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By John G. Webster (Editor)

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In the general case, when there are j mechanisms operating and each one affects only a small part of the population, the total pdf is given by k f T (t) = a j f j (t) (16) j=1 where f j(t) ϭ pdf of the jth mode aj ϭ population fraction affected by mode j An analogous formula describes FT(t). Then the hazard rate for the population is computed from f T(t) and FT(t). Such situations are described as mixed-mode models. THERMOMECHANICAL MODELS Fatigue Thermomechanical fatigue is the predominant failure mechanism of first- and second-level interconnects.

According to Huntington (49), the main contributors to Q* in a diffusion vacancy mechanism are the migration energy ⌬Hm and the vacancy energy of formation ⌬Hf , written as Q* ϭ ͱ⌬Hm Ϫ ⌬Hf . 8. 3 kJ/mol. 5 kJ/mol. Evidently, Q* is a quantity af- 206 DESIGN FOR MICROELECTRONICS RELIABILITY fected by many variables and must be determined for each material. In practice, Q* becomes part of the proportionality constant, and the experimental variables are ⌬T across the joint and average T. Gurp, deWaard, and Duchatenier (50) studied the thermomigration of indium and determined the heat of transport Q*.

For high-lead Pb-Sn, the predominant oxide formed is SnO, which covers the entire surface of the alloy despite the low Sn concentration. At temperatures above 100ЊC, some PbO also forms. Tin oxide performs a useful function for solder bumps, namely, that of protecting the joint from corrosion by lead carbonate formation. On the other hand, its presence at any stage of the process hinders solder wettability and prevents the bumps from achieving a spherical shape. Lead carbonate also increases contact resistance for pad-on-pad or edge connectors thus influencing the thermal properties and package thermal management.

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52.Reliability by John G. Webster (Editor)


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