Pump-probe transient thermoreflectance (TTR) techniques are powerful tools for measuring the thermophysical properties of thin films, such as thermal conductivity, Λ, or thermal boundary conductance, G. This paper examines the assumption of one-dimensional heating on, Λ and G, 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
.
You do not currently have access to this content.