  Using low-temperature cathodoluminescence spectroscopy, we study the
properties of N- and Al-polar AlN layers grown by molecular beam epitaxy on
bulk AlN{0001}. Compared to the bulk AlN substrate, layers of both polarities
feature a suppression of deep-level luminescence, a total absence of the
prevalent donor with an exciton binding energy of 28 meV, and a much increased
intensity of the emission from free excitons. The dominant donor in these
layers is characterized by an associated exciton binding energy of 13 meV. The
observation of excited exciton states up to the exciton continuum allows us to
directly extract the $\Gamma_{5}$ free exciton binding energy of 57 meV.
