A technique to extract in-plane thermal conductivity of thin metallic films whose thickness is comparable to electron mean free path is described. Microscale constrictions were fabricated into gold films of thicknesses 43nm and 131nm. A sinusoidal voltage excitation across the constriction results in a local temperature rise. An existing technique known as scanning joule expansion microscopy, measures the corresponding periodic thermomechanical expansion with a 10nm resolution and determines the local temperature gradient near the constriction. A three-dimensional finite-element simulation of the frequency-domain heat transfer fits the in-plane thermal conductivity to the measured data, finding thermal conductivities of 82±7.7WmK for the 43nm film and 162±16.7WmK for the 131nm film, at a heating frequencies of 100kHz and 90kHz, respectively. These values are significantly smaller than the bulk thermal conductivity value of 318WmK for gold, showing the electron size effect due to the metal-dielectric interface and grain boundary scattering. The obtained values are close to the thermal conductivity values, which are derived from electrical conductivity measurements after using the Wiedemann–Franz law. Because the technique does not require suspended metal bridges, it captures true metal-dielectric interface scattering characteristics. The technique can be extended to other films that can carry current and result in Joule heating, such as doped single crystal or polycrystalline semiconductors.

1.
Fuchs
,
K.
, 1938, “
The Conductivity of Thin Metallic Films According to the Electron Theory of Metals
,”
Proc. Cambridge Philos. Soc.
0068-6735,
34
, pp.
100
108
.
2.
Sondheimer
,
E. H.
, 1952, “
The Mean Free Path of Electrons in Metals
,”
Adv. Phys.
0001-8732,
1
, pp.
1
42
.
3.
Ziman
,
J. M.
, 1960,
Electrons and Phonons
,
Oxford University Press
,
New York
.
4.
Soffer
,
S. B.
, 1967, “
Statistical Model for the Size Effect in Electrical Conduction
,”
J. Appl. Phys.
0021-8979,
38
, pp.
1710
1715
.
5.
Namba
,
Y.
, 1970, “
Resistivity and Temperature Coefficient of Thin Metal Films With Rough Surface
,”
Jpn. J. Appl. Phys.
0021-4922,
9
, pp.
1326
1329
.
6.
Gurrum
,
S. P.
,
Joshi
,
Y. K.
,
King
,
W. P.
, and
Ramakrishna
,
K.
, 2004, “
Numerical Simulation of Electron Transport Through Constriction in a Metallic Thin Film
,”
IEEE Electron Device Lett.
0741-3106,
25
, pp.
696
698
.
7.
Mayadas
,
A. F.
, and
Shatzkes
,
M.
, 1970, “
Electrical-Resistivity Model for Polycrystalline Films: The Case of Arbitrary Reflection at External Surfaces
,”
Phys. Rev. B
0556-2805,
1
, pp.
1382
1389
.
8.
Hatta
,
I.
,
Sasuga
,
Y.
,
Kato
,
R.
, and
Maesono
,
A.
, 1985, “
Thermal Diffusivity Measurement of Thin Films by Means of an AC Calorimetric Method
,”
Rev. Sci. Instrum.
0034-6748,
56
, pp.
1643
1647
.
9.
Kemp
,
T.
,
Srinivas
,
T. A. S.
,
Fettig
,
R.
, and
Ruppel
,
W.
, 1995, “
Measurement of Thermal Diffusivity of Thin Films and Foils Using a Laser Scanning Microscope
,”
Rev. Sci. Instrum.
0034-6748,
66
,
176
181
.
10.
Langer
,
G.
,
Hartmann
,
J.
, and
Reichling
,
M.
, 1997, “
Thermal Conductivity of Thin Metallic Films Measured by Photothermal Profile Analysis
,”
Rev. Sci. Instrum.
0034-6748,
68
,
1510
1513
.
11.
Boiko
,
B. T.
,
Pugachev
,
A. T.
, and
Bratsychin
,
V. M.
, 1973, “
Method for the Determination of the Thermophysical Properties of Evaporated Thin Films
,”
Thin Solid Films
0040-6090,
17
, pp.
157
161
.
12.
Volklein
,
F.
, and
Kessler
,
E.
, 1984, “
A Method for the Measurement of Thermal Conductivity, Thermal Diffusivity, and Other Transport Coefficients of Thin Films
,”
Phys. Status Solidi A
0031-8965,
81
, pp.
585
596
.
13.
Lu
,
L.
,
Yi
,
W.
, and
Zhang
,
D. L.
, 2001, “
3ω Method for Specific Heat and Thermal Conductivity Measurements
,”
Rev. Sci. Instrum.
0034-6748,
72
,
2996
3003
.
14.
Zhang
,
X.
,
Xie
,
H.
,
Fujii
,
M.
,
Ago
,
H.
,
Takahashi
,
K.
,
Ikuta
,
T.
,
Abe
,
H.
, and
Shimizu
,
T.
, 2005, “
Thermal and Electrical Conductivity of a Suspended Platinum Nanofilm
,”
Appl. Phys. Lett.
0003-6951,
86
(
1–3
),
171912
.
15.
Yang
,
Y.
, and
Asheghi
,
M.
, 2004, “
A Novel Technique for In-Plane Thermal Conductivity Measurements of Electrically Conductive Interconnects and Nanostructures
,”
Proceedings of 2004 Inter Society Conference on Thermal Phenomena-ITHERM
,
IEEE
,
Piscataway, NJ
, pp.
