Bimaterial atomic force microscope cantilevers have been used extensively over the last 15 years as physical, chemical, and biological sensors. As a thermal sensor, the static deflection of bimaterial cantilevers, due to the mismatch of the coefficient of thermal expansion between the two materials, has been used to measure temperature changes as small as 106K, heat transfer rate as small as 40 pW, and energy changes as small as 10 fJ. Bimaterial cantilevers have also been used to measure “heat transfer-distance” curves—a heat transfer analogy of the force-distance curves obtained using atomic force microscopes. In this work, we concentrate on the characterization of heat transfer from the microcantilever. The thermomechanical response of a bimaterial cantilever is used to determine the (1) thermal conductance of a bimaterial cantilever, and (2) overall thermal conductance from the cantilever to the ambient. The thermal conductance of a rectangular gold coated silicon nitride cantilever is Gc=4.09±0.04μWK1. The overall thermal conductance from the cantilever to the ambient (at atmospheric pressure) is Ga=55.05±0.69μWK1. The effective heat transfer coefficient from the cantilever to the ambient (at atmospheric pressure) is determined to be 3400Wm2K1.

1.
Thundat
,
T.
,
Wachter
,
E. A.
,
Sharp
,
S. L.
, and
Warmack
,
R. J.
, 1995, “
Detection of Mercury Vapor Using Resonating Microcantilevers
,”
Appl. Phys. Lett.
0003-6951,
66
, pp.
1695
1697
.
2.
Gimzewski
,
J. K.
,
Gerber
,
C.
,
Meyer
,
E.
, and
Schlittler
,
R. R.
, 1994, “
Observation of a Chemical Reaction Using a Micromechanical Sensor
,”
Chem. Phys. Lett.
0009-2614,
217
, pp.
589
594
.
3.
Van Neste
,
C. W.
,
Senesac
,
L. R.
,
Yi
,
D.
, and
Thundat
,
T.
, 2008, “
Standoff Detection of Explosive Residues Using Photothermal Microcantilevers
,”
Appl. Phys. Lett.
0003-6951,
92
(
13
), p.
134102
.
4.
Mukhopadhyay
,
R.
,
Sumbayev
,
V.
,
Lorentzen
,
M.
,
Kjems
,
J.
,
Andreasen
,
P.
, and
Besenbacher
,
F.
, 2005, “
Cantilever Sensor for Nanomechanical Detection of Specific Protein Conformations
,”
Nano Lett.
1530-6984,
5
(
12
), pp.
2385
2388
.
5.
Lai
,
J.
,
Perazzo
,
T.
,
Shi
,
Z.
, and
Majumdar
,
A.
, 1997, “
Optimization and Performance of High-Resolution Micro-Optomechanical Thermal Sensors
,”
Sens. Actuators, A
0924-4247,
58
, pp.
113
119
.
6.
Varesi
,
J.
,
Lai
,
J.
,
Perazzo
,
T.
,
Shi
,
Z.
, and
Majumdar
,
A.
, 1997, “
Photothermal Measurements at Picowatt Resolution Using Uncooled Micro-Optomechanical Sensors
,”
Appl. Phys. Lett.
0003-6951,
71
, pp.
306
308
.
7.
Narayanaswamy
,
A.
,
Shen
,
S.
, and
Chen
,
G.
, 2008, “
Near-Field Radiative Heat Transfer Between a Sphere and a Substrate
,”
Phys. Rev. B
0163-1829,
78
, p.
115303
.
8.
Shen
,
S.
,
Narayanaswamy
,
A.
, and
Chen
,
G.
, 2009, “
Surface Phonon Polaritons Mediated Energy Transfer Between Nanoscale Gaps
,”
Nano Lett.
1530-6984,
9
, pp.
2909
2913
.
9.
Rousseau
,
E.
,
Siria
,
A.
,
Jourdan
,
G.
,
Volz
,
S.
,
Comin
,
F.
,
Chevrier
,
J.
, and
Greffet
,
J. -J.
, 2009, “
Radiative Heat Transfer at the Nanoscale
,”
Nat. Photonics
1749-4885,
3
, pp.
