For a dot with discrete levels, the distribution function at equilibrium
differs from the Fermi-Dirac distribution, especially at low temperatures.
The peaks in the Ohmic conductance are spaced by an amount 
.
In the I-V characteristics the effect of both the charge quantisation and
the size quantisation can be observed.
The transport through a double dot has been investigated assuming that
inelastic transport through the inter-dot barrier can take place by means
of interaction with acoustic phonons. The main peaks in the Ohmic
conductance reach a maximum at a temperature 
which is at least roughly
half the energy difference 
between the dominant levels in the two dots.
Other levels in the two dots that are well aligned can also have a
significant effect on the conductance, especially when the inter-dot coupling
is weak. The I-V characteristics may contain regions of negative
differential conductance. This is less likely to occur at low temperatures,
although its effect will be stronger than at higher temperatures.
The inter-dot spacing can be analysed spectroscopically by investigating the current through the double dot at fixed bias as a function of one of the gate voltages. This produces very narrow peaks with a width that is closely related to the intrinsic level width. This method eliminates thermal smearing of the peaks.
Figure 1: Distribution function for a dot with equally spaced
energy levels
Figure 6: Energy dependence of the inter-dot transition rate:
(a) ignoring level broadening, (b) including broadening 
.
Figure 9: Ohmic conductance through a double dot with
(
, 
, 
,
). The empty and filled circles indicate the
positions at which the average occupation increases by one
for dot 1 and 2 respectively.
Figure 8: Temperature at which a conductance peak reaches its maximum
Figure: Ohmic conductance through a double dot with
(, ,
, ).
The empty and filled circles indicate the
positions at which the average occupation increases by one
for dot 1 and 2 respectively.
Figure 11: I-V characteristics for a double dot at various temperatures
(the dots are interchanged with respect to the previous figure)
Figure 12: Energy diagram for tunnelling through two dots at fixed bias
