Investigation of the Influences of Thermal stresses and Joule Heating within a Piezoresistive MEMS Pressure Sensor using the Finite Element Modeling

In this paper, the influences of thermal stresses and Joule heating are studied in a piezoresistive MEMS pressure sensor via a 3D finite element model developed in our previous work using FreeFem++. First, a steady state equation of electric currents is solved to determine the electric potential. Second, a quasi-stationary equation of the thermal conduction under the influence of Joule heating is solved to obtain the distribution of the temperature field. Then, the Cauchy-Navier's equations subjected to thermal stresses are solved to find the elastic displacements and thus the elastic strains. As a result, the elastic stresses within the piezoresistors are found; then, using the constitutive equation of the piezoresistive material, the changes in the electrical resistance of the piezoresistors are obtained, which yields the output voltage eventually. During the simulations, the influences on the output voltage from the thermal stresses, Joule heating as well as different size parameters are studied. In the end, a modal analysis of the sensor is performed. The simulation results obtained have the potential to help the design of piezoresistive MEMS pressure sensors and also help to determine the major factors which influence the performance of the sensors.