Semiclassical Boltzmann Transport Equation Research Articles

Monolayer SnI2: An Excellent p-Type Thermoelectric Material with Ultralow Lattice Thermal Conductivity.

Using density functional theory and semiclassical Boltzmann transport equation, the lattice thermal conductivity and electronic transport performance of monolayer SnI2 were systematically investigated. The results show that its room temperature lattice thermal conductivities along the zigzag and armchair directions are as low as 0.33 and 0.19 W/mK, respectively. This is attributed to the strong anharmonicity, softened acoustic modes, and weak bonding interactions. Such values of the lattice thermal conductivity are lower than those of other famous two-dimensional thermoelectric materials such as MoO3, SnSe, and KAgSe. The two quasi-degenerate band valleys for the valence band maximum make it a p-type thermoelectric material. Due to its ultralow lattice thermal conductivities, coupled with an ultrahigh Seebeck coefficient, monolayer SnI2 possesses an ultrahigh figure of merits at 800 K, approaching 4.01 and 3.34 along the armchair and zigzag directions, respectively. The results indicate that monolayer SnI2 is a promising low-dimensional thermoelectric system, and would stimulate further theoretical and experimental investigations of metal halides as thermoelectric materials.

Calculation of thermomagnetic properties using first-principles density functional theory

The BoltzWann code uses the first-principles density-functional theory to calculate the material’s response to an electric field and temperature gradient within the constant relaxation time approximation. We extend this code to include the response of the system to a magnetic field. The carrier dynamic is described by the semi-classical Boltzmann transport equation. This equation is solved in the presence of an external magnetic field within the constant relaxation time approximation and using the Jones–Zener expansion. This is done through a Wannier interpolation of the density functional theory bands using the Boltzwann code, followed by the computation of group velocities and effective masses leading to the energy-dependent transport function. This work leads to a generalized method for the calculation of thermomagnetic properties of materials. The results are validated by comparison to the analytical solutions of the thermomagnetic properties for several simple energy dispersion types and close agreements at moderate computational costs are achieved. This method can pave the path for the discovery of materials with potentially high thermomagnetic power factor.

High Pressure and Temperature Dependence of the Structural, Electronic, Thermal and Transport Properties of U3Si2: Computational Insights

Due to its advantageous thermophysical qualities, U3Si2 piques the interest of the nuclear industry as an accident‐tolerant fuel to replace uranium dioxide (UO2). Herein, the structural, electrical, thermodynamic, and transport features of the U3Si2 compound are investigated using the full‐potential linearized augmented plane wave approach within the density functional theory, and within the generalized gradient approximation related to spin orbit and Hubbard. The ground statistic parameters that are estimated, such as the lattice constants and bulk moduli, are qualitatively consistent with previous experimental and theoretical evidence. The density of states analysis reveals that U3Si2 is a metal complex. In addition, the macroscopic thermal effects of U3Si2 are calculated using the quasi‐harmonic Debye model, which includes lattice vibrations. Experimental and theoretical findings are compared with the calculated variations in volume, heat capacity, entropy, and Debye temperature as a function of temperature in the range of 0–1500 K. Some thermal properties are projected to be pressure dependent in the range of 0–20 GPa. In the temperature range of 0–1500 K, the semiclassical Boltzmann transport equation is utilized to estimate electron transport parameters such as the Seebeck coefficient, thermal and electrical conductivity.

First-principles study of the structural, electronic, optical, and thermoelectric properties of the RhVZ (Z= Si, Ge, Sn)

In this work, we have explored half-Heusler RhVZ (Z ​= ​Si, Ge, Sn) with 18 valence electrons per unit cell within the Density Functional Theory (DFT). The structural, electronic, optical, thermoelectric, and phonon properties have been investigated. The structural properties such as lattice constant, bulk modulus, and pressure derivative of bulk modulus have been reported. All materials are semiconductors with a narrow bandgap as it is concluded from the electronic band structure, and the phonon dispersion approve the dynamical stability, meanwhile, the absorption coefficient is found to be around 104 ​cm−1 in the visible region indicating that these materials can be used in Photovoltaic applications. The semi-classical Boltzmann transport equation used to calculate the thermoelectric characteristics and all materials under investigation show high performance in the p-type region due to the valence band degeneracy. The thermoelectric analysis provided show that the power factor of the materials lies on 3.12 ​× ​10−3, 3.26 ​× ​10−3, and 6.52 ​× ​10−3 ​W/msK2 for RhVSi, RhVGe, and RhVSn respectively, the figure of merit ZT reaches the maximum value of 0.8 ​at room temperature indicating that those materials are suitable for thermo-generation application at near room temperature. However, we found that RhVSn is more suitable for thermoelectric applications with its high ZT values more than RhVSi, and RhVGe compounds.

