Phonon Reflection Research Articles

Influence of specularity factor on heat transport in nanoribbons of different sizes

In this paper, the phonon heat transfer in two-dimensional conductors with different types of phonon reflection from the boundaries is examined. Heat conductors with arbitrary ratios of width W to length L are studied assuming that the mean free path between phonon-phonon collisions is infinite. The integral equations for the angular distribution functions of the incident and reflected phonons at a specific point on the conductor boundary were proposed. To solve these integral equations a new iterative method is proposed. The proposed iterative approach formally corresponds to taking into account subsequent collisions of phonons with the edges of the conductor. It ensures the convergence of the desired solution for any W/L ratio and for any value of the specularity coefficient p. Interpolation formulae are found to describe with sufficient accuracy the solution of the system of integral equations in the entire region of the specularity coefficient p from 0 to 1, and the W/L ratios ranging from 10 to 0.01. These formulae allow the construction of the isolines of the thermal conductance coefficient values, from which it is possible to determine the necessary values of W/L and parameter p to get the desired value of the thermal conductance.

Generalization of interfacial thermal conductance based on interfacial phonon localization

Interfacial energy transport is of great engineering and scientific importance. Traditional theoretical treatment based on phonon reflection and transmission only provides qualitative understanding of the interfacial thermal conductance (G). In the interface region, the material has gradual (covalent) or abrupt (van de Waals) physical structure transition, each transition features interface-region atomic interactions that are different from those of both adjoining sides. This difference makes the interface-region phonons extremely localized. Here, by constructing an “equivalent interfacial medium” (EIM) that accounts for the extremely localized phonon region, G can be described by a universal physical model that is characterized by an “interface characteristic temperature” (Θint) and energy carrier transfer time. The EIM model fits widely reported G ∼ T (T: temperature) data with high accuracy and provides remarkable prediction of G at different temperatures based on 2–3 experimental data points. Under normalized temperature (T/Θint) and interfacial thermal conductance (G/Gmax), all literature data of G can be universally grouped to a single curve. The EIM model provides a solid correlation between G and interfacial structure and is expected to significantly advance the physical understanding and design of interfacial energy transport toward high-efficiency energy conversion, transport, and micro/nanoelectronics.

Effect of boundary roughness on the attenuation of specular phonon reflection in graphene

Effect of boundary roughness on the attenuation of specular phonon reflection in graphene

Unusual heat transfer dependence on boundary scattering in very long narrow conductors

When modeling heat transfer in nanoribbons, an unusually sharp dependence of the heat flux, and, consequently, the thermal conductivity coefficient, on the degree of specularity of phonon reflection from the lateral boundaries was found. From numerical calculations, it followed that the addition of minimally diffuse scattering should lead to an abrupt increase in the thermal resistance of the conductor. Given the importance of selecting optimal thermal parameters in nanotechnology, this short paper provides an analysis of the found dependencies, discusses the physical reasons for this anomalous behavior, and draws conclusions about the importance of achieving the quality of the nanoconductor interface to create thermal contacts with a given or optimal thermal conductivity.

Effective cross-plane thermal conductivity of metal-dielectric multilayers at low temperatures

Heat transfer in layered metal-dielectric structures is considered theoretically based on an analytical solution of the Boltzmann transfer equation for the phonon distribution function. Taking into account the size effect, the problem of effective cross-plane thermal conductivity of structures containing two metal layers is analyzed in detail. If the thickness of the metal layers is less than the phonon mean free path, interlayer heat transfer is carried out predominantly by phonons, and the effective cross-plane thermal conductivity is determined by the reflection of phonons from the metal/dielectric interfaces. In the opposite case of thick metal layers, the effective cross-plane thermal conductivity is determined both by the thermal conductivity of the metal layers and by the thermal resistance of the dielectric layers. The results obtained are generalized to multilayer structures and superlattices.

Thermal transport in kinked nanowires through simulation.

