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L. Chen et al.
substrate-control methods, which could result in additional stress into the package.
Therefore, it is necessary to develop more effective control methods based on deep
understanding of warpage control mechanism [66].
To address the thermal stress induced reliability issues (e.g., excessive warpage
and solder joint failures) at package level and provide potential solutions, this section
will first introduce analytical theories for the calculation of thermal stress and
warpage for multilayered structures under temperature loading. Then the warpage
mechanism during the packaging process is demonstrated, followed by discussion on the effectiveness of traditional warpage control methods in Sect. 15.3.3.
In Sect. 15.3.4, a new control approach is presented for achieving potential warpagefree package. Numerical modeling, as well as experimental testing, is performed to
verify the new method. Different cases are studied and the results are discussed in
details.
15.3.2 Thermal Stresses in a Multilayered Structure
As 3D chip stacks and other microelectronic devices can be conceived as multilayered
structures, analytical modeling based on the existing theories may be adopted. The
main advantage of analytical modeling is that one can perform quick calculation of
thermal stress for any multilayered systems with regular geometry, especially for
those including very thin layers.
There are several analytical methods available for calculating the thermal stress
in laminated structures or multilayered composite used in electronic packaging. One
theory introduced here is called the natural bending theory [67], which is based
on the assumptions of linear elasticity and small deformation. The basic idea of
the natural bending theory is illustrated in Fig. 15.10, where a two-layer system is
used for simplicity. Due to different CTEs of layer 1 and layer 2 (α 2 < α 1 ), thermal
mismatch is produced in the cooling process from high temperature (T H ) to room
temperature (T R ). The theory first considers a stress-free case, so that each material
will contract accordingly to their CTEs, resulting in mismatch in stress-free thermal
strain (ε
0
T 1 = α 1 T > ε
0
T 2 = a 2 T ). To accommodate the mismatch, layer 1 will
be constrained and then bonded to layer 2. After the constraint is released and the
stack will be bent. The process of natural bending theory can be used to explain how
warpage is developed by thermal stress in dissimilar materials. Note that uniform
temperature is considered in the theory.
Based on the natural bending theory, the warpage of a multilayered device can
be resulted from both thermal loading and external applied curvature. The normal
stress in x direction in each layer i of a composite can be expressed as a function of
thermal strain and applied curvature, as [67]
σ xi = ¯
E i [(κ nat + κ app )(y − h b ) + ¯
ε T + v i A − η i ε
0
i ]
(15.2)
L. Chen et al.
substrate-control methods, which could result in additional stress into the package.
Therefore, it is necessary to develop more effective control methods based on deep
understanding of warpage control mechanism [66].
To address the thermal stress induced reliability issues (e.g., excessive warpage
and solder joint failures) at package level and provide potential solutions, this section
will first introduce analytical theories for the calculation of thermal stress and
warpage for multilayered structures under temperature loading. Then the warpage
mechanism during the packaging process is demonstrated, followed by discussion on the effectiveness of traditional warpage control methods in Sect. 15.3.3.
In Sect. 15.3.4, a new control approach is presented for achieving potential warpagefree package. Numerical modeling, as well as experimental testing, is performed to
verify the new method. Different cases are studied and the results are discussed in
details.
15.3.2 Thermal Stresses in a Multilayered Structure
As 3D chip stacks and other microelectronic devices can be conceived as multilayered
structures, analytical modeling based on the existing theories may be adopted. The
main advantage of analytical modeling is that one can perform quick calculation of
thermal stress for any multilayered systems with regular geometry, especially for
those including very thin layers.
There are several analytical methods available for calculating the thermal stress
in laminated structures or multilayered composite used in electronic packaging. One
theory introduced here is called the natural bending theory [67], which is based
on the assumptions of linear elasticity and small deformation. The basic idea of
the natural bending theory is illustrated in Fig. 15.10, where a two-layer system is
used for simplicity. Due to different CTEs of layer 1 and layer 2 (α 2 < α 1 ), thermal
mismatch is produced in the cooling process from high temperature (T H ) to room
temperature (T R ). The theory first considers a stress-free case, so that each material
will contract accordingly to their CTEs, resulting in mismatch in stress-free thermal
strain (ε
0
T 1 = α 1 T > ε
0
T 2 = a 2 T ). To accommodate the mismatch, layer 1 will
be constrained and then bonded to layer 2. After the constraint is released and the
stack will be bent. The process of natural bending theory can be used to explain how
warpage is developed by thermal stress in dissimilar materials. Note that uniform
temperature is considered in the theory.
Based on the natural bending theory, the warpage of a multilayered device can
be resulted from both thermal loading and external applied curvature. The normal
stress in x direction in each layer i of a composite can be expressed as a function of
thermal strain and applied curvature, as [67]
σ xi = ¯
E i [(κ nat + κ app )(y − h b ) + ¯
ε T + v i A − η i ε
0
i ]
(15.2)