Indirect band gaps in quantum dots made from direct-gap bulk materials

The conditions under which the band gaps of free standing and embedded semiconductor quantum dots are director indirect are discussed. Semiconductor quantum dots are classified into three categories; (i) free standing dots, (ii) dots embedded in a direct gap matrix, and (iii) dots embedded in an indirect gap matrix. For each category, qualitative predictions are first discussed, followed by the results of both recent experiments and state of the art pseudopotential calculations. We show that: Free standing dots of InP, InAs, and CdSe will remain direct for all sizes, while dots made of GaAs and InSb will turn indirect below a critical size. Dots embedded within a direct gap matrix material will either stay direct (InAs/GaAs at zero pressure) or will become indirect at a critical size (InSb/InP). Dots embedded within an indirect gap matrix material will exhibit a transition to indirect gap for sufficiently small dots (GaAs/AlAs and InP/GaP quantum well) or will be always indirect (InP/GaP dots, InAs/GaAs above 43 kbar pressure and GeSi/Si dots). In indirect nanostructures, charge separation can occur with electrons and holes localized on different materials (flat InP/GaP quantum well) or with electrons and holes localized in different layers of the same material(concentric cylindrical GaAs/A1As layers).