Single-mode Relaxation Time Approximation Research Articles

Quantitative assessment of thermal resistance in graphene field-effect transistors based on a phonon hydrodynamics and van der Waals coupling approach

In the progressive miniaturization of graphene field-effect transistors (GrFETs), pronounced thermal boundary resistance (TBR) and increasing ballistic-diffusive thermal resistance pose formidable challenges to thermal management. Quantitative analysis of thermal resistance is crucial for advancing efficient thermal designs in GrFETs using state-of-the-art technology. The inherently low-dimensional structure nature of graphene means that thermal conduction in GrFETs, governed by phonon hydrodynamic transport and van der Waals (vdW) interactions, cannot be accurately described by traditional Fourier's law-based models or the single-mode relaxation time approximation. This study introduces an innovative thermal simulation framework that addresses these challenges by incorporating phonon hydrodynamics equations and considering weak vdW coupling. Our findings indicate that thermal conduction in GrFETs is predominantly facilitated by flexural (ZA) phonons, and their thermal transport efficiency is significantly influenced by substrate perturbations. Specifically, the TBR in GrFETs is closely associated with the weak vdW coupling between ZA phonons and substrate atoms. Furthermore, this study employs dimensionless thermal resistance ratios and Knudsen numbers to explore the impact of silicon's geometric dimensions, heat source size, and ballistic phenomena on the substrate's thermal resistance. These insights provide substantial theoretical support for the development of efficient thermal management strategies in GrFETs.

Thermal transport in Yb-based 1-2-20 materials

Lattice thermal-transport properties of heavy-fermion YbT2Zn20-based (T = Co, Rh, and Ir) 1-2-20 compounds are calculated with the single-mode relaxation-time approximation and the full solution of the linearized phonon Boltzmann transport equation from first-principles anharmonic phonon calculations. We predict low lattice thermal conductivity κ L with a maximum value of ∼24.16 ·K at 85.14 K, 137.29 ·K at 9.67 K, and 23.55 ·K at 67.50 K and ∼12.02, 40.04, and 10.30 ·K at room temperature for YbCo2Zn20, YbRh2Zn20, and YbIr2Zn20, respectively. Based on the analysis of the cumulative κ L as a function of the phonon mean free path and the frequency-dependent joint density of states at various temperatures, we attribute the low κ L to a rattling mode with an average characteristic rattling frequency that enhanced phonon scattering processes, which reduced the phonon mean free paths, suppressed the phonon lifetime, and enhanced the probability of three-phonon scattering events. The predicted low κ L , especially in YbCo2Zn20 and YbIr2Zn20, makes them promising candidate materials for thermoelectric applications and thermal management.

Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities

Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.

Structural Dynamics, Phonon Spectra and Thermal Transport in the Silicon Clathrates.

The potential of thermoelectric power to reduce energy waste and mitigate climate change has led to renewed interest in “phonon-glass electron-crystal” materials, of which the inorganic clathrates are an archetypal example. In this work we present a detailed first-principles modelling study of the structural dynamics and thermal transport in bulk diamond Si and five framework structures, including the reported Si Clathrate I and II structures and the recently-synthesised oC24 phase, with a view to understanding the relationship between the structure, lattice dynamics, energetic stability and thermal transport. We predict the IR and Raman spectra, including ab initio linewidths, and identify spectral signatures that could be used to confirm the presence of the different phases in material samples. Comparison of the energetics, including the contribution of the phonons to the finite-temperature Helmholtz free energy, shows that the framework structures are metastable, with the energy differences to bulk Si dominated by differences in the lattice energy. Thermal-conductivity calculations within the single-mode relaxation-time approximation show that the framework structures have significantly lower than bulk Si, which we attribute quantitatively to differences in the phonon group velocities and lifetimes. The lifetimes vary considerably between systems, which can be largely accounted for by differences in the three-phonon interaction strengths. Notably, we predict a very low for the Clathrate-II structure, in line with previous experiments but contrary to other recent modelling studies, which motivates further exploration of this system.

