Semiclassical Boltzmann Transport Equation Research Articles

Mechanical and thermoelectric response of 18-valence electron half-Heusler tellurides XFeTe (X=Ti, Hf): A theoretical perspective

To address growing global energy needs, half Heusler compounds offer a cost-effective and efficient solution for power generation applications. We present a study on the structural, electronic, magnetic, phonon, mechanical and thermoelectric (TE) properties of two hH tellurides, XFeTe (X= Ti, Hf) with 18 valence electrons. The investigation employs Density functional theory (DFT), Semi-classical Boltzmann transport equations (BTE), Quasi-harmonic approximation (QHA), Density functional perturbation theory (DFPT) and Deformation potential theory (DPT). The equilibrium lattice constants are determined to be 5.882 Å and 6.041 Å for TiFeTe and HfFeTe respectively. The electronic structures of TiFeTe and HfFeTe are modeled with generalised gradient approximation (GGA), revealing indirect band gaps of 0.93 eV and 0.79 eV, respectively. The conduction bands in TiFeTe and HfFeTe exhibit remarkably low effective masses of 0.72 me and 0.61 me, respectively, resulting in higher carrier relaxation times. The compounds are dynamically and mechanically stable. TiFeTe is ductile whereas HfFeTe is brittle. The elastic constants analysis suggests that these compounds exhibit stiffness, better hardness, elastic anisotropy and high melting point. TE parameters are investigated across a temperature range from 400 K to 1200 K. At room temperature, TiFeTe and HfFeTe exhibit lattice thermal conductivities of 25.43 Wm−1K−1 and 29.29 Wm−1K−1, respectively. At 1200 K, zT for the n-type, p-type compositions are 1.79, 1.11 for TiFeTe and 1.35, 1.06 for HfFeTe, respectively. The n-type composition not only exhibits superior TE performance compared to the p-type but also shows the peak zT at more feasible doping levels.

Effect of doping on domain suppression in the presence of hot electrons in semiconducting achiral carbon nanotubes

Effect of doping semiconducting achiral carbon nanotubes on domain suppression prerequisite for potential generation of terahertz radiations in the presence of hot electrons has been theoretically considered. This was done by solving the semiclassical Boltzmann's transport equation in the presence of hot electrons source to derive the current density as a function of constant electric field and chemical potential of semiconducting achiral carbon nanotubes (CNTs). Plots of normalized current density versus electric field strength for semiconducting achiral CNTs as the chemical potential (μ) representing the degree of doping increases from 1.4 eV to 2.0 eV (i.e. heavily doped CNT) revealed an increase in positive differential conductivity (PDC) that results in enhancement of domain suppression prerequisite for generation of terahertz radiations. Also, it has been observed that PDC which is associated with domain suppression increases as the relative thickness and carrier temperature of semiconducting CNTs increase. Therefore, the study predicts heavily doped larger radius semiconducting achiral CNT at a higher carrier temperature as a better candidate for generation of terahertz radiations whose applications are relevant in current-day technology, industry, and research.

Theoretical investigations of electronic, thermodynamic and thermoelectric properties of filled skutterudites ThFe4P12 and CeFe4P12 using DFT calculations

The structural, mechanical, electrical, thermodynamic and thermoelectric properties of CeFe4P12 and ThFe4P12employing first-principles calculations together with semi-classical Boltzmann Transport equations are investigated. It has been firmly proved that these materials fall within the category of semiconductors. The existence of band gap energies measuring 0.436 eV and 0.52 eV, respectively, supports the basis for this classification. Both materials are stable in terms of mechanics and dynamics. The Seebeck coefficient for ThFe4P12 is 762 V/K, while CeFe4P12 is 667 V/K at ambient temperature. For both materials, the electrical conductivity is on order, 106 S/m. The highest recorded figure of merit values for both materials is 0.14 for ThFe4P12and 0.10 for CeFe4P12at 900 K. Therefore, the theoretical findings provide a strong justification for future experimental investigations.

Thermalization of radiation-induced electrons in wide-bandgap materials: A first-principles approach

