In this work we present a comparison of multiband k · p models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k · p formalism, in contrast to a 6+2-band k·p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valence band states for the wide band gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure.
Compound semiconductor alloys of the type A x B 1−x C find widespread applications as their electronic bulk band gap varies continuously with x, and therefore a tayloring of the energy gap is possible by variation of the concentration. We model the electronic properties of such semiconductor alloys by a multiband sp 3 tightbinding model on a finite ensemble of supercells and determine the band gap of the alloy. This treatment allows for an intrinsic reproduction of band bowing effects as a function of the concentration x and is exact in the alloyinduced disorder. In the present paper, we concentrate on bulk Cd x Zn 1−x Se as a well-defined model system and give a careful analysis on the proper choice of the basis set and supercell size, as well as on the necessary number of realizations. The results are compared to experimental results obtained from ellipsometric measurements of Cd x Zn 1−x Se layers prepared by molecular beam epitaxy (MBE) and photoluminescence (PL) measurements on catalytically grown Cd x Zn 1−x Se nanowires reported in the literature.
The optical spectra of homogeneously alloyed colloidal CdSe x S 1−x quantum dots (QDs) for sulfur-rich compositions show additional transitions between the first and second absorption features of pure CdSe and CdS. Using tight-binding calculations for a large (N = 50) number of stochastic realizations for each composition of the alloyed QDs, we trace back this effect to transitions from deeper valence-band states to the lowest conduction-band level. These transitions are energetically degenerate with the main absorption lines in the pure systems but are shifted in between the lowest two main transitions in alloyed QDs. Moreover, the configurational disorder upon alloying distorts the symmetry properties of electron and hole wave functions, which results in a broad band of allowed transitions from these deeper valenceband states to the lowest conduction-band level. In agreement with experimental findings, the corresponding absorption feature shows a blueshift relative to the first exciton transition with decreasing sulfur to selenium ratio. Many-body calculations using the configuration interaction scheme reproduce the effect and additionally yield a bowing parameter of the optical gap in very good agreement with experimental findings from UV−vis spectra.
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