On the current gap of single-electron transistors

TL;DR

This paper provides a theoretical analysis of single-electron transistors based on gold clusters, focusing on Coulomb blockade effects, residual charge, and size-dependent current gaps, highlighting the influence of cluster shape and electron spectrum quantization.

Contribution

It introduces a theoretical framework for understanding Coulomb blockade and residual charge in molecular transistors with gold clusters, considering shape effects and size-dependent phenomena.

Findings

Residual charge depends on cluster shape and is non-integer.

Current gap shows non-monotonic size dependence.

Coulomb blockade effects influence the current-voltage characteristics.

Abstract

Effects of the single-electron tunneling and the Coulomb blockade in a cluster structure (the molecular transistor) are investigated theoretically. In the framework of the particle-in-a-box model for the spherical and disk-shaped gold clusters, the electron spectrum, the temperature dependence of the chemical potential and the residual charge are calculated. We show that the residual charge is equal to the non-integer value of elementary charge $e$ and depends on the cluster's shape. The equations for the analysis of the current-voltage characteristic are used under conservation condition for 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 the simple way. It is shown that the critical charge of the cluster in the open electron system is close to the residual charge. For single-electron 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.