Stress analysis of a micro-machined inertial sensor at dynamic load

This paper presents modeling and simulation techniques for the the dynamic behavior of inertial sensors. A detailed model of a sensor is generated at the continuous field level, which considers multiple physical domains, such as structural dynamics, fluidics and electrostatics. To reduce the large order of the problem, a compact model is derived by decomposition of the deformation field into basic mode shape functions. The dynamic behavior of the sensor structure is described by superposition of its dominant vibration mode shapes. The resulting reduced-order model (ROM) still considers all physical domains and is even able to capture nonlinear phenomena, such as stress stiffening of constraint structures or frequency and deflection dependent damping and stiffening caused by the squeezed gas in the sensor cell. The ROM algorithms were extended to account for MEMS package-transducer interactions. Process induced and thermally induced residual stresses and resulting deformation of the transducer elements are considered.