Semi-classical Boltzmann Theory Research Articles

The nature of the high thermoelectric properties of CuInX2 (X = S, Se and Te): First-principles study

CuInX2 (X = S, Se and Te) are members of Cu-based compounds with diamond-like structures. Their bonding characteristics, electronic structure and thermoelectric properties are studied using first-principles methods and the semiclassical Boltzmann theory. Due to the Cu-3d orbits in CuInX2, we use the mBJ + U method to obtain the accurate band gap and electronic structures. The analysis of the electronic structure for CuInX2 indicates that the combination of heavy and light bands near the Fermi level is conductive to achieve high thermoelectric performances. However, few literatures have reported the reason of the combination. Further study on AgGaTe2, CuGaTe2, and CuInX2 (X = S, Se and Te) shows that the stronger interaction between Cu-Te atoms leads to the combination of heavy and light bands in Cu-based compounds. These results provide a valuable theoretical guidance that the introduction of Cu-Te bonding in experimental synthesis is helpful to improve the thermoelectric properties.

Revealing optoelectronic and transport properties of potential perovskites Cs2PdX6 (X = Cl, Br): A probe from density functional theory (DFT)

Metal-halide perovskites are rapidly emerging crystalline materials that are reasonably preferred as leading aspirant for applications in optoelectronic and thermoelectric devices. In this paper, we have thoroughly reviewed and performed calculations to reveal optoelectronic and transport properties for a potential newcomer, Cs2PdX6 (X = Cl, Br) termed as Cesium Palladium Halides (CPH). Outcome of present computations are compared with available results and a reasonable agreement is recorded. Energy band gap computations performed reveal indirect band gap of 2.29 eV for Cs2PdCl6, which substantially reduces to 1.22 eV when ‘Cl’ is replaced by ‘Br’. Optical absorption spectra investigations performed here, in the energy range from 3 to 5 eV confirms effective utilization of these compounds in solar cells and other optoelectronic applications. In addition, the transport properties computations performed using semi-classical Boltzmann theory, shows constant pattern of thermo power near ambient temperature range (200–500 K), which admits possible utilization of these compounds as low temperature thermoelectric materials. Performed ZT calculations demonstrates reasonably good thermoelectric performance for both materials, as there exist minor variation (0.1) in the values over wide temperature ranges i.e. from 100 to 800 K. Further, detailed analysis of transport properties predicts p-type semiconducting nature of the present series of materials.

Semiclassical transport properties of IrGa3: a promising thermoelectric material

IrGa3 is an intermetallic compound which is expected to be a metal, but a study on the electronic properties of this material to confirm its metallic character is not available in the literature. In this work, we report for the first time a first-principles density functional theory and semiclassical Boltzmann theory study of the structural, electronic and transport properties of this material. The inclusion of the spin–orbit coupling term is crucial to calculate accurately the electronic properties of this compound. We have established that IrGa3 is an indirect semiconductor with a narrow gap of 0.07 eV. From semiclassical Boltzmann transport theory, it is inferred that this material, with the appropriate hole concentration, could have a thermoelectric figure of merit at room temperature comparable to other intermetallic compounds such as FeGa3, though the transport properties of IrGa3 are highly anisotropic.

Theoretical study on electronic structure and thermoelectric properties of PbSxTe1−x(x = 0.25, 0.5, and 0.75) solid solution**Project supported by the National Natural Science Foundation of China (Grant Nos. 11647010 and 11704020), the Higher Education and High-quality and World-class Universities (Grant No. PY201611), and the Fund for Disciplines Construction from Beijing University of Chemical Technology (Grant No. XK1702).

The electronic structure and thermoelectric (TE) properties of PbSxTe1−x(x = 0.25, 0.5, and 0.75) solid solution have been studied by combining the first-principles calculations and semi-classical Boltzmann theory. The special quasirandom structure (SQS) method is used to model the solid solutions of PbSxTe1−x, which can produce reasonable electronic structures with respect to experimental results. The maximum ɀT value can reach 1.67 for p-type PbS0.75Te0.25 and 1.30 for PbS0.5Te0.5 at 800 K, respectively. The performance of p-type PbSxTe1−x is superior to the n-type ones, mainly attributed to the higher effective mass of the carriers. The ɀT values for PbSxTe1−x solid solutions are higher than that of pure PbTe and PbS, in which the combination of low thermal conductivity and high power factor play important roles.

