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

Abstract

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-principlesbased 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.Nanostructuring has proven to be an effective strategy to improve the figure of merit of thermoelectric materials [1][2][3][4][5][6][7][8][9][10][11]. The figure of merit is proportional to the electrical conductivity (), the square of the Seebeck coefficient (S) and inversely proportional to the thermal conductivity consisting of both phonon (k p ) and electron (k e ) 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 certain energy range. There has been good progress in predicting the spectral phonon MFPs for a range of bulk single crystals and alloys [12][13][14][15][16][17][18][19][20][21][22][23][24]. However, there has been no discussion on the spectral electron MFPs from first-principles. Surprisingly, this status exists even for silicon, one of the most important materials. 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...

First-principles calculations of thermal, electrical, and thermoelectric transport properties of semiconductors

“…We will also show that without considering terms containing f    k , good agreement for the electrical properties in silicon with experiments can be achieved [36][37][38]. In essence, the momentum relaxation time is only an approximation to the full expression in Eq.…”

“…The competence between the relaxation time and the group velocity gives rise to the maximal electron mean free path. Figure 10b further shows the accumulated contribution to the electrical conductivity with respect to the electron mean free path [37]. Compared to the phonon mean free path distribution, we see that electron mean free paths span over a smaller range than those of phonons, from 10 nm to 100 nm for lightly-doped silicon and from 1 nm to 10 nm for heavily-doped silicon.…”

“…[38]. Copyright (2015) American Physical Society; Doped Si results reprinted with permission from Qiu et al [37]. Copyright (2015) Institute of Physics; GaAs results reprinted with permission from Bernardi et al [122].…”

“…The sharp cut-off of the accumulation curve for the electrical conductivity is due to the maximal electron mean free path as we have discussed above. The clear difference between the phonon mean free path and electron mean free path can be used to quantitatively examine the effect of nanostructuring techniques in reducing the phonon thermal conductivity while maintaining the electrical transport properties [37]. However such detailed mean free path information based on first-principles calculations has not been reported for other semiconducting materials.…”

“…However, up to now there are only few materials whose mobility or Seebeck coefficient has been calculated using a parameter-free first-principles approach, with examples including silicon, MoS2 and phosphorene [36][37][38]126,127]. Here we deem the use of the deformation potential model (even with deformation potential extracted from the first-principles) as an complementary but not a predictive method, because it neglects the electron-state-dependence of the electron-phonon coupling, which is hardly justified for general materials, especially considering the fact that the material search has been going towards more complex ones.…”