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

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 jellium electrodes. The results confirm that the leakage current through the (001) Si-SiO2 model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001) Ge-GeO2 model is insensitive to the dangling bond state.