The results are presented in terms of the four fields: structural, thermal, electrical, and diffusion.
Because hydrostatic stress, current density, and concentration results are not available in the Mechanical user interface, they are obtained by inserting the corresponding expressions as User Defined Results.
The following expressions are inserted: NLHPRE for hydrostatic stress, JCSUM for current density sum, and CONC for concentration. As an example, the details for NLHPRE are shown below:
Structural Result: Hydrostatic Stress
Hydrostatic stress results are in units of MPa. The gradient of hydrostatic stress produces diffusion from high to low "pressure". The stresses are due to the constraint on the top and bottom surface of the model and thermal strain incompatibility between the solder and the copper. A large negative hydrostatic stress occurs at the singularity produced by the sharp re-entrant corner at the edge of the solder/copper interface.
Thermal Result: Temperature
Because the model is very small and the materials have high thermal conductivity, the temperature reaches the steady-state in a few seconds and remains constant throughout the simulation. Therefore, the gradient of temperature does not contribute to atomic diffusion. The uniform temperature increase does affect diffusion by producing stress gradients due to constrained thermal expansion.
Electrical Result: Current Density
Current density here is in units of mA/(μm)2. To convert to pA/(μm)2 you need to multiply by 1e9.
Note the increase in current density (current crowding) at the entrance and exit of the solder ball. This is the location where metal depletion has been observed in solder balls.
Diffusion Result: Concentration
Regions with concentration values less than 1.0 may produce voids. Concentrations greater than 1.0 could produce hillocks or protrusions of metal from the surface.
Concentration versus Time
To generate charts of concentration versus time in the Mechanical user interface, right-click Solution and pick Insert > Chart.
In the Outline Selection, select the Concentration result and click Apply. In Output Quantities set Concentration (Min) to Display and set Concentration (Max) to Omit.
These settings produce a chart of minimum concentration versus time:
Now duplicate the Chart result and, in Output Quantities, set Concentration (Max) to Display and set Concentration (Min) to Omit.
These settings produce a chart of maximum concentration versus time:
The concentration plots show that the steady state occurs after 1 year (or around time = 1e7 sec).