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TECHNICAL PAPERS: Micro/Nanoscale Heat Transfer

The Compatibility of Thin Films and Nanostructures in Thermoelectric Cooling Systems

[+] Author and Article Information
Andrew Miner

 Romny Scientific, San Francisco, CA 94121miner@romny-scientific.com

J. Heat Transfer 129(7), 805-812 (Sep 11, 2006) (8 pages) doi:10.1115/1.2717941 History: Received March 21, 2006; Revised September 11, 2006

The compatibility of low-dimensional thermoelectric materials in forms such as thin films and nanowires for use in thermoelectric coolers is examined. First-order thermoelectric theory predicts that the cold and hot junction temperatures of a thermoelectric circuit are governed solely by the nondimensional figure of merit, ZT. Performance predictions based on this traditional theory have been more broadly applied to the performance of thermoelectric cooler systems, thereby implying that these coolers may be miniaturized without loss of performance and that system performance is dictated principally by ZT. A nondimensional thermoelectric system model for a cooler is developed and typical performance metrics for thermoelectric coolers are presented along with predictions from traditional theory. Performance is examined as a function of thermoelectric element length for representative system conditions. This system study shows that cooler performance may drop significantly when miniaturized, particularly if the cooling elements are realized at the scale of many recently proposed thermoelectric thin films and nanostructured materials. The system theory illustrates that performance is governed by three nondimensional parameters: an effective thermoelectric figure of merit, ZeTa, the relative ability for heat to be drawn into the cooler, and the relative ability for heat to be rejected from the cooler to the ambient environment. As cooler performance depends both on material properties (ZeTa) as well as the relative scale of the materials with respect to system thermal conductances, the applicability of some low-dimensional forms of materials such as thermoelectric elements may require reevaluation. The realization of high performance coolers based on thermoelectric effects must rely on developing high quality materials realized at an appropriate, application-dependent scale.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

A schematic diagram of a single-element pair of thermoelectric coolers. Thermoelectric materials, typically n- and p-type semiconductors, are electrically connected in series. The geometry is such that the elements are thermally in parallel, drawing heat from the left of the figure and dissipating heat to the right. A thermoelectric element-based model (or traditional model) for cooler performance is developed from the elements shown, including the material properties of the elements and the temperatures of the hot and cold junctions, Th and Tc, respectively.

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Figure 2

The minimum cold-side temperature achievable by a thermoelectric cooler (nondimensionalized as Tc,min∕Th) is shown as a function of the nondimensional figure of merit, ZTh. The dashed line illustrates ideal cooler performance as predicted by traditional thermoelectric theory. Various experimental results from literature are overlaid, based on the published experimental cooling performance, Tc∕Th and experimentally measured figure of merit, ZTh. (1,4-5,20-23). The degree of departure from the theoretically predicted performance is distinctly more significant for coolers based on low-dimensional materials.

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Figure 3

A thermoelectric cooler is shown schematically at the left. The electrically active elements are shown interconnected as in Fig. 1. Additional elements that determine cooler performance are shown including the finite thermal conductance between the source of heat to be cooled and the finite conductance between the hot junctions and the ambient environment. To the right, a one-dimensional thermal model is shown with each isothermal region labeled (Ta, Th, Tc, and Ts) and one-dimensional approximations of the thermal conductances shown (exit conductance, Kh, element array conductance, K, entry conductance, Kc).

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Figure 4

The nondimensional minimum cold-side temperature is shown as a function of the cooler’s relative exit thermal conductance. The performance predicted by thermoelectric system theory (current work) as well as traditional thermoelectric theory is shown for values of thermoelectric figure of merit, ZTh=ZeTa=0.5, 1.0, and 2.0. As the exit thermal conductance decreases (due to poor heat sinking and/or miniaturization of the thermoelectric element array), the minimum temperature approaches 1.0 (no cooling below the ambient temperature). The performance predicted by traditional theory is also shown as dashed lines.

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Figure 5

The nondimensional maximum cooling power is shown as a function of the cooler’s relative exit thermal conductance. The performance predicted by thermoelectric system theory (current work) is shown for values of thermoelectric figure of merit, ZTh=ZeTa=0.5, 1.0, and 2.0, each for two values of the relative entry thermal conductance. As the exit or entry thermal conductance is decreased (due to poor heat sinking, highly localized or poorly attached heat source, and/or miniaturization of the thermoelectric element array), cooling power is degraded. The performance predicted by traditional thermoelectric theory is also shown for each value of the figure of merit.

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Figure 6

A schematic diagram of a thermoelectric cooler is shown with elements fabricated on a substrate, which in turn is mounted on a heat sink as a means of heat removal. A single thermoelectric element pair is shown for simplicity, however multiple elements may be arrayed and utilized. To the left, two schematics of a typical cross section are shown. The upper section shows active thermoelectric elements of a certain area, Ae, as well as an electrically inactive “fill” area, Af. The lower schematic depicts a representative section from a cooler that may be fabricated from vertically aligned wire. The area between each wire as well as between the n- and p-wire arrays constitutes the electrically inactive region, Af.

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Figure 7

The nondimensional cold side temperature of a cooler is shown as a function of cooler element length, L. The cooler is modeled as dissipating heat through a substrate (λsub=150Wm−1K−1,t=300μm) on a semi-infinite heat sink (λsink=300Wm−1K−1). The predicted performance for several geometries and material properties reflecting a ZTa of 1.0 and a single representative result at ZTa=5 are shown. The degradation of performance as the element length decreases, the degree of degradation being a function of the element fill factor, β, and the relative thermal conductivity of the fill material λe∕λf. Thermal conductivity ratios are shown representing what would be found using a fill material of ambient air and silicon dioxide. The model illustrates the influence of scale and cooler structure, showing conditions where a microscale element with a ZTa of 5 may be outperformed by a cooler of larger scale and a ZTa of 1.0.

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Figure 8

Cooling power density of a cooler is shown as a function of cooler element length, L. The thermal conductance between the hot-side of the cooler and the ambient temperature is modeled as the airflow limit, Kh=ṁCp. The predicted performance for three values of cooling fluid mass flow rate are shown with all coolers having materials exhibiting a ZTa of 1.0. Performance for a heat source held at the ambient temperature (Ts∕Ta=1) and a source operating below ambient temperatures (Ts∕Ta=0.85) are shown. The loci of maximum shifts to longer element lengths as the available hot side heat dissipation decreases, contrary to the 1∕L behavior predicted by traditional thermoelectric element theory.

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