Phonon transport and thermal conductivity in two-dimensional materials

Two-dimensional materials, such as graphene, boron nitride and transition metal dichalcogenides, have attracted increased interest due to their potential applications in electronics and optoelectronics. Thermal transport in two-dimensional materials could be quite different from three-dimensional bulk materials. This article reviews the progress on experimental measurements and theoretical modeling of phonon transport and thermal conductivity in two-dimensional materials. We focus our review on a few typical two-dimensional materials, including graphene, boron nitride, silicene, transition metal dichalcogenides, and black phosphorus. The effects of different physical factors, such as sample size, strain and defects, on thermal transport in Two-dimensional materials are summarized. We also discuss the environmental effect on the thermal transport of two-dimensional materials, such as substrate and when two-dimensional materials are presented in heterostructures and intercalated with inorganic components or organic molecules.Comment: 67 pages, 18 figures. Submitted to Annual Review of Heat Transfe

Phonon Transport in Single-Layer Transition Metal Dichalcogenides: a First-Principles Study

Two-dimensional transition metal dichalcogenides (TMDCs) are finding promising electronic and optical applications due to their unique properties. In this letter, we systematically study the phonon transport and thermal conductivity of eight semiconducting single-layer TMDCs, MX2 (M=Mo, W, Zr and Hf, X=S and Se), by using the first-principles-driven phonon Boltzmann transport equation approach. The validity of the single-mode relaxation time approximation to predict the thermal conductivity of TMDCs is assessed by comparing the results with the iterative solution of the phonon Boltzmann transport equation. We find that the phononic thermal conductivities of 2H-type TMDCs are above 50 W/mK at room temperature while the thermal conductivity values of the 1T-type TMDCs are much lower, when the size of the sample is 1 {\mu}m. A very high thermal conductivity value of 142 W/mK was found in single-layer WS2. The large atomic weight difference between W and S leads to a very large phonon bandgap which in turn forbids the scattering between acoustic and optical phonon modes and thus resulting in very long phonon relaxation time.Comment: 21 pages, 7 figure

Lattice Thermal Conductivity of Organic-Inorganic Hybrid Perovskite CH3NH3PbI3

Great success has been achieved in improving the photovoltaic energy conversion efficiency of the organic-inorganic perovskite-based solar cells, but with very limited knowledge on the thermal transport in hybrid perovskites, which would affect the device lifetime and stability. Based on the potential developed from the density functional theory calculations, we studied the lattice thermal conductivity of the hybrid halide perovskite CH3NH3PbI3 using equilibrium molecular dynamics simulations. Temperature-dependent thermal conductivity is reported from 160 K to 400 K, which covers the tetragonal phase (160-330 K) and the pseudocubic phase (>330K). A very low thermal conductivity (0.50 W/mK) is found in the tetragonal phase at room temperature, whereas a much higher thermal conductivity is found in the pseudocubic phase (1.80 W/mK at 330 K). The low group velocity of acoustic phonons and the strong anharmonicity are found responsible for the relatively low thermal conductivity of the tetragonal CH3NH3PbI3

A relaxation time model for efficient and accurate prediction of lattice thermal conductivity

Prediction of lattice thermal conductivity is important to many applications and technologies, especially for high-throughput materials screening. However, the state-of-the-art method based on three-phonon scattering process is bound with high computational cost while semi-empirical models such as the Slack equation are less accurate. In this work, we examined the theoretical background of the commonly-used computational models for high-throughput thermal conductivity prediction and proposed an efficient and accurate method based on an approximation for three-phonon scattering strength. This quasi-harmonic approximation has comparable computational cost with many widely-used thermal conductivity models but had the best performance in regard to quantitative accuracy. As compared to many models that can only predict lattice thermal conductivity values, this model also allows to include Normal processes and obtain the phonon relaxation time.Comment: The supplementary materials exceed the size limit of arXiv and could be available after this paper is publishe

