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Research Papers

Impact of Self-Assembly Process Errors on Thermoelectric Performance

[+] Author and Article Information
Nathan B. Crane

Department of Mechanical Engineering,  University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620

Patrick McKnight

Department of Mechanical Engineering,  University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620ncrane@usf.edu

J. Electron. Packag 134(3), 031001 (Jul 18, 2012) (7 pages) doi:10.1115/1.4006709 History: Received January 25, 2011; Accepted April 10, 2012; Published July 18, 2012; Online July 18, 2012

Thermoelectric devices have many scaling benefits that motivate miniaturization, but assembly of small components is a significant challenge. Self-assembly provides a promising method for integrating very small elements. However, it introduces the possibility of stochastic errors with significant performance impacts. This work presents a method to estimate the impact of these errors on system performance. Equivalent thermoelectric properties are developed that adjust for the effect of missing elements in one-dimensional thermoelectric models. The models show that the thermoelectric devices can accommodate significant self-assembly errors by incorporation of redundant electrical paths. The model shows nearly linear decline in effective power factor with declining assembly accuracy, but the effective figure of merit (ZT) is relatively insensitive to assembly errors. Predictions from the modified one-dimensional model agree well with three-dimensional finite element simulations. This work identifies two basic strategies for how devices such as thermoelectric could be designed for self-assembly and demonstrates that it is possible to achieve high performance despite self-assembly process errors.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Illustration of thermoelectric structure showing alternating n- and p-type elements. For clarity, the top insulating layer is not represented.

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Figure 2

Illustration of thermoelectric elements without (top) and with (bottom) redundant electrical paths. Each grouping of elements with the same doping forms one macro-element made of one or more micro-elements.

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Figure 3

ANSYS finite element mesh and key parameters labeled with a system consisting of 36 thermoelectric elements and a redundancy factor of four

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Figure 4

Comparison of results between the 1D analytical model and 3D ANSYS numerical model. The model configuration is shown at their respective data points.

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Figure 5

Temperature profiles of TEC with missing elemnts. (a) Illustration of the paths along which the temperature is plotted. (b) Comparison of temperatures through the element thickness for different patterns of missing elements. (c) Temperature along the hot junction. (d) Temperatures along the cold junction.

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Figure 6

Variation of effective thermoelectric properties with redundancy and assembly probability. For all cases, the total number of elements (m × r = 1024). Symbols are average values from Monte Carlo simulations while the lines represent predictions from the large scale model.

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Figure 7

Comparison of average performance calculated using Monte Carlo simulation to predicted values based on the large assembly limits. Lines represent large assembly predictions. Circles are Monte Carlo estimates. (a) Entry and exit thermal conductance of 2 × 105 W/cm2 K. (b) Entry and exit thermal conductance of 2 × 104 W/cm2 K.

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