A Large-Signal Model of Ferroelectric Thin-Film Transmission Lines

This paper evaluates the microwave nonlinear properties and tuning at RF frequencies of ferroelectric Ba_0.3Sr_0.7 TiO₃ thin films by on-wafer measurements of the second- and third-order harmonics and intermodulation products of several coplanar transmission lines as a function of dc bias. We analyze these data by use of a large-signal circuit model to obtain the nonlinear distributed capacitance as a function of voltage. Whereas the model with an electric-field-dependent dielectric constant for the ferroelectric material is able to predict the tuning when a dc voltage is applied and the generated harmonics, it disagrees with the measured third-order intermodulation products at frequencies 2ω₁-ω₂ and 2ω₂-ω₁. Nonlinear effects due to self heating mechanisms are also considered, along with an additional phenomenological source of nonlinearities, to model all the observables. Interactions between the ferroelectric and self-heating components give rise to a deep null in both the measured and modeled intermodulation-distortion component.