514
517
.
10.
Binnig
,
G.
,
Despont
,
M.
,
Drechsler
,
U.
,
Häberle
,
W.
,
Lutwyche
,
M.
,
Vettiger
,
P.
,
Mamin
,
H. J.
,
Chui
,
B. W.
, and
Kenny
,
T. W.
, 1999, “
Ultrahigh-Density Atomic Force Microscopy Data Storage With Erase Capability
,”
Appl. Phys. Lett.
0003-6951,
74
, pp.
1329
1331
.
11.
Vettiger
,
P.
,
Cross
,
G.
,
Despont
,
M.
,
Drechsler
,
U.
,
Durig
,
U.
,
Gotsmann
,
B.
,
Haberle
,
W.
,
Lantz
,
M.
,
Rothuizen
,
H.
,
Stutz
,
R.
, and
Binnig
,
G.
, 2002, “
The “Millipede”—Nanotechnology Entering Data Storage
,”
IEEE Trans. Nanotechnol.
1536-125X,
1
(
1
), pp.
39
55
.
12.
Nelson
,
B. A.
,
King
,
W. P.
,
Laracuente
,
A. R.
,
Sheehan
,
P. E.
, and
Whitman
,
L. J.
, 2006, “
Direct Deposition of Continuous Metal Nanostructures by Thermal Dip-Pen Nanolithography
,”
Appl. Phys. Lett.
0003-6951,
88
(
3
), p.
033104
.
13.
Kim
,
S. -J.
,
Ono
,
T.
, and
Esashi
,
M.
, 2009, “
Thermal Imaging With Tapping Mode Using a Bimetal Oscillator Formed at the End of a Cantilever
,”
Rev. Sci. Instrum.
0034-6748,
80
(
3
), p.
033703
.
14.
Nelson
,
B. A.
, and
King
,
W. P.
, 2007, “
Measuring Material Softening With Nanoscale Spatial Resolution Using Heated Silicon Probes
,”
Rev. Sci. Instrum.
0034-6748,
78
(
2
), p.
023702
.
15.
Zhou
,
Y. X.
,
Jiang
,
F.
,
Chen
,
H.
,
Note
,
R.
,
Mizuseki
,
H.
, and
Kawazoe
,
Y.
, 2008, “
First-Principles Study of Length Dependence of Conductance in Alkanedithiols
,”
J. Chem. Phys.
0021-9606,
128
(
4
), p.
044704
.
16.
Pinnaduwage
,
L.
,
Gehl
,
A.
,
Hedden
,
D.
,
Muralidharan
,
G.
,
Thundat
,
T.
,
Lareau
,
R.
,
Sulchek
,
T.
,
Manning
,
L.
,
Rogers
,
B.
,
Jones
,
M.
, and
Adams
,
J.
, 2003, “
A Microsensor for Trinitrotoluene Vapour
,”
Nature (London)
0028-0836,
425
(
6957
), p.
474
.
17.
Ratcliff
,
G. C.
,
Erie
,
D. A.
, and
Superfine
,
R.
, 1998, “
Photothermal Modulation for Oscillating Mode Atomic Force Microscopy in Solution
,”
Appl. Phys. Lett.
0003-6951,
72
, pp.
1911
1913
.
18.
Eastman
,
T.
, and
Zhu
,
D.
, 1995, “
Influence of an AFM Tip on Interfacial Melting on Ice
,”
J. Colloid Interface Sci.
0021-9797,
172
, pp.
297
301
.
19.
Lee
,
S. -M.
, and
Cahill
,
D. G.
, 1997, “
Heat Transport in Thin Dielectric Films
,”
J. Appl. Phys.
0021-8979,
81
, pp.
2590
2595
.
20.
Zink
,
B. L.
, and
Hellman
,
F.
, 2004, “
Specific Heat and Thermal Conductivity of Low-Stress Amorphous Si-N Membranes
,”
Solid State Commun.
0038-1098,
129
, pp.
199
204
.
21.
Zink
,
B. L.
,
Revaz
,
B.
,
Cherry
,
J. J.
, and
Hellman
,
F.
