Phonon Transport Properties Research Articles

The Effect of Width-Mismatch of Modulated Nanowaveguides on the Thermoelectric Efficiency.

Width-modulated nanowaveguides are promising for thermoelectric efficiency enhancement because electron and phonon transport properties can be geometrically tuned for improved performance. The shape of the modulation profile drastically affects the transport properties. Optimization of the width modulation for simultaneous maximum thermoelectric transport and minimum thermal transport is challenging because of the interconnected electron and phonon transport properties. We addressed this problem by analysing the effect of each characteristic dimension of a single rectangular modulation unit on electron and phonon transport. We identified distinct behaviours for electrons and phonons. We reveal that whereas phonon thermal conductance decreases with increasing width-mismatch, the electron thermoelectric power factor shows a non-monotonic dependence. It is pointed out that optimal width-mismatch that maximizes thermoelectric efficiency is mainly determined by electron transport and should be identified by maximizing the thermoelectric power. Our work points to a new strategy of optimizing geometry-modulated metamaterials for maximum thermoelectric efficiency.

Strong Electron–Phonon and Phonon–Phonon Interactions Lead to High Thermoelectric Performances in Lead Phosphorene via Symmetry Breaking

AbstractUnderstanding the full electron–phonon and phonon–phonon interaction effects in semiconductors is crucial for tuning electronic and phonon transport properties with the purpose to the enhancement of thermoelectric performances. In this work, based on the detailed investigations on 2D lead phosphorene (PbP) by using the first‐principle calculations, it is demonstrated that, in , , and PbP, the electron–phonon interactions are significantly stronger than conventional group‐IV monolayers such as silicene by five orders in magnitude, and intravalley scatterings dominate over the intervalley scattering due to less degenerate band extrema near Fermi level. Based on the selection‐rule analysis, it is found that the symmetry breaking in the janus γ phase compared to the higher‐symmetry α phase allows fewer symmetry operations, leading to more allowed scattering channels for electrons and phonons, subsequently suppressing the electron and phonon transport in PbP. Due to the low Debye temperatures, and strong four‐phonon interactions, the lattice thermal conductivities at room temperature in these monolayers are sharply decreased. Finally, it is found that the maximum thermoelectric figure of merits for these three monolayers reach 0.90/0.24/1.25 at room temperature, respectively. This work not only paves the way for the promising applications of PbP monolayers in thermoelectric devices, but also suggests that symmetry breaking and strong high‐order phonon–phonon interactions are crucial to identifying excellent thermoelectric materials.

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.

Thermal conductivity of van der Waals heterostructure of 2D GeS and SnS based on machine learning interatomic potential

van der Waals heterostructures have provided an unprecedented platform to tune many physical properties for two-dimensional materials. In this work, thermal transport properties of van der Waals heterostructures formed by vertical stacking of monolayers GeS and SnS have been investigated systematically based on machine learning interatomic potential. The effect of van der Waals interface on the lattice thermal transport of 2D SnS and GeS can be well clarified by introducing various stacking configurations. Our results indicate that the van der Waals interface can strongly suppress the thermal transport capacity for the considered heterostructures, and either the average thermal conductivity per layer or the 2D thermal sheet conductance for the considered heterostructures is lower than that of corresponding monolayers. The suppressed thermal conductivity with tunable in-plane anisotropy in SnS/GeS heterostructures can be ascribed to the enhanced interface anharmonic scattering, and thus exhibits obvious interface-dependent characteristics. Therefore, this work highlights that the van der Waals interface can be employed to effectively modulate thermal transport for the 2D puckered group-IV monochalcogenides, and the suppressed lattice thermal conductivity together with interface-dependent phonon transport properties in the SnS/GeS heterostructure imply the great potential for corresponding thermoelectrical applications.

