Numerical Study on the Static Instability of a CNT-Based NEM switch

In the last decade, nanoelectromechanical systems (NEMS) have represented an exceptional technology that has caused major changes in whole industries. Carbon nanotubes (CNTs) are ideal building blocks for NEM devices and have attracted many research efforts due to their small size, low density, excellent mechanical and electronic properties such as high-tensile strength and high-flexural rigidity.A typical NEM switch is constructed from two conducting electrodes, one is typically fixed and the other is movable. The fixed and movable electrodes in our case study are graphite ground plane and nanotube, respectively. A force balance for a nanotube over a ground plane has been shown of elastostatic and van der Waals (vdW) forces without electrostatic force, shown in figure 1(a), or of these forces and electrostatic force, shown in figure1 (b). There is an inherent instability, known as pull-in phenomenon, in NEM switches. Due to vdW and/or electrostatic forces, the movable electrode displaces to the ground plane. At a certain condition, the movable electrode becomes unstable and collapses to the ground plane. The voltage and gap distance of the switches at this state are called to as the pull-in voltage and the pull-in gap respectively or together the pull-in parameters of switches.Some research groups have fabricated CNT-based NEM devices. For example, Kim and Lieber [1] developed nanotweezers. The mechanical capabilities of the nanotweezers were demonstrated by gripping and manipulating submicron clusters and nanowires. Aluru et al. [2] derived an analytical expression, based on a lumped model, to compute the pull-in voltage of cantilever and clamped–clamped switches. They investigated the importance of van der Waals interactions in the design of NEM switches. Espinosa et al. [3] nanofabricated and tested cantilever end type CNT-based NEMS. Their theory took into account the cylindrical shape of the nanotube in the evaluation of its electrical capacitance. They presented an analytical model based on the energy method in both small deformation and large deformation regimes to interpret the measurements. Espinosa et al. [4] performed other similar work on a typical clamped-clamped end type CNT-based NEM device. They presented the complete expression of the elastic line equation for it