Closed-form expressions for the relationships between stress, diaphragm deflection, and resistance change with pressure in silicon piezoresistive pressure sensors

A quasi-analytical technique which is capable of representing the relationships between stress, diaphragm deflection, and resistance change with pressure in closed-form expressions for square, thin silicon diaphragms with built-in edges is presented. As a result of this study, a simulation technique for silicon piezoresistive pressure sensors has been obtained based upon a thermoelastic plane-stress formulation of the deflection and stress equations and on a solid-state process-oriented model of the piezoresistive pressure sensors. This technique also gives a clear understanding of the basic response mechanisms in such devices.