Nanocomposites offer unique capabilities of controlling thermal transport through the manipulation of various structural aspects of the material. However, measurements of the thermal properties of these composites are often difficult, especially porous nanomaterials. Optical measurements of these properties, although ideal due to the noncontact nature, are challenging due to the large surface variability of nanoporous structures. In this work, we use a vector-based thermal algorithm to solve for the temperature change and heat transfer in which a thin film subjected to a modulated heat source is sandwiched between two thermally conductive pathways. We validate our solution with time domain thermoreflectance measurements on glass slides and extend the thermal conductivity measurements to SiO2-based nanostructured films.

1.
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
.
2.
Benedetto
,
G.
,
Boarino
,
L.
, and
Spangnolo
,
R.
, 1997, “
Evaluation of Thermal Conductivity of Porous Silicon Layers by a Photoacoustic Method
,”
Appl. Phys. A: Mater. Sci. Process.
0947-8396,
64
, pp.
155
159
.
3.
Bernini
,
U.
,
Bernini
,
R.
,
Maddalena
,
P.
,
Massera
,
E.
, and
Rucco
,
P.
, 2005, “
Determination of Thermal Diffusivity of Suspended Porous Silicon Films by Thermal Lens Techniques
,”
Appl. Phys. A: Mater. Sci. Process.
0947-8396,
81
, pp.
399
404
.
4.
Hopkins
,
P. E.
,
Rakich
,
P. T.
,
Olsson
,
R. H.
,
El-kady
,
I. F.
, and
Phinney
,
L. M.
, 2009, “
Origin of Reduction in Phonon Thermal Conductivity of Microporous Solids
,”
Appl. Phys. Lett.
0003-6951,
95
, p.
161902
.
5.
Song
,
D.
, and
Chen
,
G.
, 2004, “
Thermal Conductivity of Periodic Microporous Silicon Films
,”
Appl. Phys. Lett.
0003-6951,
84
, pp.
687
689
.
6.
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
0556-2805,
65
, p.
094205
.
7.
Hopkins
,
P. E.
,
Norris
,
P. M.
,
Phinney
,
L. M.
,
Policastro
,
S. A.
, and
Kelly
,
R. G.
, 2008, “
Thermal Conductivity in Nanoporous Gold Films During Electron-Phonon Nonequilibrium
,”
J. Nanomater.
,
2008
, p.
418050
.
8.
Cahill
,
D. G.
, 1990, “
Thermal Conductivity Measurement From 30 to 750 K: The 3ω Method
,”
Rev. Sci. Instrum.
0034-6748,
61
, pp.
802
808
.
9.
Koh
,
Y. K.
,
Singer
,
S. L.
,
Kim
,
W.
,
Zide
,
J. M. O.
,
Lu
,
H.
,
Cahill
,
D. G.
,
Majumdar
,
A.
, and
Gossard
,
A. C.
, 2009, “
Comparison of the 3ω Method and Time-Domain Thermoreflectance for Measurements of the Cross-Plane Thermal Conductivity of Epitaxial Semiconductors
,”
J. Appl. Phys.
0021-8979,
105
, p.
054303
.
10.
Olson
,
B. W.
,
Graham
,
S.
, and
Chen
,
K.
, 2005, “
A Practical Extension of the 3ω Method to Multilayer Structures
,”
Rev. Sci. Instrum.
0034-6748,
76
, p.
053901
.
11.
Borca-Tasciuc
,
T.
,
Kumar
,
A. R.
, and
Chen
,
G.
, 2001, “
Data Reduction in 3ω Method for Thin-Film Thermal Conductivity Determination
,”
Rev. Sci. Instrum.
0034-6748,
72
, pp.
2139
2147
.
12.
Norris
,
P. M.
,
Caffrey
,
A. P.
,
Stevens
,
R. J.
,
Klopf
,
J. M.
,
Mcleskey
,
J. T.
, and
Smith
,
A. N.
, 2003, “
Femtosecond Pump-Probe Nondestructive Examination of Materials
,”
Rev. Sci. Instrum.
0034-6748,
74
, pp.
400
406
.
13.
Cahill
,
D. G.
, 2004, “
Analysis of Heat Flow in Layered Structures for Time-Domain Thermoreflectance
,”
Rev. Sci. Instrum.
0034-6748,
75
, pp.
5119
5122
.
14.
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
.
15.
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
.
16.
Costescu
,
R. M.
,
Wall
,
M. A.
, and
Cahill
,
D. G.
, 2003, “
Thermal Conductance of Epitaxial Interfaces
,”
Phys. Rev. B
0556-2805,
67
, p.
054302
.
17.
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
.
18.
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
.
19.
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
.
20.
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
.
21.
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
.
22.
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
.
23.
