Phonon wave interference and thermal bandgap materials

Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. It is now accepted that thermal metamaterial-based phonon manipulation is possible, especially at sub-kelvin temperatures. In these extreme limits of low temperatures and dimensions, heat conduction enters a quantum regime where phonon exchange obeys the Landauer formalism. Phonon transport is then governed by the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here we report on ultra-sensitive thermal experiments made on ballistic 1D phonon conductors using a micro-platform suspended sensor. Our thermal conductance measurements attain a power sensitivity of 15 attoWatts \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {{\mathrm{Hz}}} \,^{ - 1}$$\end{document}Hz-1 around 100 mK. Ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. This limitation of heat transport in the quantum regime may have a significant impact on modern thermal management and thermal circuit design.

At low temperatures and dimensionality it has become possible to probe the quantum limits of heat transport. Tavakoli et al. show that heat transport through a one-dimensional device can be dominated by non-ideal transmission instead of reaching the regime of thermal conductance quantization.

Coherent control of thermal phonon transport in van der Waals superlattices

van der Waals (vdW) heterostructures are a central focus of materials science and condensed matter physics due to the novel physical phenomena and properties obtained by precisely stacking heterogeneous atomically thin layers. vdW heterostructures are expected to allow for the coherent manipulation of THz lattice vibrations and hence heat conduction due to the ability to precisely control chemical composition at the atomic scale, but little work has focused on thermal transport in these materials. Here, we report an ab initio study of thermal transport in vdW superlattices consisting of alternating transition metal dichalcogenide atomic layers. Our calculations show that the lattice vibrational spectrum and scattering rates can be precisely manipulated by the choice of each atomically thin layer, resulting in materials with novel properties such as large thermal anisotropies approaching 200 and ultralow cross-plane thermal conductivities comparable to those of amorphous materials. Our work demonstrates how coherent manipulation of phonons in vdW superlattices can expand the property space beyond that occupied by natural materials and suggests an experimental route to realize these properties.

Acoustic properties of porous microlattices from effective medium to scattering dominated regimes

Microlattices are architected materials that allow for an unprecedented control of mechanical properties (e.g., stiffness, density, and Poisson's coefficient). In contrast to their quasi-static mechanical properties, the acoustic properties of microlattices remain largely unexplored. This paper analyzes the acoustic response of periodic millimeter-sized microlattices immersed in water using experiments and numerical simulations. Microlattices are fabricated using high-precision stereolithographic three-dimensional printing in a large variety of porosities and lattice topologies. This paper shows that the acoustic propagation undergoes a frequency dependent transition from a classic poroelastic behaviour that can be described by Biot's theory to a regime that is dominated by scattering effects. Biot's acoustic parameters are derived from direct simulations of the microstructure using coupled fluid and solid finite elements. The wave speeds predicted with Biot's theory agree well with the experimental measures. Within the scattering regime, the signals show a strong attenuation and dispersion, which is characterized by a cut-off frequency. The strong dispersion results in a frequency dependent group velocity. A simplified model of an elastic cylindrical scatterer allows predicting the signal attenuation and dispersion observed experimentally. The results in this paper pave the way for the creation of microlattice materials for the control of ultrasonic waves across a wide range of frequencies.

Cross-plane coherent acoustic phonons in two-dimensional organic-inorganic hybrid perovskites

Two-dimensional Ruddlesden–Popper organic–inorganic hybrid layered perovskites (2D RPs) are solution-grown semiconductors with prospective applications in next-generation optoelectronics. The heat-carrying, low-energy acoustic phonons, which are important for heat management of 2D RP-based devices, have remained unexplored. Here we report on the generation and propagation of coherent longitudinal acoustic phonons along the cross-plane direction of 2D RPs, following separate characterizations of below-bandgap refractive indices. Through experiments on single crystals of systematically varied perovskite layer thickness, we demonstrate significant reduction in both group velocity and propagation length of acoustic phonons in 2D RPs as compared to the three-dimensional methylammonium lead iodide counterpart. As borne out by a minimal coarse-grained model, these vibrational properties arise from a large acoustic impedance mismatch between the alternating layers of perovskite sheets and bulky organic cations. Our results inform on thermal transport in highly impedance-mismatched crystal sub-lattices and provide insights towards design of materials that exhibit highly anisotropic thermal dissipation properties.

