Page 139 - Science at the nanoscale

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June 9, 2009
6.2. Electron Transport Properties in Low Dimensional Systems
Drain
Source
QD
Gate
V
sd
V g
Schematic of a quantum dot connected to source and drain
Figure 6.12.
contacts by tunnel junctions, and to a gate by a capacitor.
0D Electron Transport
6.2.3
Consider the electronic properties of a quantum dot depicted in
Fig. 6.12, which is coupled to three terminals. Electron exchange
can occur between two adjacent terminals, as indicated by the
arrows. These source and drain terminals connect the small
conductor to macroscopic current and voltage meters, and the
third terminal provides an electrostatic or capacitive coupling.
The number of electrons on this island is an integer N, i.e. the
charge on the island is quantised and equal to Ne. If we now allow
tunneling to the source and drain electrodes, then the number of
electrons N adjusts itself until the energy of the whole circuit is
minimised.
When tunneling occurs, the charge on the island suddenly 129 ch06
changes by the quantised amount e. An extra charge e changes the
2
electrostatic potential by the charging energy E C = e /C, where C
is the capacitance of the island. This charging energy becomes
important when it exceeds the thermal energy k B T. A second
requirement is that the barriers are sufficiently opaque such that
the electrons are located either in the source, in the drain, or on
the island. This means that quantum fluctuations in the num-
ber N due to tunneling through the barriers is much less than
one over the time scale of the measurement. This time scale is
roughly the electron charge divided by the current. This require-
ment translates to a lower bound for the tunnel resistances R t