Thermal transport across interfaces can play a critical role in nanosystems for thermal management and thermal energy conversion. Here, we show the dependence of the thermal boundary conductance (G) of the interface between a 70-nm Al transducer and a Si substrate on the size of a laser pump diameter (D) in the time-domain thermoreflectance (TDTR) experiments at room temperature. For D ≥ 30 μm, G approaches to a constant where diffusion dominates the heat transfer processes. When D decreases from 30 μm to 3.65 μm, G decreases from 240 to 170 MW/m2K due to the increasing nonlocal effects from nondiffusive heat transport. This finding is vital to our understanding of the thermal boundary conductance: it depends not only on inherent interfacial conditions but also on external heating conditions, which makes the accurate measurements and theoretical predictions of thermal transport across interfaces in micro/nanosystems more challenging.

References

References
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.
,
93
(
1
), p.
011305
.10.1063/1.1524305
2.
Cahill
,
D. G.
,
Braun
,
P. V.
,
Chen
,
G.
,
Clarke
,
D. R.
,
Fan
,
S. H.
,
Goodson
,
K. E.
,
Keblinski
,
P.
,
King
,
W. P.
,
Mahan
,
G. D.
,
Majumdar
,
A.
,
Maris
,
H. J.
,
Phillpot
,
S. R.
,
Pop
,
E.
, and
Shi
,
L.
,
2014
, “
Nanoscale Thermal Transport. II. 2003-2012
,”
Appl. Phys. Rev.
,
93
(
2
), pp.
794
817
.
3.
Ziman
,
J. M.
,
1960
,
Electrons and Phonons: The Theory of Transport Phenomena in Solids
,
Oxford University Press
,
New York
.
4.
Hopkins
,
P. E.
,
2013
, “
Thermal Transport Across Solid Interfaces With Nanoscale Imperfections: Effects of Roughness, Disorder, Dislocations, and Bonding on Thermal Boundary Conductance
,”
ISRN Mech. Eng.
,
2013
, p.
682586
.10.1155/2013/682586
5.
Swartz
,
E. T.
, and
Pohl
,
R. O.
,
1989
, “
Thermal-Boundary Resistance
,”
Rev. Mod. Phys.
,
61
(
3
), pp.
605
668
.10.1103/RevModPhys.61.605
6.
Chen
,
G.
, and
Zeng
,
T. F.
,
2001
, “
Nonequilibrium Phonon and Electron Transport in Heterostructures and Superlattices
,”
Microscale Thermophys. Eng.
,
5
(
2
), pp.
71
88
.
7.
Khalatnikov
,
I. M.
,
1952
, “
Teploobmen Mezhdu Tverdym Telom I Geliem-Ii
,”
Sov. Phys. JETP (Zh. Eksperimentalnoi I Teor. Fiz.)
,
22
(
6
), pp.
687
704
.
8.
Prasher
,
R. S.
, and
Phelan
,
P. E.
,
2001
, “
A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance
,”
ASME J. Heat Transfer
,
123
(
6
), pp.
105
112
.10.1115/1.1403455
9.
Loh
,
G. C.
,
Tay
,
B. K.
, and
Teo
,
E. H. T.
,
2010
, “
Flux-Mediated Diffuse Mismatch Model
,”
Appl. Phys. Lett.
,
97
(
12
), p.
121917
.10.1063/1.3491210
10.
Hopkins
,
P. E.
, and
Norris
,
P. M.
,
2007
, “
Effects of Joint Vibrational States on Thermal Boundary Conductance
,”
Nanoscale Microscale Thermophys. Eng.
,
11
(
3–4
), pp.
247
257
.10.1080/15567260701715297
11.
Beechem
,
T.
, and
Hopkins
,
P. E.
,
2009
, “
Predictions of Thermal Boundary Conductance for Systems of Disordered Solids and Interfaces
,”
J. Appl. Phys.
,
106
(
12
), p.
124301
.10.1063/1.3267496
12.
Le
,
N. Q.
,
Duda
,
J. C.
,
English
,
T. S.
,
Hopkins
,
P. E.
,
Beechem
,
T. E.
, and
Norris
,
P. M.
,
2012
, “
Strategies for Tuning Phonon Transport in Multilayered Structures Using a Mismatch-Based Particle Model
,”
J. Appl. Phys.
,
111
(
8
), p.
084310
.10.1063/1.4704681
13.
Singh
,
D.
,
Murthy
,
J. Y.
, and
Fisher
,
T. S.
,
2011
, “
Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces
,”
ASME J. Heat Transfer
,
133
(
12
), p.
122401
.10.1115/1.4004429
14.
Huang
,
Z.
,
Fisher
,
T.
, and
Murthy
,
J.
,
2011
, “
An Atomistic Study of Thermal Conductance Across a Metal-Graphene Nanoribbon Interface
,”
J. Appl. Phys.
,
109
(
7
), p.
