Research Papers: Micro/Nanoscale Heat Transfer

Heat Transfer From Freely Suspended Bimaterial Microcantilevers

[+] Author and Article Information
Arvind Narayanaswamy1

Department of Mechanical Engineering, Columbia University, New York, NY 10027arvind.narayanaswamy@columbia.edu

Ning Gu

Department of Electrical Engineering, Columbia University, New York, NY 10027


Corresponding author.

J. Heat Transfer 133(4), 042401 (Jan 06, 2011) (6 pages) doi:10.1115/1.4001126 History: Received October 10, 2009; Revised January 14, 2010; Published January 06, 2011; Online January 06, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

(a) Schematic of a cantilever. The bimaterial cantilever is attached to an AFM chip. The laser beam is incident very close to the free end of the cantilever. (b) Thermal model for the cantilever.

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Figure 2

Schematic of experimental apparatus to measure the thermal response of bimaterial cantilevers. The laser is focused at the tip of the cantilever and the reflected beam is incident on a PSD. A magnified view of the region close to the cantilever is also shown in the figure. A thermocouple (not shown in figure) is positioned very close to the AFM base to measure the temperature Tb.

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Figure 3

(a) Measuring variation in PSD signal with Tb. (b) Measurements of ST from eight measurements.

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Figure 4

(a) Measuring variation in PSD signal with incident power (dashed line). (b) Measurements of SP (in vacuum) from seven measurements.

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Figure 5

Schematic of procedure to measure absorptivity of cantilever

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Figure 6

Power in reflected and transmitted beams as a function of incident laser beam power. The reflectivity and transmissivity are given by the slopes of the two curves shown in this figure.




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