The thermal conductance of nanowires is an oft-explored quantity, but its dependence on the nanowire shape is not completely understood. The behaviour of the conductance is examined as kinks of varying angular intensity are included into nanowires. The effects on thermal transport are evaluated through molecular dynamics simulations, phonon Monte Carlo simulations and classical solutions of the Fourier equation. A detailed look is taken at the nature of heat flux within said systems. The effects of the kink angle are found to be complex, influenced by multiple factors including crystal orientation, details of transport modelling, and the ratio of mean free path to characteristic system lengths. The effect of varying phonon reflection specularity on the heat flux is also examined. It is found that, in general, the flow of heat through systems simulated through phonon Monte Carlo methods is concentrated into a channel smaller than the wire dimensions, while this is not the case in the classical solutions of the Fourier model.

Phonon interference effects in graphene nanomesh

Graphene nanomesh (GNM) is a single-layer graphene material that has a periodic distribution of nanoscale pores. GNM shows great potential applications in various fields such as thermoelectric energy conversion, energy storage, and field-effect transistors. In this study we utilize non-equilibrium molecular dynamics and lattice dynamics method to investigate the thermal transport mechanism of GNM. The thermal conductivity of GNM is mainly affected by the number of nanoscale pores and their horizontal and vertical spacing. Our study finds that as the number of nanoscale pores increases, the thermal conductivity of GNM decreases significantly. Additionally, the increase of the number of nanoscale pores causes phonon branch to be folded and confined, which results in a flatter dispersion curve, wider bandgap, and slower phonon group velocity. Moreover, the horizontal and vertical spacing of the nanoscale pores jointly affect the thermal transport process of GNM. When the horizontal spacing is small, the thermal conductivity of GNM decreases monotonically with the increase of vertical spacing, and increases monotonically with an increase of horizontal spacing. However, as the horizontal spacing increases, the interference effect caused jointly by phonon reflection and superposition leads to significant fluctuations in thermal conductivity. The analysis of the spectral heat flow, density of states, participation rate, and group velocity of GNM indicate that the variation in vertical spacing leads to different phonon contributions to heat flow, resulting in fluctuations in the thermal conductivity of GNM. These findings could serve as a reference for controlling the thermal transport of graphene nanomesh, and are of great significance in regulating the thermal conductivity and designing nanoscale pores in GNM.

Impacts of various interfacial nanostructures on spectral phonon thermal boundary conductance

Nanoengineering of interfaces has become an effective way to tune the thermal boundary conductance (TBC) of heterostructures. However, the same nanostructure design can have opposite impacts on TBCs for different systems. To provide a clue toward a unified explanation, in this work, we directly and explicitly reveal the impacts of nanostructures on mode-dependent phonon TBC contributions. We study four representative types of nanostructures, i.e., (1) an intermediate layer, (2) interfacial interlaced teeth, (3) interfacial atomic mixing, and (4) interfacial atomic defects on two example heterostructures: 28Si/Ge and 6Si/Ge, which have moderate and large phonon frequency mismatches, respectively. We find that most of these nanostructures reduce the TBC of 28Si/Ge while increasing the TBC of 6Si/Ge. Each nanostructure is found to have two competing impacts on an interface—one tends to increase TBC while the other tends to decrease TBC. For example, adding an intermediate layer provides a phonon bridging effect, which tends to increase both elastic and inelastic phonon transmission, but it adds one more interface and, thus, more phonon reflection. As a result, an interlayer decreases the TBC of the 28Si/Ge interface by decreasing the inelastic transmission while increasing both elastic and inelastic transmissions of the 6Si/Ge interface. Other nanostructures with atomic disorder can increase transmission by increasing the contact area but can also decrease transmission by phonon-disorder backscattering. This work unveils the fundamental thermal transport physics across interfaces with nanostructures and sheds light on future interface nanoengineering for electronic devices such as high-power transistors, photodiodes, and supercomputing architectures.

