Page 140 - Science at the nanoscale

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June 9, 2009
Low-Dimensional Nanostructures
130
of the barriers. To see this, consider the typical time to charge
or discharge the island ∆t = R t C. The Heisenberg uncertainty
2
relation: ∆E∆t = (e /C)R t C > h implies that R t should be much
2
= 25.813kW in order
larger than the resistance quantum h/e
for the energy uncertainty to be much smaller than the charging
energy.
To summarise, the two conditions for observing effects due to
the discrete nature of charge are:
h
(6.23)
R t ≫
2
e
2
e
≫ k B T
(6.24)
C
The first criterion can be met by weakly coupling the dot to the
source and drain leads. The second criterion can be met by mak-
ing the dot small. Recall that the capacitance of an object scales
with its radius R. For a sphere, C = 4πε r ε o R, while for a flat disc,
C = 8ε r ε o R, where ε r is the dielectric constant of the material sur-
rounding the object.
The circuit with the quantum dot in Fig. 6.12 forms the basis of
a single electron transistor (SET). The SET has two tunnel junctions
sharing one low self-capacitance quantum dot, whose electrical
potential can be tuned by the gate, which is capacitively coupled
to the dot. The energy levels of the island electrode are evenly
spaced with a separation of ∆E. ∆E is the energy needed for each
subsequent electron to tunnel to the dot.
The SET has effectively two states:
1. Blocking state: As seen in Fig. 6.13(a), no accessible energy ch06
levels are within tunneling range of the electron (red) on
the source contact. All energy levels on the island elec-
trode with lower energies are occupied.
2. Positive voltage applied to gate electrode: Energy levels of the
island electrode are lowered and the electron (green 1) can
tunnel onto the island (2), occupying a previously vacant
energy level. From there it can tunnel onto the drain elec-
trode (3) where it inelastically scatters and reaches the
drain electrode Fermi level (4).