Electromechanical Modeling and Simulation of RF MEMS Switches

The design of RF MEMS switches involves several disciplines: mechanics, materials science and electrical engineering. While significant progress has been made in the RF design of the switches, mechanical and material studies are required for mass commercialization of reliable devices. Senturia and co-workers at MIT have presented a closed form solution to describe the electromechanical behavior of a fixed-fixed switch. However, in some practical applications, multi-domain simulations are required to account for membrane shape, non-uniform state of residual stress, temperature and other effects. In this presentation, we will describe the modeling and simulation of MEMS switches and discuss their electromechanical performances. The switch, bottom electrode and surrounding air were all included and meshed in the model. Iterations between the electrostatic and structural analyses were performed until the solution converged. The developed method is applicable to all types of electrostatic switches, though the design of a capacitive coupling shunt switch has been examined. Introduction Microelectromechanical systems (MEMS) technology is on the verge of revolutionizing RF and microwave applications. The increasing demand for more flexible and functional, yet lightweight and low power consumption wireless systems, has generated the need for a technology that can dramatically reduce manufacturing cost, size, weight, and improve performance and reliability. With the potential to enable wide operational bandwidths, eliminate off-chip passive components, make inter-connect losses negligible, and produce almost ideal switches and resonators in the context of a planar fabrication process compatible with current IC processes, RF MEMS is just the technology. Micromechanical switches were first demonstrated in 1971 by Petersen [1]. Since then, different actuation mechanisms and switch topologies have been investigated and commercialization of RF MEMS switches has been initiated. Various designs include electromagnetic [2], magnetostatic [3], and electrostatic [4] actuation. Structure designs include surface micromachied cantilevers [5], double-fixed membranes [6], bulk micromachined or wafer bonded designs [7]. Among these, electrostatically-actuated membrane switches have been widely studied. Mechanical design plays an important role in the design of an RF MEMS switch, as do RF design and materials science. Grétillat et al. [8] presented the electromechanical behavior of an electrostatic microrelay. Chauffleur et al. [9] reported the effect of membrane shape on the membrane stiffness of RF switches. Chen et al. [10] proposed a method to measure the residual stress for MEMS suspended membrane structures. Espinosa et al. [11] analyzed the coupled effects of Young's modulus, residual stress and membrane shape on the mechanical response of RF switches under the loading of a nanoindenter. However, the mechanical study is far behind electric and material studies. Two key mechanical characteristics for RF switches are the actuation voltage and the reliability of the device. The stiffness and residual stress state of the switch structure are dominant to the actuation voltage. At the same time, RF switches have functioning requirements for various temperatures such as in satellite and airplane applications. Therefore, the temperature effect is of particular relevance to the reliability. However, there is no closed-form solution or even numerical simulation to account for the electromechanical coupled problems yet. In this paper, an electromechanical simulation for RF switches is discussed and some effects on the switch behavior are investigated. The rest of the paper is organized as follows: 1) operation of RF switches and the electromechanical analysis of the switch behavior are introduced; 2) development of a Finite Element Method (FEM) model and verification of the model are presented; 3) effects of membrane geometry and initial stress are discussed; 4) conclusions are drawn from the above analyses. Electromechanical Analysis of RF switch A. RF Switch Operation A typical capacitive RF MEMS switch consists of a fixedfixed thin metallic film suspended over a dielectric film deposited on top of the bottom electrode. This dielectric film serves to prevent the electric short between two conductors and provide a low impedance path for the signal. When the switch is unactuated, there is a large capacitance between the membrane and the bottom electrode, and the device is in the OFF state. When an electrostatic voltage is applied 8 Proceedings of the 4th International Symposium on MEMS and Nanotechnology, the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2-4, Charlotte, North Carolina, Session 03, Paper 190, pp. 8-11, 2003. between the two conductors, an electrostatic force is created to pull the membrane down. At a certain voltage, the membrane collapses and comes in contact with the bottom electrode, and the device is in the ON state. When a voltage is applied between the movable structure and the fixed bottom electrode, electrostatic charges are induced on both the movable structure and the bottom electrode. The electrostatic charges causes an electrostatic force, which deforms the movable structure. In consequence, such deformation results in an elastic force, which tries to restore the structure to its original shape. In general, the deformation will also result in the reorganization of all surface charges on the device. This reorganization of charges is adequate to cause further structural deformation. The device exhibits a coupled electromechanical behavior. For a certain applied voltage, an equilibrium position is defined by balance of the elastic force and the electrostatic force. In order to model and simulate this coupled behavior, numerical iterations between electrostatic energy domain and elastostatic energy domain have to be engaged. B. Closed-Form Solution The pull-in voltage is determined primarily by the stiffness of the switch structure. A first-order approximation is to model the switch as a parallel-plate capacitor. The parallel-plate capacitor is suspended above a ground plane by a linear spring. The pull-in voltage can be solved as