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.

Computing explanations for interactive constraint-based systems

Constraint programming has emerged as a successful paradigm for modelling combinatorial problems arising from practical situations. In many of those situations, we are not provided with an immutable set of constraints. Instead, a user will modify his requirements, in an interactive fashion, until he is satisfied with a solution. Examples of such applications include, amongst others, model-based diagnosis, expert systems, product configurators. The system he interacts with must be able to assist him by showing the consequences of his requirements. Explanations are the ideal tool for providing this assistance. However, existing notions of explanations fail to provide sufficient information. We define new forms of explanations that aim to be more informative. Even if explanation generation is a very hard task, in the applications we consider, we must manage to provide a satisfactory level of interactivity and, therefore, we cannot afford long computational times. We introduce the concept of representative sets of relaxations, a compact set of relaxations that shows the user at least one way to satisfy each of his requirements and at least one way to relax them, and present an algorithm that efficiently computes such sets. We introduce the concept of most soluble relaxations, maximising the number of products they allow. We present algorithms to compute such relaxations in times compatible with interactivity, achieving this by indifferently making use of different types of compiled representations. We propose to generalise the concept of prime implicates to constraint problems with the concept of domain consequences, and suggest to generate them as a compilation strategy. This sets a new approach in compilation, and allows to address explanation-related queries in an efficient way. We define ordered automata to compactly represent large sets of domain consequences, in an orthogonal way from existing compilation techniques that represent large sets of solutions.

Identifying sources of global contention in constraint satisfaction search

Much work has been done on learning from failure in search to boost solving of combinatorial problems, such as clause-learning and clause-weighting in boolean satisfiability (SAT), nogood and explanation-based learning, and constraint weighting in constraint satisfaction problems (CSPs). Many of the top solvers in SAT use clause learning to good effect. A similar approach (nogood learning) has not had as large an impact in CSPs. Constraint weighting is a less fine-grained approach where the information learnt gives an approximation as to which variables may be the sources of greatest contention. In this work we present two methods for learning from search using restarts, in order to identify these critical variables prior to solving. Both methods are based on the conflict-directed heuristic (weighted-degree heuristic) introduced by Boussemart et al. and are aimed at producing a better-informed version of the heuristic by gathering information through restarting and probing of the search space prior to solving, while minimizing the overhead of these restarts. We further examine the impact of different sampling strategies and different measurements of contention, and assess different restarting strategies for the heuristic. Finally, two applications for constraint weighting are considered in detail: dynamic constraint satisfaction problems and unary resource scheduling problems.