The Seebeck coefficient and phonon drag in silicon

Mahan, G. D.; Lindsay, Lucas; Broido, David

doi:10.1063/1.4904925

Cited by 63 publications

(61 citation statements)

References 30 publications

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“…The low doping level implies that the impurity scattering (3) as well as the phonon scattering by electrons (37) plays a negligible role. Similar to previous work (29,31), good agreement is obtained between the calculation results and the experimental data (8), from 300 K down to 80 K for electrons and to 60 K for holes (SI Appendix, Fig. S2).…”

Section: Resultssupporting

confidence: 77%

“…Compared with the variational method, it has the advantage of a more transparent interpretation of the results in terms of contributions from individual phonon modes. This approach has been applied to Si metal-oxide-semiconductor field-effect transistors and GaAs/AlGaAs heterojunctions (30) and to bulk silicon at low carrier concentrations recently by incorporating accurate phononphonon scattering rates obtained from first-principles calculation into the model (31). Although the quantitative agreement with experiments at low carrier concentrations was improved, the appearances of adjustable material-dependent parameters (i.e., the deformation potentials) for the crucial electron-phonon scattering processes still limit the predictive power and are not satisfactory for a modern mode-by-mode understanding of the phonon drag effect.…”

Section: Significancementioning

confidence: 99%

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Ab initio optimization of phonon drag effect for lower-temperature thermoelectric energy conversion

Zhou

Liao

Qiu

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Although the thermoelectric figure of merit zT above 300 K has seen significant improvement recently, the progress at lower temperatures has been slow, mainly limited by the relatively low Seebeck coefficient and high thermal conductivity. Here we report, for the first time to our knowledge, success in first-principles computation of the phonon drag effect-a coupling phenomenon between electrons and nonequilibrium phonons-in heavily doped region and its optimization to enhance the Seebeck coefficient while reducing the phonon thermal conductivity by nanostructuring. Our simulation quantitatively identifies the major phonons contributing to the phonon drag, which are spectrally distinct from those carrying heat, and further reveals that although the phonon drag is reduced in heavily doped samples, a significant contribution to Seebeck coefficient still exists. An ideal phonon filter is proposed to enhance zT of silicon at room temperature by a factor of 20 to ∼0.25, and the enhancement can reach 70 times at 100 K. This work opens up a new venue toward better thermoelectrics by harnessing nonequilibrium phonons.phonon drag | nonequilibrium phonon | electron phonon interaction | thermoelectrics | nanocluster scattering I n metals and semiconductors, lattice vibration-, or phonon-, induced electron scattering has a major influence on electronic transport properties (1). The strength of the electron-phonon interaction (EPI) depends on the distribution of electron and phonon populations. The EPI problem was first studied by Bloch (2), who assumed the phonons to be in equilibrium (so-called Bloch condition) when calculating the scattering rates of electrons caused by EPI, because of the frequent phonon-phonon Umklapp scattering. This assumption is widely adopted for the determination of electronic transport properties at higher temperatures (1, 3), including the electrical conductivity and the normal ("diffusive") Seebeck coefficient. Below the Debye temperature, however, the nonequilibrium phonons become appreciable because the phonon-phonon Umklapp scatterings are largely suppressed, and this assumption becomes questionable. The significance of nonequilibrium phonons on the Seebeck coefficient was first recognized by Gurevich (4). The experimental evidence given later (5, 6) clearly showed an "anomalous" peak of the Seebeck coefficient at around 40 K in germanium. To address this unusual observation, Herring proposed that the nonequilibrium phonons can deliver excessive momenta to the electrons via the EPI (7). This process generates an extra electrical current in the same direction as the heat flow, as if the electrons were dragged along by phonons. Therefore, this effect has been dubbed "phonon drag" (7), which makes itself distinct from the normal (diffusive) Seebeck effect. Subsequent explorations (8-13) revealed that this effect exists in various material systems. In particular, it has been suggested that phonon drag is responsible for the extremely high Seebeck coefficient S = −4,500 μV/K experimentally found i...

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Section: Resultssupporting

confidence: 77%

Section: Significancementioning

confidence: 99%

Ab initio optimization of phonon drag effect for lower-temperature thermoelectric energy conversion

Zhou

Liao

Qiu

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…This emphasizes the use of a first-principles approach for better description of coupled electron-phonon transport. These calculations [125,126] quantitatively investigated the temperature dependence of the phonon drag effect:…”

Section: Seebeck Coefficientmentioning

confidence: 99%

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

Zhou

Liao

Chen

2016

Semicond. Sci. Technol.

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Transport properties of semiconductors are keys to the performance of many solid-state devices (transistors, data storage, thermoelectric cooling and power generation devices, etc.).Understanding of the transport details can lead to material designs with better performances. In recent years simulation tools based on first-principles calculations have been greatly improved, being able to obtain the fundamental ground state properties of materials (such as band structure and phonon dispersion) accurately. Accordingly, methods have been developed to calculate the transport properties based on an ab initio approach. In this review we focus on the thermal, electrical, and thermoelectric transport properties of semiconductors, which represent the basic transport characteristics of the two degrees of freedom in solids -electronic and lattice degrees of freedom.Starting from the coupled electron-phonon Boltzmann transport equations, we illustrate different scattering mechanisms that change the transport features and review the first-principles approaches that solve the transport equations. We then present the first-principles results on the thermal and electrical transport properties of semiconductors. The discussions are grouped based on different scattering mechanisms including phonon-phonon scattering, phonon scattering by equilibrium electrons, carrier scattering by equilibrium phonons, carrier scattering by polar optical phonons, scatterings due to impurities, alloying and doping, and phonon drag effect. We show how the first-principles methods allow one to investigate the transport properties with unprecedented details and also offer new insights to the electron and phonon transport. Current status of the simulation is mentioned when appropriate and some of the future directions are also discussed.

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“…3,4 In addition to this, the role of the coupled electron-phonon dynamics on the thermoelectric properties of silicon has very recently attracted renewed interest. [11][12][13] Indeed, in this material there is a substantial enhancement, even at room temperature and in heavily doped samples, of the Seebeck coefficient induced by the drag exerted on charge carriers from phonons diffusing along a temperature gradient (phonon drag). In the past this topic has not received much attention beyond the initial experimental 14 and theoretical 15 works, but with current interest in thermoelectric energy conversion this effect might represent an interesting route to enhance thermoelectric performance.…”

Section: Introductionmentioning

confidence: 99%

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

2016

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We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearised Boltzmann transport equation, also including the effect of non-equilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to n-doped silicon. In particular, we discuss a number of thermoelectric properties such as thermal and electrical conductivities of electrons, Lorenz number and Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavours of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

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The Seebeck coefficient and phonon drag in silicon

Cited by 63 publications

References 30 publications

Ab initio optimization of phonon drag effect for lower-temperature thermoelectric energy conversion

Ab initio optimization of phonon drag effect for lower-temperature thermoelectric energy conversion

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

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

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