Simulation of single-electron transport processes in thin granulated chromium films

The results of the numerical simulation of the single-electron transport in two-dimensional granulated chromium films at low temperatures are reported. A theoretical model has been developed in which the granulated film is represented as a two-dimensional matrix of conducting metallic granules (islands), which are weakly coupled with each other through slightly transparent tunnel barriers, ensuring the transport of single electrons localized on the islands. The recently measured current-voltage characteristics of submicron rectangular chromium samples have been explained by taking into account the inhomogeneities in the nanometer sizes of the islands and their effective electron temperature depending on the flowing current. A transition from the two-dimensional regime to the quasi-one-dimensional regime of the single-electron transport leading to the experimentally observed hysteresis has been revealed in the simulated system.