Coulomb-Blockade Oscillations in Semiconductor Nanostructures

Abstract

Coulomb-blockade oscillations of the conductance are a manifestation of single-electron tunneling through a system of two tunnel junctions in series (see Fig. 1) [1]–[5]. The conductance oscillations occur as the voltage on a nearby gate electrode is varied. This setup is the SET transistor described in Sec. 6 of Chap. 2. The number N of conduction electrons on an island (or dot) between two tunnel barriers is an integer, so that the charge Q = — Ne. on the island can only change by discrete amounts e. In contrast, the electrostatic potential difference of island and leads changes continuously as the electrostatic potential φext due to the gate is varied. This gives rise to a net charge imbalance Cφext —Ne between the island and the leads, which oscillates in a saw-tooth pattern with gate voltage (C is the mutual capacitance of island and leads). Tunneling is blocked at low temperatures, except near the degeneracy points of the saw-tooth, where the charge imbalance jumps from +e/2 to φ e/2. At these points the Coulomb blockade of tunneling is lifted and the conductance exhibits a peak. In metals treated in the previous chapters, these “Coulomb-blockade oscillations” are essentially a classical phenomenon [6, 7]. Because the energy level separation ΔE in the island is much smaller than the thermal energy k B T, the energy spectrum may be treated as a continuum. Furthermore, provided that the tunnel resistance is large compared to the resistance quantum h/e 2, the number N of electrons on the island may be treated as a sharply defined classical variable.