First-principles simulation of electron mean-free-path spectra and thermoelectric properties in silicon

The mean free paths (MFPs) of energy carriers are of critical importance to the nanoengineering 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 a higher 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. editor’s choice Copyright c © EPLA, 2015 Nanostructuring has proven to be an effective strategy to improve the figure of merit of thermoelectric materials [1–11]. The figure of merit is proportional to the electrical conductivity (σ), the square of the Seebeck coefficient (S) and inversely proportional to the thermal conductivity consisting of both phonon (kp) and electron (ke) contributions. The most effective nanostructuring approach so far has been reducing the phonon thermal conductivity while maintaining the electronic performance. For this strategy to be effective, the nanostructures should be smaller than the phonon mean free path (MFP) but larger than the electron MFP so that phonons are more strongly scattered than electrons. It is understood that both electron and phonon MFPs have a distribution over a certain energy range. There has been good progress in predicting the spectral phonon MFPs for a range of bulk single crystals and alloys [12–24]. However, there has been no discussion on the spectral electron MFPs from first principles. Surprisingly, this status exists even for silicon, (a)E-mail: [email protected] (corresponding author) one of the most important materials. The existing knowledge on electron scattering, relaxation time, and MFP, is mostly based on analytical models derived from Fermi’s golden rule assuming ideal electron and phonon dispersions [25,26]. Past work on the phonon MFP distributions based on first-principles simulations, however, shows that such semi-empirical treatments on scattering lead to large error [13,21,23,27]. In this work, we compute the electron scattering rates and MFPs in silicon from first principles and examine their dependence on energy, doping concentration, and their contributions to electronic conductivity and Seebeck coefficient. We demonstrate quantitatively the large disparity in the electron and phonon MFP distributions in silicon, and use the information obtained to predict that nanostructures with size of 20 nm can result in a higher than five times enhancement in ZT for silicon, consistently with past experimental results. We consider n-doped silicon with carrier concentration between 10 and 10 cm−3 in the temperature range