Silicon-on-insulator (SOI) technology has sparked advances in semiconductor and MEMs manufacturing and revolutionized our ability to study phonon transport phenomena by providing single-crystal silicon layers with thickness down to a few tens of nanometers. These nearly perfect crystalline silicon layers are an ideal platform for studying ballistic phonon transport and the coupling of boundary scattering with other mechanisms, including impurities and periodic pores. Early studies showed clear evidence of the size effect on thermal conduction due to phonon boundary scattering in films down to 20 nm thick and provided the first compelling room temperature evidence for the Casimir limit at room temperature. More recent studies on ultrathin films and periodically porous thin films are exploring the possibility of phonon dispersion modifications in confined geometries and porous films.

Issue Section:
Experimental Techniques
Keywords:
silicon, phonon transport, thermal conductivity, nanoscale, thin films
Topics:
Phonons, Silicon, Thermal conductivity, Thin films, Silicon-on-insulator, Electromagnetic scattering, Radiation scattering, Scattering (Physics), Temperature

References

1.
Nguyen
,
B.-Y.
,
Celler
,
G.
, and
Mazure
,
C.
,
2009
, “
A Review of SOI Technology and Its Applications
,”
J. Integr. Circuit Syst.
,
4
(
2
), pp.
51
–
54
.
2.
Loncar
,
M.
,
Doll
,
T.
,
Vuckovic
,
J.
, and
Scherer
,
A.
,
2000
, “
Design and Fabrication of Silicon Photonic Crystal Optical Waveguides
,”
J. Lightwave Tech.
,
18
(
10
), pp.
1402
–
1411
.10.1109/50.887192
3.
Lutz
,
M.
,
Partridge
,
A.
,
Gupta
,
P.
,
Buchan
,
N.
,
Klaassen
,
E.
,
McDonald
,
J.
, and
Petersen
,
K.
,
2007
, “
MEMS Oscillators for High Volume Commercial Applications
,” 14th International Conference on Solid-State Sensors, Actuators and Microsystems Conference (TRANSDUCERS & EUROSENSORS '07), Lyon, France, June 10–14,
IEEE
, pp.
49
–
52
.10.1109/SENSOR.2007.4300068
4.
Goodson
,
K. E.
,
Flik
,
M. I.
,
Su
,
L. T.
, and
Antoniadis
,
D. A.
,
1995
, “
Prediction and Measurement of Temperature Fields in Silicon-on-Insulator Electronic Circuits
,”
ASME J. Heat Transfer
,
117
(3), pp.
574
–
581
.10.1115/1.2822616
5.
McConnell
,
A. D.
, and
Goodson
,
K. E.
,
2005
, “
Thermal Conduction in Silicon Micro- and Nanostructures
,”
Ann. Rev. Heat Transf.
,
14
, pp.
129
–
168
.
6.
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
(
2
), pp.
793
–
818
.10.1063/1.1524305
7.
Liu
,
W.
, and
Asheghi
,
M.
,
2004
, “
Phonon–Boundary Scattering in Ultrathin Single-Crystal Silicon Layers
,”
Appl. Phys. Lett.
,
84
(
19
), pp.
3819
–
3821
.10.1063/1.1741039
8.
Casimir
,
H. B. G.
,
1938
, “
Note on the Conduction of Heat in Crystals
,”
Physica
,
5
(
6
), pp.
495
–
500
.10.1016/S0031-8914(38)80162-2
9.
Yoneoka
,
S.
,
Liger
,
M.
,
Yama
,
G.
,
Schuster
,
R.
,
Purkl
,
F.
,
Provine
,
J.
,
Prinz
,
F. B.
,
Howe
,
R. T.
, and
Kenny
,
T. W.
,
2011
, “
ALD-Metal Uncooled Bolometer
,”
2011 IEEE 24th International Conference on Micro Electro Mechanical Systems
(
MEMS
), Jan. 23–27, pp.
676
–
679
.10.1109/MEMSYS.2011.5734515
10.
Niklaus
,
F.
,
Vieider
,
C.
, and
Jakobsen
,
H.
,
2007
, “
MEMS-Based Uncooled Infrared Bolometer Arrays: A Review
,” MEMS/MOEMS Technologies and Applications III, J.-C. Chiao, X. Chen, Z. Zhou, and X. Li, eds.,
SPIE
Proceedings, Beijing, China, Vol.
6836
, p.