Thermal decay in the one-dimensional transient thermal grating experiment using modified Debye-Callaway model

We calculate the thermal decay in the one-dimensional transient thermal grating (TTG) experiment by solving the transient Boltzmann-Peierls transport equation (BPTE) within the framework of the single-mode relaxation time approximation and using modified Debye-Callaway model in which both longitudinal and transverse phonon modes are included explicitly. We consider surface heating of an opaque thick semiconductor (SC) crystal film that we assume to have a cubic symmetry and is treated as a continuum, elastic, isotropic, and dispersionless medium. We obtain a nonuniversal spectral suppression function (SSF) in the integrand of the effective apparent thermal conductivity that is similar to the one obtained by Chiloyan et al. [Phys. Rev. B 93, 155201 (2016)] using the standard single-mode relaxation time approximation (RTA) model. Therefore, the nonuniversal character of the SSF in the TTG experiment does not depend on the form of the collision operator approximation in the BPTE: Callaway's or standard. Moreover, the analysis of the behavior of the thermal decay rate shows how the peculiar crystal momentum shuffling effect of phonon-phonon scattering Normal processes (N processes) that is captured by Callaway's model influences the onset of the nondiffusive (quasiballistic) regime in the phonon transport process in SC crystals. This effect tends independently from the other phonon scattering processes to favor the maintenance of the phonon diffusive regime over a large length-scale range, a remarkable feature that cannot be put into light with the standard RTA model used in previous works. Hence, the implicit effect of N processes has certainly an important impact on the extraction of the phonon mean-free path spectrum distribution, especially in the high-temperature regime.

First-principles phonon calculations for lattice dynamics, thermal expansion and lattice thermal conductivity of CoSi in the high temperature region

This study presents the first-principles phonon calculations to understand the experimental thermal expansion () and lattice thermal conductivity of CoSi in the high temperature region. Phonon dispersion is computed using the finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of is done under quasi-harmonic approximation. The is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. The calculated in the temperature range 0–1300 K gives a good match with existing experimental data. The calculated value of (∼8.0 W/mK) at 300 K is found to be in good agreement with the experimental value of ∼8.3 W/mK. The temperature dependence of phonon lifetime due to phonon-phonon interaction is calculated to understand the behaviour of . The present study suggests that ground state phonon dispersion obtained from DFT-based methods gives reasonably good explanation of experimental and .

Thermal transport of amorphous phase change memory materials using population-coherence theory: a first-principles study

Thermal conduction plays a vital role in applications of phase change memory (PCM) materials. Phonon-based theory and the Wiedemann–Franz–Lorenz rule have been widely utilized to describe the thermal transport in crystalline PCM materials, while the understanding of heat conduction in the amorphous phase remains insufficient. Here, we quantify the contributions of the coherences (coupling of vibrational modes) and populations (phonon-like) to the thermal conduction of amorphous Ge2Sb2Te5 (GST) and GeTe4, two kinds of typical PCM materials. The contributions of the coherences and populations are calculated using the theory proposed by Allen and Feldman (AF theory) and the single-mode relaxation time approximation of the Boltzmann transport equation based on first-principles calculations. Our results demonstrate that coherences contribute more than 97% of the total thermal conductivities for both amorphous GST and GeTe4 above Debye temperature, while the populations’ contribution is negligible. Besides, the temperature dependence of the thermal conductivities is predicted and analyzed, allowed by the AF theory with the mode linewidths-dependent broadening method introduced in this paper. The predicted positive temperature dependence of amorphous GeTe4 above Debye temperature, in good agreement with the experimental results, is due to the unique nature of coherences, i.e. larger contribution to heat conduction from stronger couplings between different normal modes at a higher temperature. Our calculation provides new insight into thermal transport in amorphous PCM materials and reveals the physical mechanisms of temperature-dependent thermal conductivities above Debye temperature, and the calculation framework can also be extended to other disordered systems.

Nanotube heat conductors under tensile strain: Reducing the three-phonon scattering strength of acoustic phonons

