Modeling and Analysis of Digital Tunable RF MEMS Capacitors
Authors: Wang Dajia , Yao Jun , Rao Qing , Zhang Li , Qiu Chuankai , Fan Tianquan 
Published: June 2009

The recent development of radio frequency (RF) microelectromechanical system (MEMS) technology has demonstrated great potential at the communication applications. The capacitors with tunable characteristics are now greatly required. Various structure designs of tunable capacitors have been reported, such as two or three parallel plates with a vertical electrostatic actuator showing a restricted tuning range due to the pull-in effect [1], comb-driven variable capacitors which can achieve a large tuning ratio but are poor at high insertion loss and controlling voltages and low Q-factor [2], and thermal-driven capacitors [3] having a disadvantage that their response speed is generally slower than that of electrostatic actuators. In this paper, we present two designs of MEMS electrostatically tunable capacitor; only one structural layer and one sacrificial layer are required. In Fig. 1, seven cantilever beams with constant length of 240μm, width of 60μm, thickness of 2μm are constructed as top electrodes on a coplanar waveguide transmission line. The separation between adjacent cantilevers is 600μm. The separated bottom electrodes, which are insulated by Si3N4 of 150nm, are 100μm length and 60μm width. The bottom electrodes and CPW transmission line are isolated by Si3N4 of 50nm, and the air gap is 2μm. The top electrodes can be driven individually by the separated bottom electrodes. Fig. 2 illustrates the second design has the varied cantilever width that changes from 60μm to 120μm. The length of bottom electrode that is directly treated as CPW transmission line is 4230μm and the width is 100μm; other structural parameters are the same as those of the first design. When an electrical potential is applied between the top and bottom electrodes of both designs, an attractive force is generated to pull the top cantilevers down, thus a variable capacitor is formed. The capacitor C is related to the overlap area A, the spacing d0-d between the top and bottom electrodes. d0 is the initial gap and d is the displacement of the top electrode. C=εAd0−d(1) The mechanical and RF performances of these two designs have been analyzed by FEA method. For the first design, when all beams are applied equal controlling voltages, the relationship between the capacitance in total and voltages is shown in Fig. 3 (a). When the voltage is 48V, the capacitance is 239.2fF but the tuning ratio is just about 1.2. Fig. 3 (b) shows the RF characteristic obtained by using HFSS when one, two, four or none of top electrodes are applied controlling voltage for a displacement of 0.6μm. The S-parameters vs. Frequency curves demonstrate that such design has a wide tunable frequency range from 0.1GHz to 70GHz, and the return loss can reach as large as −35dB at the self-resonating frequency of 15GHz and more than −20dB under 40GHz. In practical, it can be used as a distributed phase shifter. For the second design, the capacitor vs. voltage curve is shown in Fig. 4 (a). When a voltage of 48V is applied, the tuning ratio is very close to that of the first design. The main reason is that, when applied the same voltage, the displacements of cantilever beams with varied width are independent of the width and approximately have the same magnitudes. In Fig. 4 (b), S-parameter analyses have shown a wide narrow frequency range and large return loss compared to the first design when no voltage is applied.