Abstract
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 main objective of this study is to determine some classical aspects of electron tunnelling through a QD using the driven lattice gas model. 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.
Highlights
Nowadays, nanomaterial such as quantum dot (QD) have attracted much attention because of their superior electronic, optical, and magnetic properties due to confinement effects [1,2]
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
Summary
Nanomaterial such as quantum dot (QD) have attracted much attention because of their superior electronic, optical, and magnetic properties due to confinement effects [1,2]. A QD is a mesoscopic system which resembles an atom it is tens or hundreds times bigger than an actual atom, e.g. the Zeeman Effect and discrete energy levels [3], entitling the QD as an artificial atom [4] Another interesting feature is that its physical properties depend on the voltage applied to the dot, whereas an atom depends upon its valence electrons. A standard mathematical model which can be utilized to study many physical properties of dynamical systems is the totally asymmetric simple exclusion process (TASEP) in one dimension (1D) This is a simple driven lattice gas model where hard-core particles occupying a discrete lattice sites, i L, may jump to their respective right-nearest neighbour sites, (i + 1) L, provided that the right-nearest neighbour sites are not occupied by any other (hard-core) particle.
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