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...

Anderson localization in phonon heat conduction is observed in GaAs/AlAs superlattices with ErAs nanodots.

Using first principles, we calculate the lattice thermal conductivity of Bi, Sb, and Bi-Sb alloys, which are of great importance for thermoelectric and thermomagnetic cooling applications. Our calculation reveals that the ninth-neighbor harmonic and anharmonic force constants are significant; accordingly, they largely affect the lattice thermal conductivity. Several features of the thermal transport in these materials are studied: (1) the relative contributions from phonons and electrons to the total thermal conductivity as a function of temperature are estimated by comparing the calculated lattice thermal conductivity to the measured total thermal conductivity, (2) the anisotropy of the lattice thermal conductivity is calculated and compared to that of the electronic contribution in Bi, and (3) the phonon mean free path distributions, which are useful for developing nanostructures to reduce the lattice thermal conductivity, are calculated. The phonon mean free paths are found to range from 10 to 100 nm for Bi at 100 K.

Our elastic model of ErAs disordered GaAs/AlAs superlattices exhibits a local thermal conductivity maximum as a function of length due to exponentially suppressed Anderson-localized phonons. By analyzing the sample-to-sample fluctuations in the dimensionless conductance, !, the transition from diffusive to localized transport is identified as the crossover from the multi-channel to single-channel transport regime ! ≈ 1. Single parameter scaling is shown to hold in this crossover regime through the universality of the probability distribution of ! that is independent of system size and disorder strength.

Abstract:We have computed phonon scattering rates and density of states in silicon germanium alloys using Green's function calculations and density functional theory.This method contrasts with the virtual crystal approximation (VCA) used in conjunction with Fermi's golden rule, which cannot capture resonance states occurring through the interaction of substitutional impurities with the host lattice. These resonances are demonstrated by density of states and scattering rate calculations in the dilute limit and show broadening as the concentration increases.Although these deviations become significant from the VCA at high frequencies, the relaxation times obtained for these phonon modes are small in both the full scattering theory and the VCA, resulting in their negligible contribution to thermal transport.

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