Phonon transport in isotope-disordered carbon and boron-nitride nanotubes: is localization observable?

Phonon transition across an isotopic interface

Isotopic mixtures result in distinct properties of materials such as thermal conductivity and nuclear process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in atomic-scale isotopic identification. Here, using electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent phonon behavior at the h-¹⁰BN/h-¹¹BN isotope heterostructure with sub-unit-cell resolution. We find the phonons' energy changes gradually across the interface, featuring a wide transition regime. Phonons near the Brillouin zone center have a transition regime of ~3.34 nm, whereas phonons at the Brillouin zone boundary have a transition regime of ~1.66 nm. We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, the variation of phonon energy between atom layers near the interface depends on both of momentum transfer and mass change. This study provides new insights into the isotopic effects in natural materials.

Localization of the Optical Phonon Modes in Boron Nitride Nanotubes: Mixing Effect of 10B Isotopes and Vacancies

We explored the mixing effect of ¹⁰B isotopes and boron (B) or nitrogen (N) vacancies on the atomic vibrational properties of (10,0) single-wall boron nitride nanotubes (BNNTs). The forced oscillation technique was employed to evaluate the phonon modes for the entire range (0-100%) of ¹⁰B isotopes and atomic vacancy densities ranging from 0 to 30%. With increasing isotope densities, we noticed a blue shift of the Raman-active A₁ phonon peak, whereas an increased density of mixed or independent B and N vacancies resulted in the emergence of a new low-frequency peak and the annihilation of the A₁ peak in the phonon density of states. High-energy optical phonons were localized as a result of both ¹⁰B isotopes and the presence of mixing defects. We found an asymmetrical nature of the localization length with increasing ¹⁰B isotope content, which corresponds well to the isotope-inherited localization length of carbon nanotubes and monolayer graphene. The localization length falls abruptly with the increase in concentration of both atomic vacancies (B or N) and mixing defects (¹⁰B isotope and vacancies). These findings are critical for understanding heat conduction and nanoscopic vibrational investigations such as tip-enhanced Raman spectra in BNNTs, which can map local phonon energies.

Computational predictions of quantum thermal transport across nanoscale interfaces

Interfaces are essential elements in nanoscale devices and their properties can differ significantly from their bulk counterparts. Because interfaces often act as bottlenecks in heat dissipation, the prediction and control of the interfacial thermal conductance is critical to the design of nanoscale devices. In this review, we examine the recent advances in quantum interfacial thermal transport from a theoretical and computational perspective. We discuss in detail recent advances in the Atomistic Green's Function method which is an important tool for predicting interfacial thermal transport. We also discuss recent progress in the understanding of interfacial transport mechanisms, including the role of interfacial modes, the role of anharmonic phonon-phonon coupling, the role of electron-phonon interaction, and the ways to tune the interfacial thermal conductance. Finally, we give an overview of the challenges and opportunities in this research field.

Isotopic Disorder: The Prevailing Mechanism in Limiting the Phonon Lifetime in Hexagonal BN

The phonon linewidth of isotopically controlled hexagonal boron nitride (h-BN) single crystals has been determined by Raman scattering. The scattering by isotopic mass disorder induces a phonon broadening that is largest for boron 11 fractions around 0.65. Lowest-order perturbation theory does not suffice to explain the dependence of the isotopic broadening on isotopic composition. A multiple-scattering theory based on the coherent potential approximation provides a good quantitative account of the phonon shift and broadening with isotopic composition observed in the experiments. Isotopic-disorder scattering is shown to have a prominent role in limiting the optical-phonon lifetime in h-BN.

