Quantum confinement energies in zinc-blende III–V and group IV semiconductors

Abstract

Blueshift of the band gap due to quantum confinement is calculated in a tight-binding model for a series of nine III–V zinc-blende AB (A=Al, Ga, or In, B=As, P, or Sb) and two diamond group-IV (Si and Ge) semiconductor clusters. Analytic expressions for the highest occupied molecular orbital and lowest unoccupied molecular orbital energy levels are given as a function of the cluster size. Comparison is made to results obtained by the pseudopotential method and to experimental results.

Electronic Structure and Spectroscopy of Semiconductor Nanocrystals

“…The resulting band gap variation with size obeys a 1/D 1:42 function rather than the 1/D 2 relation expected on the basis of EMA. Recently Allan et al [72] calculated the quantum confinement effects for zinc blende III-V and group IV semiconducting nanocrystals using the nearest neighbor, sp 3 d 5 s* TB model with the spin-orbit interaction included. Such a model gives a much better description of the bulk semiconductor band structure and thus explains the experimental results for band gap variation more effectively than the sp 3 s* model.…”

Evolution of the electronic structure with size in II-VI semiconductor nanocrystals

“…[28,29] However, to account for the conduction bands, the inclusion of d orbitals becomes necessary. [30,34] This has been shown in the case of InP [30] Therefore, this improved model and the parametrization should provide a good starting point for calculating the electronic properties of corresponding nanocrystals, provided the model and parameters are transferable from the bulk to the cluster limit. Ab initio calculations for a CdS cluster of about 16Å diameter [37] as well as results of Ref.…”

Tight-binding model for semiconductor nanostructures

“…Simple model studies based on the effective mass approximation 15,22 or a multi-band k · pmodel 23,24,25 describe the QD by a confinement potential caused by the band offsets, for instance; they give qualitative insights into the formation of bound (hole and electron) states, but they are too crude for quantitative, material specific results or predictions. More suitable for a microscopic description are empirical pseudopotential methods 26,27,28,29 as well as empirical tight-binding models 30,31,32,33,34,35,36,37,38,39,40,41 . The empirical pseudopotential methods allow for a detailed variation of the wave functions on the atomic scale.…”

“…Semiempirical TB-models have been used already to describe "nearly" spherical InAs and CdSe NCs for which the dangling bonds at the surfaces are saturated by hydrogen 31,32,33,34 or organic ligands 37,38,39 . Also uncapped 42 and capped 35 pyramidal InAs QDs were ivestigated by use of an empirical TB-model.…”