Ab-initio Non-Equilibrium Green’s Function Formalism for Calculating Electron Transport in Molecular Devices

Abstract

The purpose of this chapter is to give a general reader an introduction to the Non Equilibrium Greens Function (NEGF) method for first principles modeling of current-voltage characteristics of molecular electronics devices. The molecular device is modeled on the atomic level, and we will use Density Functional Theory (DFT) to describe the electronic structure of the system. We will give a detailed description of all the steps involved in order to calculate the electron current. The steps involved are dividing the system into electrode and scattering region, determining the one-electron DFT Hamiltonian, setting up the NEGF, determining the charge density, and calculating the effective potential. The procedure sets up a set of selfconsistent equations, which result in an effective one-electron Hamiltonian description of the electron motion. From the one-electron Hamiltonian we can determine the electron current using the Landauer-Biittiker approach. We present results obtained with the method for calculating the conductance of molecular resistors, and we will show that there are excellent agreement with recent experimental results. The non-equilibrium current will induce an additional force on the atoms. We investigate the origin of this force and present a simple model which relates the force to the charge rearrangement around the atoms in the scattering region.