Pressure nonlinearity of micromachined piezoresistive pressure sensors with thin diaphragms under high residual stresses

Thermal residual stress plays a significant role in the performance of microelectromechanical system (MEMS) pressure sensor devices. For example, the voltage span and pressure nonlinearity (PNL) on the voltage output of a pressure sensing element can be significantly affected by the residual stresses of passivation films on the silicon diaphragm. The objective of this study is to resolve a pressure nonlinearity problem in terms of silicon nitride residual stress and diaphragm thickness in order to meet the PNL design criteria within ±3% at 25 °C. The curvatures of wafers were measured and the film residual stresses were calculated. Finite element analyses (FEA) were conducted and correlated with the PNL experimental tests. To build a design window for optimization, a central composite design (CCD) method was utilized to significantly reduce the number of FEA runs. It is concluded that the residual stress of PECVD silicon nitride needs to be optimized and controlled in order to reduce the pressure nonlinearity.