Low lattice thermal conductivity of two-dimensional monolayers of BxN (x = 2, 3, and 5) induced by complex bonding networks: A comparative study with h-BN

It is well known that different bonding networks could bring a wide variety of physical properties to the materials although they hold analogous element and structure features. In this paper, we present a first-principles calculation about the lattice dynamics and phonon transport properties of two-dimensional (2D) boron-rich material BxN (x = 2, 3, and 5). The calculations show that besides the obvious differences in electrical properties compared to h-BN, the special bonding environment in these boron-rich materials also results in quite different phonon behaviors, where their thermal conductivity is at least one order of magnitude smaller than that of h-BN. By performing bonding and lattice dynamics analysis, we reveal that such dramatic reduction of conductivity is attributed to the synergistic effect of weak bond strength (low phonon group velocity) and complex bonding network (strong phonon scattering). Relative regular residual analysis further indicates that the four-phonon process is limited in BxN, and the three-phonon scattering is sufficient to describe their anharmonicity. Starting from the basic physical mechanism, the present study sheds light on the thermal transport properties of 2D boron-rich BxN compounds, which could provide useful insight for their widespread applications in thermal management.

Intrinsically Low Thermal Conductivity in a Novel Cu-S Modified ZrS2 Compound with Asymmetric Bonding.

Materials with low thermal conductivity have received significant attention across various research fields, including thermal insulation materials, thermal barrier coatings, and thermoelectric materials. Exploring novel materials with intrinsically low thermal conductivity and investigating their phonon transport properties, chemical bonding, and atomic coordination are crucial. In this study, a novel ternary sulfide is successfully discovered, Cu2 ZrS3 , which is achieved by introducing copper ions into both the interlayer and intralayer of ZrS2 . The resulting structure encompasses various coordination forms within each layer, such as [CuS4 ], [ZrS6 ], and [CuS3 ], leading to pronounced phonon anharmonicity induced by the asymmetric bonding of tri-coordinated Cu atoms within the [ZrS6 ] layer. As a result, Cu2 ZrS3 exhibits intrinsically low lattice thermal conductivity (κL ) of about 0.83 W m-1 K-1 at 300 K and 0.35 W m-1 K-1 at 683 K, which are in the exceptionally low level among sulfides. In comparison to the conventional approach of inserting guests between layers, the substitution of atoms within layers provides a novel and effective strategy for designing low κL materials in transition metal dichalcogenides (TMDCs).

Modulated crystallographic shear structure in titanium–chromium oxides: their structure and phonon transport properties

Modulated crystallographic shear structure in titanium–chromium oxides: their structure and phonon transport properties

Determination of Seebeck coefficient originating from phonon-drag effect using Si single crystals at different carrier densities

The phonon-drag effect is useful for improving the thermoelectric performance, especially the Seebeck coefficient. Therefore, the phonon and electron transport properties of Si single crystals at different carrier densities were investigated, and the relationship between these properties and the phonon-drag effect was clarified. Phonon transport properties were determined using nanoindentation and spot-periodic heating radiation thermometry. The electron transport properties were determined based on the electrical conductivity of Si. The diffusive Seebeck coefficient derived from the electron transport properties was in good agreement with previous reports. However, the value of the phonon-drag Seebeck coefficient derived from the phonon transport properties is very low. This phenomenon suggests that phonons with a normal mean free path (MFP) do not contribute to the increase in the Seebeck coefficient; however, phonons with a long MFP and low frequency increase the Seebeck coefficient via the phonon-drag effect. Moreover, the phonon-drag effect was sufficiently pronounced even at 300 K and in the heavily doped region. These features are key in designing thermoelectric materials with enhanced performance derived from the phonon-drag effect.

3D Printing of Bi2Te3-Based Thermoelectric Materials with High Performance and Shape Controllability.

