Lead and its compounds have been widely used for many years in the electronics industry. However, the global demand to reduce the use of hazardous materials has compelled electronics manufacturers to consider the use of lead-free materials in future products. This transition has heightened the necessity for new finite element material models that can be used to evaluate the reliability of lead-free solders.

Lead solders, such as the popular tinlead variety, have been used in the electronics industry for the past 50 years. Subsequently, their long-term reliability is well understood. However, lead and its compounds are highly toxic and the entry of these materials into the environment has become an issue of great importance. In conjunction with legislation requiring the eventual use of leadfree materials, the electronics industry is working towards reducing the amount of lead in end-user equipment. This transition requires the development of new analytical capabilities for estimating the reliability of components that use lead-free solder.

Figure 1. Schematic Section View of the BGA model.
During their working lives, electronic components are subject to a large number of thermal cycles. Mismatch between the thermal expansion behaviors of the various materials may induce severe stresses that are high enough to cause plasticity and creep. In particular, solder balls are at risk because they are stressed at temperatures above half of the solder's melting point. At such temperatures, the solder creeps; after a number of thermal cycles, the accumulation of large inelastic strains may lead to failure of the solder joints. Therefore, the creep analysis of solder balls under cyclic thermal loading becomes an important part of the design phase.

The Ball-Grid-Array (BGA) model used in this application was built using an ABAQUS/CAE custom application of ABAQUS Version 6.6 finite element analysis developed at Worley Parsons PTE Limited, Singapore. Scripting and GUI toolkit interfaces of ABAQUS software allowed the development of certain classes of models to be automated.

The process of building a BGA model is captured in several icons such as the Model icon, the Material icon, and the Load icon. For example, only the dimensions for a BGA model need to be specified in the Model dialog box, and the model is built and meshed automatically.

Figure 1 shows a section of the BGA model used in the present calculations. Thirty-six solder balls connect the silicon die and the substrate, with underfill material used in the space surrounding the solder balls. All components except the substrate are encapsulated in the mold.

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 .