Another important aspect of predicting how a package will perform in any given application is reliability modeling. Thermal, electrical, and thermomechanical modeling, verified by experimental results, provide insight into system behavior, shorten package development time, predict system lifetimes, and provide an important analytical tool. In applications such as BGAs, where the interconnections are made through solder balls, the useful life of the package is, in most cases, dependent on the useful life of the solder itself. This is an area that has been studied extensively, and very accurate models for predicting both solder behavior and interpreting accelerated life testing exist.

The current methodology employed at Texas Instruments includes both extensive model refinement and constant experimental verification. For a given package, a detailed 2D finite element model (FEM) is constructed. This model is used to carry out 2D plain strain elastoplastic analysis to predict areas of high stress. These models also account for the thermal variation of material properties, such as modulus of elasticity, coefficient of thermal expansion, and Poisson’s Ratio as a function of temperature. These allow the FEM to calculate the thermomechanical plastic strains in the solder joints for a given thermal loading.

The combination of finite element analysis (FEA), accurate thermal property information, and advanced statistical methods allows prediction of the number of cycles to failure for various probability levels. Using the assumption that cyclic fatigue lifetime follows a Weibull distribution, various probability levels can be calculated. For these calculations, the Weibull shape parameter used is β = 4, which is based on experimental data calibration. It is also consistent with available experimental data found in the literature for leadless packages. This then results in Equation 1.

Using Equation 1, and using the plastic strain ξp in combination with the S–N curves, the data below is an example of the accuracy possible with this method:

Sample Finite Element Simulation and Life Prediction:

144 GGU @ T/C: -40/125°C

{Model}→ ξp = 0.353% on the outmost joint → Nf(50%)= 4434 cycles

→ Nf(1%) = 1539 cycles

{BLR Testing}→ -40/125°C (10 min/10 min)

→ Nf(1%) = 1657 cycles

Modeling is most useful in exploring changes in materials, designs, and process parameters without the need to build experimental units. For example, modeling was used to study the effects of changes in board thickness and pad size. Table 3-5 shows the simulated effects of pad size and board thickness on the fatigue life of a 144-GGU package.