Thermoelectric (TE) energy conversion technology provides a promising way to improve the efficiency of fossil energy by generating electricity from low-grade waste heat. With regard to these applications, thermoelectric generators (TEGs) should be designed from system integration perspectives to simultaneously improve heat transfer efficiency and system simplification as well as the robust mechanical properties. However, typical TEGs fabricated by conventional methods barely accomplish such requirements. Herein, high-quality TEGs were assembled by combining the well-flowable spherical bismuth telluride (BT) powdered precursors and selective laser melting (SLM) technology. By optimizing the electronic and phonon transport properties through defect engineering driven by 3D printing, a high figure of merit was accomplished for 1.27 (p-type) and 1.13 (n-type) in BT. This achievement is primarily attributed to the nonequilibrium solidification mechanism, which leads to the formation of multiscale defects during the 3D printing process. The introduction of these multiscale defects enables the effective scattering of wide frequency phonons, leading to a substantial reduction in lattice thermal conductivity. Meanwhile, robust mechanical properties were obtained in the printed p-type/n-type BT TE materials parallel to the building direction (BD) with a compressive strength reaching 257/250 MPa by employing the fine grain structure and the high density of nanotwins introduced during the SLM process. A well shape-controllable and high-performance TEG was designed using 3D-printed BT half-rings, and an output power of 134 mW was achieved at a temperature gradient of 38.9 °C. Our study opens a new route for the great potential of TE materials based on standard commercial SLM 3D printing technology for low-grade waste heat emitted from structures with heterogeneous shapes.

Electrical and Thermal Transport Properties of Ge1–xPbxCuySbyTeSe2y

AbstractBalancing the contradictory relationship between thermoelectric parameters, such as effective mass and carrier mobility, is a challenge to optimize thermoelectric performance. Herein, the exceptional thermoelectric performance is realized in GeTe through collaboratively optimizing the carrier and phonon transport via stepwise alloying Pb and CuSbSe2. The formation energy of Ge vacancy is efficiently bolstered by alloying Pb, which reduces carrier density and carrier scattering to maintain superior carrier mobility in GeTe. Additionally, CuSbSe2, acting as an n‐type dopant, further modulates carrier density and validly equilibrates carrier mobility and effective mass. Accordingly, the promising power factor of 45 µW cm−1 K−2 is achieved at 723 K. Meanwhile, point defects are found to significantly suppress phonons transport to descend lattice thermal conductivity by Pb and CuSbSe2 alloying, which barely impacts the carrier mobility. A combination with superior carrier mobility and lower lattice thermal conductivity, a maximum ZT of 2.2 is attained in Ge0.925Pb0.075Cu0.005Sb0.005TeSe0.01, which corresponds to a 100% promotion compared with that of intrinsic GeTe. This study provides a new indicator for optimizing carrier and phonon transport properties by balancing interrelated thermoelectric parameters.

Superior thermoelectric performance in non-stoichiometric Cu3SbSe4 system: Towards synergistic optimization of carrier and phonon transport

To investigate the effect of cation disorders to modulate thermoelectric performance of Cu3SbSe4 system, we attempted to tune copper content in Cu3+xSbSe4 (x = -0.06, -0.04, 0, 0.04, 0.06, and 0.08) system synthesized via solid-state reaction route. Considering the asymmetry in charge and phonon transport properties, intentional deviations from the proper stoichiometry successfully enhance the electrical transport and reduce the phonon transport simultaneously. The self-doping effect induced by the off stoichiometry in Cu3SbSe4 provides acceptor levels, thereby elevating the electrical conductivity. Modulating the Fermi level within the valence band, we could realize a power factor to the highest value of ∼232 µW/mK2 for the sample with x = -0.06 at 210 K. Considerable reduction in thermal conductivity is the key factor in enhancing the figure of merit to a maximum value of ∼0.033 (at 350 K) for the sample with x = 0.06, which about three times higher than that of the pristine sample. The present study demonstrates that non-stoichiometry plays a substantial role in modulating the thermoelectric transport of the Cu3SbSe4 system.