Two-dimensional, organic-inorganic hybrid perovskites have sustained research interest due to attractive optoelectronic and excitonic properties. Here, Guo et al. systematically investigate coherent acoustic phonon transport versus layer thickness in these materials with strong acoustic impedance mismatch

Thermal management and non-reciprocal control of phonon flow via optomechanics

Engineering phonon transport in physical systems is a subject of interest in the study of materials, and has a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to electric diodes, provide a directional flow of energy. Here, we propose an engineered nanostructured material, in which tunable non-reciprocal phonon transport is achieved through optomechanical coupling. Our scheme relies on breaking time-reversal symmetry by a spatially varying laser drive, which manipulates low-energy acoustic phonons. Furthermore, we take advantage of developments in the manipulation of high-energy phonons through controlled scattering mechanisms, such as using alloys and introducing disorder. These combined approaches allow us to design an acoustic isolator and a thermal diode. Our proposed device will have potential impact in phonon-based information processing, and heat management in low temperatures.

Phonon transport control is important for thermal and non-reciprocal devices. Here, Seif et al. combine heat transport in nanostructures and optomechanics into a platform for manipulating phonons with which they design an acoustic isolator and a thermal diode.

Thermal Conductivity of Graphene-hBN Superlattice Ribbons

Superlattices are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport. Single layer heterostructures of graphene and hexagonal boron nitride have been produced recently with sharp edges and controlled domain sizes. In this study we employ nonequilibrium molecular dynamics simulations to investigate the thermal conductivity of superlattice nanoribbons with equal-sized domains of graphene and hexagonal boron nitride. We analyze the dependence of the conductivity with the domain sizes, and with the total length of the ribbons. We determine that the thermal conductivity reaches a minimum value of 89 W m⁻¹K⁻¹ for ribbons with a superlattice period of 3.43 nm. The effective phonon mean free path is also determined and shows a minimum value of 32 nm for the same superlattice period. Our results also reveal that a crossover from coherent to incoherent phonon transport is present at room temperature for BNC nanoribbons, as the superlattice period becomes comparable to the phonon coherence length. Analyzing phonon populations relative to the smallest superlattice period, we attribute the minimum thermal conductivity to a reduction in the population of flexural phonons when the superlattice period equals 3.43 nm. The ability to manipulate thermal conductivity using superlattice-based two-dimensional materials, such as graphene-hBN nanoribbons, opens up opportunities for application in future nanostructured thermoelectric devices.

Enhancing Thermal Transport in Layered Nanomaterials

A comprehensive rational thermal material design paradigm requires the ability to reduce and enhance the thermal conductivities of nanomaterials. In contrast to the existing ability to reduce the thermal conductivity, methods that allow to enhance heat conduction are currently limited. Enhancing the nanoscale thermal conductivity could bring radical improvements in the performance of electronics, optoelectronics, and photovoltaic systems. Here, we show that enhanced thermal conductivities can be achieved in semiconductor nanostructures by rationally engineering phonon spectral coupling between materials. By embedding a germanium film between silicon layers, we show that its thermal conductivity can be increased by more than 100% at room temperature in contrast to a free standing thin-film. The injection of phonons from the cladding silicon layers creates the observed enhancement in thermal conductivity. We study the key factors underlying the phonon injection mechanism and find that the surface conditions and layer thicknesses play a determining role. The findings presented here will allow for the creation of nanomaterials with an increased thermal conductivity.

Nanostructure design for drastic reduction of thermal conductivity while preserving high electrical conductivity

The design and fabrication of nanostructured materials to control both thermal and electrical properties are demonstrated for high-performance thermoelectric conversion. We have focused on silicon (Si) because it is an environmentally friendly and ubiquitous element. High bulk thermal conductivity of Si limits its potential as a thermoelectric material. The thermal conductivity of Si has been reduced by introducing grains, or wires, yet a further reduction is required while retaining a high electrical conductivity. We have designed two different nanostructures for this purpose. One structure is connected Si nanodots (NDs) with the same crystal orientation. The phonons scattering at the interfaces of these NDs occurred and it depended on the ND size. As a result of phonon scattering, the thermal conductivity of this nanostructured material was below/close to the amorphous limit. The other structure is Si films containing epitaxially grown Ge NDs. The Si layer imparted high electrical conductivity, while the Ge NDs served as phonon scattering bodies reducing thermal conductivity drastically. This work gives a methodology for the independent control of electron and phonon transport using nanostructured materials. This can bring the realization of thermoelectric Si-based materials that are compatible with large scale integrated circuit processing technologies.

