Band convergence is considered a clear benefit to thermoelectric performance because it increases the charge carrier concentration for a given Fermi level, which typically enhances charge conductivity while preserving the Seebeck coefficient. However, this advantage hinges on the assumption that interband scattering of carriers is weak or insignificant. With first-principles treatment of electron-phonon scattering in CaMg$_{2}$Sb$_{2}$-CaZn$_{2}$Sb$_{2}$ Zintl system and full Heusler Sr$_{2}$SbAu, we demonstrate that the benefit of band convergence can be intrinsically negated by interband scattering depending on the manner in which bands converge. In the Zintl alloy, band convergence does not improve weighted mobility or the density-of-states effective mass. We trace the underlying reason to the fact that the bands converge at one k-point, which induces strong interband scattering of both the deformation-potential and the polar-optical kinds. The case contrasts with band convergence at distant k-points (as in the full Heusler), which better preserves the single-band scattering behavior thereby successfully leading to improved performance. Therefore, we suggest that band convergence as thermoelectric design principle is best suited to cases in which it occurs at distant k-points.
Thermoelectric performance of SnTe has been found to enhance with isovalent doping of alkaline and transition metal elements where most of these elements have solubility of less than 13%. We propose a strategy of doping rare earth element Yb to enhance the thermoelectric performance of SnTe. With heavy atomic mass and strong spin-orbit coupling, even the mild doping of Yb (~ 5%) is enough to create a degeneracy via band-convergence which enhances the density of states near Fermi level and improve overall performance. Our transport data and first-principles calculations corroborate that nearly …
High Seebeck coefficient by creating large density of state (DOS) around the Fermi level through either electronic structure modification or manipulating nanostructures, is commonly considered as a route to advanced thermoelectrics. However, large density of state due to flat bands leads to large effective mass, which results in a simultaneous decrease of mobility. In fact, the net effect of high effective mass is a lower thermoelectric figure of merit when the carriers are predominantly scattered by acoustic phonons according to the deformation potential theory of Bardeen-Shockley. We demonst…
Half-Heuslers, an emerging thermoelectric material group, has complex bandstructures with multiple bands that can be aligned through band engineering approaches, giving us an opportunity to improve their power factor. In this work, going beyond the constant relaxation time approximation, we perform an investigation of the benefits of band alignment in improving the thermoelectric power factor under different density of states dependent scattering scenarios. As a test case we consider the Co-based p-type half-Heuslers TiCoSb, NbCoSn and ZrCoSb. First, using simplified effective mass models comb…
We present a first principles based model of electron-phonon scattering mechanisms and thermoelectric transport at the L and $Σ$ valleys in <200b>$p$-type PbTe, accounting for their thermally induced shifts. Our calculated values of all thermoelectric transport parameters at room temperature are in very good agreement with experiments for a wide range of doping concentrations. Scattering due to longitudinal optical phonons is the main scattering mechanism in $p$-type PbTe, while scattering due to transverse optical modes is the weakest. The L valleys contribute most to thermoelectric transport…
Complex electronic band structures, with multiple valleys or bands at the same or similar energies can be beneficial for thermoelectric performance, but the advantages can be offset by inter-valley and inter-band scattering. In this paper, we demonstrate how first-principles band structures coupled with recently developed techniques for rigorous simulation of electron-phonon scattering provide the capabilities to realistically assess the benefits and trade-offs associated with these materials. We illustrate the approach using n-type silicon as a model material and show that intervalley scatter…
The newly emerging monolayer phosphorene was recently predicted to be a promising thermoelectric material. In this work, we propose to further enhance the thermoelectric performance of phosphorene by the strain-induced band convergence. The effect of the uniaxial strain on the thermoelectric properties of phosphorene was investigated by using the first-principles calculations combined with the semi-classical Boltzmann theory. When the zigzag-direction strain is applied, the Seebeck coefficient and electrical conductivity in zigzag direction can be greatly enhanced simultaneously at the critica…
Band convergence is an effective strategy to improve the thermoelectric performance of complex bandstructure thermoelectric materials. Half-Heuslers are good candidates for band convergence studies because they have multiple bands near the valence bad edge that can be converged through various band engineering approaches providing power factor improvement opportunities. Theoretical calculations to identify the outcome of band convergence employ various approximations for the carrier scattering relaxation times (the most common being the constant relaxation time approximation) due to the high c…
Achieving high valley degeneracy (i.e. "band convergence") in a material usually results in considerably enhanced thermoelectric properties. However, it is still unclear why this strategy of designing efficient thermoelectric materials is so successful, since the benefit of increased density of states may be severely degraded by intervalley scattering. Using first-principles calculations, we investigate these effects in $p$-type PbTe, where temperature induces alignment of the $L$ and $Σ$ valleys at $\sim$~620~K. We explicitly show that the thermoelectric power factor and figure of merit peak …