Tuning the lattice thermal conductivity of bilayer penta-graphene by interlayer twisting

Penta-graphene (PG) is the well-known prototype of the extensively studied 2D pentagon-based materials in recent years, and twisting strategy has been widely used to tune the properties of 2D sheets since the discovery of superconductivity in twisted bilayer graphene. However, no study is reported on how twisting affects the phonon properties of such penta-sheets. In this work, for the first time, we study the effect of twisting on the phonon transport properties of PG by using density functional theory and the phonon Boltzmann transport equation combined with two-channel transport theory and machine learning method. It is found that the in-plane lattice thermal conductivity of the twisted bilayer PG with a twist angle of 36.87° is only 96.72 W/mK at 300 K, reduced by 77.16% as compared to that of untwisted bilayer PG, and the four-phonon interaction further reduces the thermal conductivity by nearly 36%, while the coherence contribution to the thermal conductivity is enhanced to 9.69 W/mK from 0.13 W/mK by twisting. These results indicate that interlayer twisting not only can enhance three- and four-phonon scattering but also can uplift phonon coherence due to the resulted complex atomic configuration and high anharmonicity in bilayer PG.

Anharmonic and glass-like phonon transport in the Tetrahedrite-manner Ag6Si6Sn4P12

In this study, the thermal conductivity properties of the tetrahedrite-structures compound Ag6Si6Sn4P12, whose phonon properties have not been reported so far, are investigated in depth using self-consistent phonon calculations that consider up to fourth-order anharmonic terms. Compared to the previously studied Ag6Ge10P12, a tetrahedrite-manner phosphide, Ag6Si6Sn4P12 without lone pairs, has a unique feature in that it exhibits softening of the Ag and Sn phonon modes at 300 K and has a short phonon lifetime owing to its relatively high anharmonicity. This is believed to be the cause of the extremely low lattice thermal conductivity of Ag6Si6Sn4P12. Additionally, we also observed a nonnegligible contribution of the coherent component to the thermal conductivity of Ag6Si6Sn4P12 because of its wide phonon linewidth, suggesting that Ag6Si6Sn4P12 exhibits glass-like phonon transport properties.

Understanding intrinsic phonon thermal transport in two-dimensional γ-GeX (X = S, Se, Te) from first principles

Motivated by the recent experimental synthesis of a new hexagonal two-dimensional GeSe material, γ-GeSe, we systematically investigated the phonon transport properties of two-dimensional IV-VI compounds γ-GeS, γ-GeSe and γ-GeTe using first principles calculation and phonon Boltzmann transport equation. We discussed the basic phonon transport properties, including phonon spectra, group velocity, relaxation time, Grüneisen parameter, scattering phase space, phonon mean free path, potential energy change with respect to atomic displacement, and electron localization function of the three compounds. The intrinsic phonon thermal conductivities of γ-GeX (X = S, Se, Te) are quite low due to the low phonon velocity and large phonon scattering rates. Among the three compounds, γ-GeSe gives the lowest thermal conductivity (4.73 W/mK, at room temperature). The relative atomic mass difference between Ge atom and Se atom for γ-GeSe is the smallest which gives decreasing both the phonon relaxation time and phonon mean free path. This behavior is demonstrated by correlating the phonon dispersion and scattering mechanism of each compound. Besides, the potential energy change with respect to atomic displacement and the distribution of electron localization indicating the anharmonicity of γ-GeSe. This work reveals the low thermal conductivity of the two-dimensional γ-GeX (X = S, Se, Te), shedding light on future study and adding additional feature for thermal applications of two-dimensional IV-VI material.

Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals

The unique structure of two-dimensional (2D) Dirac crystals, with electronic bands linear in the proximity of the Brillouin-zone boundary and the Fermi energy, creates anomalous situations where small Fermi-energy perturbations critically affect the electron-related lattice properties of the system. The Fermi-surface nesting (FSN) conditions determining such effects via electron–phonon interaction require accurate estimates of the crystal’s response function as a function of the phonon wavevector q for any values of temperature, as well as realistic hypotheses on the nature of the phonons involved. Numerous analytical estimates of for 2D Dirac crystals beyond the Thomas–Fermi approximation have been so far carried out only in terms of dielectric response function , for photon and optical-phonon perturbations, due to relative ease of incorporating a q-independent oscillation frequency in calculation. Models accounting for Dirac-electron interaction with acoustic phonons, for which ω is linear to q and is therefore dispersive, are essential to understand many critical crystal properties, including electrical and thermal transport. The lack of such models has often led to the assumption that the dielectric response function in these systems can be understood from free-electron behavior. Here, we show that, different from free-electron systems, calculated for acoustic phonons in 2D Dirac crystals using the Lindhard model, exhibits a cuspidal point at the FSN condition. Strong variability of persists also at finite temperatures, while tend to infinity in the dynamic case where the speed of sound is small, albeit non negligible, over the Dirac-electron Fermi velocity. The implications of our findings for electron-acoustic phonon interaction and transport properties such as the phonon line width derived from the phonon self-energy will also be discussed.

Anomalous and non-monotonic strain dependent thermal conductivity of typical negative thermal expansion material ScF3

It is well known that the lattice thermal conductivity of the vast majority of bulk materials increases under compressive strain and decreases under tensile strain. In this paper, taking the typical negative thermal expansion material ScF3 as an example, we systematically investigate the effect of strain on the phonon transport properties by means of first-principles calculation combined with the Boltzmann transport equation. The results show that the thermal conductivity of ScF3 exhibits an anomalous strain dependence, where the thermal conductivity decreases under compressive strain while increasing as the tensile strain is smaller than −4.2 GPa. When the tensile strain increases further (larger than −4.2 GPa), however, the thermal conductivity of ScF3 decreases with tensile strain, presenting a non-monotonic behavior. Through analyzing the phonon mode information, we demonstrate that such anomalous and non-monotonic strain dependent thermal transport in ScF3 mainly originated from the intrinsic character of the negative Grüneisen parameter (negative thermal expansion). Moreover, the root mean square displacement is also utilized to further demonstrate the variation of phonon anharmonicity and thermal conductivity of ScF3 with strain. The findings shed light on the underlying association between thermal expansion and thermal conductivity and provide a feasible strategy for searching for materials with anomalous strain dependent thermal conductivity.

Strain driven anomalous anisotropic enhancement in the thermoelectric performance of monolayer MoS2

First principles density functional theory based calculations have been performed to investigate the strain and temperature induced tunability of the thermoelectric properties of monolayer (ML) MoS2. Modifications in the electronic and phononic transport properties, under two anisotropic uniaxial strains along the armchair (AC) and zigzag (ZZ) directions, have been explored in detail. Considering the intrinsic carrier-phonon scattering, we found that the charge carrier mobility (μ) and relaxation time (τ) increase remarkably for strains along the ZZ direction. Concomitantly, strain along the ZZ direction significantly reduces the lattice thermal conductivity (κL) of ML-MoS2. The combined effect of shortened phonon relaxation time and group velocity, and the reduced Debye temperature is found to be the driving force behind the lowering of κL. The large reduction in κL and increase in τ, associated with the strains along the ZZ direction, act in unison to result in enhanced efficiency and hence, improved thermoelectric performance. Nearly 150% enhancement in the thermoelectric efficiency can be achieved with the optimal doping concentration. We, therefore, highlight the significance of in-plane tensile strains, in general, and strains along the ZZ direction, in particular, in improving the thermoelectric performance of ML-MoS2.

