  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.
