First-principles calculation method for electron transport based on grid Lippmann-Schwinger equation

TL;DR

This paper introduces a novel first-principles electron-transport simulation method based on the Lippmann-Schwinger equation within a real-space finite-difference framework, enabling accurate modeling of semiconductor/oxide interfaces.

Contribution

The authors develop a grid-based LS method with analytical Green's function expressions, improving numerical stability and applicability to complex interface systems.

Findings

Leakage current increases with dangling-bond states in Si/SiO2 interfaces.

Ge/GeO2 interfaces are insensitive to dangling-bond states.

The method accurately simulates electron transport in semiconductor heterostructures.

Abstract

We develop a first-principles electron-transport simulator based on the Lippmann--Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor/oxide interfaces sandwiched between semi-infinite metal electrodes. The results confirm that the leakage current through the (001)Si/SiO$_2$ model becomes much larger when the dangling-bond (DB) state is induced by a defect in the oxygen layer while that through the (001)Ge/GeO$_2$ model is insensitive to the DB state.