Acoustic phonons play a special role in lattice heat transport, and confining these low-energy modes in low-dimensional materials may enable nontrivial transport phenomena. By applying lowest-order anharmonic perturbation theory to an atomistic model of a carbon nanotube, we investigate numerically and analytically the spectrum of three-phonon scattering channels in which at least one phonon is of low energy. Our calculations show that acoustic longitudinal (LA), flexural (FA), and twisting (TW) modes in nanotubes exhibit a distinct dissipative behavior in the long-wavelength limit, $|k|\ensuremath{\rightarrow}0$, which manifests itself in scattering rates that scale as ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LA}}\ensuremath{\sim}{|k|}^{\ensuremath{-}1/2}, {\mathrm{\ensuremath{\Gamma}}}_{\mathrm{FA}}\ensuremath{\sim}{k}^{0}$, and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{TW}}\ensuremath{\sim}{|k|}^{1/2}$. These scaling relations are a consequence of the harmonic lattice approximation and critically depend on the condition that tubes are free of mechanical strain. In this regard, we show that small amounts of tensile lattice strain $\ensuremath{\epsilon}$ reduce the strength of anharmonic scattering, resulting in strain-modulated rates that, in the long-wavelength limit, obey $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}{\ensuremath{\epsilon}}^{r}{|k|}^{s}$ with $r\ensuremath{\le}0$ and $s\ensuremath{\ge}1$, irrespectively of acoustic mode polarization. Under the single-mode relaxation time approximation of the linearized Peierls-Boltzmann equation (PBE), the long-tube limit of lattice thermal conductivity in stress-free and stretched tube configurations can be unambiguously characterized. Going beyond relaxation time approximations, analytical results obtained in the present study may help to benchmark numerical routines which aim at deriving the thermal conductivity of nanotubes from an exact solution of the PBE.

Thermal conductivity of ThO2: Effect of point defect disorder

Thoria (ThO2) has lately gained attention due to its potential for use as a nuclear fuel. From a physics standpoint, ThO2 is an actinide-bearing material with no 5f electrons and is thus ideally suited as a baseline material for future studies of the physical properties of actinide systems with correlated electrons. Current investigations of ThO2 as a nuclear fuel focus on the influence of radiation-induced lattice defects on its thermal properties, especially the conductivity. This work presents a first investigation of the impact of point defect disorder on phonon thermal conductivity of ThO2 by solving the Boltzmann transport equation within the single-mode relaxation time approximation. The relaxation times of intrinsic, three-phonon scattering are calculated by a rigorous sampling of k-points within the irreducible Brillouin zone of the face-centered cubic crystal structure. The effect of point defects on the thermal conductivity of ThO2 is predicted using the classic model by Klemens for phonon relaxation times that result from the change in mass and induced lattice strain associated with point defects. Within this model, the change in force constants and atomic radii are computed using input from an atomistic model of ThO2. The defects considered are uranium substitution at a thorium site, oxygen vacancies and interstitials, and thorium vacancies and interstitials. The results show that the conductivity of ThO2 is highly sensitive to intrinsic point defects and less sensitive to U substitution on the cation sublattice.

Enhancing thermoelectric properties of Janus WSSe monolayer by inducing strain mediated valley degeneracy

The Janus WSSe monolayer is a new 2D direct band gap material attracting attention due to its unique physical and chemical properties. The lattice thermal conductivity is calculated using the self-consistent approach as well as single-mode relaxation time approximation. We notice that acoustic modes contribute mainly to the lattice thermal conductivity. Thermoelectric properties are investigated using the Seebeck coefficient, electrical conductivity, thermal conductivity, power factor, and figure of merit for pristine WSSe monolayer. The effect of strain on thermoelectric properties is also investigated. Interestingly, the tensile strain resulted in a lowering of the lattice thermal conductivity from 25.37 to 9.90 W m−1K−1. The valley degeneracy with biaxial strain in the valence and conduction band edges enhances the power factor. Thus, strain ultimately, improves the figure of merit from 0.72 (0.73) to 1.06 (1.08) under biaxial strain for n(p) carriers at 5 × 1020 cm−3 and 7 × 1020 cm−3, respectively. The thermoelectric efficiency of biaxial stained monolayer based device improved about 29% at 1500 K. These studies provide an avenue to engineer the thermoelectric properties using strain mediated valley degeneracy as the external stimuli.

