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Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires

Liao, Gaohua; Luo, Ning; Yang, Zhihu; Chen, Keqiu and Xu, Hongqi LU (2015) In Applied Physics Reviews 118(9).
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... (More)
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. (Less)
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organization
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type
Contribution to journal
publication status
published
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in
Applied Physics Reviews
volume
118
issue
9
publisher
American Institute of Physics
external identifiers
  • wos:000360926500024
  • scopus:84941093347
ISSN
0021-8979
DOI
10.1063/1.4929412
language
English
LU publication?
yes
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7a2e3717-eea2-4ac4-9723-c137ceba2839 (old id 8077188)
date added to LUP
2015-10-23 09:39:12
date last changed
2017-10-08 03:09:53
@article{7a2e3717-eea2-4ac4-9723-c137ceba2839,
  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.},
  articleno    = {094308},
  author       = {Liao, Gaohua and Luo, Ning and Yang, Zhihu and Chen, Keqiu and Xu, Hongqi},
  issn         = {0021-8979},
  language     = {eng},
  number       = {9},
  publisher    = {American Institute of Physics},
  series       = {Applied Physics Reviews},
  title        = {Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires},
  url          = {http://dx.doi.org/10.1063/1.4929412},
  volume       = {118},
  year         = {2015},
}