Electronic, magnetic, elastic, thermal and thermoelectric proprieties of Co2MnZ (Z=Al, Ge, Sn)

The full-potential linearized augmented plane-wave (FLAPW) method, which is based on density functional theory using the “WIEN2k” code. The exchange-correlation functional was taken within the generalized gradient approximation (GGA), has been used to study the structural, electronic, mechanical, magnetic, and thermal properties of Co2MnZ (Z = Al, Ge, Sn) (CMZ) alloy. When using the GGA + U approximation, all compounds depict half-metallic behavior due to spin polarization at the Fermi level.Get the Curie temperature value and the magnetic moment. We find that the ferromagnetic state is more stable than the antiferromagnetic and nonmagnetic states. The effects of heat on lattice parameters, compressive modulus, volume, heat capacity and thermal expansion coefficient at several pressures were investigated. The thermoelectric performance of these systems was examined.Calculations are performed using the BoltzTrap code, that relies on the semiclassical Boltzmann transport equation. The Seebeck coefficient, electrical conductivity, thermal conductivity, and figure of merit are calculated taking into account the upper and lower spins.

Dirac dispersions, lattice dynamics and thermoelectric properties of quaternary Heusler alloys LiMgXY(X = Pt, Pd, Au; Y= Sb, Sn)

This manuscript reports the structural, mechanical, electronic, and thermoelectric properties of the LiMgYZ system Y = t, Pd, Au; Z = Sb, Sn) computed within the first-principle density functional theory combined with semi-classical Boltzmann transport equations. Comparing the relative energetic stability of type-I, type-II, and type-III atomic arrangement of basis atoms, the type-I arrangement is found to be the most stable among these. The lattice dynamics also confirm that the type-I phase is stable for all the studied alloys except LiMgAuSn. It is interesting to note that the electronic band structure of these materials exhibits the Dirac point. The temperature-dependent transport coefficients of these materials have been calculated within semi-classical Boltzmann transport formalism within constant scattering time approximation (CSTA). The number of states at the Fermi level has successfully depicted the behavior of electrical conductivity. Among all the studied alloys, LiMgPtSb shows the highest temperature coefficient of resistivity which indicates that this material can be a good candidate for temperature sensing applications.

Exceptional Thermoelectric Properties of Bilayer GeSe: First Principles Calculation.

The geometry structures, vibrational, electronic, and thermoelectric properties of bilayer GeSe, bilayer SnSe, and van der Waals (vdW) heterostructure GeSe/SnSe are investigated by combining the first-principles calculations and semiclassical Boltzmann transport theory. The dynamical stability of the considered structures are discussed with phonon dispersion. The phonon spectra indicate that the bilayer SnSe is a dynamically unstable structure, while the bilayer GeSe and vdW heterostructure GeSe/SnSe are stable. Then, the electronic structures for the bilayer GeSe and vdW heterostructure GeSe/SnSe are calculated with HSE06 functional. The results of electronic structures show that the bilayer GeSe and vdW heterostructure GeSe/SnSe are indirect band gap semiconductors with band gaps of 1.23 eV and 1.07 eV, respectively. The thermoelectric properties, including electrical conductivity, thermal conductivity, Seebeck coefficient, power factor, and figure of merit (ZT) are calculated with semiclassical Boltzmann transport equations (BTE). The results show that the n-type bilayer GeSe is a promising thermoelectric material.

