Modeling Electrochemical Migration of Sn-9Zn: Insights from Finite Difference and Finite Element Methods

Electrochemical migration (ECM) is a significant reliability concern in electronic systems, occurring when moisture is present on conductor-dielectric-conductor structures under an applied bias voltage. The process involves three primary stages: metal dissolution at the anode, ion migration through the electrolyte under the influence of an electric field, and metal deposition at the cathode, leading to the formation of conductive dendrites. These dendrites grow over time, reducing surface insulation resistance and potentially causing failure by bridging the electrodes. This study examines ion transport modeled by the Nernst-Planck equation to simulate the ECM of Sn-9Zn in deionized (DI) water under applied voltages of 3V and 5V. The finite difference method (FDM) is used for simulation, and the results are compared with previously obtained data from the finite element method (FEM). The comparison revealed that both methods could predict similar electrochemical behaviors of Sn and Zn ion transport across the gap. However, differences were noted: At 3V, FDM simulations indicated a delayed dominance of Sn ion transport compared to Zn. FDM consistently computed lower concentration values for Both ions during the transport along the gap distance at both voltage levels. These findings emphasize the importance of carefully selecting and validating numerical methods when modeling the electrochemical behavior of specific metals and alloys.