Tensile strain and finite size modulation of low lattice thermal conductivity in monolayer TMDCs (HfSe2 and ZrS2) from first-principles: a comparative study

With excellent physical and chemical properties, 2D TMDC materials have been widely used in engineering applications, but they inevitably suffer from the dual effects of strain and device size. As typical 2D TMDCs, HfSe₂ and ZrS₂ are reported to have excellent thermoelectric properties. Thermal transport properties have great significance for exerting the performance of materials, ensuring device lifetime and stable operation, but current research is not detailed enough. Here, first-principles combined with the phonon Boltzmann transport equation are used to study the phonon transport inside monolayer HfSe₂ and ZrS₂ under tensile strain and finite size, and explore the band structure properties. Our research shows that they have similar phonon dispersion curve structures, and the band gap of HfSe₂ increases monotonically with the increase of tensile strain, while the bandgap of ZrS₂ increases and then decreases with the increase of tensile strain. Thermal conductivity has obvious strain dependence: with the increase of tensile strain, the thermal conductivity of HfSe₂ gradually decreases, while that of ZrS₂ increases slightly, and then gradually decreases. Reducing the system size can limit the contribution of phonons with a long mean free path, significantly decreasing thermal conductivity through the controlling effect of tensile strain. The mode contribution of thermal conductivity is systematically investigated, and anharmonic properties including mode and frequency-level scattering rates, group velocity and Grüneisen parameters are used to explain the associated mechanism. Phonon scattering processes and channels in various cases are discussed in detail. Our research provides a detailed understanding of the phonon transport and electronic structural properties of low thermal conductivity monolayers of HfSe₂ and ZrS₂, and further completes the study of thermal transport of the two materials under strain and size tuning, which will provide a foundation for further popularization and application.

Anomalous Dynamics of Defect-Assisted Phonon Recycling in Few-Layer Mo0.5W0.5S2

Alloying has emerged as a new strategy to tune the function of 2D transition metal dichalcogenides (TMDCs). However, the lack of research on the electrical and structural properties of these alloys limits their practical applications. Here, femtosecond transient absorption spectroscopy with pump pulse tunability is performed to elucidate the ultrafast carrier dynamics in the few-layer Mo_0.5W_0.5S₂ prepared by the liquid phase exfoliation method. An anomalous rebleaching of the ground state is observed at high pump fluence by 3.1 eV excitation. We ascribe this rebleaching of the ground state to the mechanism that the carriers trapped in the defect are thermally excited back to the untrapped exciton state due to the phonon recycling, which hinders the dissipation of nonradiative energy, through comparative experiments and global analysis. Our findings demonstrate a novel energy transfer channel assisted by defect in few-layer TMDCs which is critical for their advanced applications.

Four-phonon and electron-phonon scattering effects on thermal properties in two-dimensional 2H-TaS2

Thermal transport characteristics of monolayer trigonal prismatic tantalum disulfide (2H-TaS₂) are investigated using first-principles calculations combined with the Boltzmann transport equation. Due to a large acoustic-optical phonon gap of 1.85 THz, the four-phonon (4ph) scattering significantly reduces the room-temperature phononic thermal conductivity (κ_ph). With the further inclusion of phonon-electron scattering, κ_ph reduces to 1.78 W mK^-1. Nevertheless, the total thermal conductivity (κ_total) of 7.82 W mK^-1 is dominated by the electronic thermal conductivity (κ_e) of 6.04 W mK^-1. Due to the electron-phonon coupling, κ_e differs from the typical estimation based on the Wiedemann-Franz law with a constant Sommerfeld value. This work provides new insights into the physical mechanisms for thermal transport in metallic 2D systems with strong anharmonic and electron-phonon coupling effects. The phonon scattering beyond three-phonon (3ph) scattering and even κ_e are typically overlooked in computations, and the constant Sommerfeld value is widely used for separating κ_e and κ_ph from the experimental thermal conductivity. These conclusions have implications for both the computational and experimental measurements of the thermal properties of transition metal dichalcogenides.