Heat transport in semiconductor crystals: Beyond the local-linear approximation

We extend the application of the nonlocal theory of Mahan and Claro [Phys. Rev. B 38, 1963 (1988)] to solve the steady-state Boltzmann–Peierls transport equation within the framework of the single mode relaxation time approximation using the modified Debye–Callaway model. We consider the case of a semi-infinite semiconductor (SC) crystal with a boundary condition at its top surface that can be considered reasonably representative of time domain thermoreflectance (TDTR) and frequency domain thermoreflectance (FDTR) techniques. The approach allows us to obtain three different contributions to the heat flux density current that shed further light on the fundamental role of nonlocality and nonlinearity in heat transport by phonons in SC crystals. Through their intrinsic and implicit shuffling effect of the crystal momentum, phonon–phonon Normal scattering processes play a key role in the onset of thermal conduction as they introduce the temperature Laplacian as a second driving potential force for the heat flux density current in addition to the conventional Fourier's temperature gradient. The developed model suits quite fairly to interpret the frequency behavior of the reduced effective thermal conductivity of SC crystals that is observed in TDTR and FDTR experiments. We obtain an expression of the effective thermal conductivity of the SC crystal that is characterized with a universal spectral suppression function that captures and describes the role, the weight, and the contribution of quasi-ballistic and non-diffusive phonons. The spectral suppression function only depends on the ratio between the phonon mean free path and the thermal penetration depth as defined based on the diffusive Fourier's law.

Lattice thermal conductivity of pure and doped (B, N) Graphene

In this paper, the effect of B and N doping on the phonon induced thermal conductivity of graphene has been investigated. This study is important when one has to evaluate the usefulness of electronic properties of B and N doped graphene. We have performed the calculations by employing density functional perturbation theory(DFPT) to calculate the inter-atomic forces/force constants of pristine/doped graphene. Thermal conductivity calculations have been carried out by making use of linearized Boltzmann transport equations (LBTE) under single-mode relaxation time approximation(RTA). The thermal conductivity of pristine graphene has been found to be of the order of 4000 W/mK at 100 K, which decreases gradually with an increase in temperature. The thermal conductivity decreases drastically by 96% to 190 W/mK when doped with 12.5% B and reduces by 99% to 30 W/mK with 25% B doping. When graphene is doped with N, the thermal conductivity decreases to 4 W/mK and 55 W/mK for 12.5% and 25% doping concentration, respectively. We have found that the thermal conductivity of doped graphene show less sensitivity to change in temperature. It has also been shown that the thermal conductivity of graphene can be tuned with doping and has a strong dependence on doping concentration.

Ultra-low lattice thermal conductivity and giant phonon–electric field coupling in hafnium dichalcogenide monolayers

Phonons in crystalline solids are of utmost importance in governing its lattice thermal conductivity (kL). In this work, kL in hafnium (Hf) dichalcogenide monolayers has been investigated based on ab initio DFT coupled to linearized Boltzmann transport equation together with single-mode relaxation-time approximation. Ultra-low kL found in HfS2 (2.19 W m−1 K−1), HfSe2 (1.23 W m−1 K−1) and HfSSe (1.78 W m−1 K−1) monolayers at 300 K, is comparable to that of the state-of-art bulk thermoelectric materials, such as, Bi2Te3 (1.6 W m−1 K−1), PbTe (2.2 W m−1 K−1) and SnSe (2.6 W m−1 K−1). Gigantic longitudinal-transverse optical (LO-TO) splitting of up to 147.7 cm−1 is noticed at the Brillouin zone-centre (Γ-point), which is much higher than that in MoS2 single layer (∼2 cm−1). It is driven by the colossal phonon–electric field coupling arising from the domination of ionic character in the interatomic bonds and Born effective or dynamical charges as high as 7.4e on the Hf ions, which is seven times that on Mo in MoS2 single layer. Enhancement in kL occurs in HfS2 (2.19 to 4.1 W m−1 K−1), HfSe2 (1.23 to 1.7 W m−1 K−1) and HfSSe (1.78 to 2.2 W m−1 K−1) upon the incorporation of the non-analytic correction term. Furthermore, the mode Grüneisen parameter is calculated to be as high as ∼2.0, at room temperature, indicating a strong anharmonicity. Moreover, the contribution of optical phonons to kL is found to be ∼12%, which is significantly high than that in single-layer MoS2. Large atomic mass of Hf (178.5 u), small phonon group velocities (4–5 km s−1), low Debye temperature (∼166 K), low bond and elastic stiffness (Young’s modulus ∼75 N m−1), small phonon lifetimes (∼6 ps), low specific heat capacity (∼17 J K−1 mol−1) and strong anharmonicity are collectively found to be the factors responsible for such a low kL. These findings would be immensely helpful in designing thermoelectric interconnects at the nanoscale and 2D material-based energy harvesters.