First-principle investigation on the thermoelectric properties of XCoGe (X = V, Nb, and Ta) half-Heusler compounds

Half-Heusler compound is a promising thermoelectric material due to its excellent conversion performance. In this study, we investigate the electronic structure, and thermoelectric properties of XCoGe (X = V, Nb, and Ta) compounds based on density functional theory. Combining the semi-classical Boltzmann transport equation and the deformation potential theory, the thermoelectric properties such as Seebeck coefficient, relaxation time, electrical conductivity, power factor, electronic thermal conductivity, and lattice thermal conductivity are analyzed. The NbCoGe compound possesses a large dimensionless figure of merit, which is related to the large electrical conductivity, small effective mass, and large relaxation time. The ZT values of n- and p-type NbCoGe compounds reach 1.6 and 1.3 at T = 1200 K, respectively. These findings will provide valuable guidance for exploring half-Heusler compounds with high thermoelectric performance.

A DFT study of electronic, magnetic, optical and transport properties of rare earth element (Gd, Sm)-doped GaN material

The main objective of this article is to deal with and establish a new type of transparent conducting material by doping Gallium Nitride (GaN) with rare-earth RE (Gd, Sm) elements. A theoretical study was performed by using the density functional theory (DFT) implemented in WIEN2k code and BoltzTraP package based on semi-classical Boltzmann transport equation (BTE) within constant relaxation time and rigid band approximation (RBA). The application of the modified Becke–Johnson (TB-mBJ) potential has improved the electronic structure, especially the electronic bandgap. Our simulation result matches with other computational results as well. We have compared the total energy of ferromagnetic (FM) and Anti-ferromagnetic (AFM) configurations for the doped system to analyze the magnetic ground state stability. Preferentially the most stable magnetic configuration is found to be ferromagnetic. The low value of formation energy indicates the possibility of the preparation of these materials in the lab. To further compare the results, we have also used the VNL-ATK quantumwise code based on the Linear Combination of Atomic Orbital (LCAO) approach. VNL-ATK incorporate a new functional DFT-1/2 to correct the Kohn–Sham KS eigenvalues around the minima and maxima of the conduction band, and the valence band, respectively, which enhances the bandgap. It shows the high optical absorption and the high electrical conductivity. These characteristics offer that GaN doped with rare earth elements are potential candidates for optoelectronic, solar cell, and spin-based magnetic devices.

Impressive Thermoelectric Figure of Merit in Two-Dimensional Tetragonal Pnictogens: a Combined First-Principles and Machine-Learning Approach.

Over the past decade, two-dimensional materials have gained a lot of interest due to their fascinating applications in the field of thermoelectricity. In this study, tetragonal monolayers of group-V elements (T-P, T-As, T-Sb, and T-Bi) are systematically analyzed in the framework of density functional theory in combination with the machine-learning approach. The phonon spectra, as well as the strain profile, dictate that these tetragonal structures are geometrically stable as well as they are potential candidates for experimental synthesis. Electronic analysis suggests that tetragonal pnictogens offer a band gap in the semiconducting regime. Thermal transport characteristics are investigated by solving the semiclassical Boltzmann transport equation. Exceptionally low lattice thermal conductivity has been observed as the atomic number increases in the group. The high Seebeck coefficient and electrical conductivity as well as the low thermal conductivity of T-As, T-Sb, and T-Bi lead to the generation of a very high thermoelectric figure of merit as compared to standard thermoelectric materials. Furthermore, the thermoelectric conversion efficiency of these materials has been observed to be much higher, which ensures their implications in thermoelectric device engineering.

Enhanced Thermoelectric Performance of Polycrystalline Si0.8Ge0.2 Alloys through the Addition of Nanoscale Porosity.

Engineering materials to include nanoscale porosity or other nanoscale structures has become a well-established strategy for enhancing the thermoelectric performance of dielectrics. However, the approach is only considered beneficial for materials where the intrinsic phonon mean-free path is much longer than that of the charge carriers. As such, the approach would not be expected to provide significant performance gains in polycrystalline semiconducting alloys, such as SixGe1-x, where mass disorder and grains provide strong phonon scattering. In this manuscript, we demonstrate that the addition of nanoscale porosity to even ultrafine-grained SiGe may be worthwhile. The semiclassical Boltzmann transport equation was used to model electrical and phonon transport in polycrystalline SiGe containing prismatic pores perpendicular to the transport current. The models are free of tuning parameters and were validated against experimental data. The models reveal that a combination of pores and grain boundaries suppresses phonon conductivity to a magnitude comparable with the electronic thermal conductivity. In this regime, ZT can be further enhanced by reducing carrier concentration to the electrical and electronic thermal conductivity and simultaneously increasing thermopower. Although increases in ZT are modest, the optimal carrier concentration is significantly lowered, meaning semiconductors need not be so strongly supersaturated with dopants.

