Ultrahigh Thermal Conductivity of θ-Phase Tantalum Nitride

Advancing high thermal conductivity: novel theories, innovative materials, and applications in thermal management technologies

Effective thermal management is crucial for the performance and stability of modern electronics, emphasizing the demand for high thermal conductivity (κ). This review summarizes the latest development in highκ, discussing the emerging theories, innovative materials and practical applications for interfacial heat dissipation. Unique phononic thermal transport behaviors are discussed, including four phonon-phonon scattering, hydrodynamic phonons, surface phonon-polaritons, and more. The review also highlights innovative materials with highκ, such as two-dimensional pentagonal structures, boron carbon nitrogen structures, hexagonal boron arsenide andθ-phase tantalum nitride. In addition, the potential of polymer composites reinforced with highκfillers and surface engineering for advanced electronic applications are also discussed. By integrating these theoretical approaches and material innovations, this review offers comprehensive strategies for enhancing thermal management in modern electronic devices.

Giant thermal conductivity and strain thermal response of nitrogen substituted diamane: a machine-learning-based prediction

With the ongoing trend of seeking miniaturization and enhanced performance for electronic devices, effective thermal management has emerged as a critical concern. The discovery and investigation of high thermal conductivity (κ) materials have proved to be pivotal in addressing this challenge. This study aims to explore the distinctive properties and potential applications of nitrogen substituted diamane (NCCN), a two-dimensional material with a diamond-like structure composed of carbon and nitrogen atoms. This work systematically delves into NCCN's thermal, mechanical, and electrical properties. It is predicted that NCCN exhibits an exceptional κ, ∼2288 W m-1 K-1, at room temperature (300 K) by combining the machine-learning interatomic potential method and the phonon Boltzmann transport equation, surpassing that of H-diamane and rivaling that of diamond, and an impressive electronic band gap of ∼4.47 eV (PBE). For mechanical properties, the stress-strain relationship reveals that NCCN exhibits isotropic elastic properties and anisotropic tensile strengths. Additionally, the variations in NCCN's κ and electronic energy band structure under different strains underscore its substantial potential in the field of thermoelectric applications.

Light-driven dynamical tuning of the thermal conductivity in ferroelectrics

Dynamical tuning of the thermal conductivity in crystals, κ, is critical for thermal management applications, as well as for energy harvesting and the development of novel phononic devices able to perform logic operations with phonons. Such a desired κ control can be achieved in functional materials that experience large structural and phonon variations as a result of field-induced phase transformations. However, this approach is only practical within reduced temperature intervals containing zero-bias phase transition points, since otherwise the necessary driving fields become excessively large and the materials' performances are detrimentally affected. Here, based on first-principles calculations, we propose an alternative strategy for dynamically tuning κ that is operative over broad temperature conditions and realizable in a wide class of materials. By shining light on the archetypal perovskite oxide KNbO3, we predict that ultrafast and reversible ferroelectric-to-paraelectric phase transitions are induced, yielding large and anisotropic κ variations (up to ≈30% at T = 300 K). These light-induced thermal transport shifts can take place at temperatures spanning several hundreds of kelvin and are essentially the result of anharmonic effects affecting the phonon lifetimes.

Electron-Induced Nonmonotonic Pressure Dependence of the Lattice Thermal Conductivity of θ-TaN

Recent theoretical and experimental research suggests that θ-TaN is a semimetal with high thermal conductivity (κ), primarily due to the contribution of phonons (κ_{ph}). By using first-principles calculations, we show a nonmonotonic pressure dependence of the κ of θ-TaN. κ_{ph} first increases until it reaches a maximum at around 60 GPa, and then decreases. This anomalous behavior is a consequence of the competing pressure responses of phonon-phonon and phonon-electron interactions, in contrast to the known materials BAs and BP, where the nonmonotonic pressure dependence is caused by the interplay between different phonon-phonon scattering channels. Although TaN has phonon dispersion features similar to BAs at ambient pressure, its response to pressure is different and an overall stiffening of the phonon branches takes place. Consequently, the relevant phonon-phonon scattering weakens as pressure increases. However, the increased electronic density of states near the Fermi level, and specifically the emergence of additional pockets of the Fermi surface at the high-symmetry L point in the Brillouin zone, leads to a substantial increase in phonon-electron scattering at high pressures, driving a decrease in κ_{ph}. At intermediate pressures (∼20-70  GPa), the κ of TaN surpasses that of BAs. Our Letter provides deeper insight into phonon transport in semimetals and metals where phonon-electron scattering is relevant.

