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Research Papers

Thermomechanical Modeling of Scanning Joule Expansion Microscopy Imaging of Single-Walled Carbon Nanotube Devices

[+] Author and Article Information
Jizhou Song

Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33146
e-mail: j.song8@miami.edu

Chaofeng Lu

Department of Civil Engineering and Soft Matter Research Center,
Zhejiang University,
Hangzhou 310058, China

Xu Xie, Simon Dunham

Department of Materials Science and Engineering,
Frederick Seitz Materials Research Laboratory,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Yihui Zhang, Yonggang Huang

Department of Civil and Environmental Engineering,
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Kyle L. Grosse, William P. King

Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

John A. Rogers

Department of Materials Science and Engineering,
Frederick Seitz Materials Research Laboratory,
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 16, 2013; final manuscript received February 24, 2013; accepted manuscript posted April 10, 2013; published online May 31, 2013. Assoc. Editor: Huajian Gao.

J. Appl. Mech 80(4), 040907 (May 31, 2013) (8 pages) Paper No: JAM-13-1030; doi: 10.1115/1.4024175 History: Received January 16, 2013; Revised February 24, 2013; Accepted April 10, 2013

An analytical model, validated by experiments and finite element simulations, is developed to study the thermal imaging of single-walled carbon nanotube (SWNT) devices by scanning Joule expansion microscopy (SJEM). A simple scaling law for thermal expansion at low frequencies, which only depends on two nondimensional geometric parameters, is established. Such a scaling law provides a simple way to determine the surface temperature distribution and power dissipation per unit length in an SWNT from the measured thermal expansion in experiments. The results suggest the spatial resolution of the SJEM measurement is as good as ∼50 nm.

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Figures

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Fig. 1

(a) Schematic illustration of the experimental setup for scanning Joule expansion microscopy imaging of an SWNT device, and (b) the SJEM image of an SWNT device collected at Vds=4 V, f=30 kHz and a PMMA thickness ∼25 nm

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Fig. 2

Schematic illustration of the analytically modeled system

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Fig. 3

Schematic illustration of the thermomechanical model

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Fig. 4

Surface temperature distribution along the cross sections given by the analytical model of the accurate and approximate solutions and the FEA for the power density Q0=1 W/m at f=30 kHz

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Fig. 5

Expansion profiles along the cross sections given by the analytical model of the accurate and approximate solutions and the FEA with the power density determined as Q0=7.7 W/m at f=30 kHz

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Fig. 6

The normalized FWHM (FWHM/r) versus the normalized PMMA thickness (h0/r) at different normalized SiO2 thicknesses (h1/r)

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