Oxidation-enhanced thermoelectric efficiency in a two-dimensional phosphorene oxide

We performed density functional theory calculations to investigate the thermoelectric properties of phosphorene oxide (PO) expected to form by spontaneous oxidation of phosphorene. Since thermoelectric features by nature arise from the consequences of the electron-phonon interaction, we computed the phonon-mediated electron relaxation time, which was fed into the semiclassical Boltzmann transport equation to be solved for various thermoelectric-related quantities. It was found that PO exhibits superior thermoelectric performance compared with its pristine counterpart, which has been proposed to be a candidate for the use of future thermoelectric applications. We revealed that spontaneous oxidation of phosphorene leads to a significant enhancement in the thermoelectric properties of n-doped phosphorene oxide, which is attributed to the considerable reduction of lattice thermal conductivity albeit a small decrease in electrical conductivity. Our results suggest that controlling oxidation may be utilized to improve thermoelectric performance in nanostructures, and PO can be a promising candidate for low-dimensional thermoelectric devices.

Probable thermoelectric materials for promising candidate of optoelectronics for Ba‐based complex perovskite compounds

Structural parameters, electronic band structure, optical spectra, and thermoelectric properties of trigonal Ba3B(Nb, Ta)2O9(B═Sr, Mg, Ca, Hg, Zn, Fe, Ni, Mn, Co, and Ca) compound materials are investigated. The computations are performed using density-functional calculations within the generalized gradient approximation. The calculated a and c parameters agree with those of the experiment to within 2%. The Ba3B(Nb, Ta)2O9(B=Sr,Mg,Ca, Hg, Zn, Fe, Ni, Mn, Co, and Ca) materials are found to be semiconductors with a band-gap energy varying from 0.82 to 3.17 eV. A metallic character is observed in Ba3B(Nb, Ta)2O9(B═Ni, Mn, and Co) compounds indicating the presence of conductivity features. A small carrier effective mass indicates the increase of the electron mobility leading to a high n-type conductivity. The p states dominate the lower valence band region. The optical spectra show an anisotropic character between x and z directions. The excitonic effects tend to increase the strength of the oscillator at M0 and M points. The effect is reduced when increasing the photon energy, indicating that the Ba3BB2'O9 compound can be used for devices such as Bragg's reflectors, and optical and optoelectronic devices. The calculations were performed using the BoltzTrap code, which depends on the semi-classical Boltzmann transport equation. The Seebeck coefficient, electrical conductivity, thermal conductivity, power factor, and the figure of merit for Ba3(Fe, Sr, Hg, Zn)B′2O9 are calculated. At higher temperatures, the mobility increases by reducing the electrical conductivity. Ba3(Fe, Sr, Hg, Zn) B2' O9 shows a considerable thermoelectric performance accompanied by a sign point figure of merit larger than many full perovskites reported till date.

Thermoelectric properties of Lenaite: A first principles study

The electronic and transport properties of AgFeS2 were studied using first principles. The stable magnetic state of the material was found as antiferromagnetic. The band structure and DOS was calculated. The calculations show that the AgFeS2 system has an indirect bandgap of 0.94 eV. The transport properties were studied using the BoltzTraP2 code by solving the semiclassical Boltzmann transport equation. The orientation dependent transport properties of lenaite with respect to relaxation time shows moderate Seebeck coefficient, electrical conductivity, thermal conductivity, and power factor in y-direction. Our study reveals the high Seebeck coefficient of 1542 μV/K and power factor of 1.93 × 1011 W/mK2s, respectively, for the p-type counterpart. These results show that p-doped AgFeS2 will be a potential candidate for thermoelectric applications.