Complex role of strain engineering of lattice thermal conductivity in hydrogenated graphene-like borophene induced by high-order phonon anharmonicity

Strain engineering has been used as a versatile tool for regulating the thermal transport in various materials as a result of the phonon frequency shift. On the other hand, the phononic bandgap can be simultaneously tuned by the strain, which can play a critical role in wide phononic bandgap materials due to the high-order phonon anharmonicity. In this work, we investigate the complex role of uniaxial tensile strain on the lattice thermal conductivity of hydrogenated graphene-like borophene, by using molecular dynamics simulations with a machine learning potential. Our findings highlight a novel and intriguing phenomenon that the thermal conductivity in the armchair direction is non-monotonically dependent on the uniaxial armchair strain. Specifically, we uncover that the increase of phonon group velocity and the decrease of three-phonon scattering compete with the enhancement of four-phonon scattering under armchair strain, leading to the non-monotonic dependence. The enhanced four-phonon scattering originates from the unique bridged B-H bond that can sensitively control the phononic bandgap under armchair strain. This anomalous non-monotonic strain-dependence highlights the complex interplay between different mechanisms governing thermal transport in 2D materials with large phononic bandgaps. Our study offers valuable insights for designing innovative thermal management strategies based on strain.

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

Two-dimensional materials (2DMs) continue to attract a lot of attention, particularly for their extreme flexibility and superior thermal properties. Molecular dynamics simulations are among the most powerful methods for computing these properties, but their reliability depends on the accuracy of interatomic interactions. While first principles approaches provide the most accurate description of interatomic forces, they are computationally expensive. In contrast, classical force fields are computationally efficient, but have limited accuracy in interatomic force description. Machine learning interatomic potentials, such as Gaussian Approximation Potentials, trained on density functional theory (DFT) calculations offer a compromise by providing both accurate estimation and computational efficiency. In this work, we present a systematic procedure to develop Gaussian approximation potentials for selected 2DMs, graphene, buckled silicene, and h-XN (X = B, Al, and Ga, as binary compounds) structures. We validate our approach through calculations that require various levels of accuracy in interatomic interactions. The calculated phonon dispersion curves and lattice thermal conductivity, obtained through harmonic and anharmonic force constants (including fourth order) are in excellent agreement with DFT results. HIPHIVE calculations, in which the generated GAP potentials were used to compute higher-order force constants instead of DFT, demonstrated the first-principles level accuracy of the potentials for interatomic force description. Molecular dynamics simulations based on phonon density of states calculations, which agree closely with DFT-based calculations, also show the success of the generated potentials in high-temperature simulations.

Janus β-PdXY (X/Y = S, Se, Te) materials with high anisotropic thermoelectric performance

Two-dimensional (2D) materials have garnered considerable attention as emerging thermoelectric (TE) materials owing to their unique density of states (DOS) near the Fermi level. We investigate the TE performance of Janus β-PdXY (X/Y = S, Se, Te) monolayer materials as a function of carrier concentration and temperature in the mid-range from 300 to 800 K by combining density functional theory (DFT) and semi-classical Boltzmann transport theory. The phonon dispersion spectra and AIMD simulations confirm their thermal and dynamic stability. The transport calculation results reveal the highly anisotropic TE performance of both n and p-type Janus β-PdXY monolayers. Meanwhile, the coexistence of low phonon group velocity and a converged scattering rate leads to a lower lattice thermal conductivity (K_l) of 0.80 W mK^-1, 0.94 W mK^-1, and 0.77 W mK^-1 along the y-direction for these Janus materials, while the high TE power factor is attributed to the high Seebeck coefficient (S) and electrical conductivity, which are due to the degenerate top valence bands of these Janus monolayers. The combination of lower K_l and a high-power factor at 300 K (800 K) leads to an optimal figure of merit (ZT) of 0.68 (2.21), 0.86 (4.09) and 0.68 (3.63) for p-type Janus PdSSe, PdSeTe and PdSTe monolayers, respectively. To evaluate rational electron transport properties, the effects of acoustic phonon scattering (τ_ac), impurity scattering (τ_imp), and polarized phonon scattering (τ_polar) are included in the temperature-dependent electron relaxation time. These findings indicated that the Janus β-PdXY monolayers are promising candidates for TE conversion devices.

