Tombstone Example tomb-C for the Surface Evolver

[Click for the tomb-C.fe datafile in a second window.]

This model introduces partial wetting on the pad and chip bottom. That is, there are a non-zero contact angles. As a result, the corners of the pad are bared, as is some of the underside of the chip wetting area.

Evolved surface, 9772 facets.

The solder surface by itself.

Notable features:

• The initial wetting angles are all 30 degrees. Hence the solder cannot wet into plane corners. On the bare solder picture, you can see that even under the front edge of the chip there is some indenting of the solder, although the refinement is not high enough to show rounded contact lines there.
• The contact angles are specified by parameters A_pad for the pad and A_z_minus for the bottom of the chip, in degrees.
• Since the solder is completely enclosed with facets, the wetting angles are implemented by setting the tensions of the contact facets. A command update in the read section of the datafile is defined to do this, for user convenience when changing the contact angles at runtime. The update command is then set to run when the file is loaded to set the initial tensions.
• A contact angle of less than 90 degrees means the contact facets have negative tension. This gives the potential for explosive behavior if the contact line should overrun interior contact vertices, leading to a double layer of negative tension facets!
• Since the contact lines on the pad and chip are now free to move, one-sided constraints have been defined to keep the contact lines within the proper bounds. These are constraints 11-16 for the chip and constraints 20-23 for the pad.
• The gogo command illustrates a possible asymmetry in the evolution of a supposedly symmetric surface. In particular, the u equiangulation command can destroy symmetry.
• The hessian command in hessian_normal mode can have problems with vertices on constraints, as they can squirt sideways and make big spikes. A new feature in version 2.11 is the hessian_slant_cutoff internal variable. It's effect is that if the normal to the surface is at too great an angle from the permitted motion along constraints, the vertex is treated as fixed. The value is the cosine of the angle. The read section sets hessian_slant_cutoff at .2 (by trial).
• The hessian command can have problems with one-sided constraints, as vertices bump into and off of the constraints. Here, hessian does happen to work okay. If it doesn't, one can first fix the vertices that hit one-sided constraints.