ABSTRACT
The cross section of the multilayered microstrip structure modeled is shown in Fig. 1. The multilayered microstrip structure consists of a LAO dielectric substrate, typically 254 pm thick, a ferroelectric thin film layer (its thickness varying from 300 to 2000 nm for various applications), a gold or HTS thin film (2 pm thick or 350 nm thick, respectively) for the top conductor, and a 2 pm thick gold ground plane. Important geometri cal dimensions controlling the microstrip parameters are the width-toheight ratio (W/H), thickness of the ferroelectric film (t), and the thickness of the substrate (h); these dimensions are indicated in Fig. 1. The geom etry of the multilayered microstrip was simulated using Sonnet em® and the Zeland’s IE3D software^ to model the behavior of ZQ, eeff, and IL as a function of frequency, W/H, and ferroelectric thin film’s parameters such as t, er, and tan8. Modeling was performed for microstrip lines with Z0’s of 25,50, and 75 Q, as determined in the absence of a ferroelectric film. The tunable range of erFE was chosen to be between 5000 at zero-field to 300 at high field and 77 K for the STO film, and 2000 at zero-field to 500 at high field at room temperature for the BSTO thin film based on the data obtained from low frequency capacitance measurements on test struc tures.^2, and It is important to mention that spatial variations of the relative dielectric constant of the ferroelectric film (erFE) are neglected in our modeling. The erFE varies spatially, going from fully biased under the microstrip to unbiased far away from the microstrip line, for a single microstrip. The variation is more complicated in a coupled microstrip, coupled ring resonator, filter or other more complex structure. Also, all of the circuits were modeled with a ferroelectric thin film layer present throughout the sample.
