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AF = acceleration factor NfF = number of cycles to failure in the field NfL = number of cycles to failure in the lab epF = plastic portion of the cyclic strain in the field epL = plastic portion of the cyclic strain in the lab fF = cyclic frequency fL = cyclic frequency TmaxF = maximum temperature of the thermal cycle in the field (K) TmaxL = maximum temperature of the thermal cycle in the lab (K) k = Boltzmann s constant (eV) L = lab conditions F = field conditions

Equation 59.11 can be algebraically rearranged to yield Eq. 59.12. Note that the max subscripts on the maximum temperatures have been dropped to simplify the notation. = pL pF

1/ 3

(59.12)

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With the previous results in mind, choosing k =1 we can write the spatial part of the line element as dr 2 (a) dl 2 = + r 2 d 2 + r 2 sin2 d 2 2m 1 1 r3 r 3 dr 2 2 (b) dl = + r 2 d 2 + r 2 sin2 d 2 1 1 r3 3 dr 2 2 (c) dl = + r 2 d 2 + r 2 sin2 d 2 1 1+ r3 3 If the cosmological constant is proportional to the size of the universe, say a =

AF = acceleration factor epF = plastic portion of the cyclic strain in the field epL = plastic portion of the cyclic strain in the lab fF = cyclic frequency in the field fL = cyclic frequency in the lab TF = maximum temperature of the thermal cycle in the field (K) TL = maximum temperature of the thermal cycle in the lab (K)

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When considering package interconnects of the same geometry and material set, one can reduce the strain term ep in Eq. 59.9 to the change in temperature.10 This is a key feature that enables the development of an acceleration transform. The goal of this analysis is to develop a transform that allows one to map laboratory thermal cycle loading conditions to field loading conditions for the same package. Thus it is valid to assume that the strain term can be reduced to the change in temperature, as shown in Eq. 59.13.

(59.13)

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ep = plastic portion of the cyclic strain T = difference between maximum and minimum temperature of the thermal cycle

Substitution of Eq. 59.12 (including L and F subscripts for lab and field, respectively) yields the final form of the acceleration factor relationship, which can be seen in Eq. 59.14.10 NfF NfL 1 T f 1 = L F exp 1414 x TF TL TF fL

1.9 1/ 3

(59.14)

AF = acceleration factor fF = cyclic frequency in the field fL= cyclic frequency in the lab TF = maximum temperature of the thermal cycle in the field (K) TL = maximum temperature of the thermal cycle in the lab (K) TF = difference between maximum and minimum temperature of the thermal cycle in the field TL = difference between maximum and minimum temperature of the thermal cycle in the lab

Figure 59.7 contains experimental failure data for a ceramic ball grid array (CBGA) cycled under the same two conditions. The predicted acceleration factor was calculated to be 3.2 employing Eq. 59.14. This predicted value correlates quite well with the CBGA data (acceleration factor ranges from 2.9 to 3.6). Note that this approach tends to be overly conservative when mapping large lab T into small field T (in the case of minicycles, to be discussed in a subsequent section). 59.2.4.3 Effect of Lead-Free Conversion. The acceleration factor equation (Eq. 59.14) is specifically derived from experimental data for Pb/Sn solder joints. What remains to be conclusively demonstrated is an equivalent acceleration transform for lead-free solder joints. Several studies have been performed, but there are no acceleration transforms accepted industrywide for lead-free solders. One of the acceleration transforms proposed is discussed in this section. A more comprehensive list of other field life prediction studies can be found in the appendix of IPC-9701-A.3

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