Search for thermoelectricity in Li-based half-Heusler alloys: a DFT study

In this paper, we investigate the transport properties of LiMgX; X = N, P, As half-Heusler alloys using the density functional theory and semi-classical Boltzmann theory based calculations. The electronic structure calculations have been performed within the generalized gradient approximation. The transport coefficients such as electrical conductivity, Seebeck coefficient, electronic thermal conductivity and power factor have been calculated using the semi-classical Boltzmann theory within the constant relaxation time approximation. The electronic structure calculations revealed that these compounds are indirect wide band gap semiconductors. Despite the wide band gaps, these compounds exhibit large values of Seebeck coefficient and power factor thus can be potential candidates for technological applications. Among the studied LiMgX alloys, LiMgN has large power factor of 2.31 × 1012 W m−1s−1 K−2 at 1200 K which makes it a possible promising candidate for the thermoelectric applications at high temperatures.

Anomalous Nernst effect in type-II Weyl semimetals

Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole pockets producing finite DOS at the Fermi level. The tilted conical spectrum and finite DOS at Fermi level in type-II WSMs have recently been shown to produce interesting effects such as a chiral anomaly induced longitudinal magnetoresistance that is strongly anisotropic in direction and a novel anomalous Hall effect. In this work, we consider the anomalous Nernst effect in type-II WSMs in the absence of an external magnetic field using the framework of semi-classical Boltzmann theory. Based on both a linearized model of time-reversal breaking WSM with a higher energy cut-off and a more realistic lattice model, we show that the anomalous Nernst response in these systems is strongly anisotropic in space, and can serve as a reliable signature of type-II Weyl semimetals in a host of magnetic systems with spontaneously broken time reversal symmetry.

Ab initio design of new cobalt-based half-Heusler materials for thermoelectric applications

In search of new prospects for thermoelectric materials, using ab-initio calculations and semi-classical Boltzmann theory, we have systematically investigated the electronic structure and transport properties of 18-valence electron count cobalt based half-Heusler alloys with prime focus on CoVSn, CoNbSn, CoTaSn, CoMoIn, and CoWIn. The effect of doping on transport properties has been studied under the rigid band approximation. The maximum power factor, S$^2\sigma$, for all systems is obtained on hole doping and is comparable to the existing thermoelectric material CoTiSb. The stability of all the systems is verified by phonon calculations. Based on our calculations, we suggest that CoVSn, CoNbSn, CoTaSn, CoMoIn and CoWIn could be potential candidates for high temperature thermoelectric materials.

Effects of hydrostatic pressure on the thermoelectric properties of the ϵ-polytype of InSe, GaSe, and InGaSe2 semiconductor compounds: an ab initio study

This work presents an ab initio study of the effects of hydrostatic pressure on the Seebeck coefficients and thermoelectric power factors of the ϵ-polytype of InSe, GaSe, and InGaSe2 semiconductor compounds. Our study is performed using the semi-classical Boltzmann theory and the rigid band approach. The electronic band structures of these materials are calculated using the full-potential linearized augmented plane-wave method. The obtained thermoelectric properties are discussed in terms of the results of the electronic structure calculations. As we will show, our calculated Seebeck coefficient values indicate that these materials are good alternatives to other well-studied thermoelectric systems.

Excellent thermoelectricity performance of p-type SnSe along b axis

The electronic and thermoelectric properties of SnSe were calculated using the first-principles calculations and the semiclassical Boltzmann theory. The accurate electronic structure (calculated by the TB-mBJ) resulted in the trend changing between the Seebeck coefficient and the electrical conductivity, which were in good agreement with the experimental data. During the Pnma phase, the maximal zT value increased from 0.32 to 1.62 as the temperature rose. During the Cmcm phase, the maximal zT value increased from 4.03 to 4.33 as the temperature rose. The theoretical investigation provided valuable insight into the relationship between the electronic structure and thermoelectric transport properties of SnSe material.

Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems

For the spin Hall effect arising from strong band-structure spin-orbit coupling, a semiclassical Boltzmann theory reasonably addressing the intriguing disorder effect called side-jump is still absent. In this paper we describe such a theory of which the key ingredient is the spin-current-counterpart of the semiclassical side-jump velocity (introduced in the context of the anomalous Hall effect). Applying this theory to spin Hall effects in a two-dimensional electron gas with giant Rashba spin-orbit coupling, we find largely enhanced spin Hall angle in the presence of magnetic impurities when only the lower Rashba band is partially occupied.

Ab Initio Prediction of the Structural, Electronic, Elastic, and Thermoelectric Properties of Half-Heusler Ternary Compounds TiIrX (X = As and Sb)

The structural, electronic, elastic, and thermoelectric properties of TiIrX (X = As and Sb) half-Heusler compounds with 18 valence electrons were studied using density functional theory. The generalized gradient approximation of Perdew–Burke and Ernzerhof used for calculation of the structural parameters and elastic properties of TiIrAs and TiIrSb denotes that the computed lattice constants were in excellent agreement with the available experimental data and previous theoretical works. Furthermore, the calculated elastic constants for both compounds satisfy the Born criteria indicating their mechanical stabilities. The modified Becke–Johnson potential (TB-mBJ) was used to provide a better description of the electronic structures, which indicate that both compounds are narrow-gap semiconductors. Additionally, the investigations of thermoelectric performance were carried out using the results of ab initio band-structure calculations and the semi-classical Boltzmann theory within the constant relaxation time approximations. The predicted values of the figure of merit ZT e are close to unity at room temperature. This reveals that TiIrAs and TiIrSb compounds are excellent candidates for practical applications in the thermoelectric devices.

Thermoelectric properties of tetragonal half-Heusler compounds, TiXSb (X = Ge, Si): A probe from Density Functional Theory (DFT)

We have presented the electronic and thermoelectric properties of d2/do type Heusler compounds TiXSb (X = Ge, Si) using Full Potential Linearized Augmented Plane Wave method (FP-LAPW), based on Density Functional Theory (DFT). For electron exchange, we have considered the most common Generalized Gradient Approximation (GGA), exchange potential. The electronic structure of both TiGeSb and TiSiSb showed overlapping between the valance and the conduction band, indicating their metallic nature. The transport coefficients were calculated by a post DFT treatment which involves the semi-classical Boltzmann Theory as implemented in the code BoltzTraP. The thermoelectric parameters are calculated along perpendicular and parallel directions with respect to chemical potential (μ) and temperature. Furthermore, we have also considered the phononic contribution to thermal conductivity (κp) for better understanding of the materials thermodynamics and efficiency (ZT). The calculated ZT values showed TiSiSb as potential thermoelectric candidate at room temperature and under normal conditions, whereas TiGeSb had poor thermoelectric properties.

Rashba torque beyond the Boltzmann regime

We study spin torques induced by Rashba spin-orbit coupling in two-dimensional ferromagnets under the good-metal condition $\epsilon_{F}\tau/\hbar\gg1$ ($\epsilon_{F}$ the Fermi energy, $\tau$ the electron lifetime) by employing the Kubo formula. We find that, in the presence of spin-dependent disorder the Rashba torque changes greatly as the system evolves out of the weak disorder limit where $\hbar/\tau$ is much smaller than any intrinsic energy scale characterizing the multiband structure. The antidamping-like component of Rashba torque can be comparable to and larger than the field-like one out of the weak disorder limit. The semiclassical Boltzmann theory produces the same results as microscopic linear response calculations only in the weak disorder limit. Our analysis indicates that rich behaviors of various nonequilibrium phenomena beyond the Boltzmann theory may also be present even when $\epsilon_{F}\tau/\hbar\gg1$ in multiband systems where $\epsilon_{F}$ is not the unique intrinsic energy scale.

Strain engineering on thermoelectric performance of Mg2Si

In this work, we propose to boost the thermoelectric performance of bulk magnesium silicide using isotropic strain. The effect of strain on the electronic and thermoelectric properties of Mg2Si is analyzed using first principles calculations combined with semi-classical Boltzmann theory. The Seebeck coefficient, power factor and electrical conductivity are strongly modified with strain. The lattice thermal conductivity is also tuned with strain. However, the strain effect on the lattice thermal conductivity of Mg2Si has not yet been systematically studied. The effect of strain on lattice thermal conductivity, specific heat, phonon dispersion curves and phonon density of states of Mg2Si are studied for the first time in this paper. The lattice thermal conductivity of bulk Mg2Si is shown to decrease continuously when applied strain changes from compressive to tensile. The results obtained in this paper have great importance in the thermoelectric field.

