Thermal stress testing is a common procedure used toassess

Chapter 5, Problem 5.39

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Thermal stress testing is a common procedure used toassess the reliability of an electronic package. Typi-cally, thermal stresses are induced in soldered or wiredconnections to reveal mechanisms that could causefailure and must therefore be corrected before the prod-uct is released. As an example of the procedure,consider an array of silicon chips (?ch?2300 kg/m3, cch?710 J/kg?K) joined to an alumina substrate(?sb?4000 kg/m3, csb?770 J/kg?K) by solder balls(?sd?11,000 kg/m3, csd?130 J/kg?K). Each chip ofwidth Lchand thickness tchis joined to a unit substratesection of width Lsband thickness tsbby solder balls ofdiameter D.A thermal stress test begins by subjecting the multichipmodule, which is initially at room temperature, to a hotfluid stream and subsequently cooling the module byexposing it to a cold fluid stream. The process isrepeated for a prescribed number of cycles to assess theintegrity of the soldered connections.(a) As a first approximation, assume that there isnegligible heat transfer between the components(chip/solder/substrate) of the module and thatthe thermal response of each component may bedetermined from a lumped capacitance analysis involving the same convection coefficient h.Assuming no reduction in surface area due to con-tact between a solder ball and the chip or substrate,obtain expressions for the thermal time constant ofeach component. Heat transfer is to all surfaces of achip, but to only the top surface of the substrate.Evaluate the three time constants for Lch?15 mm,tch?2 mm, Lsb?25 mm, tsb?10 mm, D?2 mm,and a value of h?50 W/m2?K, which is character- istic of an airstream. Compute and plot the temper-ature histories of the three components for theheating portion of a cycle, with Ti?20C andT??80C. At what time does each component expe-rience 99% of its maximum possible temperature rise,that is, (T?Ti)/(T??Ti)?0.99? If the maximumstress on a solder ball corresponds to the maximumdifference between its temperature and that of thechip or substrate, when will this maximum occur?(b) To reduce the time required to complete a stresstest, a dielectric liquid could be used in lieu of airto provide a larger convection coefficient ofh?200 W/m2?K. What is the corresponding sav-ings in time for each component to achieve 99% ofits maximum possible temperature rise?