We present a broadband on-wafer measurement technique for the characterization of the in-plane complex relative permittivity of a thin-film test wafer and a companion substrate test wafer from 100 Hz to 40 GHz, and potentially to 110 GHz. From 100 Hz to 300 MHz, the approach uses an ensemble of interdigitated capacitors with different interdigitated active lengths l = (0.100 mm, 0.325 mm, 0.875 mm, 1.835 mm, 2.9 mm) fabricated on both test wafers. Within this regime, from 100 Hz to 1 MHz, the measurements were performed with an inductance-capacitance-resistance meter. From 1 MHz to 300 MHz, the scattering parameters of the set of interdigitated capacitors were measured with a radio frequency vector network analyzer. In the high frequency regime, 300 MHz to 40 GHz, we measure scattering parameters of a set of coplanar waveguides of active lengths l = (0.420 mm, 1.270 mm, 2.155 mm, 3.22 mm, 3.993 mm, 5.933 mm) fabricated on the test wafers. We extracted the capacitance and conductance of the interdigitated capacitors and coplanar waveguides on the test wafers for the appropriate frequency regimes. We then obtained a mapping function from 2D finite element simulations that relates the change in capacitance of the thin-film test wafer relative to the companion substrate test wafer to the real part of the in-plane relative permittivity. The imaginary part of the in-plane relative permittivity was obtained from the real part of the in-plane relative permittivity and the in-plane loss tangent.

We applied this broadband dielectric spectroscopy technique to explore the frequency-dependent relative permittivity of unstrained Ruddlesden-Popper series Sr_n+1Ti_nO_3n+1(n=1, 2, 3) thin films as a function of temperature and dc electric field. At room temperature, the in-plane relative permittivities (K₁₁) obtained for Sr_n+1Ti_nO_3n+1(n=1, 2, 3) were 42 plus/minus 3, 54 plus/minus3, and 77 plus/minus2, respectively, and were independent of frequency. At low temperatures, K₁₁ increased with a behavior consistent with an incipient ferroelectric, and paraelectric behavior developed in Sr₄Ti₃O₁₀(n=3).

In 2004, J. H. Haeni, et al. showed that SrTiO₃ (n = infinity) on DyScO₃ (110) undergoes a ferroelectric to paraelectric phase transition around room temperature. As a means to understand the origins of the loss and tunability in strained SrTiO₃ (n = infinity), we performed our broadband dielectric spectroscopy technique on epitaxial thin-films of Ruddlesden-Popper series Sr_n+1Ti_nO_3n+1(n=2, 3, 4, 5, 6) on the rare-earth scandate substrates, DyScO₃ (110) and GdScO₃ (110). For these thin films, DyScO₃ (110) and GdScO₃ (110) corresponded to biaxial tensile strain of approximately 1% and 1.7%, respectively. The thin films were 50 nm thick on DyScO₃ (110) and 25 nm thick on GdScO₃ (110), which ensured uniform strain throughout the film. We report the dependence of the critical temperature, tunability, and loss tangent on series number and strain at 1 MHz. We also examined the broadband frequency dependent dielectric properties of these thin films as a function of temperature, electric field, series number and strain.