Use of dimensionality to enhance tunable microwave dielectrics

The miniaturization and integration of frequency-agile microwave circuits---\textit{tunable} filters, resonators, phase shifters and more---with microelectronics offers tantalizing device possibilities, yet requires thin films whose dielectric constant at GHz frequencies can be tuned by applying a quasi-static electric field. Appropriate systems, e.g., Ba$_{x}$Sr$_{1-x}$TiO$_{3}$, have a paraelectric-to-ferroelectric transition just below ambient temperature, providing high tunability. Unfortunately such films suffer significant losses arising from defects. Recognizing that progress is stymied by dielectric loss, we start with a system with exceptionally low loss---Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ phases---where in-plane crystallographic shear (SrO)$_{2}$ faults provide an alternative to point defects for accommodating non-stoichiometry. In this talk we will establish both experimentally and theoretically the emergence of a ferroelectric and highly tunable ground state in biaxially strained Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ phases with $n\ge $3 at frequencies up to 40~GHz. With increasing $n$ the (SrO)$_{2}$ faults are separated further than the ferroelectric coherence length perpendicular to the in-plane polarization, enabling tunability with a figure of merit at room temperature that rivals all known tunable microwave dielectrics.