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The mean-free-paths (MFPs) of energy carriers are of critical importance tothe nano-engineering of better thermoelectric materials. Despite significantprogress in the first-principles-based understanding of the spectraldistribution of phonon MFPs in recent years, the spectral distribution ofelectron MFPs remains unclear. In this work, we compute the energy dependentelectron scatterings and MFPs in silicon from first-principles. The electricalconductivity accumulation with respect to electron MFPs is compared to that ofthe phonon thermal conductivity accumulation to illustrate the quantitativeimpact of nanostructuring on electron and phonon transport. By combining allelectron and phonon transport properties from first-principles, we predict thethermoelectric properties of the bulk and nanostructured silicon, and find thatsilicon with 20 nm nanograins can result in more than five times enhancement intheir thermoelectric figure of merit as the grain boundaries scatter phononsmore significantly than that of electrons due to their disparate MFPdistributions.

First-Principles Simulation of Electron Mean-Free-Path Spectra and Thermoelectric Properties in Silicon