Modelling and numerical simulation of the electrical, mechanical, and thermal coupled behaviour of Multilayer capacitors (MLCs)

The modelling of non-linear coupled material characteristics has been used for finite element simulations of the integral device behaviour and mechanical and electrical stress distributions of ceramic multilayer capacitors. A two-dimensional finite element model of standard X7R-type capacitors of different sizes soldered on a printed circuit board has been developed to calculate residual, joining as well as mechanical and electrical load stresses. This model includes the experimentally measured non-linear bias field dependencies of the electric and piezoelectric characteristics of the BaTiO3 based dielectric material. The validation of the model is demonstrated by calculations of the failure probability of soldered capacitors in a four-point bending test under simultaneous electrical loading. The results allow a description and possible improvement of the short-time reliability under particular load cases.