Density of States for Warped or non-Warped Energy Bands

Scientific Reports, 2016

An angular effective mass formalism previously introduced is used to study the density of states in warped and non-warped energy bands. Band warping may or may not increase the densityof-states effective mass. Band "corrugation," referring to energy dispersions that deviate "more severely" from being twice-differentiable at isolated critical points, may also vary independently of density-of-states effective masses and band warping parameters. We demonstrate these effects and the superiority of an angular effective mass treatment for valence band energy dispersions in cubic materials. We also provide some two-dimensional physical and mathematical examples that may be relevant to studies of band warping in heterostructures and surfaces. These examples may also be useful in clarifying the interplay between possible band warping and band non-parabolicity for non-degenerate conduction band minima in thermoelectric materials of corresponding interest.

Physical Review B, 2014

Optical and transport properties of materials depend heavily upon features of electronic band structures in proximity of energy extrema in the Brillouin zone (BZ). Such features are generally described in terms of multi-dimensional quadratic expansions and corresponding definitions of effective masses. Multi-dimensional quadratic expansions, however, are permissible only under strict conditions that are typically violated when energy bands become degenerate at extrema in the BZ. Even for energy bands that are non-degenerate at critical points in the BZ there are instances in which multi-dimensional quadratic expansions cannot be correctly performed. Suggestive terms such as "band warping", "fluted energy surfaces", or "corrugated energy surfaces" have been used to refer to such situations and ad hoc methods have been developed to treat them. While numerical calculations may reflect such features, a complete theory of band warping has not hitherto been developed. We define band warping as referring to band structures that do not admit second-order differentiability at critical points in k-space and we develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass. Our theory also accounts for effects of band non-parabolicity and anisotropy, which hitherto have not been precisely distinguished from, if not utterly confused with, band warping. Based on our theory, we develop precise procedures to evaluate band warping quantitatively. As a benchmark demonstration, we analyze the warping features of valence bands in silicon using first-principles calculations and we compare those with previous semi-empirical models. As an application of major significance to thermoelectricity, we use our theory and angular effective masses to generalize derivations of tensorial transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. From that theory we discover the formal existence at critical points of transport-equivalent ellipsoidal bands that yield identical results from the standpoint of any transport property. Additionally, we illustrate with some basic multi-band models the drastic effects that band warping and anisotropy can induce on thermoelectric properties such as electronic conductivity and thermopower tensors.

Physical Review Letters, 2015

Thermoelectrics are promising to address energy issues but their exploitation is still hampered by low efficiencies. So far, much improvement has been achieved by reducing the thermal conductivity but less by maximizing the power factor. The latter imposes apparently conflicting requirements on the band structure: a narrow energy distribution and a low effective mass. Quantum confinement in nanostructures or the introduction of resonant states were suggested as possible solutions to this paradox but with limited success. Here, we propose an original approach to fulfill both requirements in bulk semiconductors. It exploits the highly-directional character of some orbitals to engineer the band-structure and produce a type of low-dimensional transport similar to that targeted in nanostructures, while retaining isotropic properties. Using first-principles calculations, the theoretical concept is demonstrated in Fe2YZ Heusler compounds, yielding power factors 4-5 times larger than in classical thermoelectrics at room temperature. Our findings are totally generic and rationalize the search of alternative compounds with a similar behavior. Beyond thermoelectricity, these might be relevant also in the context of electronic, superconducting or photovoltaic applications. PACS numbers: 71.15.-m, 71.15.Mb,

Computational Materials Science, 2014

The state-of-the-art full-potential linearized augmented-plane wave methods have been employed to study the electronic structures of four thermoelectric materials PbTe, Mg 2 Si, FeGa 3 and CoSb 3 belonging to chalcogenide, silicide, correlated systems and skutterudite group, respectively. Here we used the PBEsol exchange correlation functional, which predicts lattice parameters very close to the experimental values. The calculated bulk moduli are also found to be in fairly good agreement with the experimental ones. In comparison to the experimental values this functional underestimates the band gap of Mg 2 Si and CoSb 3 ; and overestimates the band gap of PbTe and FeGa 3 . The effect of spin-orbit coupling (SOC) on the electronic structures of these compounds is also studied in detail. There is a drastic decrement ($90%) of band gap of PbTe in the presence of SOC whereas for rest of the compounds this decrement is within 17%. The effective mass tensors are calculated for those bands which are expected to influence the transport behaviour of the compounds.

