###### Abstract
Table 1 summarizes selected studies on the dry etch rates of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N:  
Compared to dry etching, wet etching can be rather advantageous owing to its less expensive tooling. Common etchants include tetramethylammonium hydroxide (TMAH) [19; 20; 21], phosphoric acid (H\({}_{3}\)PO\({}_{4}\)) [22; 23] or phosphoric acid-based solution [21] (PWS, containing 80% H\({}_{3}\)PO\({}_{4}\), 16% H\({}_{2}\)O and 4% HNO\({}_{3}\)), potassium hydroxide (KOH) [22; 24; 25] and AZ400K Developer (contain 10 wt% of KOH) [26]. Among them, we found KOH to be rather attractive due to its availability and non-toxicity with a relatively high etch rate and high etch selectivity to silicon nitride (SiN\({}_{x}\)). The current research focusing on AlN etching in KOH is abundant, yet very few details were disclosed regarding the etching of Al\({}_{1-x}\)Sc\({}_{x}\)N, let alone a complete survey of its etch rate as a function of Sc alloying. For the data available, the etch rate varies substantially based on the temperature, crystallinity and etchant concentration. Table 2 summarizes previous studies on the etch rates of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N in aqueous KOH. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Material** & **Crystallinity** & **Echant Flow (sccm)** & **ICP/RF Power (W)** & **Pressure (m Torr)** & **Ech Rate (nm s\({}^{-1}\))** & **Rate to AlN** & **Ref.** \\ \hline AlN & & \begin{tabular}{c} BCl\({}_{3}\)/Cl\({}_{2}\)/Ar \\ (10/14/6) \\ \end{tabular} & 800/NA & 5 & 420 & 1.00 & [12] \\ Al\({}_{0.85}\)Sc\({}_{0.15}\)N & \begin{tabular}{c} BCl\({}_{3}\)/Cl\({}_{2}\)/He \\ (30/90/100) \\ \end{tabular} & 550/150 & NA & 160 & 0.64 & [13] \\ Al\({}_{0.73}\)Sc\({}_{0.27}\)N & \begin{tabular}{c} SiCI\({}_{4}\) \\ (NA) \\ \end{tabular} & 150/225 & 15 & 10 & 0.42 & [14] \\ Al\({}_{0.64}\)Sc\({}_{0.36}\)N & \begin{tabular}{c} BCl\({}_{3}\)/Cl\({}_{2}\)/Ar \\ (30/90/70) \\ \end{tabular} & 400/120 & NA & 30 & 0.10 & [15] \\ \hline AlN & \begin{tabular}{c} Single \\ Crystal \\ \end{tabular} & \begin{tabular}{c} BCl\({}_{3}\)/Cl\({}_{2}\)/Ar \\ (10/20/10) \\ \end{tabular} & 200/50 & 5 & 86.0 & 1.00 & \\ Al\({}_{0.84}\)Sc\({}_{0.16}\)N & \
\begin{tabular}{c} Cryst \\ \end{tabular} &
\begin{tabular}{c} BCl\({}_{3}\)/Cl\({}_{2}\)/Ar \\ (10/20/10) \\ \end{tabular} & 200/50 & 5 & 13.3 & 0.15 & [16] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Published dry etch rates of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N in ICP-RIE. The lack of variable control and the limited data make it difficult to draw solid conclusions on the factors affecting the etch rate, though from the AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N dry etch results and the KOH wet etch of its III-V alloy \(\text{kin Al}_{1-x}\text{In}_{x}\text{N}\)[27]/Al\({}_{1-x}\)Ga\({}_{x}\)N [29], one would assume that the etch rate decreases with the increasing Sc concentration. Moreover, even though prior etching studies reported the anisotropic nature of the etch, with preferential etching of the c-plane \(\left\{000\overline{1}\right\}\) in N-polar AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N [28; 29] while exposing the \(\left\{10\overline{1}\right\}\) planes [31] from whose boundary the sidewall that follows is the \(\left\{\overline{12}\overline{1}\overline{2}\right\}\) of the hexagonal crystal structure, lateral etch rates have not been reported. To date, there have been but a few papers [32; 33] discussing KOH etching of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N in detail, and only AlN and Al\({}_{0.80}\)Sc\({}_{0.20}\)N were studied. Therefore, we report a thorough survey on the vertical and lateral etch rates of sputtered AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N in aqueous KOH solutions vs. scandium concentrations, where the KOH concentrations and solution temperatures were strictly regulated. We found that the vertical etch rate declines steadily with increasing scandium concentration, whereas the lateral etch rate experiences a V-shaped transition with a minimum value of 0.043 \(\pm\) 0.002 nm/s at x = 0.125.