CkBooks Online – Free Online Books

The electromagnetic modeling step, familiar to most RF/microwave engineers, involves the electromagnetic analysis of the structure using a 3-D fullwave solver tool. It begins by transferring the solid model developed in the mechanical simulation tool into the EM tool and proceeds with the definition of its constituent materials and boundary conditions. The analysis yields the scattering parameters and field distributions.

While the use of 3-D EM analysis is common practice in microwave design, its application to the modeling of MEMS structures is relatively recent and, indeed, meets with some challenges [58, 59] . For example, Vietzorreck [58], who studied the modeling of the behavior of MEMS shunt capacitive switches at millimeter-wave frequencies, pointed out that these switches possess some features that make their numerical description difficult. For example, in these switches one can find, simultaneously in the direction normal to the substrate, the silicon nitride insulating the bottom electrode with a thickness of 0.1 mm, the bottom electrode with a thickness of 0.4 mm, the bridge-to-substrate distance with a thickness of 2 mm, the bridge/membrane with a thickness of 0.3 mm, the CPW ground lines with a thickness of 4 mm, the silicon dioxide insulating buffer layer with a thickness of 1 mm, and the substrate with a thickness of 545 mm. In the transverse direction, on the other hand, one finds the CPW center conductor with a width of 80 mm and a CPW ground-to-center conductor spacing of 120 mm.

This coexistence of very large and very small thicknesses (e.g., 0.1 mm and 545 mm in the direction normal to the substrate) poses a limitation when it comes to discretization in the context of limited computer memory. Another challenging aspect of the full-wave modeling of MEMS devices is that, because of their wide bandwidth, both wideband ohmic and dielectric loss behavior must be properly considered to adduce any degree of credibility to the results. Recently, Qian et al. [60] developed a parametric model for the microwave performance of the MEMS capacitive switch in terms of a series RLC circuit . The first step in developing the parametric model entailed performing a full wave electromagnetic simulation with the Ansoft High Frequency Structure Simulator (HFSS) on the idealized structure shown .

In the HFSS model, the structure was enclosed in a simulation box of size 1,200 ´ 600 ´ 600 mm on which radiation boundary conditions were imposed on all sides. The substrate was assumed to be lossless, with a relative dielectric constant of 9.8, corresponding to Alumina, and had a thickness of 600 mm. The metal structures (namely, the CPW lines and the bridge) were assumed to be perfect conductors, and the bottom electrode was assumed to be coated by a 0.1-mm-thick layer of silicon nitride with a relative dielectric constant of 7.

The second step in the model development entailed running full wave simulations of the structures to generate scattering parameters in the 1 to 60 GHz frequency range. Then, via optimization, the RLC circuit parameters were extracted. The results, comparing HFSS simulations of the switch in the off and on states and the extracted model, are shown.