## 3 Results and Analysis
### Etch Result with 30% KOH at 45 \({}^{\circ}\)C

Table 5: Scandium concentration vs. etch time (long etch in 30% KOH at 45 \({}^{\circ}\)C). The long etch time returned similar results compared with the short etch time. The etch rate experienced a transition where it reaches the lowest at x = 0.125. However, discrepancies still exist for the etch rates of x = 0.28, 0.30, 0.34 and 0.38 when compared to other films with Sc concentration x > 0.125. One explanation might be that these films were deposited in different batches as opposed to the rest of the films. As stated above, what exhibits as different etch rates here might be the result of the different chamber condition when the films were being sputtered. It was apparent that even though they do not fit in the line made from the x = 0.125, 0.15, 0.20, 0.25, 0.32 and 0.36 films, they were able to constitute their own trend line with almost has the same slope. Deeper examination revealed that the etch rate of the x = 0.28 film was lower than expected on two different films deposited in different batches, and further studies should be carried out to better understand these subtle trends in lateral etch rate. For most Sc concentrations, the sidewall angle of films remains invariant throughout the etching. As demonstrated in Figure 7, an extra-long submerge of the sample does not change the sidewall angle by a visible amount, and for the changes that could be measured, it can be attributed to the tilting of the sample itself during imaging. The sidewall is a reflection of the crystal structure of the Al\({}_{1-x}\)Sc\({}_{x}\)N films. As per the findings of [PERSON]. [PERSON] et al., due to the energy difference between crystalline planes, the c-plane \(\left\{000\overline{1}\right\}\) will be etched first prior to the deterioration of the \(\left\{10\overline{11}\right\}\) planes [31]. Hence, during the anisotropic etching process, the exposed \(\left\langle\overline{112}3\right\rangle\) slip edges between the boundary of the \(\left\{1\overline{011}\right\}\) planes forms the facets that follow the \(\left\{\overline{121}\overline{2}\right\}\) of the hexagonal crystal structure, behind which lateral etching ceases advancing (Figure 8). Figure 6: (a). Lateral etch length with respect to etch time of Al\({}_{0.64}\)Sc\({}_{0.36}\)N in 30% KOH at 45 \({}^{\circ}\)C. (b) Lateral etch rate of Al\({}_{1-x}\)Sc\({}_{x}\)N in 30% KOH at 45 \({}^{\circ}\)C (long etch time). Figure 7: (**a**) \(\rm Al_{0.90}Sc_{0.10}N\) etched for 20 s; (**b**) \(\rm Al_{0.75}Sc_{0.25}N\) etched for 60 s; (**c**) \(\rm Al_{0.64}Sc_{0.36}N\) etched for 80 s; (**d**) \(\rm Al_{0.90}Sc_{0.10}N\) etched for 10 min; (**e**) \(\rm Al_{0.75}Sc_{0.25}N\) etched for 5 min; (**f**) \(\rm Al_{0.64}Sc_{0.36}N\) etched for 20 min. All etching was performed in 30 wt% KOH at 45 \({}^{\circ}\)C. The sidewall angle is preserved after the long etch. Moreover, for a Hexagonal Close-Packed (HCP) unit cell with an axis length \(c/a\), the sidewall angle, \(\theta\) (Figure 9), of the \(\left\{\overline{1212}\right\}\) facets as a function of lattice length can be calculated as \(\theta=\arctan(c/a)\):  
Using the \(c/a\) data from the work presented by [PERSON] et al. (2017), and considering the isotropic etching of the \(\left\{10\overline{11}\right\}\) plane, the theoretical sidewall angle \(\varphi\) can be plotted against the experimental value (Figure 10). Figure 8: (**a**). Exposed \(\left\langle\overline{1}23\right\rangle\) slip edge in an Al\({}_{0.95}\)Sc\({}_{0.05}\)N film etched in 30% KOH at 45 \({}^{\circ}\)C for 10 min; (**b**) the sidewall that follows the \(\left\{\overline{1212}\right\}\) facet created by the boundary between the \(\left\{10\overline{11}\right\}\) planes of the same etch condition for 5 min. Figure 9: Crystal planes in Al\({}_{1-x}\)Sc\({}_{x}\)N HCP lattice. The absolute value of the experimental and theoretical angles follows the same trajectory with a parabolic downtrend with increasing Sc concentration until the Sc concentration exceeds 40%.