Methods for fast evaluation of self-energy matrices in tight-binding modeling of electron transport systems

Abstract

Simulation of quantum carrier transport in nanodevices with non-equilibrium Green’s function approach is computationally very challenging. One major part of the computational burden is the calculation of self-energy matrices. The calculation in tight-binding schemes usually requires dealing with matrices of the size of a unit cell in the leads. Since a unit cell always consists of several planes (for example, in silicon nanowire, four atomic planes for [100] crystal orientation and six for [111] and [112]), we show in this paper that a condensed Hamiltonian matrix can be constructed with reduced dimension (∼1/4 of the original size for [100] and ∼1/6 for [111] and [112] in the nearest neighbor interaction) and thus greatly speeding up the calculation. Examples of silicon nanowires with sp3d5s* basis set and the nearest neighbor interaction are given to show the accuracy and efficiency of the proposed methods.