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The electron-transport processes in a low-barrier Mott diode are studied by the methods of numerical simulation. The effects related to the quasi-ballistic motion of electrons are examined. The I-V characteristics of the diode are obtained. We have performed a comparative analysis of the results of the simulation, which was carried out using different approaches: the Monte Carlo method and the local-field model. The calculated I-V characteristics are compared with the experimental dependence. The applicability limits of the approaches we used are analyzed.