Ge
,
Z.
,
Cahill
,
D. G.
, and
Braun
,
P. V.
, 2006, “
Thermal Conductance of Hydrophilic and Hydrophobic Interfaces
,”
Phys. Rev. Lett.
0031-9007,
96
, p.
186101
.
24.
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
.
25.
Carslaw
,
H. S.
, and
Jaeger
,
J. C.
, 1959,
Conduction of Heat in Solids
, 2nd ed.,
Oxford University Press
,
New York
, Sec. 3.7, pp.
109
112
.
26.
Tong
,
T.
, and
Majumdar
,
A.
, 2006, “
Reexamining the 3-Omega Technique for Thin Film Characterization
,”
Rev. Sci. Instrum.
0034-6748,
77
, p.
104902
.
27.
Hopkins
,
P. E.
,
Serrano
,
J. R.
,
Phinney
,
L. M.
,
Kearney
,
S. P.
,
Grasser
,
T. W.
, and
Harris
,
C. T.
, 2010, “
Criteria for Cross-Plane Dominated Thermal Transport in Multilayer Thin Film Systems During Modulated Laser Heating
,”
ASME J. Heat Transfer
0022-1481,
132
, p.
081302
.
28.
Incropera
,
F.
, and
Dewitt
,
D. P.
, 1996,
Fundamentals of Heat and Mass Transfer
,
Wiley
,
New York
.
29.
Thomsen
,
C.
,
Grahn
,
H. T.
,
Maris
,
H. J.
, and
Tauc
,
J.
, 1986, “
Surface Generation and Detection of Phonons by Picosecond Light Pulses
,”
Phys. Rev. B
0556-2805,
34
, pp.
4129
4138
.
30.
Thomsen
,
C.
,
Strait
,
J.
,
Vardeny
,
Z.
,
Maris
,
H. J.
,
Tauc
,
J.
, and
Hauser
,
J. J.
, 1984, “
Coherent Phonon Generation and Detection by Picosecond Light Pulses
,”
Phys. Rev. Lett.
0031-9007,
53
, pp.
989
992
.
31.
Prevo
,
B. G.
,
Kuncicky
,
D. M.
, and
Velev
,
O. D.
, 2007, “
Engineered Deposition of Coatings From Nano- to Micro-Particles: A Brief Review of Convective Assembly at High Volume Fraction
,”
Colloids Surf., A
0927-7757,
311
, pp.
2
10
.
32.
Paddock
,
C. A.
, and
Eesley
,
G. L.
, 1986, “
Transient Thermoreflectance From Thin Metal Films
,”
J. Appl. Phys.
0021-8979,
60
, pp.
285
290
.
33.
Koh
,
Y. K.
, and
Cahill
,
D. G.
, 2007, “
Frequency Dependence of the Thermal Conductivity of Semiconductor Alloys
,”
Phys. Rev. B
0556-2805,
76
, p.
075207
.
34.
Gundrum
,
B. C.
,
Cahill
,
D. G.
, and
Averback
,
R. S.
, 2005, “
Thermal Conductance of Metal-Metal Interfaces
,”
Phys. Rev. B
0556-2805,
72
, p.
245426
.
35.
Persson
,
A. I.
,
Koh
,
Y. K.
,
Cahill
,
D. G.
,
Samuelson
,
L.
, and
Linke
,
H.
, 2009, “
Thermal Conductance of InAs Nanowire Composites
,”
Nano Lett.
1530-6984,
9
, pp.
4484
4488
.
36.
Franz
,
R.
, and
Wiedemann
,
G.
, 1853, “
Ueber die Warme-Leitungsfahigkeit der matalle
,”
Ann. Phys.
0003-3804,
165
, pp.
497
531
.
37.
Hopkins
,
P. E.
,
Kaehr
,
B.
,
Dunphy
,
D.
, and
Brinker
,
C. J.
, 2011, “
Estimating Density Reduction and Phonon Localization From Optical Thermal Conductivity Measurements of Porous Silica and Aerogel Thin Films
,”
Proceedings of the ASME/JSME Eighth Thermal Engineering Joint Conference
, Honolulu, HI, Paper No. 44137.
38.
Cahill
,
D. G.
, and
Pohl
,
R. O.
, 1987, “
Thermal Conductivity of Amorphous Solids Above the Plateau
,”
Phys. Rev. B
0556-2805,
35
, pp.
4067
4073
.
39.
Bruggeman
,
D. A. G.
, 1935, “
Computation of Different Physical Constants of Heterogeneous Substances. I. Dielectric Constants and Conductivenesses of the Mixing Bodies From Isotropic Substances (Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen)
,”
Ann. Phys.
0003-3804,
416
, pp.
636
664
.
You do not currently have access to this content.