Unlike in many other semiconductors, the band gap of PbTe increases considerably with temperature. We compute the thermoelectric transport properties of n-type PbTe from first principles including the temperature variation of the electronic band structure. The calculated temperature dependence of the thermoelectric quantities of PbTe is in good agreement with previous experiments when the temperature changes of the band structure are accounted for. We also calculate the optimum band gap values which would maximize the thermoelectric figure of merit of n-type PbTe at various temperatures. We sh…
Biaxial strain effects on electronic structures and thermoelectric properties of monolayer $\mathrm{PtTe_2}$ are investigated by using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) for the electron part and GGA for the phonon part. Calculated results show that small compressive strain (about -3\%) can induce semiconductor-to-metal transition, which can easily be achieved in experiment. The conduction bands convergence is observed for unstrained $\mathrm{PtTe_2}$, which can be removed by both compressive and tensile strains. Tensile strain can give rise to valence band…
It is believed that nanostructuring is an effective way to achieve excellent thermoelectric performance. In the work, by combining the first-principles calculations and semiclassical Boltzmann transport theory, we investigate the thermoelectric properties of bulk and monolayer BiTeBr including both the electron and phonon transports. The generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) is employed for the electron part, and GGA for the phonon part. It is found that SOC has important effects on electronic transport coefficients because of SOC-induced obvious influences on…
We present results of electronic band structure, Fermi surface and electron transport properties calculations in orthorhombic $n$- and $p$-type SnSe, applying Korringa-Kohn-Rostoker method and Boltzmann transport approach. The analysis accounted for temperature effect on crystallographic parameters in $Pnma$ structure as well as the phase transition to $CmCm$ structure at $T_c\sim 807 $K. Remarkable modifications of conduction and valence bands were notified upon varying crystallographic parameters within the structure before $T_c$, while the phase transition mostly leads to jump in the band g…
Rock-salt structured chalcogenides, such as PbTe, PbSe, and SnTe, are the top candidates for mid-temperature thermoelectric applications, and their p-type thermoelectric efficiencies can be enhanced via aligning the valence bands. Here, we provided comprehensive numerical investigations on the effects of band convergence on electronic properties. We found that the extra valance band can indeed significantly enhance the power factor. Nevertheless, the extra valance band can also increase the electronic thermal conductivity, which partially offsets the enhanced power factor for the overall figur…
Recent studies indicated the interesting metal-to-semiconductor transition when layered bulk GeP3 and SnP3 are restricted to the monolayer or bilayer, and SnP3 monolayer has been predicted to possess high carrier mobility and promising thermoelectric performance. Here, we investigate the biaxial strain effect on the electronic and thermoelectric properties of SnP3 monolayer. Our first-principles calculations combined with Boltzmann transport theory indicate that SnP3 monolayer has the pudding-mold-type valence band structure, giving rise to a large p-type Seebeck coefficient and a high p-type …
To better understand and enhance the thermoelectric efficiency of a new class of Mg-based thermoelectrics, using hybrid density-functional theory, we study the microscopic origins of valley degeneracies in the conduction band of the solid solution Mg2Si1-xSnx and its constituent components - namely, Mg2Si and Mg2Sn. In the solid solution of Mg2Si1-xSnx, the Mg sublattice and Si/Sn sublattice are expected to undergo either tensile or compressive strain. Interestingly, both tensile strain of Mg2Si and compressive strain of Mg2Sn enhance the conduction band valley degeneracy or band convergence, …
Strain engineering is a very effective method to tune electronic, optical, topological and thermoelectric properties of materials. In this work, we systematically study biaxial strain dependence of electronic structures and thermoelectric properties (both electron and phonon parts) of monolayer $\mathrm{PtSe_2}$ with generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) for electron part and GGA for phonon part. Calculated results show that compressive or tensile strain can induce conduction band minimum (CBM) or valence band maximum (VBM) transition, which produces important…
We have conducted temperature dependent Angle Resolved Photoemission Spectroscopy (ARPES) study of the electronic structure of n-, p- type PbTe, PbSe and PbS, which are pre- mier thermoelectric materials. Our ARPES measurements on them provide direct evidence for the light hole upper valence bands (UVBs) and the so-called heavy hole lower valence bands (LVBs), and an unusual temperature dependent relative movement between their band maxima leading to a monotonic decrease in the energy separation between LVBs and UVBs with increase in temperature. This enables convergence of these valence bands…
