Permittivity measurement of Ba0.5Sr0.5TiO3 ferroelectric thin films on multilayered silicon substrates

This paper presents a method for measuring the complex permittivity of Ba_0.5Sr_0.5TiO₃ (BST) ferroelectric thin films on a four-layered substrate at frequencies from 50 MHz to 26.5 GHz. Coplanar waveguide (CPW) lines are employed to measure the permittivity at high frequencies, whereas at low frequencies interdigital capacitors (IDCs) are used instead to avoid the calibration errors of CPW at those frequencies. A quasi-TEM transmission-line model and a lumped-element model, both on a four-layered substrate, are developed for CPW and IDC, respectively, using quasi-TEM analysis, conformal mapping, and partial-capacitance technique. The combinations of CPW model with measured transmission parameters and IDC model with measured scattering parameters allow extraction of the dielectric properties of the BST film. On-wafer through-reflect-line calibration is used to de-embed the true responses of the CPW lines. Dielectric constants of 400-600 and loss tangents of 0.05-0.1 are obtained at frequencies from 50 MHz to 26.5 GHz.