| 1. |
- Liao, Gaohua, et al.
(author)
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Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires
- 2015
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In: Applied Physics Reviews. - : AIP Publishing. - 1931-9401. ; 118:9
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Journal article (peer-reviewed)abstract
- We report on a theoretical study of the electronic structures of InSb and GaSb nanowires oriented along the [001] and [111] crystallographic directions. The nanowires are described by atomistic, tight-binding models, including spin-orbit interaction. The band structures and the wave functions of the nanowires are calculated by means of a Lanczos iteration algorithm. For the [001]-oriented InSb and GaSb nanowires, the systems with both square and rectangular cross sections are considered. Here, it is found that all the energy bands are doubly degenerate. Although the lowest conduction bands in these nanowires show good parabolic dispersions, the top valence bands show rich and complex structures. In particular, the topmost valence bands of the nanowires with a square cross section show a double maximum structure. In the nanowires with a rectangular cross section, this double maximum structure is suppressed, and the top valence bands gradually develop into parabolic bands as the aspect ratio of the cross section is increased. For the [111]-oriented InSb and GaSb nanowires, the systems with hexagonal cross sections are considered. It is found that all the bands at the Gamma-point are again doubly degenerate. However, some of them will split into non-degenerate bands when the wave vector moves away from the Gamma-point. Although the lowest conduction bands again show good parabolic dispersions, the topmost valence bands do not show the double maximum structure. Instead, they show a single maximum structure with its maximum at a wave vector slightly away from the Gamma-point. The wave functions of the band states near the band gaps of the [001]-and [111]-oriented InSb and GaSb nanowires are also calculated and are presented in terms of probability distributions in the cross sections. It is found that although the probability distributions of the band states in the [001]-oriented nanowires with a rectangular cross section could be qualitatively described by one-band effective mass theory, the probability distributions of the band states in the [001]-oriented nanowires with a square cross section and the [111]oriented nanowires with a hexagonal cross section show characteristic patterns with symmetries closely related to the irreducible representations of the relevant double point groups and, in general, go beyond the prediction of a simple one-band effective mass theory. We also investigate the effects of quantum confinement on the band structures of the [001]-and [111]-oriented InSb and GaSb nanowires and present an empirical formula for the description of quantization energies of the band edge states in the nanowires, which could be used to estimate the enhancement of the band gaps of the nanowires as a result of quantum confinement. The size dependencies of the electron and hole effective masses in these nanowires are also investigated and discussed. (C) 2015 AIP Publishing LLC.
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| 2. |
- Liao, Gaohua, et al.
(author)
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Electronic structures of [1 1 1]-oriented free-standing InAs and InP nanowires
- 2016
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In: Journal of Physics: Condensed Matter. - : IOP Publishing. - 0953-8984 .- 1361-648X. ; 28:13
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Journal article (peer-reviewed)abstract
- We report on a theoretical study of the electronic structures of the [1 1 1]-oriented, freestanding, zincblende InAs and InP nanowires with hexagonal cross sections by means of an atomistic sp3s∗, spinorbit interaction included, nearest-neighbor, tight-binding method. The band structures and the band state wave functions of these nanowires are calculated and the symmetry properties of the bands and band states are analyzed based on the C3v double point group. It is shown that all bands of these nanowires are doubly degenerate at the γ-point and some of these bands will split into non-degenerate bands when the wave vector k moves away from the γ-point as a manifestation of spin-splitting due to spinorbit interaction. It is also shown that the lower conduction bands of these nanowires all show simple parabolic dispersion relations, while the top valence bands show complex dispersion relations and band crossings. The band state wave functions are presented by the spatial probability distributions and it is found that all the band states show 2π/3-rotation symmetric probability distributions. The effects of quantum confinement on the band structures of the [1 1 1]-oriented InAs and InP nanowires are also examined and an empirical formula for the description of quantization energies of the lowest conduction band and the highest valence band is presented. The formula can simply be used to estimate the enhancement of the band gaps of the nanowires at different sizes as a result of quantum confinement.
