Gull Wing Lead Array Example for the Surface Evolver

A gull wing lead is a wire coming from a chip bending horizontally to make contact with a solder pad on a substrate. This set of examples models one such joint, beginning very simply and adding features until a fairly complex model is reached. The lead has three sections: a horizontal section above the pad, a circular section rising up at one end, then a second circular section curving over to horizontal where the lead enters the chip.

The ultimate goal here is to find the equilibrium shape of the liquid solder, and the forces exerted by the solder on the lead. Only translational forces will be done; torques will be left as an exercise for the reader.

The system of units is somewhat ideosyncratic, using the mil-kilogram-second system (1 mil = 0.001 inch), but that is what is used by some in industry and illustrates the point that the Evolver doesn't care what system of units you use as long as you are consistent.

A list of the various datafiles is below, with brief descriptions. Each datafile has its own page, which elaborates on the added features and their implementation. Note that the ordering of the datafiles is tree-like, rather than linear. The complete set of datafiles and auxiliary command files is available in gullwing-files.zip or gullwing-files.tar.

NOTE: These models require Evolver version 2.12 (March 21, 1999) or higher to run. One of the benefits of writing my own software is that if it needs features, I can add them. Some of the datafiles could run on old versions with a little editing, but some definitely need the new features.

It is assumed that you are familiar with the operation of the Surface Evolver at least to the level of the basic Evolver Tutorial examples cube.fe, cat.fe, and mound.fe. Also, it would be well to look first at the Ball Grid Array set of examples first, since that has a much simpler geometry.

The general sequence of steps in modeling a surface is:

Create a physical/mathematical model, in the sense of deciding on geometry, energies, and constraints.
Construct an initial datafile embodying the model, with appropriate variables, constraints, quantities, and geometric elements.
Figure out a good evolution script.
Write scripts for the calculation of whatever forces, torques, etc. you want as output data.
Estimate the accuracy of your data as a function of refinement, using known special cases or by looking at the convergence of a sequence of values for successive refinements.
Write scripts to automatically evolve and collect data over a range of parameters.

The Datafiles:

The sequence of datafiles starts simple and adds features. The sequence is not strictly linear; the main sequence keeps the contact surface on the chip explicitly represented by facets, and a sideline replaces those facets with edge integrals. Each datafile link here opens a commentary page, from which one can also open the datafile in a separate browser window. The idea is to be able to look at the commentary and datafile simultaneously. The datafiles themselves also contain a little commentary. You are also urged to have the Evolver running and run the models as they are discussed.

gullwing-1.fe Simplest model. Start here. Just the pad and lead, no solder.
gullwing-2.fe Adding solder completely surrounded by facets.
gullwing-3.fe Removing interface facets and replacing them with edge integrals, for more convenient evolution. Evolution, and force calculations.
gullwing-4.fe Final polishing, and using Hessian commands to show convergence.

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