Mechanical Response of a Micro Silicon Membrane: Model Validation by Finite Element Method

Abstract

Abstract In the piezoresistive pressure sensor, we need to study the stress repartition on the Silicon membrane surface. This study is very important because it allows us to determinate where the stress is maximal and to place there the four piezoresistors, which provide a maximal sensitivity to the pressure [2] . Because of the anisotropy of the Silicon, we have to study the variation of its mechanical parameters (Young Modulus and Poisson Coefficient) and piezoresistive (piezoresistive coefficients) parameters in the different crystallographic directions [4] . These studies will allow us to optimize the sensor characteristics (Sensitivity, Linearity …). In this paper, we propose to establish a mathematical model that describes the mechanical behavior of single crystal silicon micro membrane. The proposed model is based on the theory of thin plates and shell. It describes the deflection of the membrane and the stresses induced in by the effect of a homogeneous differential pressure applied to this membrane. The resolution of this model allows us to calculate the displacement of the membrane (his deflection) and to know the stress distribution as a function of the applied pressure. Finally, results are compared with those obtained by the numerical finite elements method.