13. Tunnel Junction, Coulomb Blockade, and Quantum Dot Circuit

Conceptual development regarding single electron transfer phenomena is presented. It is shown that energy necessary to place a single electronic charge on one plate of a capacitor with equal opposite charge on its opposite plate is not a clearly distinguishable event at micro- and milliscales. But it becomes a meaningful event at the nanoscale due to the significant amount of energy involved. Further, it is shown that the existence of a voltage requirement for tunneling to occur across the plates of a capacitor, the so-called Coulomb blockade effect, is a noticeable phenomenon exclusive to nanoscale. Moving further, it is found that the Coulomb blockade is observable at or near room temperatures only in the scale of nano dimensions. From this understanding, the notion of a tunnel junction is put forward as a barrier in the form of an electrical potential or thin dielectric film across which tunneling occurs. The tunnel junction is modeled as an ideal capacitor with a parallel-connected tunnel resistance whose value must be ≫4.2 kΩ for Coulomb blockade to become recognizable. The capacitor of the tunnel junction behaves in a different way from a normal capacitor. Upon excitation by a constant current source, the voltage across this capacitor oscillates between two values, which are referred to as single electron tunneling oscillations. Applying the tunnel junction model, the operation of a quantum dot circuit consisting of a quantum dot and two tunnel junctions is analyzed. In both cases, for electron tunneling into the quantum dot across one tunnel junction and for electron tunneling off the quantum dot across the other tunnel junction, Coulomb blockade occurs in a quantum dot circuit like a nanocapacitor. The energy band diagram for a small quantum dot circuit exhibits a discretized nature. The electron tunneling does not take place in a continuous fashion but in discrete voltage steps. The resulting current–voltage characteristic of the quantum dot circuit has the shape of a staircase which is called the Coulomb staircase.