Environmental Engineering Reference
In-Depth Information
The conceptual leap that is required here is that instead of a free electron in a
vacuum box of side
L
with in
nite potential walls, we have a conduction electron free
to roam about in a cube of intrinsic semiconductor of side
L
, with the electron being
con
ned to the conductor by the work function barrier. The moving carrier will be
endowed with an effective mass by its immersion in the semiconductor, and it will be
affected also by the permittivity of the semiconductor medium.
(Different wavefunction and energy equations will apply to other geometries than
a cube, for example, the quantum dots grown by molecular beam epitaxy (MBE) are
often pyramids. The wavefunctions in these cases will be different, but the differ-
ences in the end do not matter very much. Sharply de
ned energies inversely
proportional to the square of the container size will result.)
This application to semiconductor quantum dots requires
L
in the range of
3
-
5 nm, the mass
m
must be interpreted as an effective mass
m
, which may be
as small as 0.1
m
e
. The electron and hole particles are generated by light of energy
hc=
l
¼ E
n;
electron
þE
n;
hole
þE
g
:
ð
8
:
3
Þ
Here, the
first two terms are strongly dependent on particle size
L
,as
L
2
, which
allows the color of the light to be adjusted by adjusting the particle size. The bandgap
energy
E
g
is the minimum energy to create an electron and a hole in a pure
semiconductor. The electron and hole generated by light in a bulk semiconductor
may form a bound state along the lines of the Bohr model, described above, called an
exciton. However, as the size of the sample is reduced, the Bohr orbit becomes
inappropriate and the states of the particle in the 3D trap are a more correct
description.
In this context, Figure 8.6 shows levels in a quantum dot as an element of absorber
in a solar cell. The process shown is one of absorption of a high-energy photon
Figure 8.6 Multiple exciton generation in a
quantum dot [105]. Because of quantum
confinement, the energy levels for electrons and
holes are discrete. A single absorbed photon of
energy at least three times the energy difference
between the first energy levels for electrons and
holes in the quantum dot can create three
excitons, tripling the charge in the external
circuit.
