A PARAMETRIC MODEL OF LOW-LOSS RF MEMS CAPACITIVE SWITCHES

A PARAMETRIC MODEL OF LOW-LOSS RF MEMS CAPACITIVE SWITCHES

The recent developments of microelectromechanical systems (MEMS) switches and their uses at microwave frequencies have promoted exciting advancements in the field of microwave switching. In comparison with other switches, realized by FET's or p-i-n diodes, MEMS switches exhibit low-loss performance, zero power consumption and very low intermodulation distortion. To our knowledge, there is very little work which has been done to accurately describe their behaviors at microwave frequencies [2-4]. Due to the three dimensional geometry of such switches, a full wave analysis is needed to characterize MEMS switches. The result of the full wave analysis will provide scattering parameters for different switch geometries, which will allow constructing an equivalent lumped circuit model for different geometries. Based on this database, the equivalent lumped circuit model of the switch is determined. The values of the circuit elements are related to the physical dimensions of the switch as final result.

Electromagnetic model

In this paper, we will focus on the shunt capacitive MEMS switch, which consists of a thin metal membrane bridge suspended over the center conductor of a coplanar waveguide (CPW) and fixed on the ground conductor of the CPW, as schematically shown in Fig. 1(a). The full wave electromagnetic simulation of the switch is done by a finite element method using Ansoft High Frequency Structure Simulator (HFSS). After the full wave analysis is performed, S-parameters are extracted in the frequency range going from 1 GHz to 60 GHz for different width of the switch. The substrate is assumed to be high-resistivity silicon with relative dielectric constant of 11.9. The thickness of the substrate is 600μm and a 1-μm-thick layer of silicon dioxide is used as a buffer layer. The CPW conductors are treated as aluminum with thickness of 4.0 μm. The bottom electrode of the switches and the metallic membrane consists of a 0.4-μm-thick aluminum. The bottom electrode of the switches is assumed to be coated with silicon nitrate (Si3N4) having relative dielectric constant of 7 and thickness of 0.1μm. Figure 1(b) presents the first order equivalent circuit model obtained for the capacitive MEMS switch.

Equivalent circuit model of the capacitive MEMS switch

The parameters of the circuit model are optimized to fit the S-parameter obtained from the full wave electromagnetic simulation. Figure 2 shows the EM simulated and circuit model S-parameters of a 280 μm by 120 μm membrane suspended 3.5 μm over a CPW transmission line having a center conductor width of 120μm and a gap of 80μm. Since the capacitance is very small and it dominates the shunt impedance, it is very difficult to determine the resistance and inductance associated with the model in this state (off-state). The capacitance in the circuit model for this state is 0.075pF.

When the switch is in the on-state a similar procedure is used. The S-parameters obtained from the full wave analysis are compared with those obtained using our model in Fig. 3. In the circuit model, the capacitance is 9.31pF, the inductance is 5.03pH and the resistance is 0.034W. In both cases excellent agreement is obtained between the simulated data and our lumped circuit model.

By repeating this process for different switch widths, a full set of capacitance, inductance and resistance of the bridge is obtained and used to extract the parametric scalable model as explained in the next section.

Parametric scalable model

From the result of the full wave analysis, we observe as in the off-state condition of the switch the capacitance is dominating the total value of the impedance of the circuit in Fig. 1(b). For the parametric fitting we show the dependence of the switch capacitance in the off-state versus the switch width. The width of the switch is varied between 60.0μm and 180.0μm and results of the fitting are reported in Fig.4. Also Fig. 4 shows the computed capacitance corresponding to two overlapping parallel plates. It is clear from the comparison that the overlap capacitance has lower value compared to the one predicted by our model and by the full wave analysis due to the fringing field effects at the switch edges. From the curve in Fig. 4, a linear fitting for the switch capacitance versus the switch width is obtained, as reported in Eq.