Momentum-space electromagnetic induction in Weyl semimetals

We theoretically study the effect of the Berry curvature on the transport properties of Weyl semimetals in the nonadiabatic process, which results in nonlinear optical responses. In the adiabatic process, the Berry curvature, which involves the time derivative of the Bloch states, contributes to the transport properties such as the adiabatic Thouless pump. Although this effect is very weak in usual solids, it is enhanced in Weyl semimetals, where the Berry curvature contributes to observable nonlinear optical responses due to its nodal structure. In this paper, using semiclassical Boltzmann theory, we show that the d.c. photocurrent induced by the Berry curvature robustly persists even in the limit of short scattering time. We also show that the photocurrent is well explained as a consequence of the electromagnetic induction in momentum space. The results indicate that the electromagnetic induction gives rise to a non-dissipative photocurrent that is robust even when decoherence occurs within a time scale shorter than the periodicity of the light. We also discuss the second harmonic response of the a.c. current when the electron distribution is displaced from the ground state by an external field.

Electronic and thermoelectric properties of Mg2GexSn1−x (x = 0.25, 0.50, 0.75) solid solutions by first-principles calculations∗Project supported by the National Natural Science Foundation of China (Grant No. 11647010) and the Foundation from the Higher Education and High-quality and World-class Universities (Grant No. PY201611).

The electronic structure and thermoelectric (TE) properties of Mg2GexSn1−x (x = 0.25, 0.50, 0.75) solid solutions are investigated by first-principles calculations and semi-classical Boltzmann theory. The special quasi-random structure (SQS) is used to model the solid solutions, which can produce reasonable band gaps with respect to experimental results. The n-type solid solutions have an excellent thermoelectric performance with maximum zT values exceeding 2.0, where the combination of low lattice thermal conductivity and high power factor (PF) plays an important role. These values are higher than those of pure Mg2Sn and Mg2Ge. The p-type solid solutions are inferior to the n-type ones, mainly due to the much lower PF. The maximum zT value of 0.62 is predicted for p-type Mg2Ge0.25Sn0.75 at 800 K. The results suggest that the n-type Mg2GexSn1−x solid solutions are promising mid-temperature TE materials.

Electronic Structure and Thermoelectric Power Factor of NaxCoO2 from First-Principles Calculation**Supported by the Science Foundation of Henan University of Technology under Grant No 2015XTCX10.

To investigate the relationship between the electronic structure and the power factor of NaxCoO2 (, 0.5 and 1.0), the first-principles calculation is conducted by using density functional theory and the semi-classical Boltzmann theory. Our results suggest that with the decreasing Na content, a transition from semiconductor to semimetal is observed. Na0.3CoO2 possesses a higher electrical conductivity at 1000 K due to its increased density of states near the Fermi energy level. However, an optimal Seebeck coefficient at 1000 K is obtained in Na0.5CoO2 because of its broadened band gap near the Fermi energy level. Consequently, a maximum power factor is realized in Na0.5CoO2. Thus our work provides a complete understanding of the relationship between the electronic structure and the thermoelectric power factor of NaxCoO2.

Comparative investigation of electronic transport across three-dimensional nanojunctions

We carry out a layer-by-layer investigation to understand electron transport across metal-insulator-metal junctions. Interfacial structures of junctions were studied and characterized using first-principles density functional theory within the generalized gradient approximation. We found that as a function of the number of crystal layers the calculated transmission coefficients of multilayer silicene junctions decay much slower than for BN-based junctions We revisited the semiclassical Boltzmann theory of electronic transport and applied to multilayer silicene and BN-based junctions. The calculated resistance in the high-transmission regime is smaller than that provided by the Landauer formula. As the thickness of the barrier increases, results from the Boltzmann and the Landauer formulae converge. We provide a upper limit in the transmission coefficient below which, the Landauer method becomes valid. Quantitatively, when the transmission coefficient is lower than $ \sim 0.05 $ per channel, the error introduced by the Landauer formula for calculating the resistance is negligible. In addition, we found that the resistance of a junction is not entirely determined by the averaged transmission, but also by the distribution of the transmission over the first Brillouin zone.

