Next: Using SURFACE EVOLVER to Up: "SURFACE EVOLVER" AS Previous: An Example: The Shapes

# Using SURFACE EVOLVER to Determine Stability

Another example of a useful Evolver calculation is the determination of the critical volume of solder which can cause a ``short'' between two flat leads in a chip array[7].

In Figure 2, two such leads are modeled as constraints for an evolver calculation. The leads are separated by a gap, over which the solder droplet sits. The Evolver file for this calculation is not very different from the one given above, except that the entire droplet is modeled instead of using the two possible mirror planes.

The wetting angle for the solder on the lead was arbitrarily chosen as . The gap distance was 1/2 (gravity was ignored, so the length units can be ignored, but then calculation then only applies for small capillary lengths). The initial mesh was symmetric across the gap. The volume as manually adjusted until a critical amount was obtained that gave a ``stable'' Evolver solution. The amount of volume depicted in Figure 2 was 4.875 (in units of gap distance cubed) and it is slightly above the critical volume at which the droplet breaks symmetrically into two isolated droplets.

Evolver can calculate the Hessian of this current solution and one finds that it is not positive definite; so this solution is not a good determination of the critical bridging volume.

It is instructive to examine the stability using the following scheme. It may be conjectured that the solder drop will go unstable by breaking the symmetry across the gap; this can be tested by giving the vertices a ``kick'' in that direction. This is executed by typing the Evolver command set vertices x x+.05, which moves all vertices to one side, except those constrained from such motions. Subsequent iteration clearly shows (Figure 2c) that the system was in fact unstable to an asymmetric mode. Considerably more investigation is required to find the actual critical volume; note that merely calculating the droplet sizes resulting from asymetric break-up would be insufficient since hysteresis should be expected.

Imposing a mirror plane on the original calculation would lead to an unphysical estimation for the critical volume. If the lead is finite, instead of semi-infinite as in Figure 2, the stability will also be affected as the droplet contacts the other lead boundaries. Such contact problems are handled in a straightforward manner[8].

Next: Using SURFACE EVOLVER to Up: "SURFACE EVOLVER" AS Previous: An Example: The Shapes

W. Craig Carter
Wed Feb 28 11:27:46 EST 1996