074305
.10.1063/1.3556454
15.
Tian
,
Z. T.
,
Esfarjani
,
K.
, and
Chen
,
G.
,
2012
, “
Enhancing Phonon Transmission Across a Si/Ge Interface by Atomic Roughness: First-Principles Study With the Green's Function Method
,”
Phys. Rev. B
,
86
(
23
), p.
235304
.10.1103/PhysRevB.86.235304
16.
Landry
,
E. S.
, and
Mcgaughey
,
A. J. H.
,
2009
, “
Thermal Boundary Resistance Predictions From Molecular Dynamics Simulations and Theoretical Calculations
,”
Phys. Rev. B
,
80
(
16
), p.
165304
.10.1103/PhysRevB.80.165304
17.
Swartz
,
E. T.
, and
Pohl
,
R. O.
,
1987
, “
Thermal-Resistance at Interfaces
,”
Appl. Phys. Lett.
,
51
(
26
), pp.
2200
2202
.10.1063/1.98939
18.
Li
,
B. C.
,
Roger
,
J. P.
,
Pottier
,
L.
, and
Fournier
,
D.
,
1999
, “
Complete Thermal Characterization of Film-on-Substrate System by Modulated Thermoreflectance Microscopy and Multiparameter Fitting
,”
J. Appl. Phys.
,
86
(
9
), pp.
5314
5316
.10.1063/1.371520
19.
Lee
,
S. M.
, and
Cahill
,
D. G.
,
1997
, “
Heat Transport in Thin Dielectric Films
,”
J. Appl. Phys.
,
81
(
6
), pp.
2590
2595
.10.1063/1.363923
20.
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
,
127
(
3
), pp.
315
322
.10.1115/1.1857944
21.
Chen
,
G.
,
2005
,
Nanoscale Energy Transport and Conversion
,
Oxford University Press
,
New York
.
22.
Mcconnell
,
A. D.
,
Uma
,
S.
, and
Goodson
,
K. E.
,
2005
, “
Thermal Conduction in Silicon Micro and Nanostructures
,”
Annu. Rev. Heat Transfer
,
14
, pp.
129
168
.10.1615/AnnualRevHeatTransfer.v14.120
23.
Minnich
,
A. J.
,
Dresselhaus
,
M. S.
,
Ren
,
Z. F.
, and
Chen
,
G.
,
2009
, “
Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects
,”
Energy Environ. Sci.
,
2
(
5
), pp.
466
479
.10.1039/b822664b
24.
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
,
124
(
2
), pp.
223
241
.10.1115/1.1454111
25.
Brites
,
C. D. S.
,
Lima
,
P. P.
,
Silva
,
N. J. O.
,
Millan
,
A.
,
Amaral
,
V. S.
,
Palacio
,
F.
, and
Carlos
,
L. D.
,
2012
, “
Thermometry at the Nanoscale
,”
Nanoscale
,
4
(
16
), pp.
4799
4829
.10.1039/c2nr30663h
26.
Cattaneo
,
C.
,
1958
, “
Sur Une Forme De Lequation De La Chaleur Eliminant Le Paradoxe Dune Propagation Instantanee
,”
C. R. Hebd. Seances Acad. Sci.
,
247
(
4
), pp.
431
433
.
27.
Vernotte
,
P.
,
1958
, “
Les Paradoxes De La Theorie Continue De Lequation De La Chaleur
,”
C. R. Hebd. Seances Acad. Sci.
,
246
(
22
), pp.
3154
3155
.
28.
Guyer
,
R. A.
, and
Krumhansl
,
J. A.
,
1966
, “
Solution of Linearized Phonon Boltzmann Equation
,”
Phys. Rev.
,
148
(
2
), pp.
766
778
.10.1103/PhysRev.148.766
29.
Cimmelli
,
V. A.
,
Sellitto
,
A.
, and
Jou
,
D.
,
2010
, “
Nonlinear Evolution and Stability of the Heat Flow in Nanosystems: Beyond Linear Phonon Hydrodynamics
,”
Phys. Rev. B
,
82
(
18
), p.
184302
.10.1103/PhysRevB.82.184302
30.
Majumdar
,
A.
,
1993
, “
Microscale Heat-Conduction in Dielectric Thin-Films
,”
ASME J. Heat Transfer
,
115
(
1
), pp.
7
16
.10.1115/1.2910673
31.
Tamma
,
K. K.
, and
Zhou
,
X. M.
,
1998
, “
Macroscale and Microscale Thermal Transport and Thermo-Mechanical Interactions: Some Noteworthy Perspectives
,”
J. Therm. Stresses
,
21
(
3–4
), pp.
405
449
.10.1080/01495739808956154
32.
Chen
,
G.
,
2001
, “
Ballistic-Diffusive Heat-Conduction Equations
,”
Phys. Rev. Lett.