Structural, electronic, and thermoelectric properties of La2CuBiS5

The basic physical properties of La2CuBiS5 are studied by the first-principle calculations and the semiclassical Boltzmann theory. Charge density difference calculations show that electrons accumulate between Bi–S atoms, indicating considerable covalent bonding of Bi and S atoms. A similar charge density difference indicates that the Cu–S bonds also exhibit covalent character. The calculated minimum thermal conductivity of La2CuBiS5 is low, which is conducive to its use as a thermoelectric material. Owing to a bipolar effect, induced by thermal excitation, the material’s Seebeck coefficient decreases sharply at T = 800 K. For the n-type and p-type doping conditions, the largest values of S 2 σ / τ were calculated as −1.71×1011 and 1.837×1011 W K−2 ms−1, respectively. The combination of a large dispersion and a high band degeneracy along the Γ - Y direction in the band structure simultaneously induces the highest S y value and a high σ / τ y value. Thus, the thermoelectric performance of La2CuBiS5 is anisotropic and most favorable along the y direction.

Thermoelectric Properties of the Intermetallic Quasi-Two-Dimensional Layered Structure LiBe

The electronic transport coefficients of LiBe for the intermetallic quasi-two-dimensional layered structure are evaluated by means of the semi-classical Boltzmann theory and the rigid band model. It has been found that the charge carrier concentration is about −0.0026 e/uc at low temperature (T = 50 K), then it decreases with increase of temperature to reach −0.0028 e/uc at 250 K. Above this temperature the charge carriers concentration increases rapidly to reach −0.00228 e/uc at 600 K. The negative sign shows that LiBe exhibits n-type conduction at a certain value of chemical potential (μ = E F). The calculated electrical conductivity (σ/τ) at μ = E F shows that at low temperatures (50 K) LiBe exhibits low σ/τ of about 1.318 × 1021 (Ω ms)−1, this value increases rapidly with an increase of temperature to be 1.389 × 1021 (Ω ms)−1 at 300 K. Above 300 K the σ/τ reach to the saturated value of about 1.389 × 1021 (Ω ms)−1. It has been found that LiBe possesses a thermo-power (S) of about −460 μV/K at 50 K, which decreases with increase of temperatures to reach −220 μV/K at around 350 K. Increasing the temperatures above 350 K lead to a decrease S to be −190 μV/K at 600 K. It is clear that at a certain value of chemical potential LiBe exhibits n-type conduction as it has negative S in the whole temperature range; this supports our previous observation about the charge carriers concentration. It is a remarkable finding that LiBe exhibits a large Seebeck coefficient, which is attributed to the non-zero density of states at the Fermi level. The electron thermal conductivity (κ e/τ) increased linearly with the temperature, and we observed that at low temperature LiBe exhibits low κ e/τ of about 0.2 × 1016 W/mKs at 50 K. A rapid increases in κ e/τ occurs as a result of increasing the temperature to reach 2.1 × 1016 W/mKs at 600 K. The obtained values of the power factor (S 2 σ/τ) as function of temperature show that at low temperature (50 K) LiBe possesses a high S 2 σ/τ of about 2.8 × 1010 mW/mK2, and with increasing the temperature a rapid reduction in the S 2 σ/τ occurs till 350 K to reach the value of about 0.5 × 1010 mW/mK2. Above this temperature LiBe exhibits almost a stable S 2 σ/τ of about 0.6 × 1010 mW/mK2 at 600 K. Also, we have calculated the transport properties as a function of chemical potential at the vicinity of E F (±0.15 eV above and below E F) for two different temperatures. In LiBe for the quasi-two-dimensional layered structure, the Li and Be atoms are packed in zig-zag layers along the y-axis. The Li and Be layers are puckered with square nets of Li and triangular nets of Be alternating with each others along the z-axis. Given that the LiBe system exhibits two-dimensional (2-D) doping behavior, it might be justifiable to study its transport properties; however, we would like to explore the unique transport behavior arising from its 2-D electronic structure.