Pump-probe transient thermoreflectance (TTR) techniques are powerful tools for measuring the thermophysical properties of thin films, such as thermal conductivity, , or thermal boundary conductance, . This paper examines the assumption of one-dimensional heating on, and , determination in nanostructures using a pump-probe transient thermoreflectance technique. The traditionally used one-dimensional and axially symmetric cylindrical conduction models for thermal transport are reviewed. To test the assumptions of the thermal models, experimental data from Al films on bulk substrates (Si and glass) are taken with the TTR technique. This analysis is extended to thin film multilayer structures. The results show that at 11 MHz modulation frequency, thermal transport is indeed one dimensional. Error among the various models arises due to pulse accumulation and not accounting for residual heating.
1.
Paddock
, C. A.
, and Eesley
, G. L.
, 1986, “Transient Thermoreflectance From Thin Metal Films
,” J. Appl. Phys.
0021-8979, 60
, pp. 285
–290
.2.
Koh
, Y. K.
, and Cahill
, D. G.
, 2007, “Frequency Dependence of the Thermal Conductivity of Semiconductor Alloys
,” Phys. Rev. B
0163-1829, 76
, p. 075207
.3.
Lyeo
, H. -K.
, Cahill
, D. G.
, Lee
, B. -S.
, and Abelson
, J. R.
, 2006, “Thermal Conductivity of Phase-Change Material Ge2Sb2Te5
,” Appl. Phys. Lett.
0003-6951, 89
, p. 151904
.4.
Schmidt
, A. J.
, Chen
, X.
, and Chen
, G.
, 2008, “Pulse Accumulation, Radial Heat Conduction, and Anisotropic Thermal Conductivity in Pump-Probe Transient Thermoreflectance
,” Rev. Sci. Instrum.
0034-6748, 79
, p. 114902
.5.
Capinski
, W. S.
, Maris
, H. J.
, Ruf
, T.
, Cardona
, M.
, Ploog
, K.
, and Katzer
, D. S.
, 1999, “Thermal-Conductivity Measurements of GaAs/AlAs Superlattices Using a Picosecond Optical Pump-and-Probe Technique
,” Phys. Rev. B
0163-1829, 59
, pp. 8105
–8113
.6.
Chiritescu
, C.
, Cahill
, D. G.
, Nguyen
, N.
, Johnson
, D.
, Bodapati
, A.
, Keblinski
, P.
, and Zschack
, P.
, 2007, “Ultralow Thermal Conductivity in Disordered, Layered WSe2 Crystals
,” Science
0036-8075, 315
, pp. 351
–353
.7.
Costescu
, R. M.
, Cahill
, D. G.
, Fabreguette
, F. H.
, Sechrist
, Z. A.
, and George
, S. M.
, 2004, “Ultra-Low Thermal Conductivity in W/Al2O3 Nanolaminates
,” Science
0036-8075, 303
, pp. 989
–990
.8.
Gundrum
, B. C.
, Cahill
, D. G.
, and Averback
, R. S.
, 2005, “Thermal Conductance of Metal-Metal Interfaces
,” Phys. Rev. B
0163-1829, 72
, p. 245426
.9.
Hopkins
, P. E.
, Norris
, P. M.
, Stevens
, R. J.
, Beechem
, T.
, and Graham
, S.
, 2008, “Influence of Interfacial Mixing on Thermal Boundary Conductance Across a Chromium/Silicon Interface
,” ASME J. Heat Transfer
0022-1481, 130
, p. 062402
.10.
Hopkins
, P. E.
, Stevens
, R. J.
, and Norris
, P. M.
, 2008, “Influence of Inelastic Scattering at Metal-Dielectric Interfaces
,” ASME J. Heat Transfer
0022-1481, 130
, p. 022401
.11.
Stoner
, R. J.
, and Maris
, H. J.
, 1993, “Kapitza Conductance and Heat Flow Between Solids at Temperatures From 50 to 300 K
,” Phys. Rev. B
0163-1829, 48
, pp. 16373
–16387
.12.
Lyeo
, H. -K.
, and Cahill
, D. G.
, 2006, “Thermal Conductance of Interfaces Between Highly Dissimilar Materials
,” Phys. Rev. B
0163-1829, 73
, p. 144301
.13.
Stevens
, R. J.
, Smith
, A. N.
, and Norris
, P. M.
, 2005, “Measurement of Thermal Boundary Conductance of a Series of Metal-Dielectric Interfaces by the Transient Thermoreflectance Technique
,” ASME J. Heat Transfer
0022-1481, 127
, pp. 315
–322
.14.
Schmidt
, A.
, Chiesa
, M.
, Chen
, X.
, and Chen
, G.
, 2008, “An Optical Pump-Probe Technique for Measuring the Thermal Conductivity of Liquids
,” Rev. Sci. Instrum.
