Multiphysics study of electrochemical migration in ceramic capacitors

Electrochemical migration across the surface of dielectric cracks in multilayer ceramic capacitors when exposed to humidity or condensed moisture can result in the growth of dendritic filaments, thus causing increased leakage currents or even short circuit failure. This study uses measured empirical data to demonstrate that the growth rate of the dendrite accelerates nonlinearly with time, due to the increased electric field strength and ionic flux that results from the continuously decreasing distance between the anode and the tip of the cathodic dendrite, as the dendrite grows with time. A simple 1D analytic predictive model is developed that incorporates the nonlinear growth kinetics by allowing the separation between the anode and effective cathode to vary with time. The failure time predicted by this model is calibrated with the help of the experimental data, and the dendrite growth kinetics are found to have a close qualitative and quantitative match with the experiments. A comparison is also made to a calibrated fixed-separation linear TTF prediction model in the literature and the comparison shows that the nonlinear model developed in this study produces results that are physically more meaningful than the linear model.