Self-energy Models for Scattering in Semiconductor Nanoscale Devices: Causality Considerations and the Spectral Sum Rule

Abstract

ABSTRACTThe modelling of of silicon gate-all-around nanowire transistors by non-equilibrium Green function methods requires the computation of self-energies for inelastic electron-phonon interactions. It is shown that many approximations designed to reduce numerical complexityto these self-energies in fact fail because they do not satisfy appropriate causality conditions. Four familiar approximations are discussed and their failures resolved. It is also shown that a condition for the spectral density sum rule to hold (and hence accurate density of states in energy) depends on a simple causality condition.