The present study is concerned with simulating the thermalization of high-energy charge carriers (electrons and/or electron–hole pairs), generated by ionizing radiation, in diamond and β-Ga2O3. Computational tools developed by the nuclear/particle physics and electronic device communities allow for accurate simulation of charge-carrier transport and thermalization in the high-energy (exceeding ∼100 eV) and low-energy (below ∼10 eV) regimes, respectively. Between these energy regimes, there is an intermediate energy range of about 10–100 eV, which we call the “10–100 eV gap,” in which the energy-loss processes are historically not well studied or understood. To close this “gap,” we use a first-principles approach (density functional theory) to calculate the band structure of diamond and β-Ga2O3 up to ∼100 eV along with the phonon dispersion, carrier-phonon matrix elements, and dynamic dielectric function. Additionally, using the first-order perturbation theory (Fermi's golden rule/first Born approximation), we calculate the carrier-phonon scattering rates and the carrier energy-loss rates (impact ionization and plasmon scattering). With these data, we simulate the thermalization of 100-eV electrons and the generated electron–hole pairs by solving the semiclassical Boltzmann transport equation using Monte Carlo techniques. We find that electron thermalization is complete within ∼0.4 and ∼1.0 ps for diamond and β-Ga2O3, respectively, while holes thermalize within ∼0.5 ps for both. We also calculate electron–hole pair creation energies of 12.87 and 11.24 eV, respectively.

The thermoelectric power investigation of the ϒ2-graphyne molecule device

Graphyne, is an interesting carbon nanostructure, with unique properties such as high carrier mobility, thermal stability, and electronic band characteristics shaped by sp and sp2 hybridizations. Due to its intrinsic porous nature, graphyne exhibits higher phonon scattering, and lower thermal conductance compared to graphene, making it an excellent nominee to be investigated as an organic nanoscale thermoelectric material. In this study, we delve into the thermoelectric power properties of the ϒ2-Graphyne structures using the modeling and simulated approaches. Our modeling studies focus on unit cell base vector variation at temperatures higher and lower than the Fermi temperature, additionally, the hopping energy variation is calculated in the same temperatures. We have employed the semi-classical Boltzmann transport equation to analyze these effects, considering the relaxation time factor, as a way of exploring the phonon scatterings, and the changing system behavior. It is concluded structural variation leads to a change in the scattering mechanisms. ATK Quantum Wise simulations on three groups of ϒ2-Graphyne structures are carried out. In the first two groups, the influence of the electrode length and the asymmetry are investigated, but for the last group, only the main region variation is considered. Generally, the number of the unit cells in the main region is changed from one group to the other. The density of states, the transmission spectrum, and electrical conductance values are calculated moreover, the effect of the temperature on thermoelectric power for all groups of devices is simulated. The figure of merit (Z) values at room temperature for all the structures is determined and the highest value of ZT is for the device with one unit cell and asymmetric electrodes are reported.

A first-principles study of ternary metal chalcogenides [formula omitted][formula omitted] for efficient thermoelectric applications empowered by machine-learning interatomic potential

Metal chalcogenides have already been recognized as promising candidates for thermoelectric applications in the past decade. This study systematically analyzes the ternary metal chalcogenide Ba2MnX3 (X = Te,Se,S) materials to check their suitability for thermoelectric applications. Ba2MnX3 materials belong to the orthorhombic and centrosymmetric Pnma space group, with Ba atoms distributed inside the three-dimensional framework of MnX4 tetrahedron units, forming a quasi-one-dimensional crystal structure. The electronic band structures of the materials investigated using density functional theory (GGA+U) reveal that the materials have direct band gaps ranging between 1.3 eV to 1.9 eV. The structural stability and phonon transport properties are studied using a combination of density functional theory and machine-learning approach. The study shows that all Ba2MnX3 materials possess low lattice thermal conductivity (κL). For Ba2MnTe3, at 700 K κL∼0.45Wm−1K−1 is the lowest achieved κL in this work. The thermoelectric transport parameters of the materials are estimated by working out the semiclassical Boltzmann transport equation. Finally, the Figure of merit (ZT) and thermoelectric conversion efficiency values of the materials are calculated. The maximum ZT≈ 0.74 at 700 K at a carrier concentration of 2.43×1020cm−3, and an efficiency ∼8% in the temperature interval 300 – 700 K is achieved for Ba2MnSe3.

Improved thermoelectric properties of AB stacking bilayer graphene by Sr-intercalation according to chemical potential

This study investigated the use of graphene intercalation compounds as thermoelectric (TE) materials. The electronic and TE properties of AB stacking bilayer graphene (BG) with Sr-intercalation were investigated using Density Functional Theory (DFT) ab initio calculations and the self-consistent full potential linearized augmented plane wave (FP-LAPW) approach. The theoretical TE properties were calculated using the Boltztrap2 package’s semi-classical Boltzmann transport equations (BTE) approximation asset. By breaking the BG’s symmetry, The findings demonstrated that atom intercalation could impact electronic and TE properties and contribute to the lifting degeneracy between the charge neutrality point and the Fermi level. Moreover, the calculated TE properties show that the intercalation of Sr in AB stacking BG proved the high values of the Seebeck coefficient for the n-type and p-type behavior and lower values of thermal conductivity leading to an increase of figure of merit values reaching 3.3 at room temperature. These findings imply that Sr-intercalated material in BG has TE device-relevant properties. Furthermore, at very low temperatures (100 K), the Sr-intercalated material exhibits outstanding thermoelectric characteristics, making it perfect for generating electricity from waste heat or cooling microelectronics.