564
569
.
16.
Majumdar
,
A.
, 1999, “
Scanning Thermal Microscopy
,”
Annu. Rev. Mater. Sci.
0084-6600,
29
, pp.
505
585
.
17.
Ruiz
,
F.
,
Sun
,
W. D.
,
Pollak
,
F. H.
, and
Venkatraman
,
C.
, 1998, “
Determination of the Thermal Conductivity of Diamond-Like Nanocomposite Films Using a Scanning Thermal Microscope
,”
Appl. Phys. Lett.
0003-6951,
73
, pp.
1802
1804
.
18.
Gorbunov
,
V. V.
,
Fuchigami
,
N.
,
Hazel
,
J. L.
, and
Tsukruk
,
V. V.
, 1999, “
Probing Surface Microthermal Properties by Scanning Thermal Microscopy
,”
Langmuir
0743-7463,
15
, pp.
8340
8343
.
19.
Fischer
,
H.
, 2005, “
Quantitative Determination of Heat Conductivities by Scanning Thermal Microscopy
,”
Thermochim. Acta
0040-6031,
425
, pp.
69
74
.
20.
Fiege
,
G. B. M.
,
Altes
,
A.
,
Heiderhoff
,
R.
, and
Balk
,
L. J.
, 1999, “
Quantitative Thermal Conductivity Measurements With Nanometre Resolution
,”
J. Phys. D
0022-3727,
32
, pp.
L13
L17
.
21.
Pollock
,
H. M.
, and
Hammiche
,
A.
, 2001, “
Micro-Thermal Analysis: Techniques and Applications
,”
J. Phys. D
0022-3727,
34
, pp.
R23
R53
.
22.
Varesi
,
J.
, and
Majumdar
,
A.
, 1998, “
Scanning Joule Expansion Microscopy at Nanometer Scales
,”
Appl. Phys. Lett.
0003-6951,
72
, pp.
37
39
.
23.
Ashcroft
,
N. W.
, and
Mermin
,
N. D.
,
Solid State Physics
,
Holt, Rinehart, and Winston
,
Philadelphia, PA
.
24.
Cahill
,
D. G.
, 1990, “
Thermal Conductivity Measurement From 30to750K: The 3ω Method
,”
Rev. Sci. Instrum.
0034-6748,
61
, pp.
802
808
.
25.
Ju
,
Y. S.
, and
Goodson
,
K. E.
, 1999, “
Process-Dependent Thermal Transport Properties of Silicon-Dioxide Films Deposited Using Low-Pressure Chemical Vapor Deposition
,”
J. Appl. Phys.
0021-8979,
85
, pp.
7130
7134
.
26.
Segerlind
,
L. J.
, 1984,
Applied Finite Element Analysis
,
2nd ed.
,
Wiley
,
New York
.
27.
Jackson
,
J. D.
, 1998,
Classical Electrodynamics
,
3rd ed.
,
Wiley
,
New York
.
28.
Ney
,
M. M.
, 1991, “
Striction and Skin Effects on the Internal Impedance Value of Flat Conductors
,”
IEEE Trans. Electromagn. Compat.
0018-9375,
33
, pp.
321
327
.
29.
Mase
,
G. T.
, and
Mase
,
G. E.
, 1999,
Continuum Mechanics for Engineers
,
2nd ed.
,
CRC Press
,
Boca Raton, FL
.
30.
Nikanorov
,
S. P.
,
Burenkov
,
Yu. A.
, and
Stepanov
,
A. V.
, 1971, “
Elastic Properties of Silicon
,”
Sov. Phys. Solid State
0038-5654,
13
, pp.
2516
2518
.
31.
Zhao
,
J.-H.
,
Ryan
,
T.
,
Ho
,
P. S.
,
McKerrow
,
A. J.
, and
Shih
,
W.-Y.
, 1999, “
Measurement of Elastic Modulus, Poisson Ratio, and Coefficient of Thermal Expansion of On-Wafer Submicron Films
,”
J. Appl. Phys.
0021-8979,
85
, pp.
6421
6424
.
32.
Nandanpawar
,
M. I.
, and
Rajagopalan
,
S.
, 1978, “
Wachtman’s Equation and Temperature Dependence of Bulk Moduli in Solids
,”
J. Appl. Phys.
0021-8979,
49
, pp.
3976
3979
.
33.
Zhou
,
J. W. L.
,
Chan
,
H.-Y.
,
To
,
T. K. H.
,
Lai
,
K. W. C.
, and
Li
,
W. J.
, 2004, “
Polymer MEMS Actuators for Underwater Micromanipulation
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
9
, pp.
334
342
.
34.
Zhang
,
X.
,
Xie
,
H.
,
Fujii
,
M.
,
Ago
,
H.
,
Takahashi
,
K.
,
Ikuta
,
T.
,
Abe
,
H.
, and
Shimizu
,
T.
, 2005, “
Thermal and Electrical Conductivity of a Suspended Platinum Nanofilm
,”
Appl. Phys. Lett.
0003-6951,
86
,
171912
.
35.
Kline
,
S. J.
, and
McClintock
,
F. A.
, 1953, “
Describing Uncertainties in Single Sample Experiments
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
75
, pp.
3
8
.
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