The materials have different thermal expansion coefficients, causing stresses to develop when the model is subject to thermal loading. For simplicity, it is assumed that the entire model is subject to uniform thermal cycling. In a more detailed analysis, the temperature field could be obtained from a previous heattransfer analysis, or the entire simulation could be carried out as a fullycoupled temperaturedisplacement analysis. The bottom of the substrate is fixed and no other direct mechanical loading is applied.

Figure 2. Equivalent Creep Strain at the end of the loading history.
In Figure 2, the distribution of equivalent creep strain (CEEQ) at the end of the analysis (t=9900 s) is shown for the array of solder balls. The top surfaces of the solders interface with the silicon die; thermal expansion mismatch between the solder and the surrounding materials results in high creep strain near the top and bottom surfaces of the solders. In addition, the creep strain in solders at the perimeter of the array is higher than that near the center. The solders with the highest creep strains are those at the four corners, suggesting that these are the critical joints for the simulated device.

Figure 3. Stress and Strain Histories at points A and B (Fig. 2).
The time histories of the Mises stress and the equivalent creep strain at locations A and B (see Figure 2) are shown in Figure 3. Note that the modified Anand creep model was used to generate these results. In general, the Mises stress in the corner solder (location A) is slightly higher than that in the solders near the center of the device, especially during the time interval in which the temperature is held constant at 100°C. The slightly higher stress develops larger creep strains in the corner solders, and the difference in the creep strains steadily increases as the number of thermal cycles increases. Once the creep strain increment per cycle at the critical point of a solder reaches a constant, this value can be used in a fatigue law, such as the Coffin-Manson equation, to estimate the fatigue life of the solder ball.

The fast-growing application of lead-free materials in the electronics industry has brought new challenges with regards to the simulation of creep behavior. The advanced features of ABAQUS /Standard, including a large material library, extensive nonlinear analysis capability, and thermalmechanical coupling, have made it a powerful design tool for the electronics industry in the lead-free era.

This work was done by SIMULIA, Providence, RI. For more information, click here.