We report on the growth of high-electron-mobility AlGaN/GaN heterostructures on silicon (111) substrates by molecular-beam epitaxy using ammonia as the nitrogen source. Crack-free GaN layers up to 3 mum are obtained. Their optical properties are similar to those commonly obtained for films grown on sapphire, but photoluminescence spectra indicate that GaN on Si(111) is in a tensile strain state which increases with the epitaxial layer thickness. Such uncracked GaN buffer layers grown on Si(111) have been used to achieve undoped AlGaN/GaN heterostructures having electron mobilities exceeding 1600 cm(2)/V s at room temperature and 7500 cm(2)/V s at 20 K. (C) 2001 American Institute of Physics.