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

Temperature Effect on Phonon Dispersion Stability of Zirconium by Machine Learning-driven Atomistic Simulations

It is well known that conventional harmonic lattice dynamics cannot be applied to energetically unstable crystals at 0 K, such as high temperature body centered cubic (BCC) phase of crystalline Zr. Predicting phonon spectra at finite temperature requires the calculation of force constants to the third, fourth and even higher orders, however, it remains challenging to determine to which order the Taylor expansion of the potential energy surface for different materials should be cut off. Molecular dynamics, on the other hand, intrinsically includes arbitrary orders of phonon anharmonicity, however, its accuracy is severely limited by the empirical potential field used. Using machine learning method, we developed an inter-atomic potential for Zirconium crystals for both the hexagonal closed-packed (HCP) phase and the body centered cubic phase. The developed potential field accurately captures energy-volume relationship, elastic constants and phonon dispersions. The instability of BCC structure is found to originate from the double-well shape of the potential energy surface where the local maxima is located in an unstable equilibrium position. The stabilization of the BCC phase at high temperature is due to the dynamical average of the low-symmetry minima of the double well due to atomic vibrations. Molecular dynamics simulations are then performed to stochastically sample the potential energy surface and to calculate the phonon dispersion at elevated temperature. The phonon renormalization in BCC-Zr is successfully captured by the molecular dynamics simulation at 1188 K

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

Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials

Measuring thermal properties of materials is not only of fundamental importance in understanding the transport processes of energy carriers (electrons and phonons) but also of practical interest in developing novel materials with desired thermal conductivity for applications in energy, electronics, and photonic systems. Over the past two decades, ultrafast laser-based time-domain thermoreflectance (TDTR) has emerged and evolved as a reliable, powerful, and versatile technique to measure the thermal properties of a wide range of bulk and thin film materials and their interfaces. This tutorial discusses the basics as well as the recent advances of the TDTR technique and its applications in the thermal characterization of a variety of materials. The tutorial begins with the fundamentals of the TDTR technique, serving as a guideline for understanding the basic principles of this technique. A diverse set of TDTR configurations that have been developed to meet different measurement conditions are then presented, followed by several variations of the TDTR technique that function similarly as the standard TDTR but with their own unique features. This tutorial closes with a summary that discusses the current limitations and proposes some directions for future development.Comment: 82 pages, 23 figures, invited tutorial submitted to Journal of Applied Physic

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

Three-Dimensional Anisotropic Thermal Conductivity Tensor of Single Crystalline \b{eta}-Ga2O3

\b{eta}-Ga2O3 has attracted considerable interest in recent years for high power electronics, where thermal properties of \b{eta}-Ga2O3 play a critical role. The thermal conductivity of \b{eta}-Ga2O3 is expected to be three-dimensionally (3D) anisotropic due to the monoclinic lattice structure. In this work, the 3D anisotropic thermal conductivity tensor of a (010)-oriented \b{eta}-Ga2O3 single crystal was measured by using a novel time-domain thermoreflectance (TDTR) method with a highly elliptical pump beam. Our measured results suggest that at room temperature, the highest in-plane thermal conductivity is along a direction between [001] and [102], with a value of 13.3+/-1.8 W/mK, and the lowest in-plane thermal conductivity is close to the [100] direction, with a value of 9.5+/-1.8 W/mK. The through-plane thermal conductivity, which is along the [010] direction, has the highest value of 22+/-2.5 W/mK among all the directions. Temperature-dependent thermal conductivity of \b{eta}-Ga2O3 was also measured and compared with a modified Callaway model calculation to understand the temperature dependence and the role of impurity scattering.Comment: 14 pages, 4 figure

Super-stretchable borophene and its stability under straining

Recent success in synthesizing two-dimensional borophene on silver substrate attracts strong interest in exploring its possible extraordinary physical properties. By using the density functional theory calculations, we show that borophene is highly stretchable along the transverse direction. The strain-to-failure in the transverse direction is nearly twice as that along the longitudinal direction. The straining induced flattening and subsequent stretch of the flat borophene are accounted for the large strain-to-failure for tension in the transverse direction. The mechanical properties in the other two directions exhibit strong anisotropy. Phonon dispersions of the strained borophene monolayers suggest that negative frequencies are presented, which indicates the instability of free-standing borophene even under high tensile stress.Comment: 11 pages, 4 figure

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

Mechanics and Tunable Bandgap by Straining in Single-Layer Hexagonal Boron-Nitride

Current interest in two-dimensional materials extends from graphene to others systems like single-layer hexagonal boron-nitride (h-BN), for the possibility of making heterogeneous structures to achieve exceptional properties that cannot be realized in graphene.The electrically insulating h-BN and semi-metal graphene may open good opportunities to realize a semiconductor by manipulating the morphology and composition of such heterogeneous structures.Here we report the mechanical properties of h-BN and its band structures tuned by mechanical straining by using the density functional theory calculations.The elastic properties, both the Young's modulus and bending rigidity for h-BN, are isotropic.We reveal that there is a bi-linear dependence of band gap on the applied tensile strains in h-BN. Mechanical strain can tune single-layer h-BN from an insulator to a semiconductor, with a band gap in the 4.7eV to 1.5eV range.Comment: 16 pages, 5 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