Biomedical Engineering Reference
In-Depth Information
Fig. 1.15
Allowed and
forbidden electron energy
bands in the periodic
potential of a superlattice
E
c
allowed energies bands
a
Lead
Lead
Island
b
c
Island
Island
Tunnel
junctions
E
F
E
F
e
2
/
C
e
2
/
C
Fig. 1.16
(
a
) Schematic representation of an island connected to metallic leads through tunneling
junctions. (
b
) Energy gap opening at the Fermi level due to the Coulomb energy needed to tunnel
in or out of the island, (
c
) which is overcome by a bias V
D
e=C
transport in superlattices that involves nonequilibrium Green functions can be found
in
Wacker and Jauho
(
1998
).
Another interesting quantum phenomenon is encountered in tightly confined
nanostructures, in particular in quantum dots. Here, the Coulomb interaction is
considerable, and the electronic states depend on the number of electric charges
(electrons) in the dot, which takes discrete values. A manifestation of this depen-
dence is illustrated by the Coulomb blockade, in which an energy gap opens
at the Fermi level in the electron energy spectrum in small metallic clusters
or semiconductor quantum dots coupled by tunneling barriers to metallic leads;
these confined structures are generically called islands. The configuration of a
Coulomb blockade device is schematically represented in Fig.
1.16
a(
Ferry and
Goodnick 2009
). This gap in the energy spectrum, analogous to the energy gap
in semiconductors, is modeled as an additional energy needed by an electron to
tunnel in or out of the island, which originates in the Coulomb interaction between
electrons in the island.
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