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The conditions under which the band gaps of free standing and embedded semiconductor quantum dots are direct or 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 ofthe same material (concentric cylindrical GaAs/AlAs layers).
Key words: Heterostructures, nanostructures, quantum dots
INTRODUCTION
One of the most important properties used to classify the optical response of a quantum dot system is whether it has a direct or indirect band gap. In dots with direct gaps, the electron and hole wavefunctions are both confined within the dot and are both derived from the Brillouin zone center Gamma states. This produces strong oscillator strengths for optical transitions and a strong luminescence. Dots with indirect band gaps can be indirect in real space, in which case the electrons and holes are localized in different regions of the nanostructure (e.g., dot interior vs barrier), and/or indirect in reciprocal space, where the states involved in the optical transitions evolve from different kappa points in the Brillouin zone. The oscillator strengths for optical transitions in dots with indirect gaps are small, producing weak luminescence.
There are several physical factors which control whether the interband transitions in a quantum dot will be direct or indirect: As a starting point, one has...