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We investigate the synthesis of 340-nm-thick Sc$_x$Al$_{1-x}$N layers with $0 \leq x \leq 0.35$ on AlN-buffered Si(111) by plasma-assisted molecular beam epitaxy. We employ an AlN nucleation layer under conditions giving rise to single-domain N-polar [(000$\bar{1}$)-oriented] layers, as demonstrated by the ($3 \times 3$) pattern observed in reflection high-energy electron diffraction and confirmed by KOH etching. The subsequent growth of pure wurtzite Sc$_x$Al$_{1-x}$N layers with $x \leq 0.1$ is feasible at temperatures $\leq$ 740{\deg}C. However, layers with $x \geq 0.2$ grown at 740{\deg}C develop cracks due the high thermal mismatch between Sc$_x$Al$_{1-x}$N and Si. Lowering the growth temperature to 500{\deg}C not only prevents cracking but also improves the crystallinity of the layers. For Sc$_{0.3}$Al$_{0.7}$N layers grown at 500{\deg}C, additional x-ray reflections due to intermetallic AlSc and Al$_3$Sc inclusions are observed. The formation of these compounds can be inhibited by lowering the temperature further to 300{\deg}C.

We investigate the electrical properties of nominally undoped, 10-40-nm-thick ScN(111) layers grown on nearly lattice-matched GaN:Fe/Al$_2$O$_3$(0001) templates by plasma-assisted molecular beam epitaxy. Hall-effect measurements yield electron concentrations of 0.7-3.1$\times 10^{19}$ $\text{cm}^{-3}$ and mobilities of 50-160 cm$^{2}$V$^{-1}$s$^{-1}$ at room temperature. The temperature-dependent (4-360 K) conductivity exhibits two distinct regimes, suggesting two-band conduction in an impurity band and the conduction band. Assuming a single shallow donor in ScN and employing the standard two-band conduction model, we extract the carrier density and mobility in these bands. The results reveal nondegenerate characteristics for the 40-nm-thick layer, while the thinner layers are weakly degenerate. For the nondegenerate layer, the donor ionization energy amounts to approximately 12 meV. The electron mobility of the layers is limited by ionized impurity scattering and phonon scattering at low and high temperatures, respectively. Fits with an expression for optical phonon scattering developed for weakly degenerate semiconductors return an effective phonon energy of $(61 \pm 5)$ meV, in between the energies of the longitudinal optical ($\approx 84$ meV) and transverse optical ($\approx 45$ meV) phonon modes in ScN.

An accurate knowledge of the optical constants (refractive index $n$ and extinction coefficient $k$) of ScN is crucial for understanding the optical properties of this binary nitride semiconductor as well as for its use in optoelectronic applications. Using spectroscopic ellipsometry in a spectral range from far infrared to far ultraviolet (0.045-8.5 eV), we determine $n$ and $k$ of ScN layers grown on Al$_{2}$O$_{3}$(0001) substrates by plasma-assisted molecular beam epitaxy. Fits of ellipsometry data return the energies of four oscillators representing critical points in the band structure of ScN, namely, 2.03, 3.89, 5.33, and 6.95 eV. As the infrared range is dominated by free carriers, the vibrational properties of the layers are examined by Raman spectroscopy. Despite the rocksalt structure of ScN, several first-order phonon modes are observed, suggesting a high density of point defects consistent with the high electron density deduced from Hall measurements. Finally, photoluminescence measurements reveal an emission band slightly above the lowest direct bandgap. We attribute the redshift of the peak emission energy from 2.3 to 2.2 eV with increasing layer thickness to a reduction of the O concentration in the layers.

An accurate knowledge of the lattice parameters of the new nitride Sc$_\textit{x}$Al$_\textit{1-x}$N is essential for understanding the elastic and piezoelectric properties of this compound as well as for the ability to engineer its strain state in heterostructures. Using high-resolution x-ray diffractometry, we determine the lattice parameters of 100-nm-thick undoped Sc$_\textit{x}$Al$_\textit{1-x}$N layers grown on GaN(0001) templates by plasma-assisted molecular beam epitaxy. The Sc content $\textit{x}$ of the layers is measured independently by both x-ray photoelectron spectroscopy and energy-dispersive x-ray spectroscopy and ranges from 0 to 0.25. The in-plane lattice parameter of the layers linearly increases with increasing $\textit{x}$, while their out-of-plane lattice parameter remains constant. Layers with $\textit{x}$ $\approx$ 0.09 are found to be lattice matched to GaN, resulting in a smooth surface and a structural perfection equivalent to that of the GaN underlayer. In addition, a two-dimensional electron gas is induced at the Sc$_\textit{x}$Al$_\textit{1-x}$N/GaN heterointerface, with the highest sheet electron density and mobility observed for lattice-matched conditions.