Aluminum nitride, AlN, layers are grown on silicon substrates using molecular beam epitaxial (MBE) growth. The AlN layer is initially grown by subjecting the silicon substrate to background ammonia followed by repetitively alternating the flux of 1) Al without ammonia and 2) ammonia without Al. After the surface of the silicon structure is sufficiently covered with AlN, the wafer is further subjected to a flux of ammonia and aluminum applied simultaneously to continue the epitaxial growth process. The process minimizes the formation of amorphous silicon nitride, SiNx, compounds on the surface of the substrate which form due to background nitrogen levels in the molecular beam epitaxial growth apparatus. A surface free of amorphous silicon nitride is necessary for formation of high quality AlN. The AlN layer may be further used as a buffer layer for AlGaN/GaN growth. After the AlN layer is grown on the silicon structure, the silicon structure may be subjected to a flux of Ga and nitrogen to form a layer of GaN.