7 Fundamentals and Failures in Die Preparation for 3D Packaging
193
− γ
S
SV [2X 1 − (X − W )] + γ
B
SV W − γ
B
L S W
(7.27)
By considering the following geometry relationship,
l =
θ X
sin θ
; l 1 =
θ X 1
sin θ
(7.28)
mass balance,
X =
2X 1
(7.29)
and Young’s equation,
cos θ =
γ
S
SV − γ
S
L S
γ
E
LV
; cos β =
γ
B
SV − γ
B
L S
γ
E
LV
(7.30)
the Gibbs free energy change can be simplified as
G = γ
E
LV
θ
sin θ
− cos θ
√
2 − 1
X + [cos β − cos θ ]W
(7.31)
Based on energy minimization principle, dewetting occurs when the following
relationship is satisfied.
W
X
≥
θ
sin θ
− cos θ
√
2 − 1
cos θ − cos β
(7.32)
This 2D epoxy dewetting model can be further expanded as 3D epoxy dewetting
model by extending the circular segment to horizontal cylindrical segment with length
(L) and considering epoxy mass (M)
M = ρ L S = ρ L
θ
4 sin
2
θ
−
1
4 tan θ
X
2
(7.33)
where ρ is epoxy density. Epoxy dewetting will occur once the following equation
is satisfied.
W
√
M
≥
2
√
2 − 1
√
[θ − cos θ sin θ]
√
ρ L[cos θ − cos β]
(7.34)
To increase the epoxy dewetting or reduce the epoxy KOZ, the epoxy contact
angle at surface energy barrier (β) and the line width of surface energy barrier (W)