  Motivated by a recent experiment that reported the successful synthesis of
hexagonal (h) AlN [Tsipas et al. Appl. Phys. Lett. 103, 251605 (2013)] we
investigate structural, electronic and vibrational properties of bulk, bilayer
and monolayer structures of h-AlN by using first-principles calculations. We
show that the hexagonal phase of the bulk h-AlN is a stable direct-bandgap
semiconductor. Calculated phonon spectrum displays a rigid-layer shear mode at
274 cm-1 and an Eg mode at 703 cm-1 which are observable by Raman measurements.
In addition, single layer h-AlN is an indirect-bandgap semiconductor with a
nonmagnetic ground state. For the bilayer structure, AA' type stacking is found
to be the most favorable one and interlayer interaction is strong. While
N-layered h-AlN is an indirect bandgap semiconductor for N=1-10, we predict
that thicker structures (N>10) have a direct-bandgap at the Gamma-point. The
number-of-layer-dependent bandgap transitions in h-AlN is interesting in that
it is significantly different from the indirect-to- direct crossover obtained
in the transition metal dichalcogenides.