Thermal conductivity and air-mediated losses in periodic porous silicon membranes at high temperatures

Heat conduction in silicon can be effectively engineered by means of sub-micrometre porous thin free-standing membranes. Tunable thermal properties make these structures good candidates for integrated heat management units such as waste heat recovery, rectification or efficient heat dissipation. However, possible applications require detailed thermal characterisation at high temperatures which, up to now, has been an experimental challenge. In this work we use the contactless two-laser Raman thermometry to study heat dissipation in periodic porous membranes at high temperatures via lattice conduction and air-mediated losses. We find the reduction of the thermal conductivity and its temperature dependence closely correlated with the structure feature size. On the basis of two-phonon Raman spectra, we attribute this behaviour to diffuse (incoherent) phonon-boundary scattering. Furthermore, we investigate and quantify the heat dissipation via natural air-mediated cooling, which can be tuned by engineering the porosity.Nanostructuring of silicon allows acoustic phonon engineering, but the mechanism of related thermal transport in these structures is not fully understood. Here, the authors study the heat dissipation in silicon membranes with periodic nanoholes and show the importance of incoherent scattering.

Aberration-Corrected Electron Beam Lithography at the One Nanometer Length Scale

Patterning materials efficiently at the smallest length scales is a longstanding challenge in nanotechnology. Electron-beam lithography (EBL) is the primary method for patterning arbitrary features, but EBL has not reliably provided sub-4 nm patterns. The few competing techniques that have achieved this resolution are orders of magnitude slower than EBL. In this work, we employed an aberration-corrected scanning transmission electron microscope for lithography to achieve unprecedented resolution. Here we show aberration-corrected EBL at the one nanometer length scale using poly(methyl methacrylate) (PMMA) and have produced both the smallest isolated feature in any conventional resist (1.7 ± 0.5 nm) and the highest density patterns in PMMA (10.7 nm pitch for negative-tone and 17.5 nm pitch for positive-tone PMMA). We also demonstrate pattern transfer from the resist to semiconductor and metallic materials at the sub-5 nm scale. These results indicate that polymer-based nanofabrication can achieve feature sizes comparable to the Kuhn length of PMMA and ten times smaller than its radius of gyration. Use of aberration-corrected EBL will increase the resolution, speed, and complexity in nanomaterial fabrication.

Heat conduction tuning by wave nature of phonons

The world communicates to our senses of vision, hearing, and touch in the language of waves, because light, sound, and even heat essentially consist of microscopic vibrations of different media. The wave nature of light and sound has been extensively investigated over the past century and is now widely used in modern technology. However, the wave nature of heat has been the subject of mostly theoretical studies because its experimental demonstration, let alone practical use, remains challenging due to its extremely short wavelengths. We show a possibility to use the wave nature of heat for thermal conductivity tuning via spatial short-range order in phononic crystal nanostructures. Our experimental and theoretical results suggest that interference of thermal phonons occurs in strictly periodic nanostructures and slows the propagation of heat. This finding expands the methodology of heat transfer engineering to the wave nature of heat.

Phonon Surface Scattering and Thermal Energy Distribution in Superlattices

Thermal transport at small length scales has attracted significant attention in recent years and various experimental and theoretical methods have been developed to establish the reduced thermal conductivity. The fundamental understanding of how phonons move and the physical mechanisms behind nanoscale thermal transport, however, remains poorly understood. Here we move beyond thermal conductivity calculations and provide a rigorous and comprehensive physical description of thermal phonon transport in superlattices by solving the Boltzmann transport equation and using the Beckman-Kirchhoff surface scattering theory with shadowing to precisely describe phonon-surface interactions. We show that thermal transport in superlattices can be divided in two different heat transport modes having different physical properties at small length scales: layer-restricted and extended heat modes. We study how interface conditions, periodicity, and composition can be used to manipulate the distribution of thermal energy flow among such layer-restricted and extended heat modes. From predicted frequency and mean free path spectra of superlattices, we also investigate the existence of wave effects. The results and insights in this paper advance the fundamental understanding of heat transport in superlattices and the prospects of rationally designing thermal systems with tailored phonon transport properties.

Heat guiding and focusing using ballistic phonon transport in phononic nanostructures

Unlike classical heat diffusion at macroscale, nanoscale heat conduction can occur without energy dissipation because phonons can ballistically travel in straight lines for hundreds of nanometres. Nevertheless, despite recent experimental evidence of such ballistic phonon transport, control over its directionality, and thus its practical use, remains a challenge, as the directions of individual phonons are chaotic. Here, we show a method to control the directionality of ballistic phonon transport using silicon membranes with arrays of holes. First, we demonstrate that the arrays of holes form fluxes of phonons oriented in the same direction. Next, we use these nanostructures as directional sources of ballistic phonons and couple the emitted phonons into nanowires. Finally, we introduce thermal lens nanostructures, in which the emitted phonons converge at the focal point, thus focusing heat into a spot of a few hundred nanometres. These results motivate the concept of ray-like heat manipulations at the nanoscale.

