Rattling-induced suppression of thermal transport in cubic In2O3with Sn-Ga diatomic defect.

We present the first principles study of cubic In2O3with a diatomic defect composed of a Sn atom substituting the In atom at theb-site and a Ga atom embedded in the nearestc-site (structural vacancy) with lattice positions according to the Wyckoff notations. Structural, electronic, phononic and thermal properties were investigated within density functional theory formalism. The lattice anharmonicity effects were taken into account for all possible three-phonon scattering processes. The phonon transport was considered within the Peierls-Boltzmann transport equation with relaxation time approximation. In the relaxed lattice, a strong rearrangement of the initial positions of the atoms in the defect vicinity was revealed, which primarily manifests itself in the displacement of the Sn atom toward another interstitial site. Thus, a cage is formed around the defect by 12 O and 12 In atoms. The calculations of elastic constants and mean square displacements of cage region atoms showed the rattling-like behavior of the Sn atom. Bader charge analysis and electron localization function allowed a deeper understanding and explanation of such behavior. Phonon energy spectra as compared to In2O3and In2O3:(Sn) demonstrated flattening of phonon branches with spatial localization of phonon modes. They also revealed a decrease in average group velocities of phonons, including those of acoustic type, the presence of avoided-crossing features in the low energy range, and an increase of available phase space for three-phonon scattering. Accounting for all these vibrational features due to defect atoms resulted in a thermal conductivity drop at room temperature by more than seven times compared to In2O3.

Thermal Transport Evolution Due to Nanostructural Transformations in Ga-Doped Indium-Tin-Oxide Thin Films.

We report on a comprehensive theoretical and experimental investigation of thermal conductivity in indium-tin-oxide (ITO) thin films with various Ga concentrations (0-30 at. %) deposited by spray pyrolysis technique. X-ray diffraction (XRD) and scanning electron microscopy have shown a structural transformation in the range 15-20 at. % Ga from the nanocrystalline to the amorphous phase. Room temperature femtosecond time domain thermoreflectance measurements showed nonlinear decrease of thermal conductivity in the range 2.0-0.5 Wm-1 K-1 depending on Ga doping level. It was found from a comparison between density functional theory calculations and XRD data that Ga atoms substitute In atoms in the ITO nanocrystals retaining Ia-3 space group symmetry. The calculated phonon dispersion relations revealed that Ga doping leads to the appearance of hybridized metal atom vibrations with avoided-crossing behavior. These hybridized vibrations possess shortened mean free paths and are the main reason behind the thermal conductivity drop in nanocrystalline phase. An evolution from propagative to diffusive phonon thermal transport in ITO:Ga with 15-20 at. % of Ga was established. The suppressed thermal conductivity of ITO:Ga thin films deposited by spray pyrolysis may be crucial for their thermoelectric applications.

Energetic, structural and electronic features of Sn-, Ga-, O-based defect complexes in cubic In2O3.

Defect energy formation, lattice distortions and electronic structure of cubic In2O3 with Sn, Ga and O impurities were theoretically investigated using density functional theory. Different types of point defects, consisting of 1-4 atoms of Sn, Ga and O in both substitutional and interstitial (structural vacancy) positions, were examined. It was demonstrated, that formation of substitutional Ga and Sn defects are spontaneous, while formation of interstitial defects requires an activation energy. The donor-like behavior of interstitial Ga defects with splitting of conduction band into two subbands with light and heavy electrons, respectively, was revealed. Contrarily, interstitial O defects demonstrate acceptor-like behavior with the formation of acceptor levels or subbands inside the band gap. The obtained results are important for an accurate description of transport phenomena in In2O3 with substitutional and interstitial defects.

In-Plane Thermal Conductivity of Radial and Planar Si/SiOx Hybrid Nanomembrane Superlattices.