N-Type thermoelectric properties of a hexagonal SiGe polymorph superior to a cubic SiGe

The crystal structure of a material dictates many of its properties. This study focuses on a SiGe compound with a hexagonal crystal system that demonstrates superior thermoelectric properties than that of its conventional cubic polymorph. Using first-principles density functional theory (DFT) calculations combined with the semi-classical Boltzmann transport equation (BTE), we clearly elucidate the underlying mechanisms that cause the enhanced thermoelectric performance. The hexagonal SiGe compound shows different folding behavior of the electronic band structure, leading to dissimilar density of states and enhanced Seebeck coefficient, compared to the cubic counterpart. Moreover, the phonon vibrational modes of the hexagonal SiGe shorten the phonon lifetime due to the different lattice symmetry. Based on the results, we propose hexagonal SiGe as a promising material for a highly active n-type thermoelectric material with a figure of merit that is twice of its cubic analogue. Our approach demonstrates an attractive method for substantially enhancing conventional material properties without a complicated or expensive process for developing a novel material.

Electronic, magnetic, optical and transport properties of wurtzite-GaN doped with rare earth (RE= Pm, Sm, and Eu): First principles approach

A density functional theory (DFT) and semiclassical Boltzmann transport equations (BTE) has been used to explore the electronic, magnetic, optical and transport properties of Ga1−xRExN (RE=Pm, Sm, and Eu). We have studied the impact of doping of rare-earth (RE) elements on GaN wurtzite structure. In all the doped systems, the stability is ferromagnetic state with minimum ground state energy. Our theoretical calculations revealed that all the doped compounds exhibit half-metallic ferromagnet (HMF) behavior with 100% spin polarization at the Fermi level witin GGA, mBJ and Spin-orbit coupling (SOC). However, within GGA+U, Ga1−xRExN exhibits dilute magnetic semiconducting behaviour with exact integer value of total magnetic moment. A large gap was established with the concentrations of 6.25%, 12.5%. The shift of fermi energy towards the bottom of the conduction band, make these systems an n-type. The mechanism of ferromagnetism in this system has been proposed according to this positioning. The majority-spin density of states (DOS) mainly comprises of Eu-4f states appears in the energy gap. Yet, in the case of the Pm, and Sm-doped GaN, some part of the impurity states of 4f lies below Fermi energy (Ef). The optical absorption for RE-doped GaN is significantly enhanced, in the ultraviolet region. We have noticed the improvement of electrical conductivity as compared to the pristine one for both the concentrations. These features, make RE-doped GaN a transparent material for optoelectronic tools.

Intrinsic and extrinsic effects on intraband optical conductivity of hot carriers in photoexcited graphene

We present a numerical study on the intraband optical conductivity of hot carriers at quasi-equilibria in photoexcited graphene based on the semiclassical Boltzmann transport equations (BTE) with the aim of understanding the effects of intrinsic optical phonon and extrinsic coulomb scattering caused by charged impurities at the graphene--substrate interface. Instead of using full-BTE solutions, we employ iterative solutions of the BTE and the comprehensive model for the temporal evolutions of hot-carrier temperature and hot-optical-phonon occupations to reduce computational costs. Undoped graphene exhibits large positive photoconductivity owing to the increase in thermally excited carriers and the reduction in charged impurity scattering. The frequency dependencies of the photoconductivity in undoped graphene having high concentrations of charged impurities significantly deviate from those observed in the simple Drude model, which can be attributed to temporally varying charged impurity scattering during terahertz (THz) probing in the hot-carrier cooling process. Heavily doped graphene exhibits small negative photoconductivity similar to that of the Drude model. In this case, charged impurity scattering is substantially suppressed by the carrier-screening effect, and the temperature dependencies of the Drude weight and optical phonon scattering governs the negative photoconductivity. In lightly doped graphene, the appearance of negative and positive photoconductivity depends on the frequency and the crossover from negative photoconductivity to positive emerges from increasing the charged impurity concentration. This indicates the change of the dominant scattering mechanism from optical phonons to charged impurities. Our approach provides a quantitative understanding of non-Drude behaviors and the temporal evolution of photoconductivity in graphene.

