Experimental evidence of correctness of improved model of ferroelectric planar capacitor

Abstract

Planar capacitors, consisting of a thin (≈1μm) ferroelectric film and a dielectric substrate, widely used at microwaