Coulomb-Blockade Oscillations in Semiconductor Nanostructures

Coulomb-blockade oscillations of the conductance are a manifestation of singleelectron tunneling through a System of two tunnel junctions in series (see Fig. 1) [l]-[5]. The conductance oscillations occur äs the voltage on a nearby gate electrode is varied. This setup is the SET transistor described in See. 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 äs the electrostatic potential <£ext due to the gate is varied. This gives rise to a net charge imbalance C4>ext — 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 tempcratures, except near the degeneracy points of the saw-tooth, where the charge imbalance jumps from +e/2 to —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 AE in the island is much smaller than the thermal energy fcBT, the energy spectrum may be treated äs a continuum. Furthermore, provided that the tunnel resistance is large compared to the resistance quantum h/e, the number Λ^ of electrons on the island may be treated äs a sharply defined classical variable. Coulomb-blockade oscillations can now also be studied in semiconductor nanostructures, which have a discrete energy spectrum. Semiconductoi nanostructures are fabricated by lateral confinemcnt of the two-dimensional electron gas (2DEG) in Si-inversion layers, or in GaAs-AlGaAs heterostructures. At low tempeiatures, the conduction elec-