First-Principles Prediction of Phononic Thermal Conductivity of Silicene: a Comparison with Graphene

There has been great interest in two-dimensional materials, beyond graphene, for both fundamental sciences and technological applications. Silicene, a silicon counterpart of graphene, has been shown to possess some better electronic properties than graphene. However, its thermal transport properties have not been fully studied. In this paper, we apply the first-principles-based phonon Boltzmann transport equation to investigate the thermal conductivity of silicene as well as the phonon scattering mechanisms. Although both graphene and silicene are two-dimensional crystals with similar crystal structure, we find that phonon transport in silicene is quite different from that in graphene. The thermal conductivity of silicene shows a logarithmic increase with respect to the sample size due to the small scattering rates of acoustic in-plane phonon modes, while that of graphene is finite. Detailed analysis of phonon scattering channels shows that the linear dispersion of the acoustic out-of-plane (ZA) phonon modes, which is induced by the buckled structure, makes the long-wavelength longitudinal acoustic (LA) phonon modes in silicene not as efficiently scattered as that in graphene. Compared with graphene, where most of the heat is carried by the acoustic out-of-plane (ZA) phonon modes, the ZA phonon modes in silicene only have ~10% contribution to the total thermal conductivity, which can also be attributed to the buckled structure. This systematic comparison of phonon transport and thermal conductivity of silicene and graphene using the first-principle-based calculations shed some light on other two-dimensional materials, such as two-dimensional transition metal dichalcogenides.Comment: To appear in J. Appl. Phys. (2015) Vol.117 Issue 3. 50 pages, 11 figure

Phonon transport in single-layer Mo1-xWxS2 alloy embedded with WS2 nanodomains

Two-dimensional (2-D) transition metal dichalcogenides (TMDs) have shown numerous interesting physical and chemical properties, making them promising materials for electronic, optoelectronic, and energy applications. Tuning thermal conductivity of two-dimensional (2-D) materials could expand their applicability in many of these fields. In this paper, we propose a strategy of using alloying and nanodomains to suppress the thermal conductivity of 2-D materials. To predict the thermal conductivity of 2-D alloy embedded with nanodomains, we employ the Green's function approach to assess the phonon scattering strength due to alloying and nanodomain embedding. Our first-principles-driven phonon Boltzmann transport equation calculations show that the thermal conductivity of single-layer MoS2 can be reduced to less than one-tenth of its intrinsic thermal conductivity after alloying with W and introducing nanodomains due to the strong scattering for both high- and low-frequency phonons. The strategies to further reduce the thermal conductivity are also discussed.Comment: 20 pages, 6 figure

Measurement Techniques for Thermal Conductivity and Interfacial Thermal Conductance of Bulk and Thin Film Materials

Thermal conductivity and interfacial thermal conductance play crucial roles in the design of engineering systems where temperature and thermal stress are of concerns. To date, a variety of measurement techniques are available for both bulk and thin film solid-state materials with a broad temperature range. For thermal characterization of bulk material, the steady-state absolute method, laser flash diffusivity method, and transient plane source method are most used. For thin film measurement, the 3{\omega} method and transient thermoreflectance technique including both frequency-domain and time-domain analysis are employed widely. This work reviews several most commonly used measurement techniques. In general, it is a very challenging task to determine thermal conductivity and interface contact resistance with less than 5% error. Selecting a specific measurement technique to characterize thermal properties need to be based on: 1) knowledge on the sample whose thermophysical properties is to be determined, including the sample geometry and size, and preparation method; 2) understanding of fundamentals and procedures of the testing technique and equipment, for example, some techniques are limited to samples with specific geometrics and some are limited to specific range of thermophysical properties; 3) understanding of the potential error sources which might affect the final results, for example, the convection and radiation heat losses.Comment: 48 pages, 20 figures. Accepted by ASME Journal of Electronic Packagin

Thermal conductivity of intrinsic semiconductor at elevated temperature: role of four-phonon scattering and electronic heat conduction

