## 2 Experiment  
### Film Deposition  
#### 2.1.1 Growth  
Based on the crystallinity of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N, several methods can be used for film growth. Single-crystal AlN can be grown via physical vapor transport (PVT) on substrates up to 60 mm in diameter [34; 35; 36]. Single-crystal Al\({}_{1-x}\)Sc\({}_{x}\)N can be grown by molecular beam epitaxy (MBE) [9] on 100 mm wafers [37] with scandium concentration x from 0.06 to 0.36 [38]. The growth of Sc alloyed AlN via metal-organic chemical vapor deposition \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Crystallinity** & **Etchant** & **Temp (\({}^{\circ}\)C)** & **Etch Rate** & **Activation** & **Rate at 45 \({}^{\circ}\)C** & **Ref.** \\  & & & **(nm\(\cdot\)s\({}^{-1}\))** & **Energy** & **(kcal\(-\)mol\({}^{-1}\))** & **(nm\(\cdot\)s\({}^{-1}\))** & **Ref.** \\ \hline \multirow{6}{*}{AlN} & Single Crystal & AZ400K & 60 & 1.1 & 15.13 & 0.8 & [26] \\  & Single Crystal & & & & & \\  & (with high defect & AZ400K & 60 & 25.1 & 15.24 & 10.3 & \\  & density) & & & & & \\ \cline{2-6}  & \multirow{2}{*}{Polycrystal} & AZ400K & 32 & 185.0 & 15.65 & 561.40 & [26] \\  & & AZ400K & 40 & 92.20 & 2.0 \(\pm\) 0.5 & 107.93 & [27] \\  & & 45 wt\% KOH & 60 & 5.83 & NA & 1.89 & [28] \\  & & 1 wt\% KOH & 70 & 8.33 & NA & 1.34 & [29] \\ \hline \multirow{3}{*}{Al\({}_{0.80}\)Sc\({}_{0.20}\)N} & \multirow{3}{*}{Polycrystal} & 25 wt\% KOH & RT & 0.66 & \multirow{3}{*}{15.85} & \multirow{3}{*}{3.59} & [25] \\  & & 25 wt\% KOH & 40 & 2.38 & & & \\ \cline{1-1} \cline{5-5} Al\({}_{0.64}\)Sc\({}_{0.36}\)N & & 25 wt\% KOH & 80 & 33.33 & NA & 2.77 & [23] \\ \cline{1-1} \cline{5-5} Al\({}_{0.63}\)Sc\({}_{0.37}\)N & & 20 wt\% KOH & 20 & 0.42 & NA & 3.56 & [30] \\ \hline \hline \end{tabular} Note: For comparison, the etch rates were converted to 45 \({}^{\circ}\)C with activation energy \(E_{a}\) given by the author, or assuming \(E_{a}\) = 15.85 kcal/mol if data were unavailable.  
\end{table} 
Table 2: Published vertical etch rates of AlN/Al\({}_{1-x}\)Sc\({}_{x}\)N in aqueous KOH solutions. (MOCVD) had suffered from the lack of Sc precursors [39]; however, research in this field is catching up quickly, and the ability to grow 36% Sc alloyed Al\({}_{1-x}\)Sc\({}_{x}\)N films on 100 mm wafers has been demonstrated [40; 41]. High-quality polycrystalline Al\({}_{1-x}\)Sc\({}_{x}\)N films can be deposited with physical vapor deposition (PVD) methods such as magnetron sputtering. This method features a high deposition rate, low growth temperature, and the capability of up-scaling in substrate size [42; 43; 44; 45; 46], and has been adopted by a variety of tool manufacturers for industrial mass production [47]. Al\({}_{1-x}\)Sc\({}_{x}\)N depositions were performed in an Evatec CLUSTERLINE(r) 200 II Physical Vapor Deposition System (Evatec AG, Trubbach, Switzerland) at a substrate temperature of 350 \({}^{\circ}\)C with 150 kHz pulsed DC bias with an 88% duty cycle. No RF substrate bias was applied and the AlScN materials were deposited directly onto silicon substrates. No pre-cleans were applied to the substrates. Two 100 mm metal targets were used, Al (99.999%) and Sc (99.99%), with a target-to-substrate distance of 88.5 mm. Before deposition, the chamber was pumped to a base pressure lower than 1.0 \(\times\) 10\({}^{-7}\) mbar. A 15 nm AlN film was deposited first onto a 100 mm Si (100) wafer as the seed layer by sputtering Al in a pure nitrogen environment with a target power of 1000 W and N\({}_{2}\) flow of 20 sccm. Subsequently, a 35 nm linearly graded Al\({}_{1-x}\)Sc\({}_{x}\)N layer was deposited by gradually increasing the Sc target power while maintaining the Al target power constant. Finally, a 750 nm bulk Al\({}_{1-x}\)Sc\({}_{x}\)N layer was deposited by fixing both the Al and Sc target powers. The 20 sccm N\({}_{2}\) flow was maintained during the process and no Ar was used throughout. The chamber pressure remained close to 8.0 \(\times\) 10\({}^{-4}\) mbar during the deposition.