Density of states, electron-transport mechanisms, and chemical potentials in the presence of inelastic processes

We present a formulation for the estimation of the density of states for quantum structures, such as the quantum wire and the single- and multiple-barrier structures. Our formulation is based on the quantum kinetic approach as opposed to the single-particle approach; therefore, the model inherently accounts for the exclusion principle and incorporates phase randomizing and/or inelastic collisions. Also in this paper, we propose a physically meaningful decomposition of the density of states for left- and right-moving electrons. The total and the decomposed densities of states are then used to define chemical potentials that may be measured by the symmetric and asymmetric voltage probes. The present approach eliminates some unphysical features reported in earlier work and enables us to propose an alternative, but equivalent, expression to the well-known Tsu-Esaki equation for the tunneling current. In our transport equations, the usual transmission coefficients are not needed; instead, we introduce the concept of a state-current density that may be used to describe the current through tunneling barrier structures. Moreover, we use this concept of the state-current density to comment on the coherent and the sequential tunneling mechanisms for double-barrier structures.