First-principles electronic structure, phonon properties, lattice thermal conductivity and prediction of figure of merit of FeVSb half-Heusler

In this work, we have studied the electronic structure of a promising thermoelectric half-Heusler FeVSb using FP-LAPW method and SCAN meta-GGA including spin–orbit coupling. Using the obtained electronic structure and transport calculations we try to address the experimental Seebeck coefficient S of FeVSb samples. The good agreement between the experimental and calculated S suggests the band gap could be ∼0.7 eV. This is supported by the obtained mBJ band gap of ∼0.7 eV. Further, we study and report the phonon dispersion, density of states and thermodynamic properties. The effect of long range Coulomb interactions on phonon frequencies are also included by nonanalytical term correction. Under quasi-harmonic approximation, the thermal expansion behaviour up to 1200 K is calculated. Using the first-principles anharmonic phonon calculations, the lattice thermal conductivity κ ph of FeVSb is obtained under single-mode relaxation time approximation considering the phonon-phonon interaction. At 300 K, the calculated κ ph is ∼18.6 W m−1 K−1 which is higher compared to experimental value. But, above 500 K the calculated κ ph is in good agreement with experiment. A prediction of figure of merit ZT and efficiency for p-type and n-type FeVSb is made by finding out optimal carrier concentration. At 1200 K, a maximum ZT of ∼0.66 and ∼0.44 is expected for p-type and n-type FeVSb, respectively. For p-type and n-type materials, maximum efficiency of ∼12.2% and ∼6.0% are estimated for hot and cold temperature of 1200 K and 300 K, respectively. A possibility of achieving n-type and p-type FeVSb by elemental doping/vacancy is also discussed. Our study is expected to help in further exploring the thermoelectric material FeVSb.

A complete computational route to predict reduction of thermal conductivities of complex oxide ceramics by doping: A case study of La2Zr2O7

Rare-earth (RE) zirconate pyrochlores, of low thermal conductivity and high temperature stability, are widely considered as a candidate material group for thermal barrier coatings (TBCs). Doping of a RE zirconate pyrochlore has been shown to be one possible method towards additional reduction in the thermal conductivity. Focusing on lanthanum zirconate (La2Zr2O7) as a representative RE zirconate pyrochlore, we systematically investigated the effect of various doping elements, Gd, Y, Yb, In, Sc, Ce and Hf, on the thermal conductivity. A complete computational route, based on first-principles calculations, to predict the reduction of thermal conductivity by doping, has been developed. Employing first-principles calculations combined with thermodynamic modeling, the defects resulted from doping are explicitly clarified, with their concentrations determined considering the chemical environment. The phonon-defect scattering is then evaluated and the resultant reduction of thermal conductivity is determined from single-mode relaxation-time approximation. Good agreement has been achieved between our model predictions and available experimental data. The present study established a complete computational route, based on first-principles calculations, to predict the reduction of thermal conductivity by doping, not only for RE zirconate pyrochlores, but also for other complex oxide ceramics.

Structural, stability and thermoelectric properties for the monoclinic phase of NaSbS2 and NaSbSe2: A theoretical investigation

This study is the first attempt towards establishing computational insight into the structural, electronic, mechanical, dynamical and thermoelectric properties of the monoclinic phases of NaSbS2 and NaSbSe2. The mechanical properties are predicted using the Hill approximation. Dynamical stability was investigated by computing the phonon frequency to check for the absence of imaginary modes. Lattice thermal conductivity was calculated by using a single-mode relaxation-time approximation in the linearized phonon Boltzmann equation from first-principles an-harmonic lattice dynamics calculations. We found that the lattice thermal conductivity of NaSbS2 and NaSbSe2 are anisotropic, with values ranging between 0.753 and 1.173 Wm−1 K−1 at room temperature (300 K). The calculated values of the lattice thermal conductivity are small, especially along the x-axis. The charge transport properties are predicted using Boltzmann transport equations. The highest values attained for the figure of merit are high as 4.22 and 2.88 when the electron concentration is 1018 cm−3 at 600 K for NaSbS2 and NaSbSe2, respectively. This highlights the potential of using NaSbS2 and NaSbSe2 in designing thermoelectric materials since low lattice thermal conductivity and high figure of merit are a requisite for maximizing the efficiency of thermoelectric materials.