Heat dissipation in partially perforated phononic nano-membranes with periodicities below 100 nm

Understanding how thermal-phonon paths can be shaped is key for controlling heat dissipation at the nanoscale. Thermophononic crystals are periodic porous nanostructures with thermal conductivity deviating from effective medium theory, which is possible if the characteristic sizes are of the order of phonon mean free paths and/or if phonons are forced to flow in privileged directions. We investigate suspended silicon nanomembranes with a periodic array of partially perforated holes of original paraboloid shape, with all characteristic lengths below 100 nm. Results from scanning thermal microscopy, a thermal sensing technique derived from atomic force microscopy, indicate that partial perforation of the membranes impacts heat conduction moderately, with the holey crystals showing a thermal conductivity reduction by a factor 6 in comparison to the bulk and a factor 2.5 in comparison to the non-perforated membrane. The impact of the phononic shapes is analyzed in light of a complementary Monte Carlo ray-tracing estimate of the effective phonon mean free paths that include multiple phonon reflection and highlights phonon backscattering.

Investigation on the Phonon Focusing, Polaritons and Reflection of Gan with Lattice Dynamics Theory

Investigation on the Phonon Focusing, Polaritons and Reflection of Gan with Lattice Dynamics Theory

The influence of phonon boundary scattering on the thermal conductivity of a two-dimensional noninteractive phonon system of nanosized structures

One of the problems that arise when studying the thermal conductivity of low-dimensional phonon systems at low temperatures is the appearance of differences in expressions for the thermal conductivity as a function of sample size, as well as the appearance of unusual dependences of heat fluxes on temperature gradients. For example, in the generally accepted Casimir – Zaiman model, it is assumed that a linear temperature gradient is created on the lateral surface by external sources. Moreover, the Casimir model requires two conditions at the border. This is a diffuse reflection in which the phonon is reflected with an isotropic angular distribution function. The second condition is the presence of redistribution of phonons by energy, so that the distribution of reflected phonons corresponds to the radiation of an absolutely black body - that is, the reflection of phonons must be inelastic. And if the first condition can be achieved, for example, by boundaries with a certain degree of roughness, the second condition can be achieved only in the presence of thermal contact between the side edges of the sample and the thermal medium at a certain temperature distribution. In the case of thermally insulated sample boundaries (for example, when the sample is in vacuum) or at least with imperfect thermal contact, the fulfillment of the second condition is practically impossible.In this paper, we consider the problem of thermal conductivity of two-dimensional nanostructures - nanobands - in the temperature range, when the interaction between phonons can be neglected. In this ballistic mode, heat fluxes can be limited only by the interaction of phonons with the sample boundaries. A number of types of interaction of phonons with the boundaries of two-dimensional samples are considered: absorption at the boundary, finite number of reflections, absorption inside the sample on defects, impurities, etc. Explicit expressions of thermal conductivity in these cases are derived. Interpolation relations are obtained, which generalize the existing expressions of thermal conductivity in the case of mirror reflection and reflection with losses.

Annealing-based manipulation of thermal phonon transport from light-emitting diodes to graphene

We demonstrate that the thermal boundary conductivity (TBC) between graphene and GaN-based light-emitting diodes (LEDs) can be manipulated through thermal annealing, which is verified by measuring the acoustic phonons after reflection at the interface. Thermal annealing affects the interfacial morphology as evaluated by both the Raman spectra and the spatial profile of the graphene wrinkles in atomic force microscopy. By tracing the phase of ultrafast acoustic oscillations on the basis of the pump-probe scheme, we extract the phonon reflection coefficient at the interface as a function of annealing temperatures up to 400 °C. Specifically, the phase shift of transient phononic oscillations at the graphene/LED interface conveys the photoelastic response during the phonon transfer process and can be used for extracting the interfacial coupling rate, which is strongly enhanced around ≈200°C. By incorporating the heat capacity and the interfacial coupling constants into TBC, along with analytical modeling based on the phonon reflection coefficients, we show that the TBC increases with the minimized surface roughness of graphene side at 200 °C. This new comprehensive TBC extraction scheme could spark further discussion on improving the heat dissipation of LEDs.