68360D
.10.1117/12.755128
11.
Asheghi
,
M.
,
Leung
,
Y. K.
,
Wong
,
S. S.
, and
Goodson
,
K. E.
,
1997
, “
Phonon-Boundary Scattering in Thin Silicon Layers
,”
Appl. Phys. Lett.
,
71
(
13
), pp.
1798
–
1800
.10.1063/1.119402
12.
Asheghi
,
M.
,
Touzelbaev
,
M. N.
,
Goodson
,
K. E.
,
Leung
,
Y. K.
, and
Wong
,
S. S.
,
1998
, “
Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates
,”
ASME J. Heat Transfer
,
120
(
1
), pp.
30
–
36
.10.1115/1.2830059
13.
Aubain
,
M. S.
, and
Bandaru
,
P. R.
,
2011
, “
In-Plane Thermal Conductivity Determination Through Thermoreflectance Analysis and Measurements
,”
J. Appl. Phys.
,
110
(
8
), p.
084313
.10.1063/1.3647318
14.
Aubain
,
M. S.
, and
Bandaru
,
P. R.
,
2010
, “
In-Plane Thermal Conductivity Determination in Silicon on Insulator (SOI) Structures Through Thermoreflectance Measurements
,” Materials Research Society Spring Meeting, San Francisco, CA, Cambridge University Press, Vol. 1267, p.
1267-DD-01
.
15.
Aubain
,
M. S.
, and
Bandaru
,
P. R.
,
2010
, “
Determination of Diminished Thermal Conductivity in Silicon Thin Films Using Scanning Thermoreflectance Thermometry
,”
Appl. Phys. Lett.
,
97
(
25
), p.
253102
.10.1063/1.3527966
16.
Ju
,
Y. S.
,
2005
, “
Phonon Heat Transport in Silicon Nanostructures
,”
Appl. Phys. Lett.
,
87
(15), p.
153106
.10.1063/1.2089178
17.
Ju
,
Y. S.
, and
Goodson
,
K. E.
,
1999
, “
Phonon Scattering in Silicon Films With Thickness of Order 100 Nm
,”
Appl. Phys. Lett.
,
74
(
20
), pp.
3005
–
3007
.10.1063/1.123994
18.
Hao
,
Z.
,
Zhichao
,
L.
,
Lilin
,
T.
,
Zhimin
,
T.
,
Litian
,
L.
, and
Zhijian
,
L.
,
2006
, “
Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Films Using Improved Structure
,” 8th International Conference on Solid-State and Integrated Circuit Technology (
ICSICT
'06), Shanghai, China, Oct. 23–26, pp.
2196
–
2198
.10.1109/ICSICT.2006.306679
19.
Asheghi
,
M.
,
Kurabayashi
,
K.
,
Kasnavi
,
R.
, and
Goodson
,
K. E.
,
2002
, “
Thermal Conduction in Doped Single-Crystal Silicon Films
,”
J. Appl. Phys.
,
91
(
8
), pp.
5079
–
5088
.10.1063/1.1458057
20.
Kim
,
B.
,
Nguyen
,
J.
,
Clews
,
P. J.
,
Reinke
,
C. M.
,
Goettler
,
D.
,
Leseman
,
Z. C.
,
El-Kady
,
I.
, and
Olsson
,
R. H.
,
2012
, “
Thermal Conductivity Manipulation in Single Crystal Silicon via Lithographycally Defined Phononic Crystals
,” IEEE 25th International Conference on Micro Electro Mechanical Systems (
MEMS
), Paris, France, Jan. 29–Feb. 2, pp.
176
–
179
.10.1109/MEMSYS.2012.6170122
21.
Song
,
D.
, and
Chen
,
G.
,
2004
, “
Thermal Conductivity of Periodic Microporous Silicon Films
,”
Appl. Phys. Lett.
,
84
(
5
), pp.
687
–
689
.10.1063/1.1642753
22.
Sverdrup
,
P. G.
,
Sinha
,
S.
,
Asheghi
,
M.
,
Uma
,
S.
, and
Goodson
,
K. E.
,
2001
, “
Measurement of Ballistic Phonon Conduction Near Hotspots in Silicon
,”
Appl. Phys. Lett.
,
78
(
21
), pp.
3331
–
3333
.10.1063/1.1371536
23.
Chen
,
G.
,
1996
, “
Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles
,”
ASME J. Heat Transfer
,
118
(
3
), pp.
