Determination of Thermal Parameters of Nanostructures Exhibiting One-Dimensional Heat Flow Through a Thermal Transient M
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Determination of Thermal Parameters of Nanostructures Exhibiting One-Dimensional Heat Flow Through a Thermal Transient Method Anton Arriagada1, Edward T. Yu1, and Prabhakar R. Bandaru2 1 Deparment of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093-0407, U.S.A. 2 Materials Science Program, Mechanical Engineering Department, University of California at San Diego, La Jolla, CA 92093-0411, U.S.A. ABSTRACT We present an improved methodology for a thermal transient method enabling simultaneous measurement of thermal conductivity and specific heat of nanoscale structures with onedimensional heat flow. The temporal response of a sample to finite duration heat pulse inputs for both short (1 ns) and long (5 µs) pulses is analyzed and exploited to deduce the thermal properties. Excellent agreement has been obtained between the recovered physical parameters and computational simulations. INTRODUCTION Accurate thermal characterization of low-dimensional structures is necessary both for fundamental understanding of heat transport at the nano-/macro-scale and for practical purposes such as determining the figure of merit of thermoelectric materials. However, the steady-state methods typically employed suffer from difficulties with thermal gradients and also require separate experiments to determine individual values of thermal conductivity (k), specific heat (C), and thermal diffusivity (D). Transient techniques can be exploited to circumvent the above difficulties [1, 2]. An early experiment in this regard entailed monitoring heat pulse propagation at a particular location on the sample and computation of the statistical moments of the temperature (T) vs. time (t) curve to determine k and C [3]. In this case, the dispersion of a heat pulse as it travels down a sample as shown schematically in Figure 1 can be quantified through the computation of its moments and related to the thermal parameters appearing in the solution of the corresponding heat equation (obtained through Laplace transform techniques).
Figure 1. Schematic of heat pulse propagation (top) along a rectangular nanowire (bottom). The temperature (T) vs. time (t) plots show the dispersion of an input (at x=0) finite duration heat pulse as it diffuses, from left to right, along the wire.
While the original experiment using δ-function like pulses is adaptable for nanoscale structures with one-dimensional heat flow, its application has been hindered by the fact that large geometric aspect ratios (inherent to nanotubes, nanowires, and thin-films) and small energies (fJpJ) yield temperature changes (∆T) that are extremely difficult to measure. Larger temperature changes through resistive heating can be achieved by increasing the heater power, however a heater cross-sectional area large enough to avoid electromigration [4] can also lead to undesirable parasitics that complicate analyses. Alternately, increasing the applied current duration can cause deviations in the experimental temperature profiles, resulting i
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