Significant enhancement of lattice thermal conductivity of monolayer AlN under bi-axial strain: a first principles study

Using rigorous ab initio calculations within the framework of phonon Boltzmann transport theory, we have carried out a detailed investigation to probe the effects of uniform bi-axial strain and finite size on the lattice thermal conductivity (κ) of monolayer AlN. We show that implementation of bi-axial tensile strain can shoot up the value of κ of monolayer AlN by a large amount unlike in the case of analogous 2D materials. The value of κ for monolayer AlN is calculated to be 306.5 W m^-1 K^-1 at room temperature (300 K). The value of κ can be raised by one order of magnitude to up to 1500.9 W m^-1 K^-1 at 300 K by applying a bi-axial strain of about 5%. A similar trend persists when the finite size effect is incorporated in the calculation. As the sample size is varied from 10 nm to 10 000 nm along with increasing tensile strain, a huge variation of κ (from 20.7 W m^-1 K^-1 to 558.9 W m^-1 K^-1) is observed. Our study reveals that the major part of the lattice thermal conductivity of monolayer AlN comes from the contribution of the flexural acoustic (ZA) phonon modes. The anomalous trend of drastic increment in the value of κ with tensile strain is found to be a direct effect of interaction between nitrogen lone-pair electrons and bonding electrons in the ionic lattice which results in the reduction of phonon anharmonicity with increasing tensile strain. Our study provides a detailed analysis of the strain modulated and size-tuned thermal transport properties of monolayer AlN revealing that it is an impactful 2D material to be used in thermal management devices.

Thermal Properties of 2D Dirac Materials MN4 (M = Be and Mg): A First-Principles Study

Recently, a novel two-dimensional (2D) Dirac material BeN4 monolayer has been fabricated experimentally through high-pressure synthesis. In this work, we investigate the thermal properties of a new class of 2D materials with a chemical formula of MN4 (M = Be and Mg) using first-principles calculations. First, the cohesive energy and phonon dispersion curve confirm the dynamical stability of BeN4 and MgN4 monolayers. Besides, BeN4 and MgN4 monolayers have the anisotropic lattice thermal conductivities of 842.75 (615.97) W m-1 K-1 and 52.66 (21.76) W m-1 K-1 along the armchair (zigzag) direction, respectively. The main contribution of the lattice thermal conductivities of BeN4 and MgN4 monolayers are from the low frequency phonon branches. Moreover, the average phonon heat capacity, phonon group velocity, and phonon lifetime of BeN4 monolayer are 3.54 × 105 J K-1 m-3, 3.61 km s-1, and 13.64 ps, which are larger than those of MgN4 monolayer (3.42 × 105 J K-1 m-3, 3.27 km s-1, and 1.70 ps), indicating the larger lattice thermal conductivities of BeN4 monolayer. Furthermore, the mode weighted accumulative Grüneisen parameters (MWGPs) of BeN4 and MgN4 monolayers are 2.84 and 5.62, which proves that MgN4 monolayer has stronger phonon scattering. This investigation will enhance an understanding of thermal properties of MN4 monolayers and drive the applications of MN4 monolayers in nanoelectronic devices.

The thermoelectric properties of α-XP (X = Sb and Bi) monolayers from first-principles calculations

Thermoelectric (TE) materials as one of the effective solutions to the energy crisis are gaining more and more interest owing to their capability to generate electricity from waste heat without generating air pollution. In this work, the TE properties of α-XP monolayers such as the stability, electronic structure, electrical and phonon transport were thoroughly studied in combination with the first-principles calculations and Boltzmann transport equations. We found that α-SbP and α-BiP have indirect bandgaps of 0.85 eV and 0.73 eV, respectively, which are suitable for thermoelectric materials. Furthermore, due to the multiple valleys at the energy band edges and the high carrier mobility, α-XP possesses both large Seebeck coefficients and high electrical conductivities. It is also found that the lattice thermal conductivity of α-BiP is smaller than that of α-SbP due to lower phonon frequencies, smaller phonon group velocities, larger Grüneisen parameters and higher phonon relaxation times. High TE performance was achieved with the ZT values reaching 4.59 (for α-BiP at 500 K) and 1.34 (for α-SbP at 700 K). Our results quantify α-XP monolayers as promising candidates for building outstanding thermoelectric devices.

