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Research Papers

Different Conservation Laws Constructed on Warpage Analyses for Bimaterial Plates With Temperature-Dependent Properties

[+] Author and Article Information
Chih-Sung Chen1

 Corporate Engineering/Advanced Semiconductor Engineering, Inc., 26 Chin 3rd Road, Nantze Export Processing Zone, Nantze, Kaohsiung 811, Taiwand89543007@ntu.edu.tw

1

Corresponding author.

J. Electron. Packag 133(4), 041006 (Dec 09, 2011) (14 pages) doi:10.1115/1.4005293 History: Received December 02, 2010; Revised September 30, 2011; Published December 09, 2011; Online December 09, 2011

Polymeric material has been applied in electronic product extensively, especially for packaging applications, thus thermomechanical analyses for encapsulated structure are frequently encountered. However, modulus and thermally induced strain of polymeric material are not constant, but time- and temperature-dependence. For simplification of the stress constitutive models, particularly for applications on electronic packaging can be found in literature, the time-dependent behavior could be neglected. Otherwise, the property only considered as a function of temperature can achieve time saving and cost down, but to the best of the author’s knowledge, the thermomechanical analysis based on different conservation laws so far has not been studied indeed. Most of the relative studies published in literature are in strain conservation law, and recently strain–stress conservation law was formulated, so-called force-displacement incremental solution. This study has developed a stress-based conservation law regardless of derived strain and strain–stress based conservation laws for stress constitutive models applied in thermomechanical analysis; meanwhile, incorporated cross-link induced residual strain from polymer forming. Furthermore, the nonincrement approach is implemented by a concept of force and moment equilibrium on the flexural stiffness of final stage, and derived for efficiency enhancing. On the other hand, analytical solutions based on different conservation laws for bimaterial plate were utilized to compare with experimental measurements. The results indicate that warpage analysis based on stress conservation law with temperature-dependent property can be more realistically predicted over a range of temperature, whereas a large error can be caused by using approximated CTE or nonconsidering residual strain, especially for temperature above Tg .

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Concept of molding and post mold cure process

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Figure 2

Sketch of a multimaterial structure

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Figure 3

Sketch of the bimaterial beam for examples

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Figure 4

Moduli and CTE(s) based on different conservation laws

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Figure 5

Moduli and CTE(s) based on different conservation laws considered residual strain

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Figure 6

Warpage variation for different conservation laws with/without residual strain

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Warpage difference for different conservation laws if consider residual strain

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Figure 8

Moduli and CTE(s) based on different conservation laws

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Figure 9

Moduli and CTE(s) based on different conservation laws considered residual strain

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Figure 10

Warpage variation for different conservation laws with/without residual strain

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Figure 11

Warpage difference for different conservation laws and if they consider residual strain

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Sketch of bimaterial plate for experiment

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Sketch of setup for warpage measured system (phase-stepping shadow Moiré)

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Figure 14

Images reconstruction: (ac) filtered images, (d) phase-map, (e) 3D contour, and (f) rotation released 3D contour

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Figure 15

Moduli and thermal strain(s) (175 °C = 0) for materials of bimaterial plate

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Figure 16

Moduli and thermal strain(s) (175 °C = 0 for molding process) after molding process and post mold cure process, respectively

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Figure 17

Moduli and CTE(s) based on different conservation laws

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Figure 18

Moduli and CTE(s) based on different conservation laws considered residual strain

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Figure 19

Warpage comparison of different conservation laws with/without residual strain to measurement

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Figure 20

Comparison of CTE for approximate and real values in different temperature spans

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Figure 21

Moduli and CTE(s) based on different conservation laws

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Figure 22

Moduli and CTE(s) based on different conservation laws considered residual strain

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Figure 23

Warpage comparison of different conservation laws with/without residual strain to measurement

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Figure 24

Warpage difference for different conservation laws and if they consider residual strain

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