Broadband Permittivity Measurements of Ruddlesden-Popper Sr$_{n+1}$Ti$_{n}$O$_{3n+1 }$(n=1,2,3) Thin Films

In order to explore the microwave dielectric response of Sr$_{2}$TiO$_{4}$, Sr$_{3}$Ti$_{2}$O$_{7}$, and Sr$_{4}$Ti$_{3}$O$_{10}$ thin films, we have performed broadband in-plane quantitative complex permittivity($\varepsilon )$ measurements on Sr$_{n+1}$Ti$_{n}$O$_{3n+1 }$(n=1,2,3) thin films in the frequency range 100Hz-40GHz. The films, of approximately 160 nm thickness, were fabricated by molecular beam epitaxy[1], and standard lithographic techniques were used to define coplanar waveguide transmission lines and interdigitated capacitors using gold. We extracted $\varepsilon $ from the measured complex S-parameters (.01-40GHz) and the complex impedance (100Hz-.001GHz), which were measured at 70K, 150K, 200K, and 250K using a cyrogenic probe station. We found that below $\sim $10GHz the $\varepsilon $'s of these thin films were approximately constant with frequency: $\varepsilon \approx $38, 48, and 100 for Sr$_{n+1}$Ti$_{n}$O$_{3n+1 }$(n=1,2,3) respectively. In addition, the measured value for $\varepsilon $ of Sr$_{2}$TiO$_{4}$ is consistent with recent theoretical calculations [2]. We will discuss in detail the temperature and electric field dependence of the measured complex $\varepsilon $ for these material systems. [1] J.H. Haeni, \textit{et al} APL, \textbf{78}, 21 (2001) [2] C.J. Fennie and M.K. Rabe, PRB, \textbf{68}, 184111 \textbf{(}2003)