Potential thermoelectric materials: first-principles prediction of low lattice thermal conductivity of two-dimensional (2D) orthogonal ScX2 (X = C and N) compounds

Thermoelectric materials with excellent performance can efficiently and directly convert waste heat into electrical energy. In today's era, finding thermoelectric materials with excellent performance and adjusting the thermoelectric parameters are essential for the sustainable development of energy in the context of the energy crisis and global warming. Through first-principles calculations, we notice that two-dimensional (2D) orthogonal ScX₂ (X = C and N) compounds show great potential in the field of thermoelectricity. Different from most materials containing C or N atoms, which are generally accompanied by high lattice thermal conductivity (TC), the 2D o-ScX₂ exhibited a rather low and anisotropic lattice TC. The κ3L (the lattice thermal conductivity including the effect of three-phonon scattering and isotope scattering) of o-ScC₂ along the X and Y directions are 2.79 W m^-1 K^-1 and 1.55 W m^-1 K^-1, and those of o-ScN₂ are 1.57 W m^-1 K^-1 and 0.56 W m^-1 K^-1. By calculating the fourth-order interatomic force constants (IFCs), we obtain the κ3+4L with the additional four-phonon scattering effect. Our results clearly show that four-phonon scattering plays an important role in the TC of the two materials, the κ3+4L of o-ScC₂ is only half of its κ3L. Furthermore, it can be noticed that the low lattice TCs of o-ScX₂ (X = C and N) are the result of many factors, e.g., heavy atom doping, the strong anharmonicity caused by the vibration of Sc atoms in the out-of-plane direction and C(N) atoms in the in-plane direction, important four-phonon scattering and strongly polarized covalent bonds between X atoms and Sc atoms. Moreover, it is interesting to find that the thermal transport properties of o-ScX₂ are led by a different phonon mechanism, e.g., the different TCs of o-ScC₂ and o-ScN₂ are determined by the anharmonic characteristic, and the harmonic characteristic plays a more important role in the anisotropy of o-ScX₂ (X = C and N). In general, our research can be expected to provide important guidance for the application of o-ScX₂ (X = C and N) in the thermoelectric field.

Effect of pressure on thermalization of one-dimensional nonlinear chains

Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-β under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law-it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.

Ultralow lattice thermal conductivity and dramatically enhanced thermoelectric properties of monolayer InSe induced by an external electric field

With the ability to alter the inherent interatomic electrostatic interactions, modulating external electric field strength is a promising approach to tune the phonon transport behavior and enhance the thermoelectric performance of two-dimensional (2D) materials. Here, by applying an electric field (Ez = 0.1 V Å-1), it is predicted that an ultralow value of the lattice thermal conductivity (0.016 W m-1 K-1) at 300 K of 2D indium selenide (InSe) is nearly three orders of magnitude lower than that under an electric field of 0 V Å-1 (27.49 W m-1 K-1). Meanwhile, we calculated the variations in the electrical conductivities, electronic thermal conductivities, Seebeck coefficients, and figure of merit (ZT) of 2D InSe along with the carrier (hole and electron doping) concentrations under some representative electric fields. Owing to the smaller total thermal conductivity along the armchair and zigzag directions, p-type doped 2D InSe at Ez = 0.1 V Å-1 exhibits a larger ZT value (∼1.6) compared to the ZT value (∼0.1) without an electric field at room temperature. The peak ZT value (∼0.53) of the n-type 2D InSe at Ez = 0.1 V Å-1 is much higher than that without an electric field (∼0.02) at the same temperature. Our results pave the way for applying an external electric field to modulate the phonon transport properties and greatly promote the thermoelectric performance of some specific 2D semiconductor materials without altering their crystal structure.

Experimental and Computational Investigation of Layer-Dependent Thermal Conductivities and Interfacial Thermal Conductance of One- to Three-Layer WSe2

Two-dimensional materials such as graphene and transition metal dichalcogenides (TMDCs) have received extensive research interest and investigations in the past decade. In this research, we used a refined opto-thermal Raman technique to explore the thermal transport properties of one popular TMDC material WSe₂, in the single-layer (1L), bilayer (2L), and trilayer (3L) forms. This measurement technique is direct without additional processing to the material, and the absorption coefficient of WSe₂ is discovered during the measurement process to further increase this technique's precision. By comparing the sample's Raman spectroscopy spectra through two different laser spot sizes, we are able to obtain two parameters-lateral thermal conductivities of 1L-3L WSe₂ and the interfacial thermal conductance between 1L-3L WSe₂ and the substrate. We also implemented full-atom nonequilibrium molecular dynamics simulations (NEMD) to computationally investigate the thermal conductivities of 1L-3L WSe₂ to provide comprehensive evidence and confirm the experimental results. The trend of the layer-dependent lateral thermal conductivities and interfacial thermal conductance of 1L-3L WSe₂ is discovered. The room-temperature thermal conductivities for 1L-3L WSe₂ are 37 ± 12, 24 ± 12, and 20 ± 6 W/(m·K), respectively. The suspended 1L WSe₂ possesses a thermal conductivity of 49 ± 14 W/(m·K). Crucially, the interfacial thermal conductance values between 1L-3L WSe₂ and the substrate are found to be 2.95 ± 0.46, 3.45 ± 0.50, and 3.46 ± 0.45 MW/(m²·K), respectively, with a flattened trend starting the 2L, a finding that provides the key information for thermal management and thermoelectric designs.

