  NbN films are grown on c-plane sapphire substrates by molecular beam epitaxy.
The structural and superconducting properties of the film are characterized to
demonstrate that growth parameters such as substrate temperature and active
nitrogen flux effect the structural phase of films, and thereby the
superconducting critical temperature. Four phases of NbN are identified for
films grown in different conditions. In a novel finding, we demonstrate that
atomically flat and highly crystalline $\beta$-$\textrm{Nb}_2\textrm{N}$ films
can be grown at substrate temperatures of 1100 \degree C or higher, and that
the superconducting critical temperature of phase pure
$\beta$-$\textrm{Nb}_2\textrm{N}$ films is $0.35~K<T_c<0.6~K$, based on
measurements of films grown at different substrate temperatures.
