Finite Element Modelling of a Piezoelectric MEMS Pressure Sensor using FreeFem++

MEMS piezoelectric pressure sensors are widely used nowadays due to their small sizes, good performances and reliable qualities. Structural optimization are very important for the design and manufacturing of these sensors. Finite element modelling is usually used to achieve the structural optimization of these sensors. Here, a model of a MEMS piezoelectric pressure sensor is developed using the finite element method. The applied boundary condition on the top surface of the sensor is uniformly distributed pressures; while that on the bottom surface of the sensor is fixed displacements. Then, solving the mechanic equilibrium equations leads to elastic displacements. Thus, the elastic strains and stresses are obtained. Then, the distribution of the elastic stresses is used to determine the electric displacements and the electric field intensity within the PZT layer, using the constitutive relations of the piezoelectric effects. As a result, the average output voltage between the two electrodes can be calculated via integrating the electric field intensity in the PZT layer along its thickness direction. The influences of different thicknesses of the PZT layer and the underlying silicon substrate right below the PZT layer on the average output voltages are investigated. Moreover, modal analyses are also carried out to find the natural frequencies of the sensor.