Chapter 14
Nanostructures
The principles of physics, as far as I can see, do not speak against the possibility of
maneuvering things atom by atom.
R.P. Feynman, 1959 [1338]
Abstract One-dimensional nanostructures (quantum wires) and zero-dimensional ones (quantum
dots) are discussed with regard to their various fabrication methods and the tunable physical properties in such systems. Main effects covered are the modified density of states, confined energy levels,
(envelope) wave-function symmetry and the resulting novel electrical and optical properties.
14.1 Introduction
When the structural size of functional elements enters the size range of the de Broglie matter wavelength,
the electronic and optical properties are dominated by quantum-mechanical effects. The most drastic
impact can be seen from the density of states (Fig. 14.1). The quantization in a potential is ruled by the
Schrödinger equation with appropriate boundary conditions. These are simplest if an infinite potential
is assumed. For finite potentials, the wavefunction leaks out into the barrier. Besides making the
calculation more complicated (and more realistic), this allows electronic coupling of nanostructures.
Via the Coulomb interaction, a coupling is even given if there is no wavefunction overlap. In the
following, we will discuss some of the fabrication techniques and properties of quantum wires (QWR)
and quantum dots (QD). In particular for the latter, several textbooks can also be consulted [1339, 1340].
14.2 Quantum Wires
14.2.1 V-Groove Quantum Wires
Quantum wires with high optical quality, i.e. high recombination efficiency and well-defined spectra,
can be obtained by employing epitaxial growth on corrugated substrates. The technique is shown
schematically in Fig. 14.2. A V-groove is etched, using, e.g., an anisotropic wet chemical etch, into a
GaAs substrate. The groove direction is along
1 ¯
10
. Even when the etched pattern is not very sharp
on the bottom, subsequent growth of AlGaAs sharpens the apex to a self-limited radius ρ l of the order
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_14
401
Nanostructures
The principles of physics, as far as I can see, do not speak against the possibility of
maneuvering things atom by atom.
R.P. Feynman, 1959 [1338]
Abstract One-dimensional nanostructures (quantum wires) and zero-dimensional ones (quantum
dots) are discussed with regard to their various fabrication methods and the tunable physical properties in such systems. Main effects covered are the modified density of states, confined energy levels,
(envelope) wave-function symmetry and the resulting novel electrical and optical properties.
14.1 Introduction
When the structural size of functional elements enters the size range of the de Broglie matter wavelength,
the electronic and optical properties are dominated by quantum-mechanical effects. The most drastic
impact can be seen from the density of states (Fig. 14.1). The quantization in a potential is ruled by the
Schrödinger equation with appropriate boundary conditions. These are simplest if an infinite potential
is assumed. For finite potentials, the wavefunction leaks out into the barrier. Besides making the
calculation more complicated (and more realistic), this allows electronic coupling of nanostructures.
Via the Coulomb interaction, a coupling is even given if there is no wavefunction overlap. In the
following, we will discuss some of the fabrication techniques and properties of quantum wires (QWR)
and quantum dots (QD). In particular for the latter, several textbooks can also be consulted [1339, 1340].
14.2 Quantum Wires
14.2.1 V-Groove Quantum Wires
Quantum wires with high optical quality, i.e. high recombination efficiency and well-defined spectra,
can be obtained by employing epitaxial growth on corrugated substrates. The technique is shown
schematically in Fig. 14.2. A V-groove is etched, using, e.g., an anisotropic wet chemical etch, into a
GaAs substrate. The groove direction is along
1 ¯
10
. Even when the etched pattern is not very sharp
on the bottom, subsequent growth of AlGaAs sharpens the apex to a self-limited radius ρ l of the order
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_14
401