Effect of solder volume on joint shape with variable chip-to-board contact pad ratio

The objective of this paper is to investigate the effect of the pad size ratio between the chip and board end of a solder joint on the shape of that solder joint in combination with the solder volume available. The shape of the solder joint is correlated to its reliability and thus of importance. For low density chip bond pad applications Flip Chip (FC) manufacturing costs can be kept down by using larger size board pads suitable for solder application. By using “Surface Evolver” software package the solder joint shapes associated with different size/shape solder preforms and chip/board pad ratios are predicted. In this case a so called Flip-Chip Over Hole (FCOH) assembly format has been used. Assembly trials involved the deposition of lead-free 99.3Sn0.7Cu solder on the board side, followed by reflow, an underfill process and back die encapsulation. During the assembly work pad off-sets occurred that have been taken into account for the Surface Evolver solder joint shape prediction and accurately matched the real assembly. Overall, good correlation was found between the simulated solder joint shape and the actual fabricated solder joint shapes. Solder preforms were found to exhibit better control over the solder volume. Reflow simulation of commercially available solder preform volumes suggests that for a fixed stand-off height and chip-board pad ratio, the solder volume value and the surface tension determines the shape of the joint.

Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.