539
–
545
.10.1115/1.2822665
24.
Liu
,
W.
, and
Asheghi
,
M.
,
2006
, “
Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers
,”
ASME J. Heat Transfer
,
128
(
1
), pp.
75
–
83
.10.1115/1.2130403
25.
Liu
,
W.
, and
Asheghi
,
M.
,
2005
, “
Thermal Conduction in Ultrathin Pure and Doped Single-Crystal Silicon Layers at High Temperatures
,”
J. Appl. Phys.
,
98
(
12
), p.
123523
.10.1063/1.2149497
26.
Liu
,
W.
,
Etessam-Yazdani
,
K.
,
Hussin
,
R.
, and
Asheghi
,
M.
,
2006
, “
Modeling and Data for Thermal Conductivity of Ultrathin Single-Crystal SOI Layers at High Temperature
,”
IEEE Trans. Elec. Device.
,
53
(
8
), pp.
1868
–
1876
.10.1109/TED.2006.877874
27.
Bourgeois
,
O.
,
Fournier
,
T.
, and
Chaussy
,
J.
,
2007
, “
Measurement of the Thermal Conductance of Silicon Nanowires at Low Temperature
,”
J. Appl. Phys.
,
101
(
1
), p.
016104
.10.1063/1.2400093
28.
Heron
,
J. S.
,
Fournier
,
T.
,
Mingo
,
N.
, and
Bourgeois
,
O.
,
2009
, “
Mesoscopic Size Effects on the Thermal Conductance of Silicon Nanowire
,”
Nano Lett.
,
9
(
5
), pp.
1861
–
1865
.10.1021/nl803844j
29.
Heron
,
J.-S.
,
Bera
,
C.
,
Fournier
,
T.
,
Mingo
,
N.
, and
Bourgeois
,
O.
,
2010
, “
Blocking Phonons via Nanoscale Geometrical Design
,”
Phys. Rev. B
,
82
(
15
), p.
155458
.10.1103/PhysRevB.82.155458
30.
Yu
,
J.-K.
,
Mitrovic
,
S.
,
Tham
,
D.
,
Varghese
,
J.
, and
Heath
,
J. R.
,
2010
, “
Reduction of Thermal Conductivity in Phononic Nanomesh Structures
,”
Nat. Nanotechnol.
,
5
(
10
), pp.
718
–
721
.10.1038/nnano.2010.149
31.
Tang
,
J.
,
Wang
,
H.-T.
,
Lee
,
D. H.
,
Fardy
,
M.
,
Huo
,
Z.
,
Russell
,
T. P.
, and
Yang
,
P.
,
2010
, “
Holey Silicon as an Efficient Thermoelectric Material
,”
Nano Lett.
,
10
(
10
), pp.
4279
–
4283
.10.1021/nl102931z
32.
Hippalgaonkar
,
K.
,
Huang
,
B.
,
Chen
,
R.
,
Sawyer
,
K.
,
Ercius
,
P.
, and
Majumdar
,
A.
,
2010
, “
Fabrication of Microdevices With Integrated Nanowires for Investigating Low-Dimensional Phonon Transport
,”
Nano Lett.
,
10
(
11
), pp.
4341
–
4348
.10.1021/nl101671r
33.
Boukai
,
A. I.
,
Bunimovich
,
Y.
,
Tahir-Kheli
,
J.
,
Yu
,
J.-K.
,
Goddard
,
W. A.
, III, and
Heath
,
J. R.
,
2008
, “
Silicon Nanowires as Efficient Thermoelectric Materials
,”
Nature
,
451
(
7175
), pp.
168
–
171
.10.1038/nature06458
34.
Thomas
,
J. A.
,
Turney
,
J. E.
,
Iutzi
,
R. M.
,
Amon
,
C. H.
, and
McGaughey
,
A. J. H.
,
2010
, “
Predicting Phonon Dispersion Relations and Lifetimes From the Spectral Energy Density
,”
Phys. Rev. B
,
81
(
8
), p.
081411
.10.1103/PhysRevB.81.081411
35.
Henry
,
A. S.
, and
Chen
,
G.
,
2008
, “
Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics
,”
J. Comput. Theor. Nanos.
,
5
(
2
), pp.
141
–
152
.
36.
Lacroix
,
D.
,
Joulain
,
K.
,
Terris
,
D.
, and
Lemonnier
,
D.