Why thermal conductivity of CaO is lower than that of CaS: a study from the perspective of phonon splitting of optical mode

Generally speaking, for materials with the same structure, the thermal conductivity is higher for lighter atomic masses. However, we found that the thermal conductivity of CaO is lower than that of CaS, despite the lighter atomic mass of O than S. To uncover the underlying physical mechanisms, the thermal conductivity of CaM (M = O, S, Se, Te) and the corresponding response to strain is investigated by performing first-principles calculations along with the phonon Boltzmann transport equation. For unstrained system, the order of thermal conductivity is CaS > CaO > CaSe > CaTe. This order remains unchanged in the strain range of -2% to 5%. When the compressive strain is larger than 2%, the thermal conductivity of CaO surpasses that of CaS and becomes the highest thermal conductivity material among the four compounds. By analyzing the mode-dependent phonon properties, the phonon lifetime is found to be dominant over other influential factors and leads to the disparate response of thermal conductivity under strain. Moreover, the changing trend of three-phonon scattering phase space is consistent with that of phonon lifetime, which is directly correlated to the phonon frequency gap induced by the LO-TO splitting. The variation of Born effective charge is found to be opposite for CaM. The Born effective charge of CaO decreases with tensile strain increasing, demonstrating stronger charge delocalization and lower ionicity, while the Born effective charges of CaS, CaSe, and CaTe show a dramatic increase. Such variation indicates that the bonding nature can be effectively tuned by external strain, thus affecting the phonon anharmonic properties and thermal conductivity. The difference of bonding nature is further confirmed by the band structure. Our results show that the bonding nature of CaM can be modulated by external strain and leads to disparate strain dependent thermal conductivity.

First-principles calculations of phonon behaviors in graphether: a comparative study with graphene

Recently, a two-dimensional (2D) oxocarbon monolayer, graphether, has been arousing extensive attention owing to its excellent electrical properties. In this work, we calculate the lattice thermal conductivity (k) of graphether and graphene using first-principles calculations and the phonon Boltzmann transport equation. At 300 K, the lattice thermal conductivities of graphether and graphene along the armchair direction are 600.91 W m-1 K-1 and 3544.41 W m-1 K-1, respectively. Moreover, the electron localization function is employed to reveal the origin of the anisotropic k of graphether. Furthermore, the harmonic and anharmonic properties of graphether and graphene are analyzed. We attribute the lower k of graphether to the smaller phonon group velocity and shorter phonon lifetime. Finally, the size effects of phonon transport in graphether and graphene are studied, and the results show that the lattice thermal conductivities are significantly dependent on the system length. The analysis of phonon behaviors in our study contributes to an in-depth understanding of the thermal transport in graphether for the first time, which provides valuable guidelines for graphether-based phonon engineering applications and 2D nanoelectronic devices.

Phonon spectrum and thermoelectric properties of square/octagon structure of bismuth monolayer

First-principles calculation and Boltzmann transport theory have been combined to comparatively investigate the band structure, phonon spectrum, lattice thermal conductivity, electronic transport property, Seebeck coefficient, and figure of merit of square/octagon (s/o)-bismuth monolayer. Calculations reveal that the thermoelectric properties of s/o-bismuth monolayer are better than that of β-bismuth monolayer, which should be mainly due to the low lattice thermal conductivity and weakened coupling of electrons and phonons. It is also found that the phonon frequency and group velocity could play dominant roles in determining the magnitude of the lattice thermal conductivity of s/o-bismuth monolayer. Furthermore, the Seebeck coefficient and figure of merit of s/o-bismuth monolayer are higher than those of β-bismuth monolayer. The derived results are in good agreement with other theoretical results in the literature, and could provide a deep understanding of thermoelectric properties of the bismuth monolayer materials.

First-principles calculation and Boltzmann transport theory have been combined to comparatively investigate the electronic structure, phonon spectrum, and thermoelectric properties of square/octagon (s/o)-bismuth monolayer.

The first-principles and BTE investigation of phonon transport in 1T-TiSe2

Through the first-principles density functional theory and the phonon Boltzmann transport equation, we investigated the phonon transport characteristics inside 1T-TiSe₂.

