AlN constitutes the buffer layer of choice for the growth of GaN on all common substrates and its crystalline quality and surface morphology determine many of the properties of the overgrown epitaxial structure. This work systematically investigates the MOMBE growth of high quality AlN on Si (111) using trimethylaluminum and ammonia as sources of aluminum and nitrogen, respectively. Metalorganic MBE represents a hybrid growth technique that offers a combination of growth precision, in-situ monitoring and ease of source management with the promise of high material quality. We demonstrate very efficient growth, with the growth rate in excess of 500 nm/h and low ammonia consumption of less than 1 sccm. Over the entire domain of growth parameters, the surface roughness remained in the range from 12 to 53 Å rms for AlN layers up to 1000 nm thick. Here, the low values of the roughness are associated to the low growth temperature (760°C), behavior that contrasts with that usually observed in gas source MBE with elemental Al source. X-ray diffraction linewidth as narrow as 141 arcsec has been demonstrated for samples grown under stoichiometric conditions. High temperature of the ammonia injector promotes the transition to the two-dimensional growth, while reducing the growth rate, pointing out the importance of surface hydrogen. We demonstrate that hydrogen plays an important role in the MOMBE process acting as a surfactant and passivating surface nitrogen bonds.