skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Phononic thermal resistance due to a finite periodic array of nano-scatterers

Abstract

The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetric objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.

Authors:
;  [1]
  1. Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, F-69621 Villeurbanne (France)
Publication Date:
OSTI Identifier:
22597725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 120; Journal Issue: 4; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DIFFRACTION; FOURIER TRANSFORMATION; FREQUENCY DEPENDENCE; HOLES; KAPITZA RESISTANCE; PHONONS; POLARIZATION; ROUGHNESS; SILICON; TEMPERATURE DEPENDENCE; TEMPERATURE RANGE 0013-0065 K; TEMPERATURE RANGE 0065-0273 K; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Trang Nghiêm, T. T., and Chapuis, Pierre-Olivier. Phononic thermal resistance due to a finite periodic array of nano-scatterers. United States: N. p., 2016. Web. doi:10.1063/1.4959803.
Trang Nghiêm, T. T., & Chapuis, Pierre-Olivier. Phononic thermal resistance due to a finite periodic array of nano-scatterers. United States. doi:10.1063/1.4959803.
Trang Nghiêm, T. T., and Chapuis, Pierre-Olivier. 2016. "Phononic thermal resistance due to a finite periodic array of nano-scatterers". United States. doi:10.1063/1.4959803.
@article{osti_22597725,
title = {Phononic thermal resistance due to a finite periodic array of nano-scatterers},
author = {Trang Nghiêm, T. T. and Chapuis, Pierre-Olivier},
abstractNote = {The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetric objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.},
doi = {10.1063/1.4959803},
journal = {Journal of Applied Physics},
number = 4,
volume = 120,
place = {United States},
year = 2016,
month = 7
}
  • The nonlinear response to an external electric field is studied for classical noninteracting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transverse to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking.
  • A one-dimensional Fibonacci phononic crystal and a distributed Bragg reflector were constructed from porous silicon. The structures had the same number of layers and similar acoustic impedance mismatch, and were electrochemically etched in highly boron doped silicon wafers. The thickness of the individual layers in the stacks was approximately 2 μm. Both types of hypersonic band gap structure were studied by direct measurement of the transmittance of longitudinal acoustic waves in the 0.1–2.6 GHz range. Acoustic band gaps deeper than 50 dB were detected in both structures. The experimental results were compared with model calculations employing the transfer matrix method. The acoustic propertiesmore » of periodic and quasi-periodic structures in which half-wave retarding bi-layers do not consist of two quarter-wave retarding layers are discussed. The strong correlation between width and depth of gaps in the transmission spectra is demonstrated. The dominant mechanisms of acoustic losses in porous multilayer structures are discussed. The elastic constants remain proportional over our range of porosity, and hence, the Grüneisen parameter is constant. This simplifies the expression for the porosity dependence of the Akhiezer damping.« less
  • In this study, we propose a theoretical model to compute the effective thermal conductivity of metal and dielectric spherical particle reinforced composites with interfacial thermal resistance. We consider a wide range of filler volume fraction with sizes ranging from nano- to macro-scale. The model, based on the differential effective medium theory, accounts for particle interactions through two sets of volume fraction corrections. The first correction accounts for a finite volume of composite and the second correction introduces a self-crowding factor that allows us to develop an accurate model for particle interaction even for high volume fraction of fillers. The modelmore » is examined to other published models, experiments, and numerical simulations for different types of composites. We observe an excellent agreement between the model and published datasets over a wide range of particle volume fractions and material properties of the composite constituents.« less
  • Highlights: •Formulas for E/M fields radiated by continuous surface polarization distributions. •Non-local effective surface susceptibility model for periodic metafilms. •Generalized reflection and transmission coefficients for an arbitrary metafilm. •Successful treatment of non-planar scatterer arrays and spatial dispersion effects. -- Abstract: A non-local surface susceptibility model for the consistent description of periodic metafilms formed by arbitrarily-shaped, electrically-small, bianisotropic scatterers is developed in this paper. The rigorous scheme is based on the point-dipole approximation technique and is valid for any polarization and propagation direction of an electromagnetic wave impinging upon the metafilm, unlike existing approaches whose applicability is practically confined to verymore » specific cases of incidence. Next, the universal form of the resulting surface susceptibility matrix is employed for the derivation of the generalized Fresnel coefficients for such surfaces, which enable the comprehensive interpretation of several significant, yet relatively unexamined, physical interactions. Essentially, these coefficients include eight distinct terms, corresponding to the co-polarized and cross-polarized reflection and transmission coefficients for the two orthogonal eigenpolarizations of a linearly-polarized incident plane wave. The above formulas are, then, utilized for the prediction of the scattering properties of metafilms with different planar and non-planar resonators, which are characterized via the featured model and two previously reported local ones. Their comparison with numerical simulation outcomes substantiates the merits of the proposed method, reveals important aspects of the underlying physics, and highlights the differences between the various modeling procedures.« less
  • The impulsive acoustic dynamics of soft polymeric surface phononic crystals is investigated here in the hypersonic frequency range by near-IR time-resolved optical diffraction. The acoustic response is analysed by means of wavelet spectral methods and finite element modeling. An unprecedented class of acoustic modes propagating within the polymer surface phononic crystal and confined within 100 nm of the nano-patterned interface is revealed. The present finding opens the path to an alternative paradigm for characterizing the mechanical properties of soft polymers at interfaces and for sensing schemes exploiting polymers as embedding materials.