12.2.2 Single Electron Transistor
Figure 87: Single electron transistor.In fig. 87 you can see a single electron transistor with its three gold electrodes and an island (size of
1 μm) where only one electron at the time can tunnel on. The gate electrode is not connected to the
island but there is a thick insulating layer between the gold and the island where no tunnelling can
take place. But an applied voltage can induce a polarisation to the island which pulls the electrons
on the left side that causes a change in the bias across the tunnel junctions. The total capacitance of
the island is about 1 μF. If an electron tunnels on the island the voltage changes. For a capacitor the
formulaQ=CV has to be used withQ=ewhich leads to a voltage change of∆V = 10−^4 V.
Figure 88: I vs V: blue line: without Coulomb blockade; red line: with Coulomb blockade.If you apply a bias less than∆V across the whole thing no tunnelling will happen because there is
a Coulomb blockade. But a voltage change on the gate can suppress the Coulomb blockade and the
current will be linear to the applied voltage as you would expect for a tunnel junction. At other
voltages there is still the Coulomb blockade and the current will increase only at a certain voltage (see
fig. 88). For the model with the little crystals it means that at low bias voltages none of the electrons
will tunnel and the material will become an insulator.
We will discuss the single electron transistor (SET) now in more detail. In experiments a SET has
usually two gates. One where the signal comes in and one to tune whether the Coulomb blockade is