Thermoelectric properties of two-dimensional magnet CrI3

The thermoelectric, phonon transport, and electronic transport properties of two-dimensional magnet CrI₃ are systematically investigated by combining density functional theory with Boltzmann transport theory. A low lattice thermal conductivity of 1.355 W m^-1K^-1 is presented at 300 K due to the low Debye temperature and phonon group velocity. The acoustic modes dominate the lattice thermal conductivity, and the longitudinal acoustic mode has the largest contribution of 42.31% on account of its relatively large phonon group velocity and phonon lifetime. The high band degeneracy and the peaky density of states near the conduction band minimum appear for the CrI₃ monolayer, which is beneficial for forming a significantly increased Seebeck coefficient (1561 μV K^-1). Furthermore, the thermoelectric figure of merit is calculated reasonably, and the value is 1.57 for the optimal n-type doping level at 900 K. N-type doping maintains a higher thermoelectric conversion efficiency than p-type doping throughout the temperature range, while the difference gradually increases as the temperature rises. Our investigation may provide some theoretical support for the application of the CrI₃ monolayer in the thermoelectric field.

Strain-driven dynamic stability and anomalous enhancement of thermal conductivity in graphene-like IIA-VI monolayer monoxides

Graphene-like IIA-VI monolayer monoxides have been predicted to be novel two-dimensional materials with intrinsic bandgap, which makes them promising prospect for electronics and optoelectronics applications. In the field of microelectronics, heat dissipation is considered as the bottleneck that limits further development. Thus, the effective regulation in thermal transport is of great interest for designing novel devices. A systematic study in this work is carried out by first-principles method to explore thermal conductivity of these monoxides under strain. Compared with that of minimum strained MgO, CaO, SrO and BaO, the maximum thermal conductivity is increased by 3.25, 3.07, 1.50 and 1.53 times, respectively, under tensile strain. Detailed analysis shows that the weakened phonon-phonon scattering strength is the behind physical mechanism. It is also found that the tensile strain aids to improving the stability. Our work provides an attractive platform by studying the thermal transport of these monoxides under strain, suggesting the possible applications of these monolayers in novel devices.

Thermal transport properties of novel two-dimensional CSe

Recently, as a novel member of the IV-VI group compounds, two-dimensional (2D) buckled monolayer CSe has been discovered for use in high-performance light-emitting devices (Q. Zhang, Y. Feng, X. Chen, W. Zhang, L. Wu and Y. Wang, Nanomaterials, 2019, 9, 598). However, to date, the heat transport properties of this novel CSe is still lacking, which would hinder its potential application in electronic devices and thermoelectric materials that can generate electricity from waste heat. Here we systematically study the heat transport properties of monolayer CSe based on ab initio calculations and phonon Boltzmann transport theory. We find that the lattice thermal conductivity κlat of monolayer CSe is around 42 W m-1 K-1 at room temperature, which is much lower than those of black phosphorene, buckled phosphorene, MoS2, and buckled arsenene. Moreover, the longitudinal acoustic phonon mode contributes the most to the κlat, which is much larger than those of the out-of-plane phonon mode and transverse acoustic branches. The calculated size-dependent κlat shows that the sample size can significantly reduce the κlat of monolayer CSe and can persist up to 10 μm. These discoveries provide new insight into the size-dependent thermal transport in nanomaterials and guide the design of CSe-based low-dimensional quantum devices, such as thermoelectric devices.

Effects of low dimensionality on electronic structure and thermoelectric properties of bismuth

First-principles calculations and Boltzmann transport theory have been combined to comparatively investigate the band structure, phonon spectrum, lattice thermal conductivity, electronic transport properties, Seebeck coefficients, and figure of merit of the β-bismuth monolayer and bulk Bi. Calculation reveals that low dimensionality can bring about the semimetal-semiconductor transition, decrease the lattice thermal conductivity, and increase the Seebeck coefficient of Bi. The relaxation time of electrons and holes is calculated according to the deformation potential theory, and is found to be more accurate than those reported in the literature. It is also shown that compared with Bi bulk, the β-bismuth monolayer possesses much lower electrical conductivity and electric thermal conductivity, while its figure of merit seems much bigger. The derived results are in good agreement with experimental results in the literature, and could provide a deep understanding of various properties of the β-bismuth monolayer.

First-principles calculations and Boltzmann transport theory have been combined to comparatively investigate the band structure, phonon spectrum, lattice thermal conductivity, and the transport properties of the β-bismuth monolayer and bulk Bi.