A pressure-deformation analytical model for rectangular diaphragm of MEMS pressure sensors

Abstract

Rectangular diaphragm is commonly used as a pressure sensitive component in MEMS pressure sensors. Its deformation under applied pressure directly determines the performance of micro-devices, accurately acquiring the pressure–deflection relationship, therefore, plays a significant role in pressure sensor design. This paper analyzes the deflection of an isotropic rectangular diaphragm under combined effects of loads. The model is regarded as a clamped plate with full surface uniform load and partially uniform load applied on its opposite sides. The full surface uniform load stands for the external measured pressure. The partial load is used to approximate the opposite reaction of the silicon island which is planted on the diaphragm to amplify the deformation displacement, thus to improve the sensitivity of the pressure sensor. Superposition method is proposed to calculate the diaphragm deflections. This method considers separately the actions of loads applied on the simple supported plate and moments distributed on edges. Considering the boundary condition of all edges clamped, the moments are constructed to eliminate the boundary rotations caused by lateral load. The diaphragm’s deflection is computed by superposing deflections which produced by loads applied on the simple supported plate and moments distributed on edges. This method provides higher calculation accuracy than Galerkin variational method, and it is used to analyze the influence factors of the diaphragm’s deflection, includes aspect ratio, thickness and the applied force area of the diaphragm.