Silicon, although widely used in modern electronic devices, has not yet been implemented in thermoelectric applications mainly due to its high thermal conductivity, κ, which leads to an extremely low thermoelectric energy conversion efficiency (figure of merit). Here, we present an approach to manage κ of Si thin-film-based nanoarchitectures through the formation of radial and planar Si/SiOx hybrid nanomembrane superlattices (HNMSLs). For the radial Si/SiOx HNMSLs with various numbers of windings (1, 2, and 5 windings), we observe a continuous reduction in κ with increasing number of windings. Meanwhile, the planar Si/SiOx HNMSL, which is fabricated by mechanically compressing a five-windings rolled-up microtube, shows the smallest in-plane thermal conductivity among all the reported values for Si-based superlattices. A theoretical model proposed within the framework of the Born-von Karman lattice dynamics to quantitatively interpret the experimental data indicates that the thermal conductivity of Si/SiOx HNMSLs is to a great extent determined by the phonon processes in the SiOx layers.

Phonons and thermal transport in graphene and graphene-based materials.

A discovery of the unusual thermal properties of graphene stimulated experimental, theoretical and computational research directed at understanding phonon transport and thermal conduction in two-dimensional material systems. We provide a critical review of recent results in the graphene thermal field focusing on phonon dispersion, specific heat, thermal conductivity, and comparison of different models and computational approaches. The correlation between the phonon spectrum in graphene-based materials and the heat conduction properties is analyzed in details. The effects of the atomic plane rotations in bilayer graphene, isotope engineering, and relative contributions of different phonon dispersion branches are discussed. For readers' convenience, the summaries of main experimental and theoretical results on thermal conductivity as well as phonon mode contributions to thermal transport are provided in the form of comprehensive annotated tables.

Direct observation of confined acoustic phonon polarization branches in free-standing semiconductor nanowires.

Similar to electron waves, the phonon states in semiconductors can undergo changes induced by external boundaries. However, despite strong scientific and practical importance, conclusive experimental evidence of confined acoustic phonon polarization branches in individual free-standing nanostructures is lacking. Here we report results of Brillouin-Mandelstam light scattering spectroscopy, which reveal multiple (up to ten) confined acoustic phonon polarization branches in GaAs nanowires with a diameter as large as 128 nm, at a length scale that exceeds the grey phonon mean-free path in this material by almost an order-of-magnitude. The dispersion modification and energy scaling with diameter in individual nanowires are in excellent agreement with theory. The phonon confinement effects result in a decrease in the phonon group velocity along the nanowire axis and changes in the phonon density of states. The obtained results can lead to more efficient nanoscale control of acoustic phonons, with benefits for nanoelectronic, thermoelectric and spintronic devices.

Breakdown current density in h-BN-capped quasi-1D TaSe3 metallic nanowires: prospects of interconnect applications.

We report on the current-carrying capacity of the nanowires made from the quasi-1D van der Waals metal tantalum triselenide capped with quasi-2D boron nitride. The chemical vapor transport method followed by chemical and mechanical exfoliation were used to fabricate the mm-long TaSe3 wires with the lateral dimensions in the 20 to 70 nm range. Electrical measurements establish that the TaSe3/h-BN nanowire heterostructures have a breakdown current density exceeding 10 MA cm(-2)-an order-of-magnitude higher than that for copper. Some devices exhibited an intriguing step-like breakdown, which can be explained by the atomic thread bundle structure of the nanowires. The quasi-1D single crystal nature of TaSe3 results in a low surface roughness and in the absence of the grain boundaries. These features can potentially enable the downscaling of the nanowires to lateral dimensions in a few-nm range. Our results suggest that quasi-1D van der Waals metals have potential for applications in the ultimately downscaled local interconnects.

Thermal conductivity of graphene with defects induced by electron beam irradiation.

We investigate the thermal conductivity of suspended graphene as a function of the density of defects, ND, introduced in a controllable way. High-quality graphene layers are synthesized using chemical vapor deposition, transferred onto a transmission electron microscopy grid, and suspended over ∼7.5 µm size square holes. Defects are induced by irradiation of graphene with the low-energy electron beam (20 keV) and quantified by the Raman D-to-G peak intensity ratio. As the defect density changes from 2.0 × 10(10) cm(-2) to 1.8 × 10(11) cm(-2) the thermal conductivity decreases from ∼(1.8 ± 0.2) × 10(3) W mK(-1) to ∼(4.0 ± 0.2) × 10(2) W mK(-1) near room temperature. At higher defect densities, the thermal conductivity reveals an intriguing saturation-type behavior at a relatively high value of ∼400 W mK(-1). The thermal conductivity dependence on the defect density is analyzed using the Boltzmann transport equation and molecular dynamics simulations. The results are important for understanding phonon - point defect scattering in two-dimensional systems and for practical applications of graphene in thermal management.