First principles insights on the structural, mechanical, dynamical, thermoelectric and thermodynamics properties of novel topological (ScSb) semi-metal

In the present report, we have a detailed investigation of the structural, electronic, mechanical, thermoelectric thermodynamic responses of ScSb with external pressure to full potential Linearized augmented Plane-wave technique (FP-LAPW) and semi-classical Boltzmann transport equation based on density functional theory (DFT). Computed the structure of ScSb compound having ground state energy and dynamically stable. Diverse approximations were employed in electronic properties to account for precise exchange and correlation effects. The dynamically and mechanically stability structure is confirmed by the estimation of phonon and elastic constants such as Bulk modulus, Young’s modulus, Poisson's ratio, and shear anisotropy factor. For the transition of carriers from the valence band to conduction, we calculated the electron localized function (ELF), electron, and hole effective mass. Transports properties calculated against temperature, chemical potential, as well as carriers concentrations by employing the external pressure (0GP, 25 GPa, and 40 Gpa) were studied using the semi-classical equation in Boltzmann theory. Thermodynamics properties were computed with external pressure having the variation of temperature in this material which is investigated across a wide temperature range (200–1200 K). Maximum Power factor, electrical conductivity, and thermal conductivity are determined to be 0.3 × 1010 W/mK2s,3 × 1020 (Ω.m.s)-1, and 2.1 × 1015 W/mKs at 300 K against temperature respectively. Because of its non-trivial topological character, this material has a big power factor, which strongly implies that it can operate as a suitable thermoelectric material in the high-temperature zone.

Magneto-transport signatures in periodically-driven Weyl and multi-Weyl semimetals

We investigate the influence of a time-periodic driving (for example, by shining circularly polarized light) on three-dimensional Weyl and multi-Weyl semimetals, in the planar Hall and planar thermal Hall set-ups. We incorporate the effects of the drive by using the Floquet formalism in the large frequency limit. We evaluate the longitudinal magneto-conductivity, planar Hall conductivity, longitudinal thermo-electric coefficient, and transverse thermo-electric coefficient, using the semi-classical Boltzmann transport equations. We demonstrate the explicit expressions of these transport coefficients in certain limits of the system parameters, where it is possible to perform the integrals analytically. We cross-check our analytical approximations by comparing the physical values with the numerical results, obtained directly from the numerical integration of the integrals. The answers obtained show that the topological charges of the corresponding semimetals have profound signatures in these transport properties, which can be observed in experiments.

High dimensionless figure of merit of the ZrI2 monolayer identified based on intrinsic carrier concentration and bipolar effect

A 2D ZrI2 monolayer with a high dimensionless figure of merit (ZT) is analyzed in terms of intrinsic carrier concentrations, transport coefficients, and a bipolar effect. The ZrI2 monolayer with a space group of P21/m is fully optimized. The dynamic and thermal stabilities are verified by computing the phonon dispersion in addition to performing ab initio molecular dynamics simulation. The thermal conductivity of the lattice is evaluated by employing the phonon Boltzmann transport theory and the first-principle second and third force constants. The Seebeck coefficients, electronic thermal conductivities, and electric conductivities of the monolayer are determined by solving the relaxation time approximation semiclassical Boltzmann transport equation. To further explore the chance for promoting ZT, we investigate the manipulating effect of the carrier concentrations. The largest ZT with the bipolar effect can reach 7.86 at 700 K, implying that the ZrI2 monolayer has excellent thermoelectric performance.

Ab initio study of electronic and thermoelectric properties of a new B2CO monolayer

In this work, we present the thermoelectric properties of a novel two-dimensional (2D) B2CO monolayer obtained using first principles calculations. We investigated the electronic band structure and density of states based on density functional theory and using the QUANTUM ESPRESSO computational package. Thermoelectric properties were calculated using the semiclassical Boltzmann transport equation in relaxation time approximation and within Boltztrap computational package. These electrical transport properties include the electrical conductivity coefficients (sigma), thermal conductivity (κe), the Seebeck coefficient (S) and dimensionless figure of merit (ZT), which are suitable for designing thermoelectric devices. According to our results, two-dimensional (2D) B2CO monolayer indicates an indirect band gap semiconductor with value of 1.68 eV. The numerical results show almost isotropic transport properties for the 2D B2CO monolayer. In particular, the thermoelectric study shows a good thermoelectric performance of the 2D B2CO monolayer with high figure of merit, so that, the nanostructure of B2CO is an n-type semiconductor and Seebeck coefficient and figure of merit at room temperature were obtained as -2595 µV/K and 1, respectively.

