Research Papers: Micro/Nanoscale Heat Transfer

A Reexamination of Phonon Transport Through a Nanoscale Point Contact in Vacuum

[+] Author and Article Information
Li Shi

e-mail: lishi@mail.utexas.edu
Department of Mechanical Engineering,
University of Texas at Austin,
Austin, TX 78712

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 5, 2013; final manuscript received October 4, 2013; published online November 21, 2013. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 136(3), 032401 (Nov 21, 2013) (9 pages) Paper No: HT-13-1067; doi: 10.1115/1.4025643 History: Received February 05, 2013; Revised October 04, 2013

Using a silicon nitride cantilever with an integral silicon tip and a microfabricated platinum–carbon resistance thermometer located close to the tip, a method is developed to concurrently measure both the heat transfer through and adhesion energy of a nanoscale point contact formed between the sharp silicon tip and a silicon substrate in an ultrahigh vacuum atomic force microscope at near room temperature. Several models are used to evaluate the contact area critical for interpreting the interfacial resistance. Near field-thermal radiation conductance was found to be negligible compared to the measured interface thermal conductance determined based on the possible contact area range. If the largest possible contact area is assumed, the obtained thermal interface contact resistance can be explained by a nanoconstriction model that allows the transmission of phonons from the whole Brillouin zone of bulk Si with an average finite transmissivity larger than 0.125. In addition, an examination of the quantum thermal conductance expression suggests the inaccuracy of such a model for explaining measurement results obtained at above room temperature.

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Fig. 1

Ballistic thermal conductance contributions from the four lowest phonon polarizations with ωmin = 0 of a square Si nanowire with a 2 × 2 nm2 cross section [32] (solid line), shown in comparison with 4G0 (dotted line). Also shown is the ballistic thermal conductance of the three acoustic phonon 1D subbands (dash-dotted line) and of the three acoustic and three optical phonon 1D subbands (dash-dot-dot line) of bulk silicon in the Γ–X [or (100)] direction [29], the thermal conductance between a 1D silicon-like monatomic chain with 3 degrees of freedom and a 3D semi-infinite silicon-like contact [23] (thin dash-dot-dot line), shown in comparison with 3G0. Additionally, the ballistic thermal conductance for the longitudinal acoustic branch of a model 1D system constructed of an infinitely long chain of silicon atoms assuming bulk elastic constants [25] (thin dotted line), shown in comparison with G0 (thin solid line).

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Fig. 2

False color scanning electron micrographs of the AFM cantilever preparation procedure showing (a) the commercial cantilever, (b) local removal of Ti/Au using a focused Ga+ ion beam and (c) local ion beam induced metal deposition of a Pt–C resistance thermometer. The Si tip is located on the opposite side of the cantilever. Scale bars are 50 μm. (d) Electrical resistance (R) versus temperature for the Pt–C resistance thermometer.

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Fig. 3

(a) Change in dc voltage of the Pt-C resistance thermometer, Vdc, versus applied dc current, Idc, when the cantilever is out-of-contact with the substrate. (b) Corresponding change in electrical resistance, R, versus Idc determined by the measured Vdc/Idc (circles) and by fitting Vdc(Idc) with a third order polynomial, Vdc(Idc) = a3Idc3 + a2Idc2 + a1Idc + a0, and dividing Vdc(Idc) –a0 by Idc (solid line). (c) The heating induced resistance change (ΔR) plotted as a function of χ≡dRPt-C/dT(Qh+12Qb)+dRAu/dT(12Qh+13Qb). (d) The corresponding change in temperature of the Pt–C RT, ΔTh, as a function of the total Joule heat dissipation, Q = Qh + Qb.

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Fig. 4

Schematic diagram and thermal resistance circuit of the experimental method for in-contact thermal resistance measurement of a Si–Si nanopoint contact

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Fig. 5

Measured change in electrical resistance of the Pt–C RT, ΔR, when heated by a dc current and measured by a coupled ac current of frequency f, normalized by the change measured using a frequency of f = 15 kHz

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Fig. 6

Concurrently measured (a) temperature rise at the cantilever tip, ΔTh, and (b) intensity reading of the position sensitive quadrant-cell detector, IPSD, plotted as a function of laser power set point, Plaser/Plaser,max, where Plaser,max < 7 mW. The laser beam position was adjusted to maximize IPSD for each laser power set point. As can be typical with scanning probe microscopes, the emitted laser power is not a linear function of the set point for small set point values. The laser power set point used to measure cantilever deflection in this experiment is 17% and hence induces a negligible ΔTh.

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Fig. 7

(a) Normal force, FN, and (b) electrical resistance change normalized by out-of-contact electrical resistance, ΔR/R, plotted versus vertical height above the Si substrate, z. Data measured during approach (retract) are shown in filled (open) symbols for fixed a heating powers of 53.4 μW, corresponding to an out-of-contact temperature rises of 33 K above room temperature.

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Fig. 8

Sudden electrical resistance change of the Pt–C resistance thermometer when the Si tip is brought into contact with the Si substrate, ΔRcontact = Rin-contactRout-of-contact, plotted versus total heating power, Q, measured at the snap-to and pull-off contact points over several approach/retract cycles. The applied Q corresponds to out-of-contact temperature rises of ΔTh = 22–33 K above room temperature. Additionally, ΔRcontact extrapolates to 0.2 Ω at Q = 0.

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Fig. 9

(a) Front and (b) side profile scanning electron micrographs of the cantilever tip taken post-measurement. Dashed lines in (b) denote the plane of the substrate with respect to the cantilever tip. High resolution SEM images of the front and side tip profiles are displayed in the insets of (a) and (b), respectively. For the case that the tip makes contact with the flattened portion along its frontal slope, the maximum effective contact area can be described by an ellipse with major diameter d1 and minor diameter d2 shown in the two insets Scale bars are 1 μm for ((a) and (b)) and 50 nm for ((a), inset and (b), inset).

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Fig. 10

Schematic showing (a) top view and (b) side view cantilever geometry



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