Effects of Divacancy and Extended Line Defects on the Thermal Transport Properties of Graphene Nanoribbons

The effects of divacancy, including isolated defects and extended line defects (ELD), on the thermal transport properties of graphene nanoribbons (GNRs) are investigated using the Nonequilibrium Green's function method. Different divacancy defects can effectively tune the thermal transport of GNRs and the thermal conductance is significantly reduced. The phonon scattering of a single divacancy is mostly at high frequencies while the phonon scattering at low frequencies is also strong for randomly distributed multiple divacancies. The collective effect of impurity scattering and boundary scattering is discussed, which makes the defect scattering vary with the boundary condition. The effect on thermal transport properties of a divacancy is also shown to be closely related to the cross section of the defect, the internal structure and the bonding strength inside the defect. Both low frequency and high frequency phonons are scattered by 48, d5d7 and t5t7 ELD. However, the 585 ELD has almost no influence on phonon scattering at low frequency region, resulting in the thermal conductance of GNRs with 585 ELD being 50% higher than that of randomly distributed 585 defects. All these results are valuable for the design and manufacture of graphene nanodevices.

Green function, quasi-classical Langevin and Kubo-Greenwood methods in quantum thermal transport

With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo-Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo-Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon-phonon and other scatterings is summarized.

Using nanotubes to study the phonon spectrum of two-dimensional materials

We develop a method to characterize the phonon spectrum of 2D monolayers from IR and Raman measurements performed on nanotubes.

Phonon localization in heat conduction

Nondiffusive phonon thermal transport, extensively observed in nanostructures, has largely been attributed to classical size effects, ignoring the wave nature of phonons. We report localization behavior in phonon heat conduction due to multiple scattering and interference events of broadband phonons, by measuring the thermal conductivities of GaAs/AlAs superlattices with ErAs nanodots randomly distributed at the interfaces. With an increasing number of superlattice periods, the measured thermal conductivities near room temperature increased and eventually saturated, indicating a transition from ballistic to diffusive transport. In contrast, at cryogenic temperatures the thermal conductivities first increased but then decreased, signaling phonon wave localization, as supported by atomistic Greenșs function simulations. The discovery of phonon localization suggests a new path forward for engineering phonon thermal transport.

Anderson Localization of Thermal Phonons Leads to a Thermal Conductivity Maximum

Our elastic model of ErAs disordered GaAs/AlAs superlattices exhibits a local thermal conductivity maximum as a function of length due to exponentially suppressed Anderson-localized phonons. By analyzing the sample-to-sample fluctuations in the dimensionless conductance, g, the transition from diffusive to localized transport is identified as the crossover from the multichannel to single-channel transport regime g ≈ 1. Single parameter scaling is shown to hold in this crossover regime through the universality of the probability distribution of g that is independent of system size and disorder strength.

Blocking Phonon Transport by Structural Resonances in Alloy-Based Nanophononic Metamaterials Leads to Ultralow Thermal Conductivity

Understanding the design rules to obtain materials that enable a tight control of phonon transport over a broad range of frequencies would aid major developments in thermoelectric energy harvesting, heat management in microelectronics, and information and communication technology. Using atomistic simulations we show that the metamaterials approach relying on localized resonances is very promising to engineer heat transport at the nanoscale. Combining designed resonant structures to alloying can lead to extremely low thermal conductivity in silicon nanowires. The hybridization between resonant phonons and propagating modes greatly reduces the group velocities and the phonon mean free paths in the low frequency acoustic range below 4 THz. Concurrently, alloy scattering hinders the propagation of high frequency thermal phonons. Our calculations establish a rationale between the size, shape, and period of the resonant structures, and the thermal conductivity of the nanowire, and demonstrate that this approach is even effective to block phonon transport in wavelengths much longer than the size and period of the surface resonant structures. A further consequence of using resonant structures is that they are not expected to scatter electrons, which is beneficial for thermoelectric applications.

Tuning thermal transport in Si nanowires by isotope engineering

The thermal conductivity of ²⁸Si_x³⁰Si_1−x nanowires is reduced up to ∼20% (∼50%) at room (low) temperature with respect to isotope purfied nanowires.