An efficient approach to improve the thermoelectric performance of materials is to converge their electronic bands, which is known as band engineering. In this regard, lots of effort have been made to further improve the thermoelectric efficiency of bulk and exfoliated monolayers of Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$. However, ultra-high band degeneracy and thus significant improvement of power factor have not been yet realized in these materials. Using first-principles methods, we demonstrate that the valley degeneracy of Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$ can be largely improved upon s…
Using first principles calculations, we study the conduction band alignment, effective mass, and Fermi surface complexity factor of n-type Mg3Sb2-xBix (x = 0, 1, and 2) from the full ab initio band structure. We find that with increasing the Bi content the K and M band minima moves away from the conduction band minimum CB1 while the singly-degenerate $Γ$ band minimum shifts rapidly downward and approaches the conduction band minimum. But the favorable six-fold degenerate CB1 band minimum keeps dominating the conduction band minimum and there is no band crossing between the $Γ$ and CB1 band min…
Boltzmann transport calculations based on band structures generated with density functional theory (DFT) are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense ${\it k}$-point sampling of the Brillouin zone and are therefore typically limited to the generalized gradient approximation (GGA), whereas more accurate methods such as hybrid functionals would have been preferable. GGA variants, however, generally underestimate the band gap. While premature onset of minority carriers can be avoided with scissor corrections…
In this work we theoretically explore the effect of dimensionality on the thermoelectric power factor of InAs nanowires by coupling atomistic tight-binding calculations to the Linearized Boltzmann transport formalism. We consider nanowires with diameters from 40nm (bulk-like) down to 3nm (1D), which allows for the proper exploration of the power factor within a unified large-scale atomistic description across a large diameter range. We find that as the diameter of the nanowires is reduced below d < 10 nm, the Seebeck coefficient increases substantially, a consequence of strong subband quantiza…
The strategy of band convergence of multi-valley conduction bands or multi-peak valence bands has been widely used to search or improve thermoelectric materials. However, the phonon-assisted intervalley scatterings due to multiple band degeneracy are usually neglected in the thermoelectric community. In this work, we investigate the (thermo)electric properties of non-polar monolayer $β$- and $α$-antimonene considering full mode- and momentum-resolved electron-phonon interactions. We also analyze thoroughly the selection rules on electron-phonon matrix-elements using group-theory arguments. Our…
Filling the large voids in the crystal structure of the skutterudite CoSb$_3$ with rattler atoms $R$ provides an avenue for both increasing carrier concentration and disrupting lattice heat transport, leading to impressive thermoelectric performance. While the influence of $R$ on the lattice dynamics of skutterudite materials has been well studied, the phase stability of $R$-filled skutterudite materials and the influence of the presence and ordering of $R$ on the electronic structure remain unclear. Here, focusing on the Yb-filled skutterudite Yb$_x$Co$_4$Sb$_{12}$, we employ first-principles…
The band convergence strategy, which improves Seebeck coefficient by inducing multi-valley in bandstructures, has been widely used in thermoelectric performance (TE) enhancing. However, the phonon-assisted intervalley scattering effect is neglected and the mode-selection rules remain unclear. In this work, TE properties for $α$-, $β$- and $γ$-PbP are intestigated under the consideration of full mode-, energy- and momentum-resolved electron-phonon interactions (EPI). The group theory is used to analyze the selection rules for EPI matrix elements. Our calculations reveal that, the intervalley sc…
Tin-chalcogenides SnX (X = Te, Se and S) have been arousing research interest due to their thermoelectric physical properties. The two-dimensional (2D) counterparts, which are expected to enhance the property, nevertheless, have not been fully explored because of many possible structures. Generating variable composition of 2D Sn$_{1-x}$X$_{x}$ systems (X = Te, Se and S) has been performed using global searching method based on evolutionary algorithm combining with density functional calculations. A new hexagonal phase named by $β'$-SnX is found by Universal Structure Predictor Evolutionary Xta…
We have conducted temperature dependent Angle Resolved Photoemission Spectroscopy (ARPES) study of the electronic structures of PbTe, PbSe and PbS. Our ARPES data provide direct evidence for the \emph{light} hole upper valence bands (UVBs) and hitherto undetected \emph{heavy} hole lower valence bands (LVBs) in these materials. An unusual temperature dependent relative movement between these bands leads to a monotonic decrease in the energy separation between their maxima with increasing temperature, which is referred as band convergence and has long been believed to be the driving factor behin…
Resolving the structure of energy bands in transport experiments is a major challenge in condensed matter physics and material science. Sometimes, however, traditional electrical conductance or resistance measurements only provide very small signals, and thus limit the ability to obtain direct band structure information. In this case, it has been proven beneficial to employ thermoelectric measurements which are sensitive to the first derivative of the density of states with respect to energy, rather than to its value itself. Due to the large interest in topological effects these days, it is im…
