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Title: Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Abstract

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small-perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity reduction is given by 4η 2k 2 ,where η is the rms roughness and k is the acoustic wave vector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is discovered to be proportional to η 2k 4L 2 , with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of L . This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results imply that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipationmore » due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.« less

Authors:
 [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1370990
Alternate Identifier(s):
OSTI ID: 1181141
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 91; Journal Issue: 13; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; solar (photovoltaic); solar (thermal); solid state lighting; phonons; thermal conductivity; thermoelectric; defects; mechanical behavior; charge transport; spin dynamics; materials and chemistry by design; optics; synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

Maznev, A. A. Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit. United States: N. p., 2015. Web. doi:10.1103/PhysRevB.91.134306.
Maznev, A. A. Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit. United States. doi:10.1103/PhysRevB.91.134306.
Maznev, A. A. Tue . "Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit". United States. doi:10.1103/PhysRevB.91.134306. https://www.osti.gov/servlets/purl/1370990.
@article{osti_1370990,
title = {Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit},
author = {Maznev, A. A.},
abstractNote = {Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small-perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity reduction is given by 4η2k2 ,where η is the rms roughness and k is the acoustic wave vector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is discovered to be proportional to η2k4L2 , with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of L . This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results imply that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.},
doi = {10.1103/PhysRevB.91.134306},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 13,
volume = 91,
place = {United States},
year = {2015},
month = {4}
}

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Cited by: 9 works
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FIG. 1 FIG. 1: Geometry of the problem.

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Works referenced in this record:

An improved Kirchhoff formula for reflection loss at a rough ocean surface at low grazing angles
journal, February 1983

  • Chapman, D. M. F.
  • The Journal of the Acoustical Society of America, Vol. 73, Issue 2
  • DOI: 10.1121/1.388997

Interflake thermal conductance of edge-passivated graphene
journal, December 2011


Lifetimes of Confined Acoustic Phonons in Ultrathin Silicon Membranes
journal, February 2013


Coherent Phonon Heat Conduction in Superlattices
journal, November 2012


Wave scattering from rough surfaces
journal, December 1987


Lifetime of high-order thickness resonances of thin silicon membranes
journal, February 2015


Molecular Dynamics Simulation of Phonon Scattering at Silicon/Germanium Interfaces
journal, July 2010

  • Sun, Lin; Murthy, Jayathi Y.
  • Journal of Heat Transfer, Vol. 132, Issue 10
  • DOI: 10.1115/1.4001912

Phonon scattering at a rough interface between two fcc lattices
journal, January 2009

  • Zhao, Hong; Freund, Jonathan B.
  • Journal of Applied Physics, Vol. 105, Issue 1
  • DOI: 10.1063/1.3054383

Intrinsic to extrinsic phonon lifetime transition in a GaAs–AlAs superlattice
journal, July 2013


Seismic scattering from topographic irregularities
journal, October 1960


Nanoscale thermal transport. II. 2003–2012
journal, March 2014

  • Cahill, David G.; Braun, Paul V.; Chen, Gang
  • Applied Physics Reviews, Vol. 1, Issue 1
  • DOI: 10.1063/1.4832615

Mesoscale modeling of phononic thermal conductivity of porous Si: interplay between porosity, morphology and surface roughness
journal, February 2012

  • Romano, Giuseppe; Di Carlo, Aldo; Grossman, Jeffrey C.
  • Journal of Computational Electronics, Vol. 11, Issue 1
  • DOI: 10.1007/s10825-012-0390-2

Roles of atomic restructuring in interfacial phonon transport
journal, August 2010


Effective boundary conditions for a semi-infinite elastic medium bounded by a rough planar stress-free surface
journal, July 1983


Thermal conductivity of indium arsenide nanowires with wurtzite and zinc blende phases
journal, May 2011


Statistical Model for the Size Effect in Electrical Conduction
journal, March 1967

