4 Coulomb blockade

J [arb. u.]
4.3 Single-electron transistor 79
0 1 2 3 4
V
Fig. 4.6. Coulomb blockade: voltage-current curves of a symmetric junction at low
temperature (T =0.01EC) and different gate voltages VG =0,VG =0.25EC, and
VG = 0.5EC. Dashed line shows the change at higher temperature T = 0.1EC.
Voltage is in units of EC/|e|.
4.3.4 Current-voltage curve: Coulomb staircase
Now let us discuss the signatures of Coulomb blockade at finite voltage. The
results of calculations are presented in Fig. 4.6 for symmetric (νL = νR) system,
and in Fig. 4.7 for asymmetric one. First of all, the gap (called Coulomb
gap) is seen clear at low temperatures and low voltages, that is the other one
manifestation of Coulomb blockade. In agreement with conductance calculation,
this gap is closed in the degeneracy points, where the linear currentvoltage
relation is reproduced at low voltages. At higher temperatures the
gap is smeared and linear behaviour is restored.
The other characteristic feature, seen at higher voltages and more pronounced
in the asymmetric case, is called Coulomb staircase (Fig. 4.7) and
is observed due to the participation of higher charge states in transport at
higher voltage. For example, if VG = 0 the transport is blocked at low voltage
and the current appears only at |e|V/2 >EC (V/2 because the bias voltage is
divided between the left and right contacts) when the Coulomb gap is overcome
and the electron can go through the state |n =1〉. At higher voltage
|e|V/2 > 3EC the state |n =2〉 become available, and so on.
The general formula for the threshold voltages of the n-th step is
Vn = ±
2(2n − 1)EC
. (4.43)
|e|
The amplitude of the steps is decaying with n and at large voltage the Ohmic
behaviour is reproduced.