Scientific Reports, 2017

Electronic band structure is vital in determination the performance of thermoelectric materials. What is the optimum electronic structure for the largest figure of merit? To answer the question, we studied the relationship between the thermoelectric properties and the electronic band structure under the assumption of isotropic elastic scattering, within the context of Chasmar-Stratton theory. The results show that whether the anisotropic band structure and the effective mass of the carrier are beneficial to improving the thermoelectric properties. The scattering mechanism and the shape of the Fermi surface play a decisive role. Regardless of scattering mechanism type, a larger valley degeneracy is always beneficial to thermoelectric materials.

arXiv (Cornell University), 2023

The Journal of Physical Chemistry C, 2020

We theoretically unveil the unconventional possibility to achieve extremely high thermoelectric power factors in lightly doped narrow gap semiconductors with asymmetric conduction/valence bands operated in the bipolar transport regime. Specifically, using Boltzmann transport simulations, we show that narrow bandgap materials, rather than suffering from performance degradation due to bipolar conduction, if they possess highly asymmetric conduction and valence bands in terms of either effective masses, density of states, or phonon scattering rates, then they can deliver very high power factors. We show that this is reached because, under these conditions, electronic transport becomes phonon scattering limited, rather than ionized impurity scattering limited, which allows large conductivities. We explain why this effect has not been observed so far in the known narrow-gap semiconductors, interpret some recent related experimental findings, and propose a few examples from the half-Heusler materials family for which this effect can be observed and power factors even up to 50 mW/mK 2 can be reached.

Journal de Physique, 1976

2014 La formulation exacte de l'effet tunnel de Caroli et al. est utilisée pour étudier l'émission thermoionique. Le courant est calculé en présence de potentiel image en incluant des corrections quantiques. On montre que l'effet de ces corrections est négligeable. On rend compte des effets de structure de bande à l'aide d'un modèle de Krônig-Penney à une dimension. On montre alors qu'il n'est pas suffisant de remplacer m par m* dans l'expression du courant déduite d'un modèle d'électrons libres. De plus, le courant dépend fortement de la position de la limite entre le métal et le vide. Enfin, on montre que suivant la position du niveau du vide par rapport aux bandes interdites la loi de Richardson-Laue-Dushman est ou n'est pas vérifiée. Abstract. 2014 The exact treatment of tunnelling of Caroli et al. is used to study thermoemission. The current is computed in the presence of the image-force potential and quantum mechanical correction. The effect of this correction is shown to be negligible. Band structure effects are taken into account through a one-dimensional Krônig-Penney model. The current, in this situation, is not obtained simply by replacing m by m* in the expression for the current obtained when the metal is described by a free electron gas, even close to band edges. Moreover, the current depends strongly on the location of the boundary between the metal and the vacuum. It is also shown that, depending on the location of the vacuum level with respect to the band gaps, the well-accepted Richardson-Laue-Dushman law may or may not be valid.

2016

High performance thermoelectric materials are key to the development of an energy efficient technology. Unfortunately, the design and tailoring of materials for thermoelectric energy conversion is a formidable task. Electrical and heat transport coefficients must satisfy contradictory requirements that depend on the details of the electronic structure, the anharmonic terms in the vibrations, and the effects of chemical disorder and defects. We have exploited the capability of computational methods based on density functional theory to predict the thermoelectric properties of novel chemical compositions. I will discuss heuristic design rules for efficient thermoelectric energy conversion materials as derived from standard electronic structure calculations and also applications to skutterudite and oxide materials. Speaker: Edward Brown Michigan State University September 28, 2009 “Journey to the Core of a Neutron Star” Abstract: Neutron stars are composed of the densest observable mat...

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