  • Soffer, Stephen B.
  • Journal of Applied Physics, Vol. 38, Issue 4
  • DOI: 10.1063/1.1709746

Calculation of the lattice thermal conductivity in granular crystals
journal, February 2014

  • Kazan, M.; Volz, S.
  • Journal of Applied Physics, Vol. 115, Issue 7
  • DOI: 10.1063/1.4866362

Reflection of electromagnetic waves from slightly rough surfaces
journal, August 1951

  • Rice, Stephen O.
  • Communications on Pure and Applied Mathematics, Vol. 4, Issue 2-3
  • DOI: 10.1002/cpa.3160040206

Transition between ballistic and diffusive heat transport regimes in silicon materials
journal, September 2012

  • Maldovan, Martin
  • Applied Physics Letters, Vol. 101, Issue 11
  • DOI: 10.1063/1.4752234

Thermal boundary resistance
journal, July 1989


Assessment of phonon boundary scattering from light scattering standpoint
journal, September 2012

  • Jin Lee, Hyun; Sik Jin, Jae; Jae Lee, Bong
  • Journal of Applied Physics, Vol. 112, Issue 6
  • DOI: 10.1063/1.4752871

Room-temperature phonon boundary scattering below the Casimir limit
journal, September 2011


Thermal Transport across a Substrate–Thin-Film Interface: Effects of Film Thickness and Surface Roughness
journal, August 2014


The attenuation of rayleigh surface waves by surface roughness
journal, September 1976


Specular Scattering Probability of Acoustic Phonons in Atomically Flat Interfaces
journal, December 2009


Note on the conduction of heat in crystals
journal, June 1938


Thermal conductivity of bulk and thin-film silicon: A Landauer approach
journal, May 2012

  • Jeong, Changwook; Datta, Supriyo; Lundstrom, Mark
  • Journal of Applied Physics, Vol. 111, Issue 9
  • DOI: 10.1063/1.4710993

Enhancing phonon transmission across a Si/Ge interface by atomic roughness: First-principles study with the Green's function method
journal, December 2012


Thermal boundary conductance across rough interfaces probed by molecular dynamics
journal, February 2014


Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes
journal, July 2010


Surface roughness and thermal conductivity of semiconductor nanowires: Going below the Casimir limit
journal, August 2011


Perturbation analysis of acoustic wave scattering at rough solid-solid interfaces
journal, January 2012

  • Sun, Huarui; Pipe, Kevin P.
  • Journal of Applied Physics, Vol. 111, Issue 2
  • DOI: 10.1063/1.3676250

Spectral Phonon Scattering from Sub-10 nm Surface Roughness Wavelengths in Metal-Assisted Chemically Etched Si Nanowires
journal, March 2013

  • Ghossoub, M. G.; Valavala, K. V.; Seong, M.
  • Nano Letters, Vol. 13, Issue 4
  • DOI: 10.1021/nl3047392

Time-domain dynamic surface response of an anisotropic elastic solid to an impulsive line force
journal, March 1997


Direct Measurements of Surface Scattering in Si Nanosheets Using a Microscale Phonon Spectrometer: Implications for Casimir-Limit Predicted by Ziman Theory
journal, January 2014

  • Hertzberg, Jared B.; Aksit, Mahmut; Otelaja, Obafemi O.
  • Nano Letters, Vol. 14, Issue 2
  • DOI: 10.1021/nl402701a

Effect of surface roughness on the universal thermal conductance
journal, April 2001


    Works referencing / citing this record:

    Probing ballistic thermal conduction in segmented silicon nanowires
    journal, January 2019

    • Anufriev, Roman; Gluchko, Sergei; Volz, Sebastian
    • Nanoscale, Vol. 11, Issue 28
    • DOI: 10.1039/c9nr03863a

    Minimizing Coherent Thermal Conductance by Controlling the Periodicity of Two-Dimensional Phononic Crystals
    journal, July 2019


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