Theoretical analysis of cross-plane lattice thermal conduction in graphite**Project supported by the National Natural Science Foundation of China (Grant No. 51376094) and Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents.

A theoretical analysis of the cross-plane lattice thermal conduction in graphite is performed by using first-principles calculations and in the single-mode relaxation time approximation. The out-of-plane phonon acoustic mode ZA and optical mode have almost 80% and 20% of contributions to cross-plane heat transfer, respectively. However, these two branches have a small part of total specific heat above 300 K. Phonons in the central 16% of Brillouin zone contribute 80% of cross-plane transport. If the group velocity angle with respect to the graphite layer normal is less than 30°, then the contribution is 50% at 300 K. The ZA phonons with long cross-plane mean free path are focused in the cross-plane direction, and the largest mean free path is on the order of several micrometers at room temperature. The average value of cross-plane mean free path at 300 K is 112 nm for ZA phonons with group velocity angle with respect to the layer normal being less than 15°. The average value is dropped to 15 nm when phonons of all branches in the whole Brillouin zone are taken into account, which happens because most phonons have small or even no contributions.

Born effective charge removed anomalous temperature dependence of lattice thermal conductivity in monolayer GeC

Due to potential applications in nano- and opto-electronics, two-dimensional (2D) materials have attracted tremendous interest. Their thermal transport properties are closely related to the performance of 2D materials-based devices. Here, the phonon transports of monolayer GeC with a perfect planar hexagonal honeycomb structure are investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). Without inclusion of Born effective charges (Z*) and dielectric constants (), the lattice thermal conductivity () decreases almost linearly above 350 K, deviating from the usual law. The underlying mechanism is because the contribution to from high-frequency optical phonon modes increases with increasing temperature, and the contribution exceeds one from acoustic branches at high temperature. These can be understood by huge phonon band gap caused by large difference in atom mass between Ge and C atoms, which produces important effects on scattering process involving high-frequency optical phonon. When considering Z* and , the phonon group velocities and phonon lifetimes of high-frequency optical phonon modes are obviously reduced with respect to ones without Z* and . The reduced group velocities and phonon lifetimes give rise to small contribution to from high-frequency optical phonon modes, which produces the the traditional relation in monolayer GeC. Our works highlight the importance of Z* and to investigate phonon transports of monolayer GeC, and motivate further theoretical or experimental efforts to investigate thermal transports of other 2D materials.

Low lattice thermal conductivity and high thermoelectric figure of merit in Na2MgSn

Thermoelectric materials enables the harvest of waste heat and directly conversion into electricity. In search of high efficient thermoelectric materials, low thermal conductivity of a material is essential and critical. Here, we have theoretically investigated the lattice thermal conductivity and thermoelectric properties of layered intermetallic Na$_2$MgSn and Na$_2$MgPb based on the density functional theory and linearized Boltzmann equation with the single-mode relaxation-time approximation. It is found that both materials exhibit very low and anisotropic intrinsic lattice thermal conductivity. Despite of the very low mass density and simple crystal structure of Na$_2$MgSn, its lattice thermal conductivities along $a$ and $c$ axes are only 1.75 and 0.80 W/m$\cdot$K respectively at room temperatures. When Sn is replaced by the heavier element Pb, its lattice thermal conductivities decrease remarkably to 0.51 and 0.31 W/m$\cdot$K respectively along $a$ and $c$ axes at room temperatures. We show that the low lattice thermal conductivities of both materials are mainly due to their very short phonon lifetimes, which are roughly between 0.4 to 4.5 ps. Combined with previous experimental measurements, the metallic Na$_2$MgPb can not be a good thermoelectric material. However, we predict that the semiconducting Na$_2$MgSn is a potential room-temperature thermoelectric material with a considerable $ZT$ of 0.34 at 300 K. Our calculations not only imply that the intermetallic Na$_2$MgSn is a potential thermoelectric material, but also can motivate more theoretical and experimental works on the thermoelectric researches in simple layered intermetallic compounds.

A theoretical investigation of structural, mechanical, electronic and thermoelectric properties of orthorhombic CH3NH3PbI3

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH3NH3PbI3 have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm−1K−1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.