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

Abstract

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...

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

“…In a later study using a full first-principles calculation with both electron and phonon relaxation times extracted from DFT calculations, the Seebeck coefficient including the phonon drag was predicted with excellent agreements compared to the experiment [126], as shown in Fig. 11a.…”

“…It was shown that at room temperature in lightly-doped n-type (p-type) silicon the phonon drag contribute to 30% (40%) of the total Seebeck coefficient [126]. As we have mentioned, phonon drag effect can be understood as the momentum transfer from non-equilibrium phonons with long mean free paths to the electron system.…”

“…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:…”

“…For example, one can enhance the thermoelectric performance by filtering out short-mean-free-path phonons, in which case the phonon drag will be retained but the thermal conductivity can be reduced, a strategy recently proposed in Ref. [126]. Furthermore, by considering the phonon scattering by electrons in the phonon relaxation time calculation, the reduction of the phonon drag effect at higher carrier concentrations, known as the saturation effect [39], can also be captured by the fully first-principles approach [126], with a good agreement with the experiment shown in Fig.…”

“…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.…”