Nonequilibrium Green's function formalism applicable to discrete impurities in semiconductor nanostructures

A theoretical framework for the nonequilibrium Green's function (NEGF) scheme is presented to account for the discrete nature of impurities doped in semiconductor nanostructures. The short-range part of the impurity potential is included as scattering potential in the self-energy due to spatially localized impurity scattering, and the long-range part of the impurity potential is treated as the self-consistent Hartree potential by coupling with the Poisson equation. The position-dependent impurity scattering rate under inhomogeneous impurity profiles is systematically derived so that its physical meaning is clarified. The position dependence of the scattering rate turns out that it is represented by the ``center of mass'' coordinates in the Wigner coordinates, rather than the real-space coordinates. Consequently, impurity scattering is intrinsically nonlocal in space. The proposed framework is applied to cylindrical thin wires under the quasi-one-dimensional approximation. We show explicitly how the discrete nature of impurities affects the transport properties such as electrostatic potential, local density of states, carrier density, scattering rates, and mobility.