Nonequilibrium Green's Function Formalism Applicable to Discrete Impurities in Semiconductor Nanostructures

TL;DR

This paper introduces a novel NEGF framework for modeling discrete impurities in semiconductor nanostructures, capturing their nonlocal effects on transport properties.

Contribution

It develops a comprehensive NEGF approach that includes both short-range impurity scattering and long-range Coulomb interactions, with a focus on impurity position dependence.

Findings

Impurity scattering rate depends on 'center of mass' coordinates in Wigner space.

Discrete impurities significantly influence electrostatic potential and carrier mobility.

The framework is demonstrated on quasi-1D cylindrical nanowires.

Abstract

A new 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 impurity potential is included as scattering potential in the self-energy due to spatially localized impurity scattering, and the long-range part of 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 to be 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 (quasi-1D) 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.