Investigation of laser modulated thermoelectric power of chiral carbon nanotubes

We investigated laser modulated thermopower in chiral carbon nanotubes . This was achieved by solving the Boltzmann transport equation with energy dispersion relation obtained in the tight-binding approximation. Analytical expressions were obtained for the differential thermoelectric power ( α ) along the axial ( α zz ) direction of the nanotubes. We have also noted that laser intensities above a threshold value of 4.6 × 10 7 V/m lower the thermopower, otherwise there is no substantial change. Varying the real overlapping integrals for jumps along the nanotube axis (Δ z ) and base helix (Δ s ) changes the thermopower from a positive to negative type. Our results suggest the possibility of on-demand tuning of the electronic and thermoelectric properties of single wall nanotubes (SWNTs) in the presence of a laser source. • Laser modulated thermopower of chiral carbon nanotubes has been studied using semi-classical Boltzmann's transport equation. • Below threshold laser intensity of 4.6 × 10 7 V/m, thermopower of nanotubes increases with increasing intensity of the applied laser field. • Under some unique conditions, nanotubes behave as either n-type or p-type semiconductors. • Laser induced on-demand tuning of electronic and thermoelectric properties of nanotubes for optoelectronic applications is possible.

Enhanced thermoelectric ZT in the tails of the Fermi distribution via electron filtering by nanoinclusions: Model electron transport in nanocomposites

Silicon carbide nanoparticles with diameters around 8 nm and narrow size distribution have been finely mixed with doped silicon nanopowders and sintered into bulk samples to investigate the influence of nanoinclusions on electrical and thermal transport properties. We have compared the thermoelectric properties of samples ranging from 0%--5% volume fraction of silicon carbide. The silicon carbide nanoinclusions lead to a significant improvement in the thermoelectric figure of merit ZT largely due to an enhancement of the Seebeck coefficient. A semiclassical Boltzmann transport equation is used to model the electrical transport properties of the Seebeck coefficient and electrical conductivity. The theoretical analysis confirms that the enhancements in the thermoelectric properties are consistent with the energy selective scattering of electrons induced by the offset between the silicon Fermi level and the carbide conduction band edge. This study proves that careful engineering of the energy-dependent electron scattering rate can provide a route towards relaxing long-standing constraints in the design of thermoelectric materials.

Strain-Enhanced Thermoelectric Performance in GeS2 Monolayer.

Strain engineering has attracted extensive attention as a valid method to tune the physical and chemical properties of two-dimensional (2D) materials. Here, based on first-principles calculations and by solving the semi-classical Boltzmann transport equation, we reveal that the tensile strain can efficiently enhance the thermoelectric properties of the GeS2 monolayer. It is highlighted that the GeS2 monolayer has a suitable band gap of 1.50 eV to overcome the bipolar conduction effects in materials and can even maintain high stability under a 6% tensile strain. Interestingly, the band degeneracy in the GeS2 monolayer can be effectually regulated through strain, thus improving the power factor. Moreover, the lattice thermal conductivity can be reduced from 3.89 to 0.48 W/mK at room temperature under 6% strain. More importantly, the optimal ZT value for the GeS2 monolayer under 6% strain can reach 0.74 at room temperature and 0.92 at 700 K, which is twice its strain-free form. Our findings provide an exciting insight into regulating the thermoelectric performance of the GeS2 monolayer by strain engineering.

Enhanced thermoelectric performance from bulk to monolayer BiSbS3 from first principle study

The electronic structure and thermoelectric properties of bulk to monolayer BiSbS3 are studied by density functional theory and semi-classical Boltzmann transport equation. Meanwhile, it is clear that bulk and monolayer BiSbS3 are semiconductors with indirect band gaps by using the TB-mBJ scheme, respectively. Further, it can be known that the phonon spectrum of thin film BiSbS3 has no negative frequency, and it can be inferred further that thin film BiSbS3 is stable. Monolayer BiSbS3 studied in this paper has extremely low lattice thermal conductivity at room temperature, which is lower than that of single quintuple layer Bi2Te3, bulk Sb2Te3, single-QL Bi2Se3 and Bi2Te3S at room temperature. The maximum figure of merit of p-type monolayer BiSbS3 is obtained at a temperature of 1100 K and carrier concentration of 1 × 1020 cm−3. The optimal figure of merit, which is procured from n-type monolayer BiSbS3 within the range of carrier concentration interval considered in this paper, is obtained at 1500 K and 5 × 1019 cm−3.

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.