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

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strain rate sensitivity. The evolution equation describes the strain hardening or softening of the<br />

material:<br />

a ds d<br />

o B <br />

p<br />

hoB <br />

dt B <br />

dt<br />

(5-2)<br />

o 1 *<br />

S<br />

B (5-3)<br />

S<br />

dp <br />

dt Q <br />

exp<br />

<br />

A kT <br />

<br />

* <br />

S S<br />

represented steady state creep behavior by a double power law model as equation (5) shown<br />

101<br />

n<br />

(5-4)<br />

where ho is the hardening/softening constant, a is the strain rate sensitivity of hardening/softening,<br />

the quantity s* represents a saturation value of de<strong>for</strong>mation resistance, sˆ is a coefficient <strong>for</strong><br />

de<strong>for</strong>mation resistance saturation value, and n is the strain rate sensitivity <strong>for</strong> s saturation.<br />

Anand’s model has been shown to provide reasonable results when compared to a combination<br />

of plasticity and creep model [Tunga et al, 2002]. It has been used in the ANSYS program as the<br />

standard option to describe viscoplastic elements. Nine material parameters (A, Q, m, n, ξ, sˆ, a,<br />

ho, and so,) need to be determined to model the material behavior of solder.<br />

Creep Model: The elastic-creep model (Creep) incorporates the creep effect on solder<br />

material and all inelastic de<strong>for</strong>mation is induced by creep phenomena.<br />

Wiese et al. [92] studied the creep behavior of flip chip solder joint samples with<br />

Sn4.0Ag0.5Cu solder and the bulk solder specimen sample (a dog-hone type specimen), PCB<br />

specimen sample (copper wire soldered into a printed circuit board). They identified two<br />

mechanisms <strong>for</strong> steady state creep de<strong>for</strong>mation <strong>for</strong> the bulk and PCB samples, and attributed<br />

these to low stress (climb controlled) and high stress (combined glide/climb) mechanisms. They

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