Analytical Die Stress Modeling and Hysteresis Compensation in MEMS Sensors
Analytical die stress modeling isolates mechanical package strain from sensor signals while hysteresis compensation algorithms eliminate viscoelastic offset drift.
Suhir Stress Model
Analytical Formulation
An analytical model calculates the thermal and mechanical stresses in multi-layered microelectronic assemblies with finite boundaries. Within this engineering framework, the Suhir stress model evaluates the shearing and peeling stresses that develop in bonded assemblies due to mismatches in thermal expansion. This formulation is widely applied to sensor packaging and joint design.
It provides a closed-form solution that avoids the need for complex numerical simulations in the early design phase.
Mathematical Concept
The formulation modifies classical beam theory by incorporating compliant interface layers that absorb some of the differential thermal strain. By calculating the stress distribution along the bonded interfaces, the Suhir stress model identifies the locations of maximum load, which typically occur at the assembly edges. This calculation helps packaging designers choose materials with compatible thermal expansion coefficients.
The analytical equations use the geometric dimensions and mechanical properties of each layer to calculate the interfacial compliance. This calculation enables rapid evaluation of different package configurations. It is particularly useful for optimizing the thickness of adhesive layers used to secure sensing elements.
Design Limit
High shearing stresses at the edges can lead to delamination of the active layers. This failure mode is prevented by applying the Suhir stress model to optimize layer dimensions.
Validation Technique
Finite element analysis is often used to confirm the results of the closed-form calculations. This comparative analysis ensures the reliability of the Suhir stress model in practical designs.