  The mean-free-paths (MFPs) of energy carriers are of critical importance to
the nano-engineering of better thermoelectric materials. Despite significant
progress in the first-principles-based understanding of the spectral
distribution of phonon MFPs in recent years, the spectral distribution of
electron MFPs remains unclear. In this work, we compute the energy dependent
electron scatterings and MFPs in silicon from first-principles. The electrical
conductivity accumulation with respect to electron MFPs is compared to that of
the phonon thermal conductivity accumulation to illustrate the quantitative
impact of nanostructuring on electron and phonon transport. By combining all
electron and phonon transport properties from first-principles, we predict the
thermoelectric properties of the bulk and nanostructured silicon, and find that
silicon with 20 nm nanograins can result in more than five times enhancement in
their thermoelectric figure of merit as the grain boundaries scatter phonons
more significantly than that of electrons due to their disparate MFP
distributions.