Modelling of thermal transport through a nanocellular polymer foam: toward the generation of a new superinsulating material

Superinsulating materials play a pivotal role in achieving the sustainable development of our modern world by improving energy efficiency, and reducing energy consumption and CO₂ emission. Nanocellular polymer foams have been considered as a promising superinsulating material, but their development is yet to be achieved. The understanding of thermal transport through the nanocellular foam is crucial for developing this superinsulating material. Herein, we report an accurate mathematical model for the first time to quantitatively estimate thermal transport through the nanocellular polymer foam. This is realized by taking into account the phonon scattering effect, the Knudsen effect and the thin-film interference effect in modeling the thermal transport through solid conduction, gas conduction and thermal radiation, respectively. We demonstrate a quantitative relationship between the cellular structure and the equivalent thermal conductivity and present the optimum cellular structure scope for achieving the superinsulating performance. In particular, the significance of thermal radiation in the nanocellular polymer foam is emphasized. This mathematical model offers a very useful tool for deeply understanding thermal transport through the nanocellular polymer foams, and guiding the development of the new generation of superinsulating materials.

Ballistic thermal transport in silicon nanowires

We have experimentally investigated the impact of dimensions and temperature on the thermal conductivity of silicon nanowires fabricated using a top-down approach. Both the width and temperature dependences of thermal conductivity agree with those in the existing literature. The length dependence of thermal conductivity exhibits a transition from semi-ballistic thermal phonon transport at 4 K to fully diffusive transport at room temperature. We additionally calculated the phonon dispersion in these structures in the framework of the theory of elasticity and showed that the thermal conductance increases with width. This agrees with our experimental observations and supports the pertinence of using the modified phonon dispersion at low temperatures.

Investigation of phonon coherence and backscattering using silicon nanomeshes

Phonons can display both wave-like and particle-like behaviour during thermal transport. While thermal transport in silicon nanomeshes has been previously interpreted by phonon wave effects due to interference with periodic structures, as well as phonon particle effects including backscattering, the dominant mechanism responsible for thermal conductivity reductions below classical predictions still remains unclear. Here we isolate the wave-related coherence effects by comparing periodic and aperiodic nanomeshes, and quantify the backscattering effect by comparing variable-pitch nanomeshes. We measure identical (within 6% uncertainty) thermal conductivities for periodic and aperiodic nanomeshes of the same average pitch, and reduced thermal conductivities for nanomeshes with smaller pitches. Ray tracing simulations support the measurement results. We conclude phonon coherence is unimportant for thermal transport in silicon nanomeshes with periodicities of 100 nm and higher and temperatures above 14 K, and phonon backscattering, as manifested in the classical size effect, is responsible for the thermal conductivity reduction.

Anomalous Lattice Dynamics of EuSi_{2} Nanoislands: Role of Interfaces Unveiled

We report a systematic lattice dynamics study of EuSi_{2} films and nanoislands by in situ nuclear inelastic scattering on ^{151}Eu and ab initio theory. The Eu-partial phonon density of states of the nanoislands exhibits anomalous excess of phonon states at low and high energies, not present in the bulk and at the EuSi_{2}(001) surface. We demonstrate that atomic vibrations along the island-substrate interface give rise to phonon states both at low and high energies, while atomic vibrations across the island-island interface result in localized high-energy phonon modes.

Engineered metabarrier as shield from seismic surface waves

Resonant metamaterials have been proposed to reflect or redirect elastic waves at different length scales, ranging from thermal vibrations to seismic excitation. However, for seismic excitation, where energy is mostly carried by surface waves, energy reflection and redirection might lead to harming surrounding regions. Here, we propose a seismic metabarrier able to convert seismic Rayleigh waves into shear bulk waves that propagate away from the soil surface. The metabarrier is realized by burying sub-wavelength resonant structures under the soil surface. Each resonant structure consists of a cylindrical mass suspended by elastomeric springs within a concrete case and can be tuned to the resonance frequency of interest. The design allows controlling seismic waves with wavelengths from 10-to-100 m with meter-sized resonant structures. We develop an analytical model based on effective medium theory able to capture the mode conversion mechanism. The model is used to guide the design of metabarriers for varying soil conditions and validated using finite-element simulations. We investigate the shielding performance of a metabarrier in a scaled experimental model and demonstrate that surface ground motion can be reduced up to 50% in frequency regions below 10 Hz, relevant for the protection of buildings and civil infrastructures.

