and from the island on the second electrode or from the second electrode on the island. The relating
change in energy is as follows:
∆E 1 R(n) = eV 1 −e(−ne+Q 0 +C 1 V 1 +C 2 V 2 +Cg 1 Vg 1 +Cg 2 Vg 2 )/CΣ+e^2
2 CΣ(197)
∆E 1 L(n) = −eV 1 +e(−ne+Q 0 +C 1 V 1 +C 2 V 2 +Cg 1 Vg 1 +Cg 2 Vg 2 )/CΣ+
e^2
2 CΣ(198)
∆E 2 R(n) = −eV 2 +e(−ne+Q 0 +C 1 V 1 +C 2 V 2 +Cg 1 Vg 1 +Cg 2 Vg 2 )/CΣ+
e^2
2 CΣ(199)
∆E 2 L(n) = eV 2 −e(−ne+Q 0 +C 1 V 1 +C 2 V 2 +Cg 1 Vg 1 +Cg 2 Vg 2 )/CΣ+e^2
2 CΣ. (200)
If the change in energy is negative the electron will tunnel. Figure 90 shows a plot where all four of
them are plotted as a function of the bias and the gate voltage. All other voltages are held constant.
The shaded regions show where none of the tunnel events can decrease the energy which is called the
Figure 90: Coulomb blockade; shaded region: Coulomb blockade is active - none of the four tunnel
events decrease the energy; the number in the region says how many electrons are allowed
to tunnel on the island.
Coulomb blockade regime. The region labelled with 0 determines the bias and gate voltage range
where no electron is allowed to tunnel on or off the island. But if you increase the gate voltage you
come to a region where one electron can tunnel on the island because the positive gate voltage pulls
one electron on it. The higher the gate voltage the more electrons can tunnel. But if you increase the
bias voltage nothing happens until you get to the region that is labelled with 0 , 1 which shows us that
at a given numbernof electrons eithernorn+ 1electrons are allowed on the islands. It depends now
on the number of electrons on the island which tunnel processes decrease or increase the energy.
This illustration is important to interpret experimental data (see fig. 91). In the Coulomb blockade
regime there is no current flowing but if you increase the bias voltage you get into a regime where there
is a current that changes periodically with the change of the gate voltage (instead of linear compared
to usual transistors).