Fundamental Aspects of Semiconductor Device Modeling Associated With Discrete Impurities: Nonequilibrium Green’s Function Scheme

A new theoretical framework for the nonequilibrium Green’s function (NEGF) scheme is presented to account for the discrete nature of impurities doped in semiconductors. Since the impurity potential is singular, the short-range screened impurity potential is included as the self-energy due to spatially localized impurity scattering. The long-range part of the impurity potential is treated as the self-consistent Hartree potential. The present framework is applied to cylindrical wires under the quasi-one-dimensional (quasi-1D) approximation. We show explicitly how the discrete nature of impurities affects transport properties such as electrostatic potential, local density of states (LDOSs), carrier density, and scattering rates. Furthermore, we demonstrate that the present scheme allows for the quantitative analysis of variabilities in transport characteristics of nanoscale thin wires.