While using first-principles-based Boltzmann transport equation approach to predict the thermal conductivity of crystalline semiconductor materials has been a routine, the validity of the approach is seldom tested for high-temperature conditions. Most previous studies only focused on the phononic contribution, and neglected the electronic part. Meanwhile, the treatment on phonon transport is not rigorous as a few ingredients, such as four-phonon scatterings, phonon renormalization and thermal expansion, are ignored. In this paper, we present a Boltzmann transport equation study on high-temperature thermal conduction in bulk silicon by considering the effects of both phonons and electrons, and explore the role of the missing parts in the previous studies on the thermal conductivity at elevated temperature. For the phonon transport, four-phonon scattering is found to considerably reduce the thermal conductivity when the temperature is larger than 700 K, while the effects of phonon renormalization and thermal expansion on phononic thermal conductivity are negligible. Bipolar contribution to the electronic thermal conductivity calculated from first-principles is implemented for the first time. More than 25% of heat is shown to be conducted by electrons at 1500 K. The computed total thermal conductivity of silicon faithfully reproduces the measured data. The approach presented in this paper is expected to be applied to other high-temperature functional materials, and the results could serve as benchmarks and help to explain the high-temperature phonon and electron transport phenomena.Comment: 6 figures, 23 page

How does the accuracy of interatomic force constants affect the prediction of lattice thermal conductivity

Solving Peierls-Boltzmann transport equation with interatomic force constants (IFCs) from first-principles calculations has been a widely used method for predicting lattice thermal conductivity of three-dimensional materials. With the increasing research interests in two-dimensional materials, this method is directly applied to them but different works show quite different results. In this work, classical potential was used to investigate the effect of the accuracy of IFCs on the predicted thermal conductivity. Inaccuracies were introduced to the third-order IFCs by generating errors in the input forces. When the force error lies in the typical value from first-principles calculations, the calculated thermal conductivity would be quite different from the benchmark value. It is found that imposing translational invariance conditions cannot always guarantee a better thermal conductivity result. It is also shown that Gr\"uneisen parameters cannot be used as a necessary and sufficient criterion for the accuracy of third-order IFCs in the aspect of predicting thermal conductivity.Comment: 26 pages, 9 figure

Phonon transmission across Mg2Si/Mg2Si1-xSnx interfaces: A first-principles-based atomistic Green's function study

Phonon transmission across interfaces of dissimilar materials has been studied intensively in the recent years by using atomistic simulation tools owing to its importance in determining the effective thermal conductivity of nanostructured materials. Atomistic Green's function (AGF) method with interatomic force constants from the first-principles (FP) calculations has evolved to be a promising approach to study phonon transmission in many not well-studied material systems. However, the direct FP calculation for interatomic force constants becomes infeasible when the system involves atomic disorder. Mass approximation is usually used, but its validity has not been tested. In this paper, we employ the higher-order force constant model to extract harmonic force constants from the FP calculations, which originates from the virtual crystal approximation but considers the local force-field difference. As a feasibility demonstration of the proposed method that integrates higher-order force constant model from the FP calculations with the AGF, we study the phonon transmission in the Mg2Si/Mg2Si1-xSnx systems. When integrated with the AGF, the widely-used mass approximation is found to overpredict phonon transmission across Mg2Si/Mg2Sn interface. The difference can be attributed to the absence of local strain field-induced scattering in the mass approximation, which makes the high-frequency phonons less scattered. The frequency-dependent phonon transmission across an interface between a crystal and an alloy, which often appears in high efficiency "nanoparticle in alloy" thermoelectric materials, is studied. The interfacial thermal resistance across Mg2Si/Mg2Si1-xSnx interface is found to be weakly dependent on the composition of Sn when the composition x is less than 40%, but increases rapidly when it is larger than 40% due to the transition of high-frequency phonon DOS in Mg2Si1-xSnx alloys.Comment: 44 pages, 11 figure