We present a new model for predicting thermal boundary conductance in the classical limit. This model takes a different form than those of the traditionally used mismatch theories in the fact that the temperature dependence of thermal boundary conductance is driven by the phononic scattering mechanisms of the materials comprising the interface as opposed to the heat capacities of those materials. The model developed in this work assumes that a phonon on one side of an interface may not scatter at the interface itself but instead scatter with phonons in the adjacent material via the scattering processes intrinsic in the adjacent material. We find that this model is in good agreement with classical molecular dynamics simulations of phonon transport across a Si/Ge interface.

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
(
2
), pp.
793
818
.
2.
Swartz
,
E. T.
, and
Pohl
,
R. O.
, 1989, “
Thermal Boundary Resistance
,”
Rev. Mod. Phys.
0034-6861,
61
(
3
), pp.
605
668
.
3.
Hopkins
,
P. E.
,
Norris
,
P. M.
, and
Stevens
,
R. J.
, 2008, “
Influence of Inelastic Scattering at Metal-Dielectric Interfaces
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
022401
.
4.
Hopkins
,
P. E.
,
Norris
,
P. M.
,
Stevens
,
R. J.
,
Beechem
,
T. E.
, 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
.
5.
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
.
6.
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
0556-2805,
48
(
22
), pp.
16373
16387
.
7.
Costescu
,
R. M.
,
Wall
,
M. A.
, and
Cahill
,
D. G.
, 2003, “
Thermal Conductance of Epitaxial Interfaces
,”
Phys. Rev. B
0556-2805,
67
, p.
054302
.
8.
Cahill
,
D. G.
,
Bullen
,
A.
, and
Lee
,
S. -M.
, 2000, “
Interface Thermal Conductance and the Thermal Conductivity of Multilayer Thin Films
,”
High Temp. - High Press.
0018-1544,
32
, pp.
135
142
.
9.
Costescu
,
R. M.
,
Cahill
,
D. G.
,
Fabreguette
,
F. H.
,
Sechrist
,
Z. A.
, and
George
,
S. M.
, 2004, “
Ultra-Low Thermal Conductivity in W/Al2O2 Nanolaminates
,”
Science
0036-8075,
303
, pp.
989
990
.
10.
Lyeo
,
H. -K.
, and
Cahill
,
D. G.
, 2006, “
Thermal Conductance of Interfaces Between Highly Dissimilar Materials
,”
Phys. Rev. B
0556-2805,
73
, p.
144301
.
11.
Alvarez-Quintana
,
J.
, and
Rodríguez-Viejo
,
J.
, 2008, “
Interfacial Effects on the Thermal Conductivity of a-Ge Thin Films Grown on Si Substrates
,”
J. Appl. Phys.
0021-8979,
104
(
7
), p.
074903
.
12.
Stevens
,
R. J.
,
Zhigilei
,
L. V.
, and
Norris
,
P. M.
, 2007, “
Effects of Temperature and Disorder on Thermal Boundary Conductance at Solid-Solid Interfaces: Nonequilibrium Molecular Dynamics Simulations
,”
Int. J. Heat Mass Transfer
0017-9310,
50
, pp.
3977
3989
.
13.
Landry
,
E. S.
, and
McGaughey
,
A. J. H.
, 2009, “
Thermal Boundary Resistance Predictions From Molecular Dynamics Simulations and Theoretical Calculations
,”
Phys. Rev. B
0556-2805,
80
(
16
), p.
165304
.
14.
Reddy
,
P.
,
Castelino
,
K.
, and
Majumdar
,
A.
, 2005, “
Diffuse Mismatch Model of Thermal Boundary Conductance Using Exact Phonon Dispersion
,”
Appl. Phys. Lett.
0003-6951,
87
, p.
211908
.
15.
Chen
,
Y.
,
Li
,
D.
,
Yang
,
J.
,
Wu
,
Y.
,
Lukes
,
J. R.
, and
Majumdar
,
A.
