Coupled Non-Equilibrium Green’s Function (NEGF) Electron-Phonon Interaction in Thermoelectric Materials

Abstract

Over the last decade, nano-structured materials have shown a promising avenue for enhancement of the thermoelectric figure of merit. These performance enhancements in most cases have been a direct result of selectively modifying certain geometric attributes that alter the thermal or electrical transport in a desirable fashion. More often, models used to study the electrical and/or thermal transport are calculated independent of each other. However, studies have suggested electrical and thermal transport are intimately linked at the nanoscale. This provides an argument for a more rigorous treatment of the physics in an effort to capture the response of both electrons and phonons simultaneously. A simulation method has been formulated to capture the electron-phonon interaction of nanoscale electronics through a coupled non-equilibrium Greens function (NEGF) method. This approach is unique because the NEGF electron solution and NEGF phonon solution have only been solved independently and have never been coupled to capture a self-consistent inelastic electron-phonon scattering. One key aspect of this formalism is that the electron and phonon description is derived from a quantum point of view and no correction terms are necessary to account for the probabilistic nature of the transport. Additionally, because the complete phonon description is solved, scattering rates of individual phonon frequencies can be investigated to determine how electron-phonon scattering of particular frequencies influences the transport. This computational method is applied to the study of Si/Ge nanostructured superlattice thermoelectric materials.