Ballistic heat conduction and mass disorder in one dimension

It is well-known that in the disordered harmonic chain, heat conduction is subballistic and the thermal conductivity (κ) scales asymptotically as lim(L--> ∞) κ ∝ L(0.5) where L is the chain length. However, using the nonequilibrium Green's function (NEGF) method and analytical modelling, we show that there exists a critical crossover length scale (LC) below which ballistic heat conduction (κ ∝ L) can coexist with mass disorder. This ballistic-to-subballistic heat conduction crossover is connected to the exponential attenuation of the phonon transmittance function Ξ i.e. Ξ(ω, L) = exp[-L/λ(ω)], where λ is the frequency-dependent attenuation length. The crossover length can be determined from the minimum attenuation length, which depends on the maximum transmitted frequency. We numerically determine the dependence of the transmittance on frequency and mass composition as well as derive a closed form estimate, which agrees closely with the numerical results. For the length-dependent thermal conductance, we also derive a closed form expression which agrees closely with numerical results and reproduces the ballistic to subballistic thermal conduction crossover. This allows us to characterize the crossover in terms of changes in the length, mass composition and temperature dependence, and also to determine the conditions under which heat conduction enters the ballistic regime. We describe how the mass composition can be modified to increase ballistic heat conduction.

Thermal and thermoelectric properties of graphene

The subject of thermal transport at the mesoscopic scale and in low-dimensional systems is interesting for both fundamental research and practical applications. As the first example of truly two-dimensional materials, graphene has exceptionally high thermal conductivity, and thus provides an ideal platform for the research. Here we review recent studies on thermal and thermoelectric properties of graphene, with an emphasis on experimental progresses. A general physical picture based on the Landauer transport formalism is introduced to understand underlying mechanisms. We show that the superior thermal conductivity of graphene is contributed not only by large ballistic thermal conductance but also by very long phonon mean free path (MFP). The long phonon MFP, explained by the low-dimensional nature and high sample purity of graphene, results in important isotope effects and size effects on thermal conduction. In terms of various scattering mechanisms in graphene, several approaches are suggested to control thermal conductivity. Among them, introducing rough boundaries and weakly-coupled interfaces are promising ways to suppress thermal conduction effectively. We also discuss the Seebeck effect of graphene. Graphene itself might not be a good thermoelectric material. However, the concepts developed by graphene research might be applied to improve thermoelectric performance of other materials.

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.

Thermal conductivity of isotopically modified graphene

In addition to its exotic electronic properties graphene exhibits unusually high intrinsic thermal conductivity. The physics of phonons--the main heat carriers in graphene--has been shown to be substantially different in two-dimensional (2D) crystals, such as graphene, from in three-dimensional (3D) graphite. Here, we report our experimental study of the isotope effects on the thermal properties of graphene. Isotopically modified graphene containing various percentages of 13C were synthesized by chemical vapour deposition (CVD). The regions of different isotopic compositions were parts of the same graphene sheet to ensure uniformity in material parameters. The thermal conductivity, K, of isotopically pure 12C (0.01% 13C) graphene determined by the optothermal Raman technique, was higher than 4,000 W mK(-1) at the measured temperature T(m)~320 K, and more than a factor of two higher than the value of K in graphene sheets composed of a 50:50 mixture of 12C and 13C. The experimental data agree well with our molecular dynamics (MD) simulations, corrected for the long-wavelength phonon contributions by means of the Klemens model. The experimental results are expected to stimulate further studies aimed at a better understanding of thermal phenomena in 2D crystals.

Thermal conductivity reduction through isotope substitution in nanomaterials: predictions from an analytical classical model and nonequilibrium molecular dynamics simulations

We introduce an analytical model to rapidly determine the thermal conductivity reduction due to mass disorder in nanomaterials. Although this simplified classical model depends only on the masses of the different atoms, it adequately describes the changes in thermal transport as the concentrations of these atoms vary. Its predictions compare satisfactorily with nonequilibrium molecular dynamics simulations of the thermal conductivity of (14)C-(12)C carbon nanotubes as well as with previous simulations of other materials. We present it as a simple tool to quantitatively estimate the thermal conductivity decrease that is induced by isotope substitution in various materials.

Universality and diversity in a phonon-transmission histogram of isotope-disordered carbon nanotubes

Universal fluctuations in phonon transmission and other features of phonon-transmission histograms are investigated by performing numerical simulations of coherent-phonon transport in isotope-disordered carbon nanotubes. Interestingly, the phonon-transmission fluctuation in the diffusive regime is universal, irrespective of the average phonon transmission, the tube chirality, and the concentrations, and masses of isotopes. We also find that the histogram, which has a Gaussian distribution in the diffusive regime, has a log-normal distribution in the localization regime.

