Linear and Nonlinear Frequency Analysis of Single and Multibeam MEMS Arrays

Microelectromechanical system, MEMS, and nanoelectromechanical system (NEMS) employ electric power for actuation and sensing. However, the sensitivity and performance of these devices heavily depend on the linear frequency, nonlinear frequency, and quality factor of their mechanical elements. Until recently, most of these devices employ the parallel plate configuration for computing electrical forces, thereby neglecting other terms such as fringing field effect, nearest neighbor effect, etc. Moreover, due to the exural motion of the mechanical element, the parallel plate assumption no longer holds. Hence the accurate computation of resonance frequency in submicron or nano scale regime requires consideration of various effects like fringing feeld effect, nearest neighbor effect, nonlocal effect, surface effect, etc. In this thesis, we first derive generalized numerical expressions for computing capacitance as well as electrostatic force in simple and complex configurations consisting of an array of beams and electrodes. These expressions consider the direct and fringing electrostatic field effect, nearest neighbor effect