Modeling spatial strain gradient effects in thermo-mechanical fatigue of copper microstructures

Copper microvias play a key role as electrical interconnects in high density wiring substrates used in microsystems packaging. These microvia structures experience low-cycle fatigue due to thermo-mechanical loads during processing and operating environments. To predict the thermo-mechanical fatigue life of the microvias through physics-based models accurate estimation of damage metrics, such as plastic strain and total strain range is critical. Experimental evidence indicates that the plastic deformation in metals and polymers at small scales depends not only on the state variables of stress and strain, but also on the higher-order spatial strain gradients. As the diameter of the microvia structures reduce to accommodate high density wiring, the wall thickness of these structures correspondingly reduces to the order of microns, where scale effects in plasticity are predominant. In this work a spatial strain gradient-based hardening algorithm is developed and employed in a commercial finite element code to study the thermo-mechanical deformation of copper microvia structures. In-house thermal cycling results are used to validate the numerical results. The thermo-mechanical reliability and low-cycle fatigue analysis demonstrate the influence of incorporating strain gradient effects in predicting the evolution of plastic deformation and low-cycle fatigue life in the copper microvia structures.