Bonding Heterogeneity Leads to Hierarchical and Ultralow Lattice Thermal Conductivity in Sodium Metavanadate

Sodium metavanadate (NaVO₃) is a promising low-cost candidate as a cathode material for sodium-ion batteries (SIBs) owing to its high cycle performance. Its thermal transport, although being a central factor limiting its practical applications, remains scarce. Herein, we comprehensively investigate the intrinsic thermal transport properties of the two phases of NaVO₃ using the unified theory. Importantly, we identify a hierarchical thermal transport mechanism in NaVO₃ and the significant contribution of diffusive thermal transport. With the combined two channels, we reveal that NaVO₃ has the anisotropic and ultralow thermal conductivity κ, which is derived from the bonding heterogeneity with the coexistence of strong V-O bonds and weak Na-O bonds, implying the possibility of engineering the κ of SIBs by spatially tuning the sodium concentration distribution. Our work establishes a fundamental understanding of the intrinsic thermal transport of NaVO₃ and provides guidance toward designing tunable thermal conductivity cathode materials for SIBs.

Phase Stability, Strong Four-Phonon Scattering, and Low Lattice Thermal Conductivity in Superatom-Based Superionic Conductor Na3OBH4

Superatom-based superionic conductors are of current interest due to their promising applications in solid-state electrolytes for rechargeable batteries. However, much less attention has been paid to their thermal properties, which are vital for safety and performance. Motivated by the recent synthesis of superatom-based superionic conductor Na₃OBH₄ consisting of superhalogen cluster BH₄, we systematically investigate its lattice dynamics and thermal conductivity using the density functional theory combined with a self-consistent phonon approach. We reveal the bonding hierarchy features by studying the electron localization function and potential energy surface and further unveil the rattling effect of the BH₄ superatom, which introduces strong quartic anharmonicity and induces soft phonon modes in low temperatures by assisting Na displacements, thus calling for the necessity of quartic renormalization and four-phonon scattering in calculating the lattice thermal conductivity. We find that the contribution of four-phonon processes to the lattice thermal conductivity increases from 13 to 32% when the temperature rises from 200 to 400 K. At room temperature (300 K), the phonon scattering phase space is enlarged by 133% due to the four-phonon interactions, and the lattice thermal conductivity is evaluated to be 5.34 W/mK, reduced by 24% as compared with a value of 6.99 W/mK involving three-phonon scattering only. These findings provide a better understanding of the lattice stability and thermal transport properties of superionic conductor Na₃OBH₄, shedding light on the role of strong quartic anharmonicity played in superatom-based materials.

Novel insights into lattice thermal transport in nanocrystalline Mg3Sb2 from first principles: the crucial role of higher-order phonon scattering

Zintl phase Mg₃Sb₂, which has ultra-low thermal conductivity, is a promising anisotropic thermoelectric material. It is worth noting that the prediction and experiment value of lattice thermal conductivity (κ) maintain a remarkable difference, troubling the development and application. Thus, we firstly included the four-phonon scattering processes effect and performed the Peierls-Boltzmann transport equation (PBTE) combined with the first-principles lattice dynamics to study the lattice thermal transport in Mg₃Sb₂. The results showed that our theoretically predicted κ is consistent with the experimentally measured, breaking through the limitations of the traditional calculation methods. The prominent four-phonon scatterings decreased phonon lifetime, leading to the κ of Mg₃Sb₂ at 300 K from 2.45 (2.58) W m^-1 K^-1 to 1.94 (2.19) W m^-1 K^-1 along the in (cross)-plane directions, respectively, and calculation accuracy increased by 20%. This study successfully explains the lattice thermal transport behind mechanism in Mg₃Sb₂ and implies guidance to advance the prediction accuracy of thermoelectric materials.