, 2005, “
Measurement of Thermal Conductivity of Thin Films With a Si-N Membrane-Based Microcalorimeter
,”
Rev. Sci. Instrum.
0034-6748,
76
, p.
024901
.
22.
Sultan
,
R.
,
Avery
,
A. D.
,
Stiehl
,
G.
, and
Zink
,
B. L.
, 2009, “
Thermal Conductivity of Micromachined Low-Stress Silicon-Nitride Beams From 77 to 325 K
,”
J. Appl. Phys.
0021-8979,
105
(
4
), p.
043501
.
23.
Shi
,
L.
, and
Majumdar
,
A.
, 2002, “
Thermal Transport Mechanisms at Nanoscale Point Contacts
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
329
337
.
24.
Park
,
K.
,
Cross
,
G. L. W.
,
Zhang
,
Z. M.
, and
King
,
W. P.
, 2008, “
Experimental Investigation on the Heat Transfer Between a Heated Microcantilever and a Substrate
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
102401
.
25.
Thiery
,
L.
,
Toullier
,
S.
,
Teyssieux
,
D.
, and
Briand
,
D.
, 2008, “
Thermal Contact Calibration Between a Thermocouple Probe and a Microhotplate
,”
ASME J. Heat Transfer
0022-1481,
130
, p.
091601
.
26.
Lefèvre
,
S.
,
Volz
,
S.
, and
Chapuis
,
P. -O.
, 2006, “
Nanoscale Heat Transfer at Contact Between a Hot Tip and a Substrate
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
251
258
.
27.
Chapuis
,
P. -O.
,
Greffet
,
J. -J.
,
Joulain
,
K.
, and
Volz
,
S.
, 2006, “
Heat Transfer Between a Nano-Tip and a Surface
,”
Nanotechnology
0957-4484,
17
(
12
), pp.
2978
2981
.
28.
Lee
,
J.
, and
King
,
W. P.
, 2007, “
Microcantilever Hotplates: Design, Fabrication, and Characterization
,”
Sens. Actuators, A
0924-4247,
136
(
1
), pp.
291
298
.
29.
Shen
,
S.
,
Narayanaswamy
,
A.
,
Goh
,
S.
, and
Chen
,
G.
, 2008, “
Thermal Conductance of AFM Bi-Material Cantilevers
,”
Appl. Phys. Lett.
0003-6951,
92
, p.
063509
.
30.
Young
,
W. C.
, 1989,
Roark’s Formulas for Stress and Strain
,
McGraw-Hill
,
New York
.
31.
Kim
,
K. J.
, and
King
,
W. P.
, 2009, “
Thermal Conduction Between a Heated Microcantilever and a Surrounding Air Environment
,”
Appl. Therm. Eng.
1359-4311,
29
, pp.
1631
1641
.
32.
Lee
,
J.
,
Wright
,
T. L.
,
Abel
,
M. R.
,
Sunden
,
E. O.
,
Marchenkov
,
A.
,
Graham
,
S.
, and
King
,
W. P.
, 2007, “
Thermal Conduction From Microcantilever Heaters in Partial Vacuum
,”
J. Appl. Phys.
0021-8979,
101
(
1
), p.
014906
.
33.
Park
,
K.
,
Lee
,
J.
,
Zhang
,
Z.
, and
King
,
W.
, 2007, “
Frequency-Dependent Electrical and Thermal Response of Heated Atomic Force Microscope Cantilevers
,”
J. Microelectromech. Syst.
1057-7157,
16
(
2
), pp.
213
222
.
34.
Hu
,
X. J.
,
Jain
,
A.
, and
Goodson
,
K. E.
, 2008, “
Investigation of the Natural Convection Boundary Condition in Microfabricated Structures
,”
Int. J. Therm. Sci.
1290-0729,
47
(
7
), pp.
820
824
.
35.
Yovanovich
,
M. M.
, 1998,
Handbook of Heat Transfer
,
McGraw-Hill
,
New York
, Chap. 3.
36.
Yovanovich
,
M. M.
, and
Marotta
,
E. E.
, 2003,
Heat Transfer Handbook
,
Wiley
,
New York
, Chap. 4.
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