## 4 Results and Discussion
### Influence of Annealing Temperature  
To estimate the influence of annealing temperature on the HSQ-NW mechanical properties, a set of samples with _\"pyramidal\"_ NW morphology similar to Figure 5 and different annealing temperatures (300 \({}^{\circ}\)C, 400 \({}^{\circ}\)C and 500 \({}^{\circ}\)C) has been fabricated and experimentally studied. These three samples have been grown at different growth runs, therefore they exhibit some variation of NW density and of the rough layer. To assure a comparability of the HSQ-NW parameters, we have prescribed the thicknesses of the sublayers based on the scan in Figure 5a: \(h_{1}=150\,\mathrm{nm}\), \(h_{2,1}=350\,\mathrm{nm}\), \(h_{2,2}=550\,\mathrm{nm}\) (\(M=4\)). The first layer is thicker than the CrPt coating itself (\(\approx\)25-30 nm). It includes a zone of surface roughness and a bit of a HSQ-NW top part. Therefore, in the course of minimization, its parameters were also variable except the prescribed \(h_{1}=150\,\mathrm{nm}\). This explains why the obtained Young moduli of the coating layer are different in different samples.  
The results are summarised in Table 4; the corresponding slowness dispersion curves and the experimental points are shown in Figure 11.  
It is known that the material hardness of HSQ polymer increases with the annealing temperature [24]. Therefore, one would expect to observe an increase of Young moduli between samples annealed at 300 \({}^{\circ}\)C, 400 \({}^{\circ}\)C and 500 \({}^{\circ}\)C. However, the obtained dependence of the effective  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline  & \(\mathbf{C_{11}}\) & \(\mathbf{C_{33}}\) & \(\mathbf{C_{13}}\) & \(\mathbf{C_{44}}\) & \(\mathbf{C_{66}}\) & \(\rho\) & \(\mathbf{h}\) & \(\mathbf{E_{x}}\) & \(\mathbf{E_{z}}\) & \(\mathbf{\mu_{z}}\) & \(\mathbf{\
u_{x}}\) & \(\mathbf{\
u_{z}}\) \\ \hline \(t=300\)\({}^{\circ}\)C & & & & & & & & & & & & \\ CrPt & 490 & 490 & 366 & 61.7 & 61.7 & 20.6 & 150 & 176 & 176 & 61.7 & 0.48 & 0.48 \\
2.1 & 54.4 & 70.6 & 14.9 & 3.05 & 17.0 & 3.25 & 350 & 45.5 & 64.7 & 3.05 & 0.34 & 0.20 \\
2.2 & 39.2 & 90.9 & 4.14 & 150 & 19.1 & 3.05 & 550 & 39.0 & 90.0 & 150 & 0.02 & 0.10 \\ \hline \(t=400\)\({}^{\circ}\)C & & & & & & & & & & & & \\ CrPt & 357 & 357 & 230 & 63.7 & 63.7 & 19.0 & 150 & 177 & 177 & 63.7 & 0.39 & 0.39 \\
2.1 & 47.7 & 80.8 & 5.94 & 3.18 & 18.9 & 3.21 & 350 & 45.4 & 79.5 & 3.18 & 0.20 & 0.10 \\
2.2 & 97.1 & 111 & 16.8 & 442 & 39.3 & 2.77 & 550 & 91.9 & 106 & 442 & 0.17 & 0.15 \\ \hline \(t=500\)\({}^{\circ}\)C & & & & & & & & & & & & \\ CrPt & 335 & 335 & 184 & 75.1 & 75.1 & 13.9 & 150 & 204 & 204 & 75.1 & 0.36 & 0.36 \\
2.1 & 50.1 & 56.3 & 29.3 & 17.3 & 11.1 & 2.88 & 350 & 30.1 & 33.3 & 17.3 & 0.36 & 0.38 \\
2.2 & 56.2 & 73.7 & 6.66 & 1504 & 27.5 & 1.48 & 550 & 55.7 & 72.1 & 1504 & 0.01 & 0.12 \\ \hline \end{tabular}
\end{table}
Table 4: Effective parameters of the samples with the same NW _\"pyramidal\"_ morphology (Figure 5a) fabricated with different annealing temperatures \(t\), 4-layer model, fixed \(h_{1}=150\), \(h_{2}=350\), and \(h_{3}=550\,\mathrm{[nm]}\).  
Figure 10: Dispersion curves calculated for the sample shown in Figure 2 within (**a**) \(M=3\) and (**b**) \(M=4\) models with the effective parameters from Table 3.  
HSQ-NW constants is not monotone. We attribute this discrepancy to the variation of the NW morphology between the three samples. Indeed, the Young modulus on GaN is much lager than the one on HSQ. Therefore, a small variation of the NW density produces a stronger effect than the variation of the HSQ parameters with annealing. Nevertheless, it is seen in Figure 11 that the dispersion curves smoothly transform with the annealing temperature, which allows to trace the variation of the behavior of guided waves in such composite structures.