Engineering of the thermodynamic properties of bilayer graphene by atomic plane rotations: the role of the out-of-plane phonons.

We investigated theoretically the specific heat of graphene, bilayer graphene and twisted bilayer graphene taking into account the exact phonon dispersion and density of states for each polarization branch. It is shown that contrary to a conventional belief the dispersion of the out-of-plane acoustic phonons - referred to as ZA phonons - deviates strongly from a parabolic law starting from the frequencies as low as ∼100 cm(-1). This leads to the frequency-dependent ZA phonon density of states and the breakdown of the linear dependence of the specific heat on temperature T. We established that ZA phonons determine the specific heat for T ≤ 200 K while contributions from both in-plane and out-of-plane acoustic phonons are dominant for 200 K ≤ T ≤ 500 K. In the high-temperature limit, T > 1000 K, the optical and acoustic phonons contribute approximately equally to the specific heat. The Debye temperature for graphene and twisted bilayer graphene was calculated to be around ∼1861-1864 K. Our results suggest that the thermodynamic properties of materials such as bilayer graphene can be controlled at the atomic scale by rotation of the sp(2)-carbon planes.

Thermal conductivity of twisted bilayer graphene.

We have investigated experimentally the thermal conductivity of suspended twisted bilayer graphene. The measurements were performed using an optothermal Raman technique. It was found that the thermal conductivity of twisted bilayer graphene is lower than that of monolayer graphene and the reference, Bernal stacked bilayer graphene in the entire temperature range examined (∼300-700 K). This finding indicates that the heat carriers - phonons - in twisted bilayer graphene do not behave in the same manner as that observed in individual graphene layers. The decrease in the thermal conductivity found in twisted bilayer graphene was explained by the modification of the Brillouin zone due to plane rotation and the emergence of numerous folded phonon branches that enhance the phonon Umklapp and normal scattering. The results obtained are important for understanding thermal transport in two-dimensional systems.

Anomalous size dependence of the thermal conductivity of graphene ribbons.

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to an unusual nonmonotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p > 0.5). Our results also suggest that, contrary to what was previously thought, the bulk-like three-dimensional phonons in graphite make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ∼30 µm, as log(L), while for larger L, the thermal conductivity approaches a finite value following the dependence K(0) - A × L(-1/2), where K(0) and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.

Two-dimensional phonon transport in graphene.

Properties of phonons-quanta of the crystal lattice vibrations-in graphene have recently attracted significant attention from the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature, while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in a quasi-two-dimensional system such as graphene compared to the basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates into unusual heat conduction in graphene and related materials. In this review, we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes, and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent results for the phonon thermal conductivity of single-layer graphene and few-layer graphene, and the effects of the strain, defects, and isotopes on phonon transport in these systems.

Dimensional crossover of thermal transport in few-layer graphene.

Graphene, in addition to its unique electronic and optical properties, reveals unusually high thermal conductivity. The fact that the thermal conductivity of large enough graphene sheets should be higher than that of basal planes of bulk graphite was predicted theoretically by Klemens. However, the exact mechanisms behind the drastic alteration of a material's intrinsic ability to conduct heat as its dimensionality changes from two to three dimensions remain elusive. The recent availability of high-quality few-layer graphene (FLG) materials allowed us to study dimensional crossover experimentally. Here we show that the room-temperature thermal conductivity changes from approximately 2,800 to approximately 1,300 W m(-1) K(-1) as the number of atomic planes in FLG increases from 2 to 4. We explained the observed evolution from two dimensions to bulk by the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering. The obtained results shed light on heat conduction in low-dimensional materials and may open up FLG applications in thermal management of nanoelectronics.