Modeling of Spring Constant and Pull-down Voltage of Non uniform RF MEMS Cantilever Shimul Chandra Saha Ulrik Hanke Geir Uri Jensen Trond Sæther Department of Electronics and Institute for Microsystems SINTEF ICT Department of electronics and Telecommunications (IET), Technology, Vestfold Gaustadalleen 23, Telecommunications (IET), Norwegian University of Science University College, 0371 Oslo Norwegian University of Science and Technology (NTNU), 3103 Tønsberg Norway and Technology (NTNU), 7491 Trondheim, Norway Norway 7491 Trondheim, Norway shimul.saha@iet.ntnu.no Ulrik.Hanke@hive.no Geir.Jensen@sintef.no trond.saether@iet.ntnu.no ABSTRACT In this paper, we are going to present a model of spring constant and pull down voltage for non uniform RF MEMS cantilever. In order to reduce the pull down voltage, it is usual to use a beam, which is narrower close to anchor and wider at the end or electrode area for a cantilever. Compare to uniform beam, this beam will have lower spring constant which will reduce the pull down voltage. A comprehensive model for spring constant and pull down voltage of the non uniform cantilever is developed through basic force deflection mechanism of the suspended beam. 1. INTRODUCTION Nowadays RF MEMS components are becoming popular, due to their very good performance at RF and microwave frequencies. RF MEMS switches have very low insertion loss at on state and very high isolation at off state. The operating principle of an electrostatic actuated RF MEMS switch is very simple. A beam (bridge or cantilever) is suspended from the anchor with an actuation electrode placed underneath. When a DC voltage is applied between the beam and actuation electrode the beam moves down due to an electrostatic force. The DC actuation voltage, at which the beam fully moves down, is called the pull down voltage. Usually the actuation voltage for RF MEMS switches is higher than their solid-state counterparts. In order to reduce the pull down voltage for RF MEMS switches, techniques like folded spring, narrower beam close to the anchor than actuation electrode are used [1]. To calculate the required pull down voltage for a beam, it is necessary to have an accurate mechanical model for the spring constant of the beam. The spring constant will determine the pull down voltage. The pull down voltage (spring constant) also depends on the position and orientation of the actuation electrode. The model of the spring constant and the pull down voltage for a uniform beam is presented in the literature [1]. For non uniform beam, some work has been published recently [2, 3]. In the work presented in [2], the model assumes that the force is concentrated on the tip of the cantilever. Therefore the accuracy strongly depends on the size and position of the actuation electrode. In [3], a comparison of pull down voltage between uniform and non uniform beam is presented using numerical simulations. It shows that a non uniform beam may have a lower pull down voltage than a uniform beam. In this paper we develop an analytical model for the spring constant and pull down voltage for a non uniform cantilever taking into account that the force may be distributed along the beam. The model will be very useful for analysis of spring constant and pull down voltage of non uniform beam, using simple mathematical program. It will be much faster and simpler compared to the commercial tools using 3-D modeling. The model of the spring constant and its verification is described in section 2.The modeled pull down voltage is compared with CoventorWare simulation in section 3. The paper is concluded in section 4 followed by an appendix. 2. MODELING OF CANTILEVER There are two basic types of RF MEMS switches, fixed- fixed bridge and cantilever. Usually the spring constant of fixed-fixed bridge is higher than cantilever, because the bridges are rigidly anchored at both sides. In circuit point of view, bridges are more useful in shunt configuration and cantilevers are more useful in series configuration. The cantilever can be used both as a DC and capacitive contact switch. For DC contact switch, a separate actuation electrode is required. For capacitive contact switch the same electrode may be used both for actuation and capacitive contact. In this section we are going to develop the model for the spring constant of a non 0-7803-9742-8/06/$20.00 © 2006 IEEE. 56