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Chip Scale Review May • June • 2019

[ChipScaleReview.com]
**Wafer warpage**

The following sections discuss predicting

warpage and model validation.

**Prediction of warpage.**

In the search for a

suitable EMC that causes minimal warpage,

close collaboration between the equipment

supplier and the EMC supplier is needed. The

EMC supplier can manufacture several small

batches of test EMCs with a low coefficient

of thermal expansion (CTE), a low viscosity,

and a good particle distribution. The

feedback from the equipment supplier to the

EMC supplier after doing the molding tests is

crucial for the development of the best EMC

for wafer-level transfer molding. Even with a

close collaboration, soon there are many types

of EMCs that should be tested. Finite element

method (FEM) analysis in combination with

a trial and error testing method works well [1],

however a faster selection method is possible

by doing some simple calculus in advance

and predicting which EMC will have the best

warpage behavior.

Traditionally one uses the material

properties of the wafer and EMC for the

prediction of warpage. For the wafer, the

CTE (α_wafer ) is the only parameter that

is used. For the EMC, one uses the material

properties α1_emc , α2_emc and Tg, where

α1_emc and α2_emc are the CTEs below and

above the glass transition temperature Tg,

respectively. In order to predict the warpage,

one calculates the difference in effective

length change ΔL of the EMC when the

EMC cools down from mold temperature to

ambient temperature relative to the wafer.

The smaller the effective length change

ΔL between wafer and EMC, the better the

warpage will be. Graphically this can be seen

in

**Figure 2**

. At mold temperature Tmold,

both the wafer and EMC have the same

length L0. When they cool down to ambient

temperature, Tamb, the diameter of the wafer

decreases equal to a slope of α_wafer,

while the EMC length decreases first

with a slope of α2_emc, and below

Tg with a slope α1_emc. At Tamb, a

difference in length will remain, which

will cause warpage. Using this graphical

method in practice does not always work

well, because important parameters

like the thickness and Young’s modulus

of the wafer and mold cap have been

neglected, which have a significant

influence on the warpage.

A more accurate method to predict

the warpage, whereby the thickness

and Young’s modulus of the materials

is taken into account, is Timoshenko’s formula of the bimetallic strip [2]. The bimetallic strip

consists of two layers of materials with different properties as can be seen in

**Figure 3**

. With

this formula, one can calculate the radius of curvature, κ, as a function of the material and

geometric properties of a bimetallic rectangular strip:

Where E

1

and h

1

are the Young’s modulus and thickness of material one (wafer material);

and E

2

and h

2

are the Young’s modulus and thickness of material two (EMC material) as can be

seen in

**Figure 3**

. ε is equal to the misfit strain and can be calculated by:

ε = (α

1_emc

- α

_wafer

) * ΔT

Here, α1_emc is equal to the CTE

of the EMC below its glass transition

temperature, and α_wafer is equal to

the CTE of the wafer. ΔT is equal to the

current temperature minus the glass

transition temperature, Tg. Tg is used

under the assumption that above Tg,

no significant stresses will be built up

that contribute to the warpage due to

the much lower Young’s modulus. In

this formula, the curvature (κ) shows

a dependency of the thickness of the

mold cap (h

2

) and wafer (h

1

). This

makes it very useful to see if the ratio

between mold cap thickness and wafer

thickness has been balanced to reduce

warpage. In

**Figure 4**

one can see a

three-dimensional plot of Timoshenko’s

formula for a silicon wafer with an

EMC mold cap. When the value of the curvature becomes high, a highly warped wafer can be

expected. This is the case when a thin wafer of for instance, 50μm, is used in combination with

a 100μm EMC layer.

**Validation.**

Although the Timoshenko formula has been derived for a rectangular strip, it

will give a qualitative estimation of the warpage of a circular wafer with a mold cap. Therefore,

it is suitable to make a comparison among the different EMC types, without giving the exact

value of the warpage. In order to prove this comparison method, an experiment is done where

several EMC types are molded on a 12” silicon wafer using several cap heights (h2) and EMCs

(

**Table 1**

). Based on the calculations with Timoshenko’s formula, the four most promising

EMCs have been selected, which give a variety in the calculated κ values. After molding, the

warpage of the wafers were measured, which can be seen in the last row of

**Table 1**

. Clearly,

a strong correlation can be observed between the calculated curvature and the amount of

**Figure 2:**

The shrinkage of the wafer and EMC

during the cool down process. The distance ΔL is

generally assumed to be a measure for the warpage.

**Figure 3:**

A bimetallic strip. With Timoshenko’s formula,

one can calculate the curvature

κ

.

**Figure 4:**

A three-dimensional plot of Timoshenko’s for-

mula. The curvature as a function of the layer thickness of

the wafer and mold cap is shown in this plot.