,
2006
, “
Monte Carlo Simulation of Phonon Confinement in Silicon Nanostructures: Application to the Determination of the Thermal Conductivity of Silicon Nanowires
,”
Appl. Phys. Lett.
,
89
(
10
), p.
103104
.10.1063/1.2345598
37.
Schelling
,
P. K.
,
Phillpot
,
S. R.
, and
Keblinski
,
P.
,
2002
, “
Comparison of Atomic-Level Simulation Methods for Computing Thermal Conductivity
,”
Phys. Rev. B
,
65
(
14
), p.
144306
.10.1103/PhysRevB.65.144306
38.
Volz
,
S. G.
, and
Chen
,
G.
,
1999
, “
Molecular Dynamics Simulation of Thermal Conductivity of Silicon Nanowires
,”
Appl. Phys. Lett.
,
75
(
14
), pp.
2056
–
2058
.10.1063/1.124914
39.
Ziman
,
J. M.
,
1960
,
Electrons and Phonons
,
Oxford University Press
,
London
.
40.
Baillis
,
D.
, and
Randrianalisoa
,
J.
,
2009
, “
Prediction of Thermal Conductivity of Nanostructures: Influence of Phonon Dispersion Approximation
,”
Int. J. Heat Mass Transf.
,
52
(
11–12
), pp.
2516
–
2527
.10.1016/j.ijheatmasstransfer.2009.01.017
41.
Holland
,
M. G.
,
1963
, “
Analysis of Lattice Thermal Conductivity
,”
Phys. Rev.
,
132
(
6
), pp.
2461
–
2471
.10.1103/PhysRev.132.2461
42.
Hopkins
,
P. E.
,
Reinke
,
C. M.
,
Su
,
M. F.
,
Olsson
,
R. H.
,
Shaner
,
E. A.
,
Leseman
,
Z. C.
,
Serrano
,
J. R.
,
Phinney
,
L. M.
, and
El-Kady
,
I.
,
2010
, “
Reduction in the Thermal Conductivity of Single Crystalline Silicon by Phononic Crystal Patterning
,”
Nano Lett.
,
11
(
1
), pp.
107
–
112
.10.1021/nl102918q
43.
Sondheimer
,
E. H.
,
1952
, “
The Mean Free Path of Electrons in Metals
,”
Adv. Phys.
,
1
(
1
), pp.
1
–
42
.10.1080/00018735200101151
44.
Berman
,
R.
,
Foster
,
E. L.
, and
Ziman
,
J. M.
,
1955
, “
Thermal Conduction in Artificial Sapphire Crystals at Low Temperatures. I. Nearly Perfect Crystals
,”
Pr. Roy. Soc. Lond. A Mat.
,
231
(
1184
), pp.
130
–
144
.10.1098/rspa.1955.0161
45.
Ho
,
C. Y.
,
Powell
,
R. W.
, and
Liley
,
P. E.
,
1972
, “
Thermal Conductivity of the Elements
,”
J. Phys. Chem. Ref. Data
,
1
(
2
), pp.
279
–
421
.10.1063/1.3253100
46.
Torres
,
C. M. S.
,
Zwick
,
A.
,
Poinsotte
,
F.
,
Groenen
,
J.
,
Prunnila
,
M.
,
Ahopelto
,
J.
,
Mlayah
,
A.
, and
Paillard
,
V.
,
2004
, “
Observations of Confined Acoustic Phonons in Silicon Membranes
,”
Phys. Status Solidi C
,
1
(
11
), pp.
2609
–
2612
.10.1002/pssc.200405313
47.
Cuffe
,
J.
,
Chávez
,
E.
,
Shchepetov
,
A.
,
Chapuis
,
P.-O.
,
El Boudouti
,
E. H.
,
Alzina
,
F.
,
Kehoe
,
T.
,
Gomis-Bresco
,
J.
,
Dudek
,
D.
,
Pennec
,
Y.
,
Djafari-Rouhani
,
B.
,
Prunnila
,
M.
,
Ahopelto
,
J.
, and
Sotomayor Torres
,
C. M.
,
2012
, “
Phonons in Slow Motion: Dispersion Relations in Ultrathin Si Membranes
,”
Nano Lett.
,
12
(7), pp.
3569
–
3573
.10.1021/nl301204u
48.
Johnson
,
J. A.
,
Maznev
,
A. A.
,
Eliason
,
J. K.
,
Minnich
,
A.
,
Collins
,
K.
