Effect of dielectric layer on the response times of electrostatic MEMS switches

Electrostatic MEMS switches have become prevalent because of low power consumption and ease of integration in micro-fabrication technology. The equations governing their dynamic response obtained by energy methods are nonlinear differential equations. Even the unit-step response of these devices requires numerical computation. Depending on the magnitude of the applied step voltage and the presence of dielectric in the actuator, the response could be recurring or non-recurring. Estimating the period time and the switching time in these cases proves to be hard because one has to solve the energy equation numerically which could be time consuming or difficult to converge if it is not posed properly. Elata et al. have developed excellent methods to obtain these times on a logarithmic scale of voltage more easily for the undamped case. This paper extends their work for the case when the bottom plate is covered with a dielectric layer. The stagnation time occurring before dynamic pull-in, and the switching time thereafter are first shown as nonlinear graphs with the dielectric permittivity as a parameter. They are also linearized on an exponential scale and made useful for quick look up and convenience of designers.