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Title: Reconstruction of phonon relaxation times from systems featuring interfaces with unknown properties

Abstract

We present a method for reconstructing the phonon relaxation-time function $$τ_ω = τ(ω)$$ (including polarization) and associated phonon free-path distribution from thermal spectroscopy data for systems featuring interfaces with unknown properties. Our method does not rely on the effective thermal-conductivity approximation or a particular physical model of the interface behavior. The reconstruction is formulated as an optimization problem in which the relaxation times are determined as functions of frequency by minimizing the discrepancy between the experimentally measured temperature profiles and solutions of the Boltzmann transport equation for the same system. Interface properties such as transmissivities are included as unknowns in the optimization; however, because for the thermal spectroscopy problems considered here the reconstruction is not very sensitive to the interface properties, the transmissivities are only approximately reconstructed and can be considered as byproducts of the calculation whose primary objective is the accurate determination of the relaxation times. The proposed method is validated using synthetic experimental data obtained from Monte Carlo solutions of the Boltzmann transport equation. The method is shown to remain robust in the presence of uncertainty (noise) in the measurement.

Authors:
 [1];  [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)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1470629
Alternate Identifier(s):
OSTI ID: 1438957
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 19; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 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

Forghani, Mojtaba, and Hadjiconstantinou, Nicolas G. Reconstruction of phonon relaxation times from systems featuring interfaces with unknown properties. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.97.195440.
Forghani, Mojtaba, & Hadjiconstantinou, Nicolas G. Reconstruction of phonon relaxation times from systems featuring interfaces with unknown properties. United States. doi:10.1103/PhysRevB.97.195440.
Forghani, Mojtaba, and Hadjiconstantinou, Nicolas G. Thu . "Reconstruction of phonon relaxation times from systems featuring interfaces with unknown properties". United States. doi:10.1103/PhysRevB.97.195440. https://www.osti.gov/servlets/purl/1470629.
@article{osti_1470629,
title = {Reconstruction of phonon relaxation times from systems featuring interfaces with unknown properties},
author = {Forghani, Mojtaba and Hadjiconstantinou, Nicolas G.},
abstractNote = {We present a method for reconstructing the phonon relaxation-time function $τ_ω = τ(ω)$ (including polarization) and associated phonon free-path distribution from thermal spectroscopy data for systems featuring interfaces with unknown properties. Our method does not rely on the effective thermal-conductivity approximation or a particular physical model of the interface behavior. The reconstruction is formulated as an optimization problem in which the relaxation times are determined as functions of frequency by minimizing the discrepancy between the experimentally measured temperature profiles and solutions of the Boltzmann transport equation for the same system. Interface properties such as transmissivities are included as unknowns in the optimization; however, because for the thermal spectroscopy problems considered here the reconstruction is not very sensitive to the interface properties, the transmissivities are only approximately reconstructed and can be considered as byproducts of the calculation whose primary objective is the accurate determination of the relaxation times. The proposed method is validated using synthetic experimental data obtained from Monte Carlo solutions of the Boltzmann transport equation. The method is shown to remain robust in the presence of uncertainty (noise) in the measurement.},
doi = {10.1103/PhysRevB.97.195440},
journal = {Physical Review B},
number = 19,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

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Works referenced in this record:

Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport
journal, November 2012


Experimental metrology to obtain thermal phonon transmission coefficients at solid interfaces
journal, May 2017


Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams
journal, November 2009

  • Siemens, Mark E.; Li, Qing; Yang, Ronggui
  • Nature Materials, Vol. 9, Issue 1
  • DOI: 10.1038/nmat2568

Silicon nanowires as efficient thermoelectric materials
journal, January 2008

  • Boukai, Akram I.; Bunimovich, Yuri; Tahir-Kheli, Jamil
  • Nature, Vol. 451, Issue 7175, p. 168-171
  • DOI: 10.1038/nature06458

Heat Generation and Transport in Nanometer-Scale Transistors
journal, August 2006


High-performance flat-panel solar thermoelectric generators with high thermal concentration
journal, May 2011

  • Kraemer, Daniel; Poudel, Bed; Feng, Hsien-Ping
  • Nature Materials, Vol. 10, Issue 7, p. 532-538
  • DOI: 10.1038/nmat3013

Cross-plane phonon transport in thin films
journal, December 2010

  • Sellan, D. P.; Turney, J. E.; McGaughey, A. J. H.
  • Journal of Applied Physics, Vol. 108, Issue 11
  • DOI: 10.1063/1.3517158

Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
journal, August 2011


The Transport of heat Between Dissimilar Solids at low Temperatures
journal, March 1959

  • Little, W. A.
  • Canadian Journal of Physics, Vol. 37, Issue 3
  • DOI: 10.1139/p59-037

Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
journal, September 2013

  • Collins, Kimberlee C.; Maznev, Alexei A.; Tian, Zhiting
  • Journal of Applied Physics, Vol. 114, Issue 10
  • DOI: 10.1063/1.4820572

Heat transport in silicon from first-principles calculations
journal, August 2011


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

Thermal Conductivity of Ge and Ge–Si Core–Shell Nanowires in the Phonon Confinement Regime
journal, December 2011

  • Wingert, Matthew C.; Chen, Zack C. Y.; Dechaumphai, Edward
  • Nano Letters, Vol. 11, Issue 12
  • DOI: 10.1021/nl203356h

Heat transport in thin dielectric films
journal, March 1997

  • Lee, S. -M.; Cahill, David G.
  • Journal of Applied Physics, Vol. 81, Issue 6
  • DOI: 10.1063/1.363923

Enhanced thermoelectric performance of rough silicon nanowires
journal, January 2008

  • Hochbaum, Allon I.; Chen, Renkun; Delgado, Raul Diaz
  • Nature, Vol. 451, Issue 7175, p. 163-167
  • DOI: 10.1038/nature06381

Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements
journal, August 2014


Heat Transfer in Thermoelectric Materials and Devices
journal, May 2013

  • Tian, Zhiting; Lee, Sangyeop; Chen, Gang
  • Journal of Heat Transfer, Vol. 135, Issue 6
  • DOI: 10.1115/1.4023585

Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation
journal, October 2016

  • Forghani, Mojtaba; Hadjiconstantinou, Nicolas G.; Péraud, Jean-Philippe M.
  • Physical Review B, Vol. 94, Issue 15
  • DOI: 10.1103/PhysRevB.94.155439

Dispersion Relations for Phonons in Aluminum at 80 and 300°K
journal, May 1966


Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations
journal, November 2011


Thermal boundary resistance
journal, July 1989


Spectral mapping of thermal conductivity through nanoscale ballistic transport
journal, June 2015

  • Hu, Yongjie; Zeng, Lingping; Minnich, Austin J.
  • Nature Nanotechnology, Vol. 10, Issue 8
  • DOI: 10.1038/nnano.2015.109

Reduction of thermal conductivity in phononic nanomesh structures
journal, July 2010

  • Yu, Jen-Kan; Mitrovic, Slobodan; Tham, Douglas
  • Nature Nanotechnology, Vol. 5, Issue 10
  • DOI: 10.1038/nnano.2010.149

High-performance bulk thermoelectrics with all-scale hierarchical architectures
journal, September 2012

  • Biswas, Kanishka; He, Jiaqing; Blum, Ivan D.
  • Nature, Vol. 489, Issue 7416, p. 414-418
  • DOI: 10.1038/nature11439

An alternative approach to efficient simulation of micro/nanoscale phonon transport
journal, October 2012

  • Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
  • Applied Physics Letters, Vol. 101, Issue 15
  • DOI: 10.1063/1.4757607

Elastic modulus and in-plane thermal diffusivity measurements in thin polyimide films using symmetry-selective real-time impulsive stimulated thermal scattering
journal, May 1994

  • Rogers, J. A.; Yang, Y.; Nelson, K. A.
  • Applied Physics A Solids and Surfaces, Vol. 58, Issue 5
  • DOI: 10.1007/BF00332448

Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics
journal, February 2008

  • Henry, Asegun S.; Chen, Gang
  • Journal of Computational and Theoretical Nanoscience, Vol. 5, Issue 2
  • DOI: 10.1166/jctn.2008.2454

Phonon Dynamics at Surfaces and Interfaces and Its Implications in Energy Transport in Nanostructured Materials—An opinion Paper
journal, April 2015


A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency
journal, March 2015

  • Hoogeboom-Pot, Kathleen M.; Hernandez-Charpak, Jorge N.; Gu, Xiaokun
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 16
  • DOI: 10.1073/pnas.1503449112

Thermometry and Thermal Transport in Micro/Nanoscale Solid-State Devices and Structures
journal, December 2001

  • Cahill, David G.; Goodson, Kenneth; Majumdar, Arunava
  • Journal of Heat Transfer, Vol. 124, Issue 2
  • DOI: 10.1115/1.1454111

Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation
journal, December 2011


A Simplex Method for Function Minimization
journal, January 1965


Adjoint-based deviational Monte Carlo methods for phonon transport calculations
journal, June 2015


Onset of nondiffusive phonon transport in transient thermal grating decay
journal, November 2011


Monte Carlo Methods for Solving the Boltzmann Transport Equation
journal, January 2014


Nanoscale thermal transport
journal, January 2003

  • Cahill, David G.; Ford, Wayne K.; Goodson, Kenneth E.
  • Journal of Applied Physics, Vol. 93, Issue 2, p. 793-818
  • DOI: 10.1063/1.1524305