, 2004, “
Molecular Dynamics Study of the Lattice Thermal Conductivity of Kr/Ar Superlattice Nanowires
,”
Physica B
0921-4526,
349
(
1–4
), pp.
270
280
.
16.
Ong
,
Z. -Y.
, and
Pop
,
E.
, 2010, “
Molecular Dynamics Simulation of Thermal Boundary Conductance Between Carbon Nanotubes and SiO2
,”
Phys. Rev. B
0556-2805,
81
(
15
), p.
155408
.
17.
Salaway
,
R. N.
,
Hopkins
,
P. E.
,
Norris
,
P. M.
, and
Stevens
,
R. J.
, 2008, “
Phonon Contribution to Thermal Boundary Conductance at Metal Interfaces Using Embedded Atom Method Simulations
,”
Int. J. Thermophys.
0195-928X,
29
, pp.
1987
1996
.
18.
Zhang
,
W.
,
Fisher
,
T. S.
, and
Mingo
,
N.
, 2007, “
Simulation of Interfacial Phonon Transport in Si–Ge Heterostructures Using an Atomistic Green’s Function Method
,”
ASME J. Heat Transfer
0022-1481,
129
(
4
), pp.
483
491
.
19.
Schelling
,
P. K.
,
Phillpot
,
S. R.
, and
Keblinski
,
P.
, 2002, “
Phonon Wave-Packet Dynamics at Semiconductor Interfaces by Molecular-Dynamics Simulation
,”
Appl. Phys. Lett.
0003-6951,
80
(
14
), pp.
2484
2486
.
20.
Pettersson
,
S.
, and
Mahan
,
G. D.
, 1990, “
Theory of the Thermal Boundary Resistance Between Dissimilar Lattices
,”
Phys. Rev. B
0556-2805,
42
(
12
), pp.
7386
7390
.
21.
Hopkins
,
P. E.
, 2009, “
Multiple Phonon Processes Contributing to Inelastic Scattering During Thermal Boundary Conductance at Solid Interfaces
,”
J. Appl. Phys.
0021-8979,
106
(
1
), p.
013528
.
22.
Duda
,
J. C.
,
Smoyer
,
J. L.
,
Norris
,
P. M.
, and
Hopkins
,
P. E.
, 2009, “
Extension of the Diffuse Mismatch Model for Thermal Boundary Conductance Between Isotropic and Anisotropic Materials
,”
Appl. Phys. Lett.
0003-6951,
95
, p.
031912
.
23.
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
0022-1481,
123
, pp.
105
112
.
24.
Prasher
,
R.
, 2008, “
Thermal Boundary Resistance and Thermal Conductivity of Multiwalled Carbon Nanotubes
,”
Phys. Rev. B
0556-2805,
77
, p.
075424
.
25.
Beechem
,
T.
,
Graham
,
S.
,
Hopkins
,
P.
, and
Norris
,
P.
, 2007, “
Role of Interface Disorder on Thermal Boundary Conductance Using a Virtual Crystal Approach
,”
Appl. Phys. Lett.
0003-6951,
90
, p.
054104
.
26.
Hopkins
,
P. E.
, and
Norris
,
P. M.
, 2007, “
Effects of Joint Vibrational States on Thermal Boundary Conductance
,”
Nanoscale Microscale Thermophys. Eng.
1556-7265,
11
(
3
), pp.
247
257
.
27.
Hopkins
,
P. E.
, and
Norris
,
P. M.
, 2009, “
Relative Contributions of Inelastic and Elastic Diffuse Phonon Scattering to Thermal Boundary Conductance Across Solid Interfaces
,”
ASME J. Heat Transfer
0022-1481,
131
(
2
), p.
022402
.
28.
Beechem
,
T.
, and
Hopkins
,
P. E.
, 2009, “
Predictions of Thermal Boundary Conductance for Systems of Disordered Solids and Interfaces
,”
J. Appl. Phys.
0021-8979,
106
, p.
124301
.
29.
Duda
,
J. C.
,
Hopkins
,
P. E.
,
Beechem
,
T. E.
,
Smoyer
,
J. L.
, and
Norris
,
P. M.
, 2010, “
Inelastic Phonon Interactions at Solid-Graphite Interfaces
,”
Superlattices Microstruct.
