GaN quantum dots (QDs) in an AlN matrix have been grown on Si(111) by molecular-beam epitaxy. The growth of GaN deposited at 800 degrees C on AlN has been investigated in situ by reflection high-energy electron diffraction. It is found that a growth interruption performed at GaN thicknesses larger than three molecular monolayers (8 Angstrom) instantaneously leads to the formation of three-dimensional islands. This is used to grow GaN/AlN QDs on Si(111). Depending on their sizes, intense room-temperature photoluminescence is observed from blue to orange. Finally, we demonstrate that stacking of QD planes with properly chosen dot sizes gives rise to white light emission. (C) 1999 American Institute of Physics. [S0003-6951(99)01533-8].