38 Chip Scale Review November • December • 2019 [ChipScaleReview.com] Should temperature cycling accelerated testing for SJIs be replaced? In the effort reduced to practice under a project with NASA Jet Propulsion Lab, random vibrations were considered as a white noise of the given level, characterized as the ratio of the acceleration amplitudes squared to the vibration frequency. Testing has been carried out for two printed circuit boards (PCBs), with surface-mounted packages on them, at the same level (with the mean value of 50g) of three-dimensional random vibrations. One board was subjected to the low temperature of -20° C and another to a temperature of -100° C . It has been found by preliminary calculations that the joints tested at -20° C will still perform within the elastic range, while the joints at -100° C will experience appreciable inelastic strains. No wonder that no failures were detected in the joints of the board tested at -20° C , while the joints of the board tested at -100° C failed after several hours of testing. Using the BAZ model, the probability of non-failure of the SJI experiencing inelastic strains during temperature cycling can be sought in the form (see Figure 3 ): (2) Here U 0 , eV , is the activation energy that characterizes the propensity of the solder material to fracture, W , eV , is the damage caused in the solder material by a single temperature cycle and measured, in accordance with Hall’s concept [28,29], by a hysteresis loop a r ea for t he g iven i n e l a s t i c s t r a i n , T 0 , K is the absolute temperature (say, the me a n t empe r at u r e of the cycle), n is the number of cycles, k , eV/K is Boltzmann’s constant, t , sec , is time, R, Ω, is the measured (monitored) electrical resistance at the joint location, and γ is the sensitivity factor for the measured electrical resistance. Equation (2) makes physical sense. Indeed, the probability P of non-failure is “one” at the initial moment of time and when electrical resistance of the solder joint structure is zero. This probability decreases with time because of the material aging and structural degradation, and not necessarily only because of temperature cycling; it is lower for higher electrical resistance (a resistance as high as, say, 450Ω, can be viewed as an indication of an irreversible mechanical failure of the joint); materials with higher activation energy U 0 have a higher probability of non-failure; the increase in the number n of cycles leads to lower effective energy U 0 - nW , and so does the energy W of a single cycle. It could be shown that the maximum entropy of the distribution (2) takes place at the mean time to failure (MTTF) τ expressed as: (3) Me ch a n i c a l f a i l u r e , b e c a u s e of temperature cycling, takes place, when the number n of cycles is W h e n failure occurs, the temperature in the denominator in the parenthesis in equation (2) becomes irrelevant, and this equation yields: (4) Here P f is the measured probability of non- failure for the situation, when failure takes place, and is the MTTF. If, e.g., 20 dev ice s have been t empe r at u re cycled and the high resistance R f = 450Ω, considered as an indication of failure was detected in 15 of them, then P f = 0.25. If the number of cycles during such FOAT was, say, n f = 2000, and each cycle lasted, say, for 20min=1200sec., then the predicted time t f at failure is t f = 2000 x 1200 = 24 x 10 5 sec, the factor γ is a n d t h e MTTF is According to Hall’s concept, the energy, W , of a single cycle should be evaluated by running a specially designed test, in which strain gages should be used. As an example, in the above tests this energy (the area of the hysteresis loop) was W = 2.5 x 10 -4 eV . Then the stress-free activation energy of the solder material is U 0 = n f W = 2000 x 2.5 x 10 -4 = 0.5 eV. In order to assess the number of cycles to failure in actual operating conditions one could assume that the temperat u re range in these conditions is, say, half the accelerated test range, and that the area, W , of the hysteresis loop is proportional to the temperature range. Then the number of cycles to failure is If the duration of one cycle in actual operating conditions is one day, then the time to failure will be t f = 2000 days = 5.48 years . Summary There are several effective ways to relieve stresses and strains in SJIs of IC packages. Future work should include experimentations to confirm the obtained findings and recommendations. References Contact the author for the complete list of references (firstname.lastname@example.org ). Biography Ephraim Suhir is on the faculty of Portland State U., Portland, OR, and is also CEO of ERS Co., Los Altos, CA, USA. He has authored 400+ publications, presented numerous keynote and invited talks worldwide, and received many professional awards, including 1996 Bell Labs DMTS Award, 2004 ASME Worcester Read Warner Medal (he is the third “Russian American,” after S. Timoshenko and I. Sikorsky, who received this prestigious award), 2019 IEEE EPS Field award for seminal contributions to mechanical reliability engineering and 2019 IMAPS Life Achievement Award for making exceptional, visible, and sustained impact on the microelectronics packaging industry in technology, business or both. Email email@example.com; www.ERSuhir.com Figure 3: Hysteresis loop obtained for one cycle of SJI testing: P. M. Hall’s approach [28,29].