0749-6036,
47
, pp.
550
555
.
30.
Phelan
,
P. E.
, 1998, “
Application of Diffuse Mismatch Theory to the Prediction of Thermal Boundary Resistance in Thin-Film High-Tc Superconductors
,”
ASME J. Heat Transfer
0022-1481,
120
, pp.
37
43
.
31.
Kosevich
,
Y. A.
, 1995, “
Fluctuation Subharmonic and Multiharmonic Phonon Transmission and Kapitza Conductance Between Crystals With Very Different Vibrational Spectra
,”
Phys. Rev. B
0556-2805,
52
(
2
), pp.
1017
1024
.
32.
Little
,
W. A.
, 1959, “
The Transport of Heat Between Dissimilar Solids at Low Temperatures
,”
Can. J. Phys.
0008-4204,
37
(
3
), pp.
334
349
.
33.
Norris
,
P. M.
, and
Hopkins
,
P. E.
, 2009, “
Examining Interfacial Diffuse Phonon Scattering Through Transient Thermoreflectance Measurements of Thermal Boundary Resistance
,”
ASME J. Heat Transfer
0022-1481,
131
, p.
043207
.
34.
Duda
,
J. C.
,
Hopkins
,
P. E.
,
Smoyer
,
J. L.
,
Bauer
,
M. L.
,
English
,
T. E.
,
Saltonstall
,
C. B.
, and
Norris
,
P. M.
, 2010, “
On the Assumption of Detailed Balance in Prediction of Diffusive Transmission Probability During Interfacial Transport
,”
Nanoscale Microscale Thermophys. Eng.
1556-7265,
14
(
1
), pp.
21
33
.
35.
Cahill
,
D. G.
,
Watson
,
S. K.
, and
Pohl
,
R. O.
, 1992, “
Lower Limit to the Thermal Conductivity of Disordered Crystals
,”
Phys. Rev. B
0556-2805,
46
(
10
), pp.
6131
6140
.
36.
Hopkins
,
P. E.
, and
Piekos
,
E. S.
, 2009, “
Lower Limit to Phonon Thermal Conductivity of Disordered, Layered Solids
,”
Appl. Phys. Lett.
0003-6951,
94
, p.
181901
.
37.
Roberts
,
N. A.
, and
Walker
,
D. G.
, 2010, “
Phonon Wave-Packet Simulations of Ar/Kr Interfaces for Thermal Rectification
,”
J. Appl. Phys.
0021-8979,
108
(
12
), p.
123515
.
38.
Duda
,
J. C.
,
Beechem
,
T. E.
,
Smoyer
,
J. L.
,
Norris
,
P. M.
, and
Hopkins
,
P. E.
, 2010, “
Role of Dispersion on Phononic Thermal Boundary Conductance
,”
J. Appl. Phys.
0021-8979,
108
, p.
073515
.
39.
Landry
,
E. S.
, 2009, “
Thermal Transport by Phonons Across Semiconductor Interfaces, Thin Films, and Superlattices
,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
40.
Beechem
,
T.
,
Duda
,
J. C.
,
Hopkins
,
P. E.
, and
Norris
,
P. M.
, 2010, “
Contribution of Optical Phonons to Thermal Boundary Conductance
,”
Appl. Phys. Lett.
0003-6951,
97
(
6
), p.
061907
.
41.
Dames
,
C.
, and
Chen
,
G.
, 2004, “
Theoretical Phonon Thermal Conductivity of Si/Ge Superlattice Nanowires
,”
J. Appl. Phys.
0021-8979,
95
(
2
), pp.
682
693
.
42.
Ward
,
A.
, and
Broido
,
D. A.
, 2010, “
Intrinsic Phonon Relaxation Times From First-Principles Studies of the Thermal Conductivities of Si and Ge
,”
Phys. Rev. B
0556-2805,
81
(
8
), p.
085205
.
You do not currently have access to this content.