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59.2.6.2 Map Package A Lifetime into Package B Thermal Loading Conditions. Using Eq. 59.10, one would derive Eq. 59.18. AF = where NfAA NfAB (59.18)
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AF = acceleration factor NfAA = number of cycles to failure in package A cycled from 10 to 125 C (condition A) NfAB = number of cycles to failure in package A cycled from 0 to 100 C (condition B)
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Equation 59.14 can be rearranged to yield Eq. 59.19. T AF = B TA where
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1 fA 1 exp 1414 TA TB fB
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(59.19)
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AF = acceleration factor fA = cyclic frequency for condition A (1 cycle/hr) fB = cyclic frequency for condition B (1 cycle/hr) TA = maximum temperature for condition A (110 C, 383 K) TB = maximum temperature for condition B (100 C, 373 K) TA = difference between maximum and minimum temperature of condition A (120) TB = difference between maximum and minimum temperature of condition B (100)
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Substitution of the values in Table 59.4 into Eq. 59.19 yields an acceleration factor of 0.641. Package A would be expected to survive 3,574 cycles (NfAB = NfAA/AF = 2,291/0.641) if subjected to condition B thermal loading conditions. The packages appear to be comparable. 59.2.6.3 Assessing Expected Field Life of a New Package Based on Thermal Cycle Data Given: Thermal cycle qualification data for a new ball grid array package (use package B in Table 59.4) and estimates of field loading conditions (see Table 59.5)
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TABLE 59.5 Field Conditions for Example Power cycle Tmax ( C) Tmin ( C) T ( C) Frequency 65 25 40 1 cycle per 30 days, 30 min. duration Minicycle 80 65 15 4 cycles per day, 60 min. duration
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Solution: The process for solving this problem is as follows. The experimentally obtained qualification data (presented in Table 59.4) must be mapped into number of power cycles to failure and number of minicycles to failure. These estimates assume that only power cycles occur and that only minicycles occur (that is the underlying assumption when mapping the experimental data to the end-use power cycle and minicycle conditions). After mapping the experimental data into field conditions, Miner s rule is employed to assess the number of cycles to fail based on the simultaneous occurrence of both power cycles and minicycles throughout the package lifetime. When employing Eq. 59.14 to map power cycles and minicycles, it is important to consider the implications of how the frequency term is interpreted. The Norris-Landzberg approach assumes that the frequency corresponds to the duration of the cycle, not how often that cycle occurs.
COMPONENT-TO-PWB RELIABILITY
Equation 59.14 can be employed to determine the acceleration factors. Equations 59.20 and Eq. 59.21 contain the expressions for power cycles and minicycles, respectively. T AF = L TP where
f 1 1 P exp 1414 TP TL ff
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(59.20)
AF = acceleration factor fP = cyclic frequency for a power cycle (2 cycles/hr) fL = cyclic frequency in the lab (1 cycle/hr) TP = maximum temperature of a power cycle (65 C, 338 K) TL = maximum temperature of the thermal cycle in the lab (100 C, 373 K) TP = difference between maximum and minimum temperature of a power cycle (40) TL = difference between maximum and minimum temperature of the thermal cycle in the lab (100) 1 T f 1 AF = L M exp 1414 TM fL TM TL
1.9 1/ 3
(59.21)
where
AF = acceleration factor fM = cyclic frequency for a minicycle (1 cycle/hr) fL = cyclic frequency in the lab (1 cycle/hr) TM = maximum temperature of a minicycle (80 C, 353 K) TL = maximum temperature of the thermal cycle in the lab (100 C, 373 K) TM = difference between maximum and minimum temperature of a minicycle (15) TL = difference between maximum and minimum temperature of the thermal cycle in the lab (100)
Substitution of the data in Tables 59.4 and 59.5 yields a power cycle acceleration factor of 10.6 and a minicycle acceleration factor of 45.6. Equation 59.10 can be rearranged to yield Eq. 59.22. Nfi = AFi NfL where Nfi = number of cycles to fail under minicycle (i) or power cycle (i) NfL = number of cycles to fail in the lab AFi = acceleration factor for minicycle (i) or power cycle (i) (59.22)
Substitution of the lab number of cycles to fail from Table 59.4 into Eq. 59.22 for minicycle and power cycles yields 37,895 power cycles to fail (assuming only power cycles occur) and 163,020 minicycles to fail (assuming only minicycles occur). Miner s rule (Eq. 59.17) can now be applied to determine the actual number of cycles to fail. It is important to note that at this stage the number of minicycles to fail if only minicycles occur and the actual number of power cycles to fail if only power cycles occur is known. The actual number of minicycles and power cycles to fail remains unknown; thus Eq. 59.17 is only one equation, whereas two unknowns still exist: Npoweractual and Nminiactual. Therefore, it is important to consider the number of minicycles that occur per power cycle. In this case, there is one power cycle per 30 days and 4 minicycles per day. This equates to 120 minicycles per power cycle. Equation 59.17 can now be written as shown in Eq. 59.23. Npoweractual/Npoweronly + K* Npoweractual/Nminionly = 1.0 (59.23)
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