Molecular beam epitaxial growth of III-V semiconductor ... - KOBRA

Theoretical Background of Semiconductor Nanostructures
Structure Degree of connement Dimension of the structure
Bulk 0 3D
Quantum well (QW) 1 2D
Quantum wire (QWR) 2 1D
Quantum dot (QD) 3 0D
Table 2.1: Classication of semiconductor nanostructures and their degree of quantum
connement.
According to Eq. 2.1 if one-dimension of a bulk semiconductor (assuming,
box geometry) (L x , L y , L z ) is in the order of the de-Broglie wavelength (λ B ) or
smaller (Eq. 2.2), the quantum size eect gets signicant. The wave-like behavior
of electrons are also important on much longer dimensions, if you have to care on
coherent phenomena. This is also true for band-structure formation caused by the
coherent interaction with the periodic potential of the lattice and is valid in the
whole solid. You would not understand this without using quantum mechanics
[19].
L x , L y , L z ≤ λ B (2.2)
2.3.1 Density of States Function of Low-Dimensional Systems
In quantum physics, the electronic structure is often analyzed in terms of the
density of electron states (DOS). The DOS function, at a given value E of energy,
is dened such that g(E)∆E is equal to the number of states (i.e. solutions of
Schrödinger equation) in the interval energy ∆E around E. However, if the
dimensions L i (i = x, y, z) are macroscopic and if proper boundary conditions are
chosen, the energy levels can be treated as quasi-continuous [19]. On the other
hand, in the case where any of the dimensions L i gets small enough, the DOS
function becomes discontinuous. Fig. 2.2 describes how the density of states
changes as a function of dimensionality. It is clear that the density of state
function (DOS) in Fig. 2.2 gets sharper as the dimension of the structure becomes
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