Epitaxy of Ge on sapphire

Ge was grown on sapphire (α-Al2O3 single crystals) by molecular beam epitaxy. On the (0001) surface (basal plane) of sapphire as well as on the (112̄0) surface (prism plane), Ge forms islands with a unique orientation relationship to the substrate. On the (11̄02) surface (rhombohedral plane), however, Ge grows with a fibre texture: While the grains have a unique crystallographic direction parallel to the substrate normal, the crystal lattices of the individual grains are rotated more or less randomly about this axis. It is attempted to compare the experimentally observed orientation relationships with those of a model that considers the ‘reciprocal space overlap’ of the substrate and the overgrowth