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Research Papers: Micro/Nanoscale Heat Transfer

Electrothermal Characterization of Doped-Si Heated Microcantilevers Under Periodic Heating Operation

[+] Author and Article Information
Sina Hamian

Department of Mechanical Engineering,
University of Utah,
Salt Lake City, UT 84112

Andrew M. Gauffreau, Timothy Walsh

Department of Mechanical, Industrial,
and Systems Engineering,
University of Rhode Island,
Kingston, RI 02881

Jungchul Lee

Department of Mechanical Engineering,
Sogang University,
Seoul 121-742, South Korea

Keunhan Park

Department of Mechanical Engineering,
University of Utah,
Salt Lake City, UT 84112
e-mail: kpark@mech.utah.edu

1S. Hamian and A. M. Gauffreau contributed equally to this work.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 20, 2015; final manuscript received December 31, 2015; published online February 9, 2016. Assoc. Editor: Gennady Ziskind.

J. Heat Transfer 138(5), 052401 (Feb 09, 2016) (9 pages) Paper No: HT-15-1136; doi: 10.1115/1.4032531 History: Received February 20, 2015; Revised December 31, 2015

This paper reports the frequency-dependent electrothermal behaviors of a freestanding doped-silicon heated microcantilever probe operating under periodic (ac) Joule heating. We conducted a frequency-domain finite-element analysis (FEA) and compared the steady periodic solution with 3ω experiment results. The computed thermal transfer function of the cantilever accurately predicts the ac electrothermal behaviors over a full spectrum of operational frequencies, which could not be accomplished with the 1D approximation. In addition, the thermal transfer functions of the cantilever in vacuum and in air were compared, through which the frequency-dependent heat transfer coefficient of the air was quantified. With the developed FEA model, design parameters of the cantilever (i.e., the size and the constriction width of the cantilever heater) and their effects on the ac electrothermal behaviors were carefully investigated. Although this work focused on doped-Si heated microcantilever probes, the developed FEA model can be applied for the ac electrothermal analysis of general microelectromechanical systems.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematic of the 3ω experimental setup with the SEM image of a doped-Si heated microcantilever and (b) its FEA model with an environment box. The cantilever base was anchored to the wall of the environment box while the remaining cantilever facets were spaced 100 μm away from the other side walls.

Grahic Jump Location
Fig. 2

Normalized (a) in-phase and (b) out-of-phase thermal transfer functions of the cantilever from the experimental (square marks) and computational (solid line) results. The dashed curve and the dotted curve are associated with the RC model of the leg and the heater, respectively.

Grahic Jump Location
Fig. 3

The in-phase and out-of-phase components and the magnitude of the ac temperature distributions of the cantilever under the periodic heating operation in vacuum at various frequencies: (a) 90 Hz, (b) 1 kHz, (c) 10 kHz, and (d) 34 kHz. (e) The normalized temperature distributions along the centerline of the cantilever for different frequencies. They are normalized by the magnitude of the tip temperature at each frequency.

Grahic Jump Location
Fig. 4

The in-phase and out-of-phase components and the magnitude of the ac temperature distributions of the cantilever under the periodic heating operation in air at various frequencies: (a) 90 Hz, (b) 1 kHz, (c) 10 kHz, and (d) 34 kHz. (e) The normalized temperature distributions along the centerline of the cantilever for different frequencies.

Grahic Jump Location
Fig. 5

(a) In-phase and (b) out-of-phase thermal transfer functions of the cantilever for the vacuum and the air environments. Results are normalized using the thermal resistance in vacuum. The discrepancy indicates the effect of heat conduction to the air on the ac thermoelectric behaviors of the cantilever.

Grahic Jump Location
Fig. 6

The magnitude and phase of the complex heat transfer coefficient for the (a) constriction region and (b) leg region. Both magnitude and phase increase as the frequency increases, indicating that the thermal response of the air is confined to the cantilever surface and becomes more out-of-phase.

Grahic Jump Location
Fig. 7

(a) The effect of the heater size to the in-phase and out-of-phase thermal transfer functions of the cantilever. The inset images illustrate different heater sizes used in the analysis. The number next to each image is the percentage of the heater size as compared to the original cantilever design. (b) The effect of the constriction width to the in-phase and out-of-phase thermal transfer functions of the cantilever. The inset images illustrate different constriction widths used in the analysis. The number next to each image is the percentage of the constriction width as compared to the original cantilever design. The constriction width significantly affects the high-frequency behaviors where the heater plays a dominant role.

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