Two-Dimensional Phononic Crystals: Disorder Matters

The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder.

Nondestructive Complete Mechanical Characterization of Zinc Blende and Wurtzite GaAs Nanowires Using Time-Resolved Pump-Probe Spectroscopy

We have developed and demonstrated an experimental method, based on the picosecond acoustics technique, to perform nondestructive complete mechanical characterization of nanowires, that is, the determination of the complete elasticity tensor. By means of femtosecond pump-probe spectroscopy, coherent acoustic phonons were generated in an ensemble of nanowires and their dynamics was resolved. Specific phonon modes were identified and the detection mechanism was addressed via wavelength dependent experiments. We calculated the exact phonon dispersion relation of the nanowires by fitting the experimentally observed frequencies, thus allowing the extraction of the complete elasticity tensor. The elasticity tensor and the nanowire diameter were determined for zinc blende GaAs nanowires and were found to be in a good agreement with literature data and independent measurements. Finally, we have applied this technique to characterize wurtzite GaAs nanowires, a metastable phase in bulk, for which no experimental values of elastic constants are currently available. Our results agree well with previous first principle calculations. The proposed approach to the complete and nondestructive mechanical characterization of nanowires will allow the efficient mechanical study of new crystal phases emerging in nanostructures, as well as size-dependent properties of nanostructured materials.

Temperature Trapping: Energy-Free Maintenance of Constant Temperatures as Ambient Temperature Gradients Change

It is crucial to maintain constant temperatures in an energy-efficient way. Here we establish a temperature-trapping theory for asymmetric phase-transition materials with thermally responsive thermal conductivities. Then we theoretically introduce and experimentally demonstrate a concept of an energy-free thermostat within ambient temperature gradients. The thermostat is capable of self-maintaining a desired constant temperature without the need of consuming energy even though the environmental temperature gradient varies in a large range. As a model application of the concept, we design and show a different type of thermal cloak that has a constant temperature inside its central region in spite of the changing ambient temperature gradient, which is in sharp contrast to all the existing thermal cloaks. This work has relevance to energy-saving heat preservation, and it provides guidance both for manipulating heat flow without energy consumption and for designing new metamaterials with temperature-responsive or field-responsive parameters in many disciplines such as thermotics, optics, electromagnetics, acoustics, mechanics, electrics, and magnetism.

Femtosecond electron imaging of defect-modulated phonon dynamics

Precise manipulation and control of coherent lattice oscillations via nanostructuring and phonon-wave interference has the potential to significantly impact a broad array of technologies and research areas. Resolving the dynamics of individual phonons in defect-laden materials presents an enormous challenge, however, owing to the interdependent nanoscale and ultrafast spatiotemporal scales. Here we report direct, real-space imaging of the emergence and evolution of acoustic phonons at individual defects in crystalline WSe2 and Ge. Via bright-field imaging with an ultrafast electron microscope, we are able to image the sub-picosecond nucleation and the launch of wavefronts at step edges and resolve dispersion behaviours during propagation and scattering. We discover that the appearance of speed-of-sound (for example, 6 nm ps(-1)) wavefronts are influenced by spatially varying nanoscale strain fields, taking on the appearance of static bend contours during propagation. These observations provide unprecedented insight into the roles played by individual atomic and nanoscale features on acoustic-phonon dynamics.

Simultaneous Thermoelectric Property Measurement and Incoherent Phonon Transport in Holey Silicon

Block copolymer patterned holey silicon (HS) was successfully integrated into a microdevice for simultaneous measurements of Seebeck coefficient, electrical conductivity, and thermal conductivity of the same HS microribbon. These fully integrated HS microdevices provided excellent platforms for the systematic investigation of thermoelectric transport properties tailored by the dimensions of the periodic hole array, that is, neck and pitch size, and the doping concentrations. Specifically, thermoelectric transport properties of HS with a neck size in the range of 16-34 nm and a fixed pitch size of 60 nm were characterized, and a clear neck size dependency was shown in the doping range of 3.1 × 10(18) to 6.5 × 10(19) cm(-3). At 300 K, thermal conductivity as low as 1.8 ± 0.2 W/mK was found in HS with a neck size of 16 nm, while optimized zT values were shown in HS with a neck size of 24 nm. The controllable effects of holey array dimensions and doping concentrations on HS thermoelectric performance could aid in improving the understanding of the phonon scattering process in a holey structure and also in facilitating the development of silicon-based thermoelectric devices.