How Hydrodynamic Phonon Transport Determines the Convergence of Thermal Conductivity in Two-Dimensional Materials

The phonon Boltzmann transport equation combined with first-principles calculation has achieved great success in exploring the lattice thermal conductivity (κ) of various materials. However, the convergence of the predicted κ is a critical issue, leading to quite scattered results recorded in the literature, even for the same material. In this paper, we explore the origin for the convergence of thermal conductivity in two-dimensional (2D) materials. Two kinds of typical 2D materials, graphene and silicene, are studied, and the bulk silicon is also compared as a control system for a three-dimensional material. The effect of the cutoff radius (rc) in the third-order interatomic force constants on κ is studied for these three materials. It is found that that κ of these three materials exhibits diverse convergence behaviors with respect to rc, which coincides very well with the strength of hydrodynamic phonon transport. By further analyzing the phonon lifetime and scattering rates, we reveal that the dominance of the normal scattering process gives rise to the hydrodynamic phonon transport in both graphene and silicene, which results in long-range interaction and a large lifetime of low-frequency flexural acoustic phonons, while the same phenomenon is absent in bulk silicon. Our study highlights the importance of long-range interaction associated with hydrodynamic phonon transport in determining the thermal conductivity of 2D materials.

Four-Phonon Scattering Effect and Two-Channel Thermal Transport in Two-Dimensional Paraelectric SnSe

In recent years, increased attention has been paid to the study of four-phonon interactions and diffusion transport in three-dimensional (3D) thermoelectric materials because they play an essential role in understanding the thermal transport process. In this work, we study four-phonon scattering and diffusion transport in two-dimensional (2D) thermoelectric materials using the paraelectric phase of 2D SnSe as an example. The inherent soft phonon modes are treated by the self-consistent phonon theory, which considers the temperature-induced renormalization of the phonons. Based on density functional theory and the Peierls-Boltzmann transport equation for phonons, we show that the four-phonon interactions can reduce the thermal conductivity of the 2D SnSe sheet by nearly 40% due to the collapse of soft optical modes, and the contribution of diffusion transport to the total thermal conductivity accounts for 14% at a high temperature of 800 K due to the short phonon mean free path approaching the Ioffe-Regel limit, suggesting the two-channel transport in this system. The results are further confirmed by using the machine learning-assisted molecular dynamics simulations. This work provides a new insight into the physical mechanisms for thermal transport in 2D systems with strong anharmonic effects.

3-X Structural Model and Common Characteristics of Anomalous Thermal Transport: The Case of Two-Dimensional Boron Carbides

Improving the reliability of electronic devices requires effective heat management, and the key is the relationship between the thermal transport and temperature. Inspired by synthesized T-carbon and H-boron, the 3-X structural models are proposed to unify the two-dimensional (2D) multitriangle materials. Employing structural searches, we identify the stability of the 3-X configuration in 2D boron carbides as 3-9 BC₃ monolayer, which, unexpectedly, exhibits a linear thermal conductivity versus temperature, not the traditional ∼1/T trend. We summarize the common characteristics and explore why this behavior is absent in 3-9 AlC₃ and graphene via investigating the optical modes. We show that the linear behavior is a direct consequence of the special oscillation modes by the 3-X model associated with the largest group velocity. We find that 2D materials with such behavior usually share a relatively low thermal conductivity. Our work paves the way to deeply understand the lattice thermal transport and to widen nanoelectronic applications.

High Thermal Conductivity of Wurtzite Boron Arsenide Predicted by Including Four-Phonon Scattering with Machine Learning Potential

Materials with high thermal conductivity are of great importance to the thermal management of modern electronic devices. Recently, it was found that cubic boron arsenide (c-BAs) is a high thermal conductivity (κ) material with a value of ∼1300 W/(m·K) at room temperature (RT), where four-phonon scattering plays a crucial role in limiting the κ. In this work, with four-phonon scattering included, we find that the κ of wurtzite BAs (w-BAs) reaches as high as 1036 W/(m·K) along the a-b plane at RT, decreasing by 43% compared to the calculation without considering four-phonon scattering. The similar phonon transport properties between c-BAs and w-BAs can be understood in terms of similar projected density of states and scattering rates, which have the origin in crystal structural resemblance. To accelerate the calculation, the moment tensor potential derived from machine learning is adopted and proven to be a reliable and efficient method to obtain high-order interatomic force constants.

