Uncertainty Considerations for Nonlinear Dynamics of a Class of MEMS Switches Undergoing Tip Contact Bouncing

Abstract

Batch fabrication processes used to produce micro-electro-mechanical systems (MEMS) are prone to uncertainties in the system geometrical and contact parameters as well as material properties. However, since the common design method for these systems is typically based on precise deterministic assumptions, it is necessary to get more insight into their variations. To this end, understanding the influences of uncertainties accompanied by these processes on the system performance and reliability is warranted. The present paper focuses on predictions of uncertainty measures for MEMS switches based on the transient dynamic response, in particular, the bouncing behavior. To understand and quantify the influence of pertinent parameters on the bouncing effects, suitable mathematical model that captures the bouncing dynamics as well as the forces that are dominant at this micron scale are employed. Measure of performance in terms of second-order statistics is performed, particularly for the beam as well as beam tip parameters since excessive tip bounce is known to degrade switch performance. Thus, the present study focusses on the influence of uncertainties in the beam tip geometry parameters such as beam tip length/width as well as contact asperity variables such as the area asperity density and the radius of asperities. In addition to beam tip parameters, this study quantifies the effects of uncertainties in Young's modulus, beam thickness as well as actuation voltage. These influences on significant switch performance parameters such as initial contact time and maximum bounce height have been quantified in the presence of interactive system nonlinearities.

Bouncing dynamics of electrostatically actuated NEM switches

“…The dynamic pull-in voltage is determined for such switches and verified with that presented in a previous work [20]. It is worth noting that in the modeling of MEM switches, a realistic asperity-based contact model that has been used previously in many studies (see, e.g., [37]) is adopted here for the NEM switch model with the consideration of surface effects to represent the contact force along with the repulsive van der Waals force. However, it was demonstrated that the elastic forces due to asperities had negligible or no influence on the bouncing behavior.…”