## 3 Results and Analysis
### Formation of Vertical Sidewall in Al\({}_{0.875}\)Sc\({}_{0.125}\)N  
While differences can be observed across the spectrum, the lateral etch rate unanimously reaches its lowest point when the Sc concentration is at 12.5%. An inspection of the etch results have shown that during the etching, a more vertical side wall can be formed, as shown in Figure 12.  
Figure 11: (**a**) Lateral etch rate at elevated temperature and lower etchant concentration. (**b**) Sidewall angle at elevated temperature and lower etchant concentration.  
Although (a) was etched with different parameters compared to (b-d)--plus, (b-d) were etched for almost the same time--we conjecture that these images are demonstrating the transient response of the same etching dynamics. The KOH etch is slowed significantly at the Si \(\{111\}\) plane and the Al\({}_{0.875}\)Sc\({}_{0.125}\)N \(\{10\overline{11}\}\) plane due to the low etch rate. Because of the energy differences between removing \(\{10\overline{11}\}\) Al\({}_{0.875}\)Sc\({}_{0.125}\)N and \(\{111\}\) Si, the KOH slowly etches Si \(\{111\}\) until it comes into contact with the Al\({}_{0.875}\)Sc\({}_{0.125}\)N \(\{1\overline{1}00\}\) planes, which requires lower energy to react than the \(\{10\overline{11}\}\) planes. As a result, the etchant begins to remove and simultaneously etch Si \(\{111\}\) and \(\{1\overline{1}00\}\) AlScN. By the time the entire \(\{1\overline{1}00\}\) planes were exposed, a vertical sidewall was formed. It is possible that the slow lateral etch rate is necessary but not sufficient for the exposure of the \(\{1\overline{1}00\}\) AlScN to occur. This has been demonstrated with the lateral etching of Al\({}_{0.85}\)Sc\({}_{0.15}\)N and Al\({}_{0.72}\)Sc\({}_{0.28}\)N, which have slightly higher lateral etch rates than Al\({}_{0.875}\)Sc\({}_{0.125}\)N. As shown below (Figure 13), the etchant may preferentially etch Si \(\{111\}\) instead of m-plane Al\({}_{1-\infty}\)Sc\({}_{\infty}\)N.  
Figure 12: Lateral etch of Al\({}_{0.875}\)Sc\({}_{0.125}\)N in (a) 30% KOH at 45 \({}^{\circ}\)C for 10 min; (b–d) 10% KOH at 65 \({}^{\circ}\)C for 20 min.  
The \(\{\overline{1}\overline{1}00\}\) plane etching has been reported before in single-crystal GaN [57] and Al\({}_{1-x}\)Ga\({}_{x}\)N [58], and as per the findings of [PERSON]. [PERSON] et al. [57], the preference of its etching in GaN is a result of its smaller dangling bond density, which makes it more stable in KOH than the \(\{10\overline{1}\overline{1}\}\) plane. Therefore, one explanation might be that the Al\({}_{0.875}\)Sc\({}_{0.125}\)N film has the highest activation energy in terms of the lateral etching, which was calculated to be 23.14 kcal/mol based on the data available. Nevertheless, this is one of the limited examples where this is reported in sputtered Al\({}_{1-x}\)Sc\({}_{x}\)N, and more research needs to be conducted to reveal the mechanism behind the vertical sidewall formation. This method, combined with BCl\({}_{3}\)/Cl\({}_{2}\) dry etching, could potentially be applied in fabricating vertical side walls using a two-step fabrication process, which will benefit the research and production of LWR, laser mirrors, UV LEDs and a variety of MEMS devices.  
Figure 13: (a) Al\({}_{0.85}\)Sc\({}_{0.15}\)N etched for 20 min in 10 wt% KOH, etch front of AlScN approaching Si \(\{111\}\); (b) KOH preferentially etches Si \(\{111\}\) instead of \(\{\overline{1}\overline{2}\overline{1}\overline{2}\}\) AlScN; (c) Al\({}_{0.72}\)Sc\({}_{0.28}\)N etched for 20 min in 10 wt% KOH, etch front of AlScN aligned with Si \(\{111\}\); (d) KOH preferential etching of Si \(\{111\}\) instead of \(\{\overline{1}\overline{2}\overline{1}\overline{2}\}\) AlScN. All etches were performed at 60 \({}^{\circ}\)C.