ABSTRACTMicrowave properties of coplanar waveguide (CPW) transmission lines fabricated on high dielectric materials, such as ferroelectric Ba1−xSrxTiO3 films, are highly sensitive on the dimension and shape of electrodes. A small change in device dimension affects the total electrical length of the CPW, which may mislead the effective dielectric constant of the dielectric layer. Furthermore, extracting dielectric constant of high-k thin films from the measured microwave properties, such as S-parameters, is very difficult. The well known a modified conformal mapping method frequently exhibits an inconsistent dielectric constant for CPW on high-k materials. CPW transmission lines were fabricated on high-k thin films, ferroelectric Ba0.6Sr0.4TiO3, which were deposited by the pulsed laser deposition with partial oxygen backgrounds. A large phase shift angle of 100° at 10 GHz was observed from the CPW (gap = 4 μm, length = 3 mm) with a 40 V of dc bias, which supports that the idea of the tunable microwave device application using ferroelectrics films. The dielectric constant of the thin ferroelectric film was extracted from the dimension of the CPW (gap, width, length) and the measured S-parameters by a modified conformal mapping. However, the dielectric constant of the ferroelectric thin film calculated by a modified conformal mapping exhibits a gap dependency; dielectric constant (990 ∼ 830) decreases with increasing gap size (4 ∼ 19 μm, respectively). For comparison, dielectric properties have been extracted by extensive EM-simulation using a HFSS™ (Ansoft) with observed dimensions of CPW devices. Total phase, which is closely related with the dielectric constant of the film, is strongly affected by gap size, film thickness, and slanted angle of CPW.
Appendix F Averaging the Effective Dielectric Constant in EBG-Based Transmission Lines