0034-6748, 79
, p. 064902
.15.
Palik
, E. D.
, 1985, Handbook of Optical Constants of Solids
, Academic
, Orlando, FL
.16.
Cahill
, D. G.
, 2004, “Analysis of Heat Flow in Layered Structures for Time-Domain Thermoreflectance
,” Rev. Sci. Instrum.
0034-6748, 75
, pp. 5119
–5122
.17.
Carslaw
, H. S.
, and Jaeger
, J. C.
, 1959, “Steady Periodic Temperature in Composite Slabs
,” Conduction of Heat in Solids
, 2nd ed., Oxford University Press
, New York
, pp. 109
–112
.18.
Feldman
, A.
, 1999, “Algorithm for Solutions of the Thermal Diffusion Equation in a Stratified Medium With a Modulated Heating Source
,” High Temp. - High Press.
0018-1544, 31
, pp. 293
–298
.19.
Costescu
, R. M.
, Wall
, M. A.
, and Cahill
, D. G.
, 2003, “Thermal Conductance of Epitaxial Interfaces
,” Phys. Rev. B
0163-1829, 67
, p. 054302
.20.
Chiritescu
, C.
, Cahill
, D. G.
, Heibeman
, C.
, Lin
, Q.
, Mortensen
, C.
, Nguyen
, N. T.
, Johnson
, D.
, Rostek
, R.
, and Bottner
, H.
, 2008, “Low Thermal Conductivity in Nanoscale Layered Materials Synthesized by the Method of Modulated Elemental Reactants
,” J. Appl. Phys.
0021-8979, 104
, p. 033533
.21.
Costescu
, R. M.
, Bullen
, A. J.
, Matamis
, G.
, O’hara
, K. E.
, and Cahill
, D. G.
, 2002, “Thermal Conductivity and Sound Velocities of Hydrogen-Silsequioxane Low-k Dielectrics
,” Phys. Rev. B
0163-1829, 65
, p. 094205
.22.
Koh
, Y. K.
, Cao
, Y.
, Cahill
, D. G.
, and Jena
, D.
, 2009, “Heat-Transport Mechanisms in Superlattices
,” Adv. Funct. Mater.
1616-301X, 19
, pp. 610
–615
.23.
Hopkins
, P. E.
, 2009, “Effects of Electron-Boundary Scattering on Changes in Thermoreflectance in Thin Metal Films Undergoing Intraband Transitions
,” J. Appl. Phys.
0021-8979, 105
, p. 093517
.24.
Ezzahri
, Y.
, Grauby
, S.
, Dilhaire
, S.
, Rampnoux
, J. M.
, and Claeys
, W.
, 2007, “Cross-Plan Si/SiGe Superlattice Acoustic and Thermal Properties Measurement by Picosecond Ultrasonics
,” J. Appl. Phys.
0021-8979, 101
, p. 013705
.25.
Cahill
, D. G.
, Ford
, W. K.
, Goodson
, K. E.
, Mahan
, G. D.
, Majumdar
, A.
, Maris
, H. J.
, Merlin
, R.
, and Phillpot
, S. R.
, 2003, “Nanoscale Thermal Transport
,” J. Appl. Phys.
0021-8979, 93
, pp. 793
–818
.26.
Cahill
, D. G.
, Goodson
, K. E.
, and Majumdar
, A.
, 2002, “Thermometry and Thermal Transport in Micro/Nanoscale Solid-State Devices and Structures
,” ASME J. Heat Transfer
0022-1481, 124
, pp. 223
–241
.27.
Stevens
, R. J.
, Smith
, A. N.
, and Norris
, P. M.
, 2006, “Signal Analysis and Characterization of Experimental Setup for the Transient Thermoreflectance Technique
,” Rev. Sci. Instrum.
0034-6748, 77
, p. 084901
.28.
Schmidt
, A. J.
, 2008, “Optical Characterization of Thermal Transport From the Nanoscale to the Macroscale
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.29.
Schmidt
, A. J.
, Cheaito
, R.
, and Chiesa
, M.
, 2009, “A Frequency-Domain Thermoreflectance Method for the Characterization of Thermal Properties
,” Rev. Sci. Instrum.
0034-6748, 80
, p. 094901
.30.
Lee
, S. -M.
, and Cahill
, D. G.
, 1997, “Heat Transport in Thin Dielectric Films
,” J. Appl. Phys.
0021-8979, 81
, pp. 2590
–2595
.31.
Incropera
, F.
, and Dewitt
, D. P.
, 1996, Fundamentals of Heat and Mass Transfer
, Wiley
, New York
.32.
Norris
, P. M.
, and Hopkins
, P. E.
, 2009, “Examining Interfacial Diffuse Phonon Scattering Through Transient Thermoreflectance Measurements of Thermal Boundary Conductance
,” ASME J. Heat Transfer
0022-1481, 131
, p. 043207
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