Lattice Thermal Transport in the Homogeneous Cage-Like Compounds Cu3 VSe4 and Cu3 NbSe4 : Interplay between Phonon-Phase Space, Anharmonicity, and Atomic Mass

Understanding the correlation between crystal structure and thermal conductivity in semiconductors is very important for designing heat-transport-related devices, such as high-performance thermoelectric materials and heat dissipation in micro-nano-scale devices. In this work, the lattice thermal conductivity ( κ L ) of the cage-like compounds Cu₃ VSe₄ and Cu₃ NbSe₄ was investigated by experimental measurements and first-principles calculations. The experimental κ L of Cu₃ NbSe₄ is approximately 25 % lower than that of Cu₃ VSe₄ at 300 K. The relevant important physical parameters, including the sound velocity, heat capacity, weighted phonon phase space (W), and third-order force constants along with atomic mass were theoretically analyzed. It is found that W is the dominant parameter in determining the κ L , and the other factors only play a minor role. The physical origin is the relatively "soft" lattice of Cu₃ NbSe₄ with heavier atomic mass. This research provides deep insight into the correlation between the thermal conductivity and crystal structure and paves the way for discovering high-performance thermal management device and thermoelectric materials with intrinsically low κ L .

A differential thin film resistance thermometry method for peak thermal conductivity measurements of high thermal conductivity crystals

High thermal conductivity materials are useful for thermal management applications and fundamental studies of phonon transport. Past measurements of several ultrahigh thermal conductivity materials were not able to obtain the peak thermal conductivity, which is expected to appear at a low temperature and contains insight into the competition between extrinsic phonon-defect and phonon-boundary scattering with intrinsic phonon-phonon processes. Here, we report a peak thermal conductivity measurement method based on differential Wheatstone bridge measurement of the small temperature drop between two thin film resistance thermometers patterned directly on the sample. With the use of a mesoscale silicon bar sample as the calibration standard, this method is able to obtain results that agree with past measurements of large bulk silicon crystals at high temperatures and first-principles calculation results that account for additional phonon-boundary scattering in the sample. The agreement demonstrates the accuracy of this measurement method for peak thermal conductivity measurements of high thermal conductivity materials.

Study on the Electrical, Structural, Chemical and Optical Properties of PVD Ta(N) Films Deposited with Different N2 Flow Rates

By reactive DC magnetron sputtering from a pure Ta target onto silicon substrates, Ta(N) films were prepared with different N2 flow rates of 0, 12, 17, 25, 38, and 58 sccm. The effects of N2 flow rate on the electrical properties, crystal structure, elemental composition, and optical properties of Ta(N) were studied. These properties were characterized by the four-probe method, X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and spectroscopic ellipsometry (SE). Results show that the deposition rate decreases with an increase of N2 flows. Furthermore, as resistivity increases, the crystal size decreases, the crystal structure transitions from β-Ta to TaN(111), and finally becomes the N-rich phase Ta3N5(130, 040). Studying the optical properties, it is found that there are differences in the refractive index (n) and extinction coefficient (k) of Ta(N) with different thicknesses and different N2 flow rates, depending on the crystal size and crystal phase structure.

Exposing the hidden influence of selection rules on phonon-phonon scattering by pressure and temperature tuning

Selection rules act to restrict the intrinsic anharmonic interactions between phonons in all crystals. Yet their influence on phonon propagation is hidden in most materials and so, hard to interrogate experimentally. Using ab initio calculations, we show that the otherwise invisible impact of selection rules on three-phonon scattering can be exposed through anomalous signatures in the pressure (P) and temperature (T) dependence of the thermal conductivities, κ, of certain compounds. Boron phosphide reveals such underlying behavior through an exceptionally sharp initial rise in κ with increasing P, which may be the steepest of any material, and also a peak and decrease in κ at high P. These features are in stark contrast to the measured behavior for many solids, and they occur at experimentally accessible conditions. These findings give a deep understanding of phonon lifetimes and heat conduction in solids, and motivate experimental efforts to observe the predicted behavior.