  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.
