Study about static and dynamic modeling of the cantilever-type nano mechanical switch

Abstract

As the physical gap between the cantilever beam and the bottom electrode becomes several tens nanometer scale, the mechanical switch is influenced by intermolecular force such as van der Waals force. In this thesis, cantilever-type nanoelectromechanical (NEM) switch for an emerging memory device is characterized through static and dynamic modeling. Previous approach about the modeling of the NEM switch is based on one dimensional spring model and two dimensional beam model using Green’s function. However, there is discrepancy between the spring model and the real behavior of the switch in gate voltage-displacement relation even in micrometer scale. The two dimensional beam model using Green’s function underestimates electrostatic force due to uniform load approximation. Proposed model uses Euler-Bernoulli beam equation with the quadratically increasing load model. This one shows better agreement compared with the result of the FEM simulation in micrometer scale than the previous ones. Moreover, drain bias effect on the pull-in voltage of the switch is considered. Previous design limit of the NEM switch starts from zero pull-in voltage. However, the influence of the van der Waals force becomes dominant when the switch is on state. Thus, from guessing pull-out voltage of the switch, more strict design limit of the NEM switch is proposed. Dynamic behavior of the NEM switch is estimated numerically utilizing finite difference method. Theoretical switching time and bouncing of the tip of the switch can be obtained from it. In sum, with consideration of the van der Waals force, the behavior of nano mechanical switch is modeled using Euler-Bernoulli beam equation. The author hopes that this work helps to predict the static and dynamic behavior of the NEM switch.