Casimir effect on the pull-in parameters of nanometer switches

Abstract

Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam. IntroductionThe nanoelectromechanical systems (NEMS), as an extension of microelectromechanical systems (MEMS), have turned into the hot research topic in recent years. In MEMS and NEMS, with the geometric dimension decreasing, the surface forces [1][2][3][4][5][6], replacing the body forces, take over the dominant position, which become more important for the nano-scales. In this paper, we just consider Casimir force and electrostatic force. Casimir [7] predicted an attractive force between objects. Kenneth et al. [8] have extended these considerations to real-world materials.NEM switches are fundament building blocks for the design of NEMS applications. However, the pull-in phenomenon, an inherent instability of MEM and NEM switches, is one of annoying problems in design. By applying a voltage difference between the two electrodes, an electrostatic force is formed. At certain voltage the switches lost its stability and the gap between the switches rapidly decrease, until the two electrodes adhere. The voltage and deformation of the switches at this state are referred to as the pull-in voltage and the critical pull-in gap respectively, or shortly as the pull-in parameters of switches. Therefore, an analytical expression of the pull-in parameters could guide the design.An analytical expression of the pull-in parameters has been given about the MEMS switches in [9]. A lumped two degrees of freedom (L2DOF) pull-in model was presented in [10]. The pull-in parameters for electrostatic torsion actuators are the pull-in voltage and pull-in angle [11,12]. The pull-in phenomenon is widely applied in many micromachined devices that require bi-stability for their operation [13,14]. In the above references [9][10][11][12][13][14], the Casimir and van der Waals effects are neglected. The significant effect of van der Waals force has been shown on the pull-in voltage of NEMS switches, but the effect on the critical pull-in gap has been omitted [15].The Casimir effect in MEMS was studied in [16] and measured in [17]. In [18], a micromachined torsional device is used to determine the Casimir effect in MEMS. Casimir force has a profound influence on the oscillatory behavior of nanostructures [19].The maximum length that will not stick to the substrate, also called detachment length is basic design parameter [20,21].The objective of the present paper is to study the effect of Casimir force on the pull-in parameters. An approximate analytical expression of the critical pull-in gap is obtained by the perturbation theory and the detachment length...

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

“…(17) and using the dimensionless parameters in Eq. (27), the nondimensional governing equation of the paddle-type actuator is: …”

“…The LPM assumes a uniform force distribution along the wire [27]. The mechanical resistance of nanowire is…”

“…Finally, by using dimensionless relations (Eqs. (27) and (31)), the relation between dimensionless wire tip de ection, w tip , and applied voltage, , is determined by Eqs. (46) and (47) To examine the impact of geometry on the behavior of the double-sided actuator, the variations of PI and pull-in de ection (ŵ PI (x = 1)) as a function of are presented in Figure 2 for various values of Casimir parameter .…”

“…For precise modeling of the pull-in performance of the aforementioned nanostructures, the Casimir force should be included in the model [26][27][28]. Almost all previous investigations in this area have been devoted to those devices with planar con gurations, while only few investigations have considered it in actuators which are fabricated from nanowires with cylindrical geometries [29,30].…”

Nonlinear behavior for nanoscale electrostatic actuators with Casimir force

“…Because of its fundamental nature, the Casimir effect motivates extensive researches in the last decade. Potential applications of Casimir effect in nanoelectromechanical systems (NEMS) and nanotechnology are studied theoretically and experimentally [2][3][4][5][6][7][8][9][10]. It finds [5] that movable components in NEMS devices fabricated at distances less than 100 nm between each other often stick together due to strong Casimir force.…”