Pull-in voltage calculations for MEMS sensors with cantilevered beams

MEMS sensors, such as acoustic, noise and vibration transducers often employ a diaphragm or cantilevered structure as part of a variable capacitance sensor geometry. A bias voltage is necessary to ensure a linear force-capacitance range of operation. The calculation of the pull-in voltage whereby the sensing structure collapses due to electrostatic forces is an important design requirement. A linearized, uniform approximate model of the nonlinear electrostatic pressure has been developed and used in conjunction with the load deflection model of a MEMS cantilever beam under uniform pressure to develop a highly accurate model to calculate the pull-in voltage. The new model improves sensor design methodology by evaluating the pull-in voltage for a cantilever beam with a maximum deviation of less than 1% from the finite element analysis results for wide beams and for narrow beams with extreme fringing fields.