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Research Papers: Micro/Nanoscale Heat Transfer

# Experimental Investigation on the Heat Transfer Between a Heated Microcantilever and a Substrate

[+] Author and Article Information
Keunhan Park

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Graham L. Cross

School of Physics and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland

Zhuomin M. Zhang1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332zhuomin.zhang@me.gatech.edu

William P. King1

Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801wpk@uiuc.edu

1

Corresponding authors.

J. Heat Transfer 130(10), 102401 (Aug 08, 2008) (9 pages) doi:10.1115/1.2953238 History: Received July 25, 2007; Revised November 12, 2007; Published August 08, 2008

## Abstract

This work describes the heat transfer process from a heated microcantilever to a substrate. A platinum-resistance thermometer with a $140nm$ width was fabricated on a $SiO2$-coated silicon substrate. The temperature coefficient of resistance estimated from the measurement was $7×10−4K−1$, about one-fifth of the bulk value of platinum. The temperature distribution on the substrate was obtained from the thermometer reading, as the cantilever raster scanned the substrate. Comparison between the measurement and calculation reveals that up to 75% of the cantilever power is directly transferred to the substrate through the air gap. From the force-displacement experiment, the effective tip-specimen contact thermal conductance was estimated to be around $40nW∕K$. The findings from this study should help understand the thermal interaction between the heated cantilever and the substrate, which is essential to many nanoscale technologies using heated cantilevers.

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## Figures

Figure 1

(a) SEM image of a heated microcantilever. The cantilever is made of single-crystal silicon, with a high phosphorus concentration in the leg region and a low phosphorus concentration in the heater region. (b) Top views of the fabricated PRT, obtained with SEM with different magnifications. The sensing probe is 140nm in width and 29μm in length. The thickness is approximately 35nm.

Figure 2

(a) The experimental setup in an AFM platform. While the cantilever scans the specimen, the AFM controller simultaneously measures the surface topography, the cantilever voltage, and the PRT resistance. (b) The bridge circuits used in the measurements of the cantilever (left) and PRT (right).

Figure 3

(a) Schematic of the cantilever and the specimen (not to scale). The air gap between the cantilever and the specimen is assumed to be parallel, through which qg is transferred to the SiO2 film and eventually the Si substrate. (b) The calculation results of the specimen surface temperature distribution when the cantilever resistance is 1.75kΩ.

Figure 4

The characteristics of the heated cantilever when it is off the specimen and on the specimen. (a) The cantilever resistance versus heater temperature measured with a micro-Raman spectroscope. (b) The cantilever dc characteristic curves are compared between the off-specimen and on-specimen cases. (c) The calculation reveals that up to 75% of the cantilever power is transferred to the substrate via the air gap and SiO2 film.

Figure 5

The characteristics of the PRT. (a) The thermometer resistance change is linearly proportional to the cantilever power. The slope difference between parallel and perpendicular alignments is attributed to the effective heat transfer area. (b) By comparison of the measurement and the calculation, the TCR of the thermometer is estimated to be between 6.76×10−4K−1 and 7.74×10−4K−1.

Figure 6

AFM images when the cantilever scans over the thermometer in parallel and perpendicular alignments while maintaining its resistance at 1.75kΩ. (a) The thermometer topographic image, (b) cantilever voltage image, (c) thermometer resistance image in parallel alignment, and (d) thermometer resistance image in perpendicular alignment. The calculation results of the thermometer resistance are shown together in (c) and (d).

Figure 7

The cantilever signals and thermometer signals when the cantilever resistance is controlled with different values. As the cantilever is maintained with higher resistance, more heat is transferred between the cantilever and substrate, resulting in (a) an increase in ΔVC, (b) an increase in ΔRth for parallel alignment, and (c) an increase in ΔRth for perpendicular alignment.

Figure 8

The force-displacement experiment results when the cantilever is aligned with the nanothermometer in parallel and controlled with the cantilever resistance. (a) The deflection signal shows that as the cantilever resistance increases, the cantilever bends down due to electrostatic and thermal forces. (b) The cantilever voltage increases as the cantilever approaches the substrate to maintain the temperature. (c) As a result, the thermometer resistance increases as the cantilever approaches the substrate.

Figure 9

The force-displacement experiment result at Rc=2.0kΩ, which is magnified on the moment of contact. There is a jump on the cantilever and thermometer signals when the cantilever contacts the substrate, from which the effective contact conductance can be estimated to be around 40nW∕K.

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