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Quantum-confinement-induced Γ→ X transition in GaAs/AlGaAs quantum films, wires, and dots

1995; American Physical Society; Volume: 52; Issue: 20 Linguagem: Inglês

10.1103/physrevb.52.14664

1095-3795

Alberto Franceschetti, Alex Zunger,

Semiconductor Quantum Structures and Devices

Large GaAs domains embedded in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As matrix act as potential wells for both electrons and holes, resulting in a direct band-gap system. When the GaAs domains become small, however, quantum-confinement effects may push the \ensuremath{\Gamma}-like conduction-band state localized on GaAs above the X-like conduction-band state of the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy, leading to an indirect band-gap system. Using a pseudopotential band-structure method, as well as the conventional one-band effective-mass approximation, we investigate the nature of the direct\ensuremath{\rightarrow}indirect (\ensuremath{\Gamma}\ensuremath{\rightarrow}X) transition in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum films, wires, and dots. In the case of an isolated GaAs quantum structure embedded in AlAs, we find that the critical size for the onset of the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition increases from \ensuremath{\sim}31 \AA{} in a two-dimensional film through \ensuremath{\sim}56 \AA{} in a one-dimensional cylindrical wire to \ensuremath{\sim}80 \AA{} in a zero-dimensional spherical dot. The interaction between GaAs quantum structures tends to reduce the critical size for the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition. We further study the effect of the alloy composition on the \ensuremath{\Gamma}\ensuremath{\rightarrow}X transition, finding that the critical size decreases when the Ga concentration of the alloy increases. In the case of spherical GaAs quantum dots embedded in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy, we show that, as a function of the dot radius and the alloy composition, different alignments of the band-edge states lead to different regimes of the lowest-energy optical transition.