Highly Accurate Analytic Modeling of Dispersive Field Distributions in MIM Capacitances With Electrodes Thinner Than Skin Depth

Rapid dielectric characterization and modeling play an essential role in developing new technologies and materials for RF systems. In RF frontends, flexible impedance matching and frequency tuning can be introduced by deploying tunable capacitors (varactors), e.g., in metal-insulator–metal (MIM) configuration. On the physical side, test structures are available that only require patterning of the top layer and allow a fast characterization. On the modeling side, still, time-consuming 3-D EM simulations are necessary to extract the corresponding material properties. While analytic/schematic modeling would be fast, no accurate models that closely fit the dispersive characteristic are available up to now. In this article, we present a novel analytic model derived from the common $RLC$ model, which splits the electrode’s contribution into two parts and adds a parallel substrate impedance. Other than the common $RLC$ model, it is consistent for varying thickness of the dielectric and electrode, electrode conductivity, and dielectric properties. This model is verified by systematic, multivariate simulations and a large set of measured test structures. The analysis shows that the root mean squared error (RMSE) can be decreased by orders with our model.