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.

References

References
1.
Chen
,
C.-S.
,
Wang
,
T. H.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2008, “
Warpage Analyses of Integral Methodologies With Temperature-Dependent Material Property on wBGA
,”
Proceedings of the 2008 Taiwan ANSYS User Conference
, Taipei, Taiwan.
2.
Chen
,
C.-S.
,
Wang
,
T. H.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2008, “
Different Integral Methodology of Thermomechanical Analysis With Temperature Dependent Elastic Model for Warpage of a Bi-Material Structure
,”
Proceedings of the 25th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
3.
Chen
,
C.-S.
,
Wang
,
T. H.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2008, “
Warpage Evaluation for Package-on-Package Stacking Assembly Using Total Integral of Quasi-Static Thermomechanical Analysis
,”
Proceedings of the 25th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
4.
Chen
,
C.-S.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2009, “
Warpage Analysis of MAP PoP Used Processing Model by Stress Conservation Law
,”
Proceedings of the 26th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
5.
Chen
,
C.-S.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2009, “
Warpage Optimization of MAP PoP on Die Thickness and Core Type by Trend Plot of Numerical Method
,”
Proceedings of the 26th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
6.
Chen
,
C.-S.
,
Lee
,
C.-C.
, and
Lai
,
Y.-S.
, 2009, “
Warpage Optimization of FC TFBGA on Material Type and Design of Substrate by Trend Plot of Numerical Method
,”
Proceedings of the 26th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
7.
Chen
,
C.-S.
, 2010, “
Warpage Optimization of Flip-Chip Package on Underfill-Core-Ring Types by Material-Selection Trend Plot
,”
Proceedings of the 27th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
8.
Chen
,
C.-S.
, 2010, “
Material Alignment and Warpage Optimization for XFBGA With Different Package- and Die-Size by Trend Plot of Material Selection
,”
Proceedings of the 27th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
9.
Chen
,
C.-S.
, 2010, “
Warpage Optimization of XFBGA on Die Thickness by Iterative Algorithm of Structure Design
,”
Proceedings of the 27th Chinese Society of Mechanical Engineers Conference
, Taiwan (in Chinese).
10.
Chen
,
C.-S.
, 2010, “
Different Conservation Laws as Thermo-Mechanical Analysis for Bi-Material Plate With Temperature-Dependent Properties
,”
Proceedings of the 34th National Conference on Applied Mechanics
, Taiwan (in Chinese).
11.
Chen
,
C.-S.
, 2010, “
Warpage Analysis of TRD PoP Used Processing Model by Stress Conservation Law
,”
Proceedings of the 34th National Conference on Applied Mechanics
, Taiwan (in Chinese).
12.
Chen
,
C.-S.
, 2010, “
Material Alignment and Warpage Optimization for Different PoP Types by Different Die Thickness
,”
Proceedings of the 34th National Conference on Applied Mechanics
, Taiwan (in Chinese).
13.
Chen
,
C.-S.
, 2010, “
Warpage Optimization for an 8 inch FO-WLP in a Sequential High Temperature Process
,”
Proceedings of the 2010 Taiwan ANSYS User Conference
, Taipei, Taiwan.
14.
Chen
,
C.-S.
, 2010, “
Stress Conservation Law of Linear Elasticity on In-Plane Displacement Analysis for the Reconstituted MW of FO-WLP
,”
Proceedings of the 2010 Taiwan ANSYS User Conference
, Taipei, Taiwan.
15.
Chen
,
C.-S.
, 2010, “
Simply Linear Equations Applied on In-Plane Displacement as Pre-Compensation for the Reconstituted MW of FO-WLP
,”
Proceedings of the 2010 Taiwan ANSYS User Conference
, Taipei, Taiwan.
16.
Chen
,
C.-S.
, 2010, “
Analytical Solutions and Back Analysis Constructed for Automatic Pre-Compensation on In-Plane Displacement of the Reconstituted MW of FO-WLP
,”
Proceedings of the 2010 Taiwan ANSYS User Conference
, Taipei, Taiwan.
17.
Chen
,
C.-S.
, 2010, “
Warpage Analyses Based on Different Conservation Laws for Polymeric Structures With Temperature-Dependent Properties
,”
Proceedings of the 2010 Taiwan COMSOL User Conference
, Taipei, Taiwan.
18.
Chen
,
C.-S.
, 2010, “
Warpage Prediction Utilized Different Conservation Laws for MAP PoP With Temperature-Dependent Properties
,”
Proceedings of the 2010 Taiwan COMSOL User Conference
, Taipei, Taiwan.
19.
Pan
,
T. Y.
, and
Pao
,
Y. H.
, 1990, “
Deformation in Multi-Layer Stacked Assemblies
,”
ASME J. Electron. Packag.
,
112
, pp.
30
34
.
20.
Timoshenko
,
S.
, 1925, “
Analysis of Bi-Metal Thermostats
,”
J. Opt. Soc. Am.
,
11
, pp.
233
255
.
You do not currently have access to this content.