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RESEARCH PAPERS

Multiscale Mechanics in Microelectronics: A Paradigm in Miniaturization

[+] Author and Article Information
M. G. Geers

Department of Mechanical Engineering,  Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsm.g.d.geers@tue.nl

V. Kouznetsova1

Department of Mechanical Engineering,  Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

W. A. Brekelmans

Department of Mechanical Engineering,  Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

1

Also at Netherlands Institute for Metals Research, P.O. Box 5008, 2600 GA Delft, The Netherlands

J. Electron. Packag 127(3), 255-261 (Jun 24, 2004) (7 pages) doi:10.1115/1.1939007 History: Received February 03, 2003; Revised June 24, 2004

This paper reviews the inherent change in the observed mechanical behavior of electronic components, structures, and multimaterials as a result of the ongoing miniaturization. In general, the size of microstructures is no longer negligible with respect to the component size in micro and submicron applications. Additionally, surface layers start to play a more prominent role in the mechanical response. Microstructural effects, macroscopically triggered gradient effects, and surface effects jointly appear and constitute the various size effects that can be observed. Classical continuum mechanics theories fail to describe these phenomena, and higher-order multiscale theories are required to arrive at an appropriate prediction of the mechanical behavior of miniaturized structures.

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Hall-Petch effect and its limits

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Figure 2

Gradient effects in small-scale components

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Figure 3

Strengthening for a decreasing foil thickness, reproduced from (5)

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Figure 4

Surface layers influencing the mechanical response

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Figure 5

Four-point bending on multilayered PCB boards

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Figure 6

Observed size effect in the mechanical response of bended PCB boards

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Figure 7

Second-order multiscale homogenization

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Figure 8

Second-order versus first-order multiscale homogenization in bending

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Figure 9

Gradient size effects in a microstructure

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Figure 10

Surface effects in a constrained thin shear layer for various ratios of H∕d

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Figure 11

Constrained thin film loaded in shear

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Figure 12

Macroscopic shear stress as a function of averaged shear for various ratios of H∕d

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Figure 13

Fine-scale microstructural deformation patterns in a thin layer for H∕d=5

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