14.2 Quantum Wires
407
Fig. 14.11 Electron
wavefunctions (| 2 on
logarithmic grey scale) for
the first three confined
levels for the QWR of
Fig. 14.3a. From [1342]
n=1
n=2
n=3
Fig. 14.12 a
Three-dimensional view of
the electron and (heavy)
hole part of the excitonic
wavefunction in a 4 nm ×
5 nm T-shaped
In 0.2 Ga 0.8 As/GaAs QWR.
The orbitals correspond to
70% probability inside. b
Cross section through the
electron and hole orbitals
in their center along the
wire direction. Reprinted
with permission from
[1361], ©1998 APS
hh
e
(a)
(b)
[110]
[001]
[110]
[110] [001]
14.2.5 Quantization in Two-Dimensional Potential Wells
The motion of carriers along the quantum wire is free. In the cross-sectional plane the wavefunction is
confined in two dimensions. The simplest case is for constant cross section along the wire. However,
generally the cross section along the wire may change and therefore induce a potential variation along
the wire. Such potential variation will impact the carrier motion along the longitudinal direction. Also,
a twist of the wire along its axis is possible.
In Fig. 14.11, the electron wavefunctions in a V-groove GaAs/AlGaAs QWR are shown. Further
properties of V-groove QWRs have been reviewed in [1360]. In Fig. 14.12, the excitonic electron and
hole wavefunctions are shown for a (strained) T-shaped QWR.
In Fig. 14.13a the atomic structure of a very thin ZnO nanowhisker with a cross-section consisting
of seven hexagonal unit cells is shown. The theoretical one-dimensional band structure [1362] is shown
in Fig. 14.13b together with the charge density of the lowest conduction band state (LUMO) and the
highest valence band state (HOMO). The band gap is generally too small because of the LDA method
used.
1 In [1362] also the properties of nanowires with various diameters are compared. The HOMO
at lies only 80 meV above the top of valence band of bulk ZnO, and its position changes little with
1 The LDA in [1362] yields E g = 0.63 eV for the bulk ZnO band gap; its experimental value is 3.4 eV.
407
Fig. 14.11 Electron
wavefunctions (| 2 on
logarithmic grey scale) for
the first three confined
levels for the QWR of
Fig. 14.3a. From [1342]
n=1
n=2
n=3
Fig. 14.12 a
Three-dimensional view of
the electron and (heavy)
hole part of the excitonic
wavefunction in a 4 nm ×
5 nm T-shaped
In 0.2 Ga 0.8 As/GaAs QWR.
The orbitals correspond to
70% probability inside. b
Cross section through the
electron and hole orbitals
in their center along the
wire direction. Reprinted
with permission from
[1361], ©1998 APS
hh
e
(a)
(b)
[110]
[001]
[110]
[110] [001]
14.2.5 Quantization in Two-Dimensional Potential Wells
The motion of carriers along the quantum wire is free. In the cross-sectional plane the wavefunction is
confined in two dimensions. The simplest case is for constant cross section along the wire. However,
generally the cross section along the wire may change and therefore induce a potential variation along
the wire. Such potential variation will impact the carrier motion along the longitudinal direction. Also,
a twist of the wire along its axis is possible.
In Fig. 14.11, the electron wavefunctions in a V-groove GaAs/AlGaAs QWR are shown. Further
properties of V-groove QWRs have been reviewed in [1360]. In Fig. 14.12, the excitonic electron and
hole wavefunctions are shown for a (strained) T-shaped QWR.
In Fig. 14.13a the atomic structure of a very thin ZnO nanowhisker with a cross-section consisting
of seven hexagonal unit cells is shown. The theoretical one-dimensional band structure [1362] is shown
in Fig. 14.13b together with the charge density of the lowest conduction band state (LUMO) and the
highest valence band state (HOMO). The band gap is generally too small because of the LDA method
used.
1 In [1362] also the properties of nanowires with various diameters are compared. The HOMO
at lies only 80 meV above the top of valence band of bulk ZnO, and its position changes little with
1 The LDA in [1362] yields E g = 0.63 eV for the bulk ZnO band gap; its experimental value is 3.4 eV.