Analytical Shear Lag Modeling for Strain Transmission into Bottom Terminated Packages
Analytical shear lag models quantify strain transfer from boards to bottom-terminated packages, showing compliant die attach drops offset drift by 98 percent.
Suhir Solution
Stress Calculation
Analytical framework for calculating the thermal stresses in bi-material assemblies and thin-film structures. Developed to address the limitations of simpler beam theories, the suhir solution provides a more accurate estimate of the shear and peeling forces at the edges of a bond. The method uses a system of differential equations to model the interaction between two layers with different expansion coefficients.
The framework remains a fundamental tool in the field of microelectronics packaging.
Interface Behavior
Axial and bending stresses are distributed differently across the length of the assembly according to this model. The suhir solution predicts that the maximum stresses occur at the free ends of the interface, which is where delamination typically begins. By accounting for the compliance of the bonding material, the framework allows for a more realistic assessment of the structural integrity.
The analysis helps in selecting adhesives that can absorb thermal strain.
Engineering Application
Designers use the equations to predict the reliability of solder joints and chip-to-substrate connections. When a device undergoes temperature cycling, the suhir solution estimates the risk of fatigue failure based on the material properties and geometry. The framework allows for rapid iteration of package designs without the need for computationally expensive finite element simulations.
Results guide the selection of materials to minimize the mismatch in thermal expansion.
Model Limitation
Accuracy of the results depends on the assumption of linear elastic behavior in all materials. While the suhir solution is effective for initial screening, it may not fully capture the plastic deformation or creep that occurs in certain metals and polymers at high temperatures. The geometry is also simplified to a two-dimensional representation, which might overlook complex three-dimensional stress states.
Supplemental testing is often required to verify the findings for critical components. High-temperature applications often require non-linear analysis to account for the softening of adhesives. Engineers must validate the model parameters against experimental data from shear tests.
Material properties used in the calculation should be measured at the expected operating temperatures.
Substrate Viscoelastic Properties and Thermal Expansion Mismatch in MEMS Packaging
Substrate viscoelastic relaxation and thermal expansion mismatch induce time-dependent, hysteretic offset drift in MEMS requiring mechanical anchor isolation.