Effects of charging and tunnelling in a structure based on magic and non-magic metal clusters

The effects of charging and single-electron tunnelling in a metal cluster structure are investigated theoretically. In the framework of the particle-in-a-box model for spherical and disc-shaped gold clusters, the electron spectrum and the temperature dependence of the electron chemical potential are calculated. The difference between the electron chemical potentials of massive electrodes and islands leads to the noticeable charging of the electrode. We show that the effective residual charge is equal to the non-integer value of the elementary charge e and depends on the shape of the cluster. The equations for the analysis of the current-voltage characteristic are used under the conditions of conservation of the total energy of the structure, taking into account the contact potential difference. Restrictions associated with the Coulomb instability of a cluster are introduced into the theory in a simple way. It is shown that the critical charge of the cluster in an open electron system is close to the effective residual charge. For single-electron molecular transistors based on small gold clusters the current gap and its voltage asymmetry are computed. We demonstrate that the current gap exhibits non-monotonic size dependences which are related to the quantization of the electron spectrum and the Coulomb blockade.