contacts, which were thicker this time and had different overlap with the NWs.