The conduction-band alignments of Ge1-xSix/Ge and Ge1-xSix/Si heterostructures grown on (111) and (001) crystallographic planes, respectively, are analysed. We have obtained the selection rules for interband dipole optical transitions in the heterostructures, and discussed the possibilities for specifying the types of the lowest conduction-band minima. We show that this can be done by, for example, exploring the polarization of different phonon-assisted band-edge optical transitions. The conduction-band minima may be at different L or Delta points of the Brillouin zone, depending on the structure parameters. Although bulk Ge, Si, and their alloy are indirect-gap semiconductors, the heterostructures Ge1-xSix/Ge and Ge1-xSix/Si can have a direct band gap. We found the parameter regions where type-I and type-II band alignment were realized, and those where the band gap was direct in quantum well (QW) structures. It is shown that in direct-gap QW structures grown on (001) planes, direct interband optical transitions between the nearest electron and hole subbands are allowed, but the same transitions are forbidden for direct-gap structures grown on (111) planes.