Bidirectional Modulation of Contact Thermal Resistance between Boron Nitride Nanotubes from a Polymer Interlayer.

Enhancing the thermal conductivity of polymer composites could improve their performance in applications requiring fast heat dissipation. While significant progress has been made, a long-standing issue is the contact thermal resistance between the nanofillers, which could play a critical role in the composite thermal properties. Through systematic studies of contact thermal resistance between individual boron nitride nanotubes (BNNTs) of different diameters, with and without a poly(vinylpyrrolidone) (PVP) interlayer, we show that the contact thermal resistance between bare BNNTs is largely determined by reflection of ballistic phonons. Interestingly, it is found that a PVP interlayer can either enhance or reduce the contact thermal resistance, as a result of converting the ballistic phonon dominated transport into diffusion through the PVP layer. These results disclose a previously unrecognized physical picture of thermal transport at the contact between BNNTs, which provides insights into the design of high thermal conductivity BNNT-polymer composites.

Phonon Reflections from Nanostructured Interfaces Imaged by Momentum- Averaged and Resolved Vibrational EELS

Phonon Reflections from Nanostructured Interfaces Imaged by Momentum- Averaged and Resolved Vibrational EELS

Temperature dependence of the optical phonon reflection band in GaP

We explore the effect of temperatures between 80 and 720 K on the energy and linewidth of zone-center transverse (TO) and longitudinal (LO) optical phonons in bulk gallium phosphide (GaP) using Fourier transform infrared ellipsometry from 0.03 to 0.60 eV. We extract the optical phonon parameters of GaP by fitting the ellipsometric angles with the Lowndes–Gervais model, which applies two different broadening parameters to the TO and LO phonons. In GaP, the two-phonon density of states is larger for the decay of TO phonons than for LO phonons. Therefore, we observed a larger TO phonon broadening (compared to the LO phonon) and an asymmetric reststrahlen line shape. This would lead to a negative imaginary part of the dielectric function just above the LO phonon energy but the addition of two-phonon absorption avoids this. We find a temperature-dependent redshift and broadening of TO and LO phonons with increasing temperature due to thermal expansion and anharmonic phonon-phonon scattering, involving three and four phonon decay processes. We also investigate the temperature dependence of the high-frequency dielectric constant. Its variation is explained by thermal expansion and the temperature dependence of the Penn gap.

Phononic Thermal Transport along Graphene Grain Boundaries: A Hidden Vulnerability.

While graphene grain boundaries (GBs) are well characterized experimentally, their influence on transport properties is less understood. As revealed here, phononic thermal transport is vulnerable to GBs even when they are ultra‐narrow and aligned along the temperature gradient direction. Non‐equilibrium molecular dynamics simulations uncover large reductions in the phononic thermal conductivity (κ p) along linear GBs comprising periodically repeating pentagon‐heptagon dislocations. Green's function calculations and spectral energy density analysis indicate that the origin of the κ p reduction is hidden in the periodic GB strain field, which behaves as a reflective diffraction grating with either diffuse or specular phonon reflections, and represents a source of anharmonic phonon–phonon scattering. The non‐monotonic dependence with dislocation density of κ p uncovered here is unaccounted for by the classical Klemens theory. It can help identify GB structures that can best preserve the integrity of the phononic transport.

