Simulation of Electron Transmission through Graphene with Inelastic Scattering

Abstract

Real-space time evolution of an electron wave packet through single- and multi-layer graphene is numerically calculated with taking the effect of inelastic scattering into account for the first step of numerical simulation of graphene-insulator-semiconductor (GIS)-structured electron source. The incident electron energy is ∼10 eV supposing the typical experimental condition. Wave packet inevitably introduces an energy uncertainty, which is rather preferable for the simulation of real electron source with energy spread. The graphene potential for the incident electron is calculated from the electron density obtained by the density functional method and the screened Coulomb potential. The inelastic scattering effect is included in the calculation by assuming the imaginary potential proportional to the real graphene potential with a proportionality constant a. Comparing the obtained simulation results with the experimental ones, the inelastic parameter is determined as a ≃ 0.03. Simulation of realistic three-layer GIS structure remains as a future work, where the effects of inelastic scattering should be included by the above method with a ≃ 0.03.