AlN epitaxial layers in a thickness range of 0.065 to 0.6 microns have been grown on double-side polished c-plane sapphire by molecular beam epitaxy (MBE) using either RF nitrogen or ammonia as the nitrogen source. The samples were characterized by XRD, room temperature (RT) and low temperature (2K) optical absorption (transmission) measurements. The XRD (0002) peak FWHM diminishes from 380 arcsec to 84 arcsec when the thickness of the AlN films is increased from 65 nm towards 0.6 μm. All the samples grown with ammonia (NH3), representing N-rich conditions, exhibited optical bandgap exceeding 6 eV at RT. For samples grown with RF nitrogen source, we find that higher nitrogen flow (partial pressure of 8.3-9.4 × 10-5 Torr) results in optical bandgap values larger than 6.0 eV, regardless of the XRD results. The bandgap is found to be smaller than 6.0 eV for the samples grown with lower nitrogen partial pressure (1.0-3.5 x 10-5 Torr), regardless of sample thickness and the XRD data.