Investigation of nanoscale heat transport in sub-10 nm carbon nanotube field-effect transistors based on the finite element method

During the past few years, computational approaches and engineering thermal optimizations have been investigated due to its essential role in heat conduction problems related to the next-generation transistors. This paper probes the significance of thermal management applications in carbon nanotube field-effect transistors (CNTFETs). In this work, we refer to the phonon hydrodynamic model for thermal modeling of sub-10nm CNTFETs. Here, we report the nanoscale heat transport within CNTFETs based on the finite-element method (FEM). The excellent agreement between the phonon Boltzmann transport equation (BTE) and our model prediction provides the validity of the present methodology. Our computation techniques suggest that limiting the heat propagation can be ensured by increasing specular phonon reflection inside the channel region. In addition, enhancing the thermal conductivity of CNTs with a small thermal boundary resistance is a feasible way to improve the heat dissipation ability.

An improved smoothed molecular dynamics method with high‐order shape function

AbstractAs an efficient molecular simulation method, the smoothed molecular dynamics (SMD) method introduces background mesh and mapping process into molecular dynamics (MD) procedure to suppress high‐frequency modes, so that a much larger time step than that of MD can be adopted. SMD method can achieve a nice overall accuracy, but local atomic disorders cannot be described very well with original SMD method for smoothing out high‐frequency motions. An improved SMD method with two kinds of high‐order shape functions is proposed. A parameter indicating the smoothing degree in SMD method is also presented to assess the mapping process. The efficiency and the accuracy of the improved method are discussed in detail, and the proposed method is validated with several examples. The results demonstrate obvious improvement in accuracy, and more high‐frequency atomic motions can be captured. When the high‐order SMD method is coupled with the MD method, the non‐physical phonon reflection, which may occur at the interface in the coupling of MD and original SMD method, will decrease remarkably even if no transition scheme is employed.

Specular transmission and diffuse reflection in phonon scattering at grain boundary

It is widely assumed in the literature that the specularity parameters for phonon transmission (forward scattering) and reflection (backward scattering) at a boundary are identical, i.e., the statistical distributions of the transition probabilities between an incident phonon and the range of outgoing phonon modes are the same for both transmission and reflection. However, it is hypothesized by Li and McGaughey that separate specularity parameters are needed to describe the behavior of transmitted and reflected phonons in superlattices and polycrystalline materials correctly. We test this hypothesis by analyzing the mode-resolved specularity parameters computed separately for transmission and reflection processes at a graphene grain boundary. Our results show that backward scattering is considerably more diffuse than forward scattering at most frequencies and polarizations, providing strong evidence for Li and McGaughey's hypothesis, and shed new light on how surfaces and interfaces modify phonon transport within and between domains in nanostructured materials.

Double-humped phonon resonance in doubly resonant vibration systems: Phonon metamaterials analogy with doubly resonant electromagnetic structures

Phononic metamaterial which consists of two (or several) nanolayers separated by a planar defect of atomic-scale thickness is studied, under the assumption that the two-channel phonon interference mechanism of the transverse (cross-plane) heat flux control is dominant at high temperatures. An analytically exactly solvable discrete three-dimensional (3D) model of the multilayer interface between two semi-infinite bcc-lattice crystals is used to simulate phononic metamirror, metafilter, and meta-absorber. Two options of the general model in which two-path phonon interference reveals itself as double-humped resonance in the interface phonon absorption at weak dissipation or as total phonon transmission and total phonon reflection in the lossless limit are considered. An analogy is discussed between doubly resonant dissipative vibration systems and earlier investigated doubly resonant electromagnetic structure exhibiting both types of behavior: induced transparency and superscattering. It is shown that triple-peaked absorption resonance may arise from superposition of two-path phonon interference and Fabry-P\'erot-type interference in the system with triple defect layer. The existence conditions of double-peaked and triple-peaked resonances as well as total interface absorption are analyzed in terms of nondissipative phonon scattering properties and dissipative parameters. Also additional peculiarities relevant to the thermal interface resistance problem are described. The study provides insight into heat management in phononic nanostructures and metamaterials like metamirrors, metafilters, and meta-absorbers.