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| 3. |
- Liao, Gaohua, et al.
(author)
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Electronic Structures of Free-Standing Nanowires made from Indirect Bandgap Semiconductor Gallium Phosphide
- 2016
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In: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 6
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Journal article (peer-reviewed)abstract
- We present a theoretical study of the electronic structures of freestanding nanowires made from gallium phosphide (GaP) - a III-V semiconductor with an indirect bulk bandgap. We consider [001]-oriented GaP nanowires with square and rectangular cross sections, and [111]-oriented GaP nanowires with hexagonal cross sections. Based on tight binding models, both the band structures and wave functions of the nanowires are calculated. For the [001]-oriented GaP nanowires, the bands show anti-crossing structures, while the bands of the [111]-oriented nanowires display crossing structures. Two minima are observed in the conduction bands, while the maximum of the valence bands is always at the Γ-point. Using double group theory, we analyze the symmetry properties of the lowest conduction band states and highest valence band states of GaP nanowires with different sizes and directions. The band state wave functions of the lowest conduction bands and the highest valence bands of the nanowires are evaluated by spatial probability distributions. For practical use, we fit the confinement energies of the electrons and holes in the nanowires to obtain an empirical formula.
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| 4. |
- Luo, Ning, et al.
(author)
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Band-inverted gaps in InAs/GaSb and GaSb/InAs core-shell nanowires
- 2016
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In: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 6
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Journal article (peer-reviewed)abstract
- The [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires have been studied by the 8 × 8 Luttinger-Kohn "Equation missing" Hamiltonian to search for non-vanishing fundamental gaps between inverted electron and hole bands. We focus on the variations of the band-inverted fundamental gap, the hybridization gap, and the effective gap with the core radius and shell thickness of the nanowires. The evolutions of all the energy gaps with the structural parameters are shown to be dominantly governed by the effect of quantum confinement. With a fixed core radius, a band-inverted fundamental gap exists only at intermediate shell thicknesses. The maximum band-inverted gap found is ~4.4 meV for GaSb/InAs and ~3.5 meV for InAs/GaSb core-shell nanowires, and for the GaSb/InAs core-shell nanowires the gap persists over a wider range of geometrical parameters. The intrinsic reason for these differences between the two types of nanowires is that in the shell the electron-like states of InAs is more delocalized than the hole-like state of GaSb, while in the core the hole-like state of GaSb is more delocalized than the electron-like state of InAs, and both favor a stronger electron-hole hybridization.
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| 5. |
- Luo, Ning, et al.
(author)
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k.p theory of freestanding narrow band gap semiconductor nanowires
- 2016
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In: AIP Advances. - : AIP Publishing. - 2158-3226. ; 6:12
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Journal article (peer-reviewed)abstract
- We report on a theoretical study of the electronic structures of freestanding nanowires made from narrow band gap semiconductors GaSb, InSb and InAs. The nanowires are described by the eight-band k.p Hamiltonians and the band structures are computed by means of the finite element method in a mixture basis consisting of linear triangular elements inside the nanowires and constrained Hermite triangular elements near the boundaries. The nanowires with two crystallographic orientations, namely the [001] and [111] orientations, and with different cross-sectional shapes are considered. For each orientation, the nanowires of the three narrow band gap semiconductors are found to show qualitatively similar characteristics in the band structures. However, the nanowires oriented along the two different crystallographic directions are found to show different characteristics in the valence bands. In particular, it is found that all the conduction bands show simple, good parabolic dispersions in both the [001]- and [111]-oriented nanowires, while the top valence bands show double-maximum structures in the [001]-oriented nanowires, but single-maximum structures in the [111]-oriented nanowires. The wave functions and spinor distributions of the band states in these nanowires are also calculated. It is found that significant mixtures of electron and hole states appear in the bands of these narrow band gap semiconductor nanowires. The wave functions exhibit very different distribution patterns in the nanowires oriented along the [001] direction and the nanowires oriented along the [111] direction. It is also shown that single-band effective mass theory could not reproduce all the band state wave functions presented in this work.
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