Coulomb Blockade

The tunnel junction is a conductor-insulator-conductor device. Suppose a very small tunnel junction is operated at very low temperatures so that thermal fluctuations do not contribute to electron tunneling across the junction. Now connect the tunnel junction to a source of constant electrical charge. Will the flow of current across the junction be steady?

Answer

No, the current across the junction will not be a steady current. There will be single electron tunneling (SET), with the voltage across the junction changing periodically with a frequency equal to the current divided by the fundamental unit of charge e.

The tunnel junction is a conductor-insulator-conductor device, so transferred charge flows through the conductor to accumulate on the surface of the electrode against the insulating layer of the junction. An opposite surface charge of equal amount accumulates on the other electrode across the junction. The actual amount of surface charge has a continuous change in value as the charge accumulates, including fractional values such as +0.8642 e, because the electrons near this surface can adjust their positions slightly.

However, only discrete amounts of charge can tunnel through the insulating layer that is, each electron tunneling through changes the surface charge by +e or –e, depending on the direction of tunneling. The tunneling process is energy-dependent. If the charge at the junction is greater than +e/2, an electron can tunnel through to reduce the surface charge by e, thus reducing the electrostatic energy of the system. And if the surface charge is less than –e/2, an electron can tunnel in the opposite direction to decrease the energy. But if the surface charge value is greater than –e/2 or less than +e/2, tunneling would not occur because the system energy would increase. This tunneling suppression is known as the Coulomb blockade, first studied in the 1950s.

The tunnel junction connected to a constant current source begins in the Coulomb blockade condition, then reaches tunneling for the one-electron condition, then back to the Coulomb blockade, then one-electron tunneling, etc. The analogue may be a dripping faucet.

Many electronic devices are being made with SET operation. For example, an SET transistor can switch on or off the flow of billions of electrons per second when the charge on the middle electrode is changed by only half the charge of an electron!