Mitigating the Effect of Nanoscale Porosity on Thermoelectric Power Factor of Si

The addition of porosity to thermoelectric materials can significantly increase the figure of merit, ZT, by reducing the thermal conductivity. Unfortunately, porosity is also detrimental to the thermoelectric power factor in the numerator of the figure of merit ZT. In this manuscript we derive strategies to recoup electrical performance in nanoporous Si by fine tuning the carrier concentration and through judicious design of the pore size and shape so as to provide energy selective electron filtering. In this study, we considered phosphorus doped silicon containing discrete pores that are either spheres, cylinders, cubes, or triangular prisms. The effects from these pores are compared with those from extended pores with circular, square and triangular cross sectional shape, and infinite length perpendicular to the electrical current. A semiclassical Boltzmann transport equation is used to model Si thermoelectric power factor. This model reveals three key results: The largest enhancement in Seebeck coefficient occurs with cubic pores. The fractional improvement is about 15% at low carrier concentration ($< 10^{20}\ \mathrm{1/cm^3}$) up to 60% at high carrier population with characteristic length around $\sim 1\ \mathrm{nm}$. To obtain the best energy filtering effect at room temperature, nanoporous Si needs to be doped to higher carrier concentration than is optimal for bulk Si. Finally, in $n$-type Si thermoelectrics the electron filtering effect that can be generated with nanoscale porosity is significantly lower than the ideal filtering effect; nevertheless, the enhancement in the Seebeck coefficient that can be obtained is large enough to offset the reduction in electrical conductivity caused by porosity.

Monte Carlo Solution of High Electric Field Hole Transport Processes in Avalanche Amorphous Selenium.

Amorphous selenium lacks the structural long-range order present in crystalline solids. However, the stark similarity in the short-range order that exists across its allotropic forms, augmented with a shift to non-activated extended-state transport at high electric fields beyond the onset of impact ionization, allowed us to perform this theoretical study, which describes the high-field extended-state hole transport processes in amorphous selenium by modeling the band-transport lattice theory of its crystalline counterpart trigonal selenium. An in-house bulk Monte Carlo algorithm is employed to solve the semiclassical Boltzmann transport equation, providing microscopic insight to carrier trajectories and relaxation dynamics of these non-equilibrium “hot” holes in extended states. The extended-state hole–phonon interaction and the lack of long-range order in the amorphous phase is modeled as individual scattering processes, namely acoustic, polar and non-polar optical phonons, disorder and dipole scattering, and impact ionization gain, which is modeled using a power law Keldysh fit. We have used a non-parabolic approximation to the density functional theory calculated valence band density of states. To validate our transport model, we calculate and compare our time of flight mobility, impact ionization gain, ensemble energy and velocity, and high field hole energy distributions with experimental findings. We reached the conclusion that hot holes drift around in the direction perpendicular to the applied electric field and are subject to frequent acceleration/deceleration caused by the presence of high phonon, disorder, and impurity scattering. This leads to a certain determinism in the otherwise stochastic impact ionization phenomenon, as usually seen in elemental crystalline solids.

Ab initio prediction of thermoelectric performance of monolayer BiSbTe3

The transport properties on the monolayer BiSbTe3 were studied by density functional theory and Semi-classical Boltzmann Transport equation. For monolayer BiSbTe3, the band gap with TB-mBJ can be improved for monolayer BiSbTe3 comparing with GGA. There is no imaginary frequency for the phonon band structure of monolayer BiSbTe3, which guarantees its dynamic stability. The heavy elements and small band gap between the acoustic mode and the optical mode causes lower lattice thermal conductivity for monolayer BiSbTe3. Due to the flat valence band near Fermi level, p-type doping produces higher S values than n-type doping. The monolayer BiSbTe3 with TB-mBJ can’t improve electrical conductivities, but TB-mBJ can reduce the electronic thermal conductivity. Compared with other well-known two-dimensional materials, monolayer BiSbTe3 have larger ZT. ZT of monolayer BiSbTe3 with n ​= ​1020 ​cm−3 calculated by GGA is 1.002 ​at 900 ​K.