Scaling issues in ferroelectric barium strontium titanate tunable planar capacitors

We report on the geometric limits associated with tunability of interdigitated capacitors, specifically regarding the impact of a parasitic non-tunable component that necessarily accompanies a ferroelectric surface capacitor, and can dominate the voltage-dependent response as capacitor dimensions are reduced to achieve the small capacitance values required for impedance matching in the X band. We present a case study of simple gap capacitors prepared and characterized as a function of gap width (i.e., the distance between electrodes) and gap length (i.e., the edge-to-edge gap distance). Our series of measurements reveals that for gap widths in the micrometer range, as gap lengths are reduced to meet sub-picofarad capacitance values, the non-tunable parasitic elements limit the effective tunability. These experimental measurements are supported by a companion set of microwave models that clarify the existence of parallel parasitic elements.