,
86
(
11
), pp.
2297
2300
.10.1103/PhysRevLett.86.2297
33.
Tzou
,
D. Y.
,
2011
, “
Nonlocal Behavior in Phonon Transport
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
475
481
.10.1016/j.ijheatmasstransfer.2010.09.022
34.
Wang
,
H. D.
,
Cao
,
B. Y.
, and
Guo
,
Z. Y.
,
2012
, “
Non-Fourier Heat Conduction in Carbon Nanotubes
,”
ASME J. Heat Transfer
,
134
(
5
), p.
051004
.10.1115/1.4005634
35.
Wang
,
M.
, and
Guo
,
Z. Y.
,
2010
, “
Understanding of Temperature and Size Dependences of Effective Thermal Conductivity of Nanotubes
,”
Phys. Lett. A
,
374
(
42
), pp.
4312
4315
.10.1016/j.physleta.2010.08.058
36.
Wang
,
M. R.
,
Yang
,
N.
, and
Guo
,
Z. Y.
,
2011
, “
Non-Fourier Heat Conductions in Nanomaterials
,”
J. Appl. Phys.
,
110
(
6
), p.
064310
.10.1063/1.3634078
37.
Wilson
,
R. B.
,
Feser
,
J. P.
,
Hohensee
,
G. T.
, and
Cahill
,
D. G.
,
2013
, “
Two-Channel Model for Nonequilibrium Thermal Transport in Pump-Probe Experiments
,”
Phys. Rev. B
,
88
(
14
), p.
144305
.10.1103/PhysRevB.88.144305
38.
Liang
,
L. H.
,
Wei
,
Y. G.
, and
Li
,
B. W.
,
2008
, “
Size-Dependent Interface Phonon Transmission and Thermal Conductivity of Nanolaminates
,”
J. Appl. Phys.
,
103
(
8
), p.
084314
.10.1063/1.2910828
39.
Regner
,
K. T.
,
Mcgaughey
,
A. J. H.
, and
Malen
,
J. A.
,
2014
, “
Analytical Interpretation of Nondiffusive Phonon Transport in Thermoreflectance Thermal Conductivity Measurements
,”
Phys. Rev. B
,
90
(
6
), p.
064302
.10.1103/PhysRevB.90.064302
40.
Wilson
,
R. B.
, and
Cahill
,
D. G.
,
2014
, “
Anisotropic Failure of Fourier Theory in Time-Domain Thermoreflectance Experiments
,”
Nat. Commun.
,
5
, p.
6075
.10.1038/ncomms6075
41.
Gorham
,
C. S.
,
Hattar
,
K.
,
Cheaito
,
R.
,
Duda
,
J. C.
,
Gaskins
,
J. T.
,
Beechem
,
T. E.
,
Ihlefeld
,
J. F.
,
Biedermann
,
L. B.
,
Piekos
,
E. S.
,
Medlin
,
D. L.
, and
Hopkins
,
P. E.
,
2014
, “
Ion Irradiation of the Native Oxide/Silicon Surface Increases the Thermal Boundary Conductance Across Aluminum/Silicon Interfaces
,”
Phys. Rev. B
,
90
(
2
), p.
024301
.10.1103/PhysRevB.90.024301
42.
Ding
,
D.
,
Chen
,
X.
, and
Minnich
,
A. J.
,
2014
, “
Radial Quasiballistic Transport in Time-Domain Thermoreflectance Studied Using Monte Carlo Simulations
,”
Appl. Phys. Lett.
,
104
(
14
), p.
143104
.10.1063/1.4870811
43.
Ma
,
Y.
,
2014
, “
A Two-Parameter Nondiffusive Heat Conduction Model for Data Analysis in Pump-Probe Experiments
,”
J. Appl. Phys.
,
116
(24), p.
243505
.10.1063/1.4904355
44.
Cahill
,
D. G.
,
2004
, “
Analysis of Heat Flow in Layered Structures for Time-Domain Thermoreflectance
,”
Rev. Sci. Instrum.
,
75
(
12
), pp.
5119
5122
.10.1063/1.1819431
45.
Schmidt
,
A. J.
,
Chen
,
X. Y.
, and
Chen
,
G.
,
2008
, “
Pulse Accumulation, Radial Heat Conduction, and Anisotropic Thermal Conductivity in Pump-Probe Transient Thermoreflectance
,”
Rev. Sci. Instrum.
,
79
(
11
), p.
114902
.10.1063/1.3006335
46.
Guo
,
L.
,
Hodson
,
S. L.
,
Fisher
,
T. S.
, and
Xu
,
X. F.
,
2012
, “
Heat Transfer Across Metal-Dielectric Interfaces During Ultrafast-Laser Heating
,”
ASME J. Heat Transfer
,
134
(
4
), p.
042402
.10.1115/1.4005255
You do not currently have access to this content.