In some today's and future electronic and optoelectronic packaging systems (assemblies), including those intended for aerospace applications, the package (system's component containing active and passive devices and interconnects) is placed (sandwiched) between two substrates. In an approximate stress analysis these substrates could be considered, from the mechanical (physical) standpoint, identical. Such assemblies are certainly bow-free, provided that all the stresses are within the elastic range and remain elastic during testing and operation. Ability to remain bow-free is an important merit for many applications. This is particularly true in optical engineering, where there is always a need to maintain high coupling efficiency. The level of thermal stresses in bow-free assemblies of the type in question could be, however, rather high. High thermal stresses are caused by the thermal contraction mismatch of the dissimilar materials of the assembly components and occur at low temperature conditions. These stresses include normal stresses acting in the component cross-sections and interfacial shearing and peeling stresses. The normal stresses in the component cross-sections determine the reliability of the component materials and the devices embedded into the inner component (package). The interfacial stresses affect the adhesive and cohesive strength of the assembly, i.e. its integrity. It should be pointed out that although the assembly as a whole is bow-free, the peeling stresses in it, whether thermal or mechanical, are not necessarily low: the two outer components (substrates) might exhibit appreciable warpage with respect to the bow-free inner component (package). While there is an incentive for using bow-free assemblies, there is also an incentive for narrowing the temperature range of the accelerated reliability testing: elevated temperature excursions might produce an undesirable shift in the modes and mechanisms of failure, i.e. lead to failures that will hardly occur in actual operation conditions. Failure oriented accelerated test (FOAT) specimens are particularly vulnerable, since the temperature range in these tests should be broad enough to lead to a failure, and, if a shift in the modes and mechanisms of failures takes place during significant temperature excursions, the physics of such failures might be quite different of those in actual operation conditions. Mechanical pre-stressing can be an effective means for narrowing the range of temperature excursions during accelerated testing and, owing to that, - for obtaining consistent and trustworthy information. If pre-stressing is considered, the ability to predict the thermo-mechanical stresses in the test specimen is certainly a must. Accordingly, the objective of this analysis is to obtain simple, easy-to-use, physically meaningful and practically useful closed form solutions for the evaluation of stresses in a bow-free test specimen of the type in question. The emphasis is on the role of compliant attachments, if any, between the inner and the two outer components. The developed model can be used at the design and accelerated test stages of the development of bow-free electronic and optoelectronic products. The compliant attachments, if any, could be particularly comprised of beamlike solder joint interconnections that, if properly designed, have a potential to relieve the thermal stresses to an extent that the low-cycle-fatigue state-of-stress is avoided.
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