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

Theoretical Background of Semiconductor Nanostructures
the order of 0.01 eV . In contrast, Frenkel excitons are found in materials with
a small dielectric constant, the Coulomb interaction between an electron and a
hole may be strong and the excitons thus tend to be small, of the same order as
the size of the unit cell. Molecular excitons may even be entirely located on the
same molecule. These Frenkel excitons has a typical binding energy on the order
of 0.1 to 1 eV and found mostly in insulator and molecular crystals [23]. They
are also other exciton types like surface excitons, where the hole is inside the solid
and the electron is in the vacuum. These electron-hole pairs (surface-excitons)
can only move along the surface. Alternatively, an exciton may be thought of
as an excited state of an atom, ion, or molecule, the excitation wandering from
one cell of the lattice to another this later type called atomic or molecular excitons.
An electron is said to be found in the lowest unoccupied orbital and an
electron hole in the highest occupied molecular orbital, and since they are found
within the same molecular orbital manifold, the electron-hole state is said to be
bound. Molecular excitons typically have characteristic lifetimes on the order of
nanoseconds, after which the ground electronic state is restored and the molecule
undergoes photon or phonon emission [25].
The eect of quantum connement on excitons in semiconductors of lowdimensions
have been intensively investigated for many years [26, 27, 28]. Two
factors are responsible for the exciton properties in a quantum dot. The rst
is the Coulomb interaction between the electron and hole.
The second is the
connement by the quantum dot three-dimensional potential. The connement
is ruled by the size and shape of the dot as well as by the dot and barrier material
to produce various bands osets. In the quantum dots, the connement also
inuences binding energy. Therefore, both factors inuence the energy and oscillator
strength of exciton in a complex way [23]. As the size of the quantum dots
approaches the Bohr radius of bulk exciton, quantum connement eects become
apparent. There are two limiting cases depending upon the ratio between the
radius of the quantum dot (r) and the eective Bohr radius of the bulk exciton
(B eff ) described in Eq. 2.7:
B eff =
2 ɛ
m ∗ e 2 (2.7)
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