Competition between phonon-vacancy and four-phonon scattering in cubic boron arsenide by machine learning interatomic potential

Point defects can strongly suppress the thermal conductivity $\ensuremath{\kappa}$ of solid materials, which is crucial for a broad range of applications, such as thermal management of electronic devices and thermoelectrics. Understanding thermal transport in materials containing point defects often relies on atomistic simulations based on density functional theory (DFT) or empirical potentials (EPs). However, modeling thermal transport in defective materials using DFT is very computationally expensive or even prohibitive due to the breaking of crystal symmetry while EPs suffer from low accuracy. Recently, machine learning has been applied to the development of interatomic potentials, offering opportunities to model defective systems accurately and efficiently. Here, we present a Gaussian approximation potential (GAP) developed for crystalline cubic boron arsenide (c-BAs) with vacancies, which can achieve DFT-level accuracy in predicting its $\ensuremath{\kappa}$ and phonon transport properties at four orders of magnitude reduced computational cost, especially for phonon-vacancy and four-phonon scatterings. Particularly, we applied the GAP to investigate the effect of vacancies on the $\ensuremath{\kappa}$ of c-BAs by considering both three-phonon and four-phonon scattering. Special attention was paid to the competition between phonon-vacancy and four-phonon scattering, which tend to decrease and increase the temperature dependence of $\ensuremath{\kappa}$, respectively. Specifically, when the vacancy concentration is much lower than $0.07%$ $(2.56\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$, four-phonon scattering plays stronger roles in determining the temperature dependence of $\ensuremath{\kappa}$. As the vacancy concentration increases to $0.07%$, the temperature dependence of $\ensuremath{\kappa}$ becomes close to that considering only three-phonon scattering, indicating the comparable effect of phonon-vacancy and four-phonon scattering. As the vacancy concentration further increases, the phonon-vacancy scattering becomes more dominant and pushes the $\ensuremath{\kappa}$ towards a temperature-independent behavior. Our work deepens the understanding of the phonon scattering landscape in c-BAs with vacancies and will be helpful for tailoring its thermal properties. Atomistic simulations combined with machine learning interatomic potentials are expected to be able to greatly advance the understanding of thermal transport in defective materials.

High thermoelectric performance of TlInSe3 with ultra-low lattice thermal conductivity

Thermoelectric (TE) materials with an excellent thermoelectric figure of merit (ZT) provide an effective way to alleviate energy pressure and protect the environment. By applying the first-principles method, this paper makes a systematic study of the electronic and phonon transport properties of two-dimensional (2D) novel TlInSe3 utilizing the Boltzmann transport theory (BTE). The calculation results reveal that 2D TlInSe3 has an excellent power factor (0.81 × 10−2 W/mK2) and ultra-low lattice thermal conductivity (0.46 W/mK) at 300 K. We find that the low phonon group velocity and strong anharmonicity are the main factors leading to the ultra-low lattice thermal conductivity of TlInSe3. Meanwhile, by discussing the acoustic-optical scattering, we attribute low phonon group velocity and strong anharmonicity to the increase of scattering rates between acoustic mode and optical mode, which further suppresses the lattice thermal conductivity. In the analysis of electron and phonon transport properties, 2D TlInSe3, as a novel TE material, exhibits a ZT value as high as 4.15 at 500 K. Our research results show that TlInSe3 is a potential TE material, and the relevant analysis is significant in exploring new TE materials.

Temperature-dependent thermal phonon relaxation time and its influence on ballistic-diffusive heat transport in SOI transistor

A simple model of the average thermal phonon relaxation time including its temperature dependency for silicon (Si) is proposed and incorporated with the gray version of the phonon Boltzmann transport equation to investigate its effect on the temperature distribution of the Si-layer in a silicon-on-insulator (SOI) transistor with heat generation (qv). Our analysis showed that the peak temperatures both in the nonlocal heating region and at the Si/SiO2 interface increase quadratically with increasing values of qv, while in the case of the temperature-independent, however, they show a linear increase with increasing qv. The results from this work will help in understanding the phonon transport at the device-level based on Si and will provide a way how to do an efficient thermal analysis of the device-level including all the frequency and temperature dependencies of the phonon transport properties.