,
Chen
,
G.
,
Cuffe
,
J.
,
Kehoe
,
T.
,
Torres
,
C. M. S.
, and
Nelson
,
K. A.
,
2011
, “Experimental Evidence of Non-Diffusive Thermal Transport in Si and GaAs,”
MRS
Proceedings, San Francisco, CA, Apr. 25–29, Cambridge University Press, Vol. 1347.10.1557/opl.2011.1333
49.
Johnson
,
J. A.
,
Maznev
,
A.
,
Cuffe
,
J.
,
Eliason
,
J. K.
,
Minnich
,
A. J.
,
Kehoe
,
T.
,
Sotomayor Torres
,
C. M.
,
Chen
,
G.
, and
Nelson
,
K. A.
,
2012
, “
Direct Measurement of Room Temperature Non-Diffusive Thermal Transport Over Micron Distances in a Silicon Membrane
,” ArXiv eprint No. arXiv:1204.4735.
50.
Marconnet
,
A. M.
,
Kodama
,
T.
,
Asheghi
,
M.
, and
Goodson
,
K. E.
,
2012
, “
Phonon Thermal Conduction in Periodically Porous Silicon Nanobridges
,”
Microscale Nanoscale Therm. Eng.
,
16
(
4
), pp.
199
–
219
.10.1080/15567265.2012.732195
51.
Nordheim
,
L. W.
,
1934
, “
Die Theorie Der Thermoelektrischen Effekte
,”
Actes Scientifiques et Industrielles
, Vol. 131, Hermann & Cie, Paris.
52.
Hochbaum
,
A. I.
,
Chen
,
R.
,
Delgado
,
R. D.
,
Liang
,
W.
,
Garnett
,
E. C.
,
Najarian
,
M.
,
Majumdar
,
A.
, and
Yang
,
P.
,
2008
, “
Enhanced Thermoelectric Performance of Rough Silicon Nanowires
,”
Nature
,
451
(
7175
), pp.
163
–
167
.10.1038/nature06381
53.
Li
,
D.
,
Wu
,
Y.
,
Kim
,
P.
,
Shi
,
L.
,
Yang
,
P.
, and
Majumdar
,
A.
,
2003
, “
Thermal Conductivity of Individual Silicon Nanowires
,”
Appl. Phys. Lett.
,
83
(
14
), pp.
2934
–
2936
.10.1063/1.1616981
54.
Josell
,
D.
,
Burkhard
,
C.
,
Li
,
Y.
,
Cheng
,
Y. W.
,
Keller
,
R. R.
,
Witt
,
C. A.
,
Kelley
,
D. R.
,
Bonevich
,
J. E.
,
Baker
,
B. C.
, and
Moffat
,
T. P.
,
2004
, “
Electrical Properties of Superfilled Sub-Micrometer Silver Metallizations
,”
J. Appl. Phys.
,
96
(
1
), pp.
759
–
768
.10.1063/1.1757655
55.
Dingle
,
R. B.
,
1950
, “
The Electrical Conductivity of Thin Wires
,”
Pr. Roy. Soc. Lond. A Mat.
,
201
(
1067
), pp.
545
–
560
.10.1098/rspa.1950.0077
56.
Gong
,
Y.
,
Ellis
,
B.
,
Shambat
,
G.
,
Sarmiento
,
T.
,
Harris
,
J. S.
, and
Vuckovic
,
J.
,
2010
, “
Nanobeam Photonic Crystal Cavity Quantum Dot Laser
,”
Optics Exp.
,
18
(
9
), pp.
8781
–
8789
.10.1364/OE.18.008781
57.
Makarova
,
M.
,
Yiyang
,
G.
,
Szu-Lin
,
C.
,
Nishi
,
Y.
,
Yerci
,
S.
,
Rui
,
L.
,
Negro
,
L. D.
, and
Vuckovic
,
J.
,
2010
, “
Photonic Crystal and Plasmonic Silicon-Based Light Sources
,”
IEEE J. Quant. Electron.
,
16
(
1
), pp.
132
–
140
.10.1109/JSTQE.2009.2030777
58.
Laude
,
S.
,
Beugnot
,
J. C.
,
Benchabane
,
S.
,
Pennec
,
Y.
,
Djafari-Rouhani
,
B.
,
Papanicolaou
,
N.
, and
Martinez
,
A.