Enhanced thermopower of graphene films with oxygen plasma treatment

In this work, we show that the maximum thermopower of few layers graphene (FLG) films could be greatly enhanced up to ∼700 μV/K after oxygen plasma treatment. The electrical conductivities of these plasma treated FLG films remain high, for example, ∼10(4) S/m, which results in power factors as high as ∼4.5 × 10(-3) W K(-2) m(-1). In comparison, the pristine FLG films show a maximum thermopower of ∼80 μV/K with an electrical conductivity of ∼5 × 10(4) S/m. The proposed mechanism is due to generation of local disordered carbon that opens the band gap. Measured thermopowers of single-layer graphene (SLG) films and reduced graphene oxide (rGO) films were in the range of -40 to 50 and -10 to 20 μV/K, respectively. However, such oxygen plasma treatment is not suitable for SLG and rGO films. The SLG films were easily destroyed during the treatment while the electrical conductivity of rGO films is too low.

Impacts of doping on thermal and thermoelectric properties of nanomaterials

Thermal transport in nanoscale structures has attracted an increasing interest in the last two decades. On the one hand, the low dimensional nanostructured materials are platforms for testing novel phonon transport theories. On the other hand, nanomaterials are promising candidates for nanoscale on-chip coolers. This review is focused on the thermal conductance, thermoelectric property, and impacts of doping on these properties.

Precise control of thermal conductivity at the nanoscale through individual phonon-scattering barriers

The ability to precisely control the thermal conductivity (kappa) of a material is fundamental in the development of on-chip heat management or energy conversion applications. Nanostructuring permits a marked reduction of kappa of single-crystalline materials, as recently demonstrated for silicon nanowires. However, silicon-based nanostructured materials with extremely low kappa are not limited to nanowires. By engineering a set of individual phonon-scattering nanodot barriers we have accurately tailored the thermal conductivity of a single-crystalline SiGe material in spatially defined regions as short as approximately 15 nm. Single-barrier thermal resistances between 2 and 4 x 10(-9) m(2) K W(-1) were attained, resulting in a room-temperature kappa down to about 0.9 W m(-1) K(-1), in multilayered structures with as little as five barriers. Such low thermal conductivity is compatible with a totally diffuse mismatch model for the barriers, and it is well below the amorphous limit. The results are in agreement with atomistic Green's function simulations.

Thermal transport in isotopically disordered carbon nanotubes: a comparison between Green's functions and Boltzmann approaches

We present a study of the phononic thermal conductivity of isotopically disordered carbon nanotubes. In particular, the behaviour of the thermal conductivity as a function of the system length is investigated, using Green's function techniques to compute the transmission across the system. The method is implemented using linear scaling algorithms, which allow us to reach systems of lengths up to L = 2.5 µm (with up to 200 000 atoms). As for 1D systems, it is observed that the conductivity diverges with the system size L. We also observe a dramatic decrease of the thermal conductance for systems of experimental sizes (roughly 80% at room temperature for L = 2.5 µm), when a large fraction of isotopic disorder is introduced. The results obtained with Green's function techniques are compared to results obtained with a Boltzmann description of thermal transport. There is a good agreement between both approaches for systems of experimental sizes, even in the presence of Anderson localization. This is particularly interesting since the computation of the transmission using Boltzmann's equation is much less computationally expensive, so that larger systems may be studied with this method.

Turning carbon nanotubes from exceptional heat conductors into insulators

Thermal conductivity (kappa) of isolated carbon nanotubes (CNTs) is higher than the kappa of diamond; however, in this Letter we show that the kappa of a packed bed of three-dimensional random networks of single and multiwall CNTs is smaller than that of thermally insulating amorphous polymers. The thermoelectric power (Sigma) of the random network of CNTs was also measured. The Sigma of a single wall nanotube network is very similar to that of isolated nanotubes and, in contrast with kappa, Sigma shows a strong dependence on the tube diameter.