Enhanced Polymer Passivation Layer for Wafer Level Chip Scale ...

cycles for the crack to propagate across a solder joints diameter. The number of cycles before
crack initiation N0 is calculated as:
N CW 0 1
C2
ave
106
(5-9)
where ∆Wave is the incremental inelastic energy per cycle at the stable cycle, and at the solder
joint in concern, C1 and C2 are constants. The crack growth rate (da/dN) per cycle was also
calculated in the similar equation as:
d dN C W
(5-10)
C4
a 3 ave
and the total number of cycles before failure (Na) can thus be written as:
a
Na N (5-11)
0 d dN
a
where a is the total distance the crack has to travel before failure. For a solder joint, it can be
conveniently interpreted as the solder diameter at the solder die interface. The viscoplastic strain
energy density ∆Wave (in psi) is defined by averaged quantity across the element along the solder joint
interface where the crack propagates. Because Darveauxs model was developed in English Unit, the unit
of a and ∆Wave have been converted from a Metric Unit (mm and MPa) to an English Unit (in and psi)
during the calculation of the fatigue life prediction. ∆Wave was introduced and defined by:
W n
i1
ave n
dWV
i1
V
i i
i
(5-12)
where dWi is the incremental inelastic energy of element i at the first stable cycle, n is the total
number of elements considered and Vi is the calculated volume of element i.