,
2010
, “
Design of Waveguides in Silicon Phoxonic Crystal Slabs
,”
IEEE
Ultrasonics Symposium (IUS), San Diego, CA, Oct. 11–14, pp.
527
–
530
.10.1109/ULTSYM.2010.5935703
59.
Sadat-Saleh
,
S.
,
Benchabane
,
S.
,
Baida
,
F. I.
,
Bernal
,
M.-P.
, and
Laude
,
V.
,
2009
, “
Tailoring Simultaneous Photonic and Phononic Band Gaps
,”
J. Appl. Phys.
,
106
(
7
), p.
074912
.10.1063/1.3243276
60.
Olsson
,
R. H.
, III, and
El-Kady
,
I.
,
2009
, “
Microfabricated Phononic Crystal Devices and Applications
,”
Measure. Sci. Tech.
,
20
(
1
), p.
012002
.10.1088/0957-0233/20/1/012002
61.
El-Kady
,
I.
,
Su
,
M. F.
,
Reinke
,
C. M.
,
Hopkins
,
P. E.
,
Goettler
,
D.
,
Leseman
,
Z. C.
,
Shaner
,
E. A.
, and
Olsson
,
R. H.
, III,
2011
, “
Manipulation of Thermal Phonons: A Phononic Crystal Route to High-ZT Thermoelectrics
,” Photonic and Phononic Properties of Engineered Nanostructures, A. Adibi, S.-Y. Lin, and A. Scherer, eds.,
Proc. SPIE
, San Francisco, CA, Jan. 22–27, p. 794615.10.1117/12.891066
62.
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.
,
95
(
16
), p.
161902
.10.1063/1.3250166
63.
Hopkins
,
P. E.
,
Phinney
,
L. M.
,
Rakich
,
P. T.
,
Olsson
,
R. H.
, and
El-Kady
,
I.
,
2010
, “
Phonon Considerations in the Reduction of Thermal Conductivity in Phononic Crystals
,”
Appl. Phys. A
,
103
(
3
), pp.
575
–
579
.10.1007/s00339-010-6189-8
64.
Benchabane
,
S.
,
Khelif
,
A.
,
Daniau
,
W.
,
Robert
,
L.
,
Petrini
,
V.
,
Assouar
,
B.
,
Vincent
,
B.
,
Elmazria
,
O.
,
Kruger
,
J.
, and
Laude
,
S.
,
2005
, “
Silicon Phononic Crystal for Surface Acoustic Waves
,”
IEEE
Ultrasonics Symposium, Rotterdam, Netherlands, Sept. 18–21, Vol. 2, pp.
922
–
925
.10.1109/ULTSYM.2005.1603001
65.
Lee
,
J.-H.
,
Galli
,
G. A.
, and
Grossman
,
J. C.
,
2008
, “
Nanoporous Si as an Efficient Thermoelectric Material
,”
Nano Lett.
,
8
(
11
), pp.
3750
–
3754
.10.1021/nl802045f
66.
Mohammadi
,
S.
,
Eftekhar
,
A. A.
,
Hunt
,
W. D.
, and
Adibi
,
A.
,
2008
, “
Demonstration of Large Complete Phononic Band Gaps and Waveguiding in High-Frequency Silicon Phononic Crystal Slabs
,”
IEEE
International Frequency Control Symposium, Honolulu, HI, May 19–21, pp.
768
–
772
.10.1109/FREQ.2008.4623103
67.
El-Kady
,
I.
,
Olsson
,
R. H.
, III,
Hopkins
,
P. E.
,
Leseman
,
Z. C.
,
Goettler
,
D. F.
,
Kim
,
B.
,
Reinke
,
C. M.
, and
Su
,
M. F.
,
2012
, “
Phonon Manipulation With Phononic Crystals
,” Sandia National Labs, Albuquerque, NM, Report No. SAND2012-0127.
68.
Reinke
,
C. M.
,
Su
,
M. F.
,
Davis
,
B. L.
,
Kim
,
B.
,
Hussein
,
M. I.
,
Leseman
,
Z. C.
,
Olsson
,
R. H.
, III, and
El-Kady
,
I.
,
2011
, “
Thermal Conductivity Prediction of Nanoscale Phononic Crystal Slabs Using a Hybrid Lattice Dynamics-Continuum Mechanics Technique
,”
AIP Adv.
,
1
(4), p.
041403
.10.1063/1.3675918
Copyright © 2013 by ASME
You do not currently have access to this content.