Simulation of a Piezoelectric MEMS Accelerometer using Finite Element Modeling with Freefem++

In this paper, a two-dimensional finite element model of a piezoelectric MEMS accelerometer is developed and analyzed using FreeFem++. First, a steady state equation of the thermal conduction is solved to obtain the temperature field. Then the quasi-stationary Cauchy-Navier’s equations with thermal stresses present are solved to determine the distribution of the total stresses. As a result, the electric displacement along the vertical direction of the PZT piezoelectric layer is calculated using the constitutive equation of the piezoelectric material. Finally, the total output electric charge on the two top electrodes are determined. The influences of thicknesses of the silicon diaphragm and the PZT layer, as well as the areas of the top two electrodes on the total output charge are studied. The effects of the temperature field are also studied and finally a modal analysis of the accelerometer is performed. The simulation results obtained via finite element modelling has the potential of helping the design of piezoelectric MEMS accelerometers and thus, improve their performances.