On the classical aspects of electrons tunnelling through a quantum dot via a driven lattice gas model in one dimension
A theoretical study of classical aspects, i.e.: density, current density, and average speed of electrons tunnelling through a quantum dot (QD) via a simple driven lattice gas model have been carried out. The study is conducted by considering a resemblance between the components of the QD with the components of the totally asymmetric simple exclusion process (TASEP) that consists of only a single site and open boundary conditions. The former consists of a source, an island, and a drain, which corresponds respectively to the left reservoir (i = 0), site i = 1, and the right reservoir (i = 2) of the latter. Explicit expressions of the density, current densities, and average speed for electrons tunnelling through the QD in the classical regime are obtained. At the steady state, the density of electrons tunnelling through the dot is 0.5 and the current density becomes v/2, where v is the speed of the electrons. Furthermore, the speed of the electrons may be obtained as functions of temperature and the difference between gate and source-drain potentials. For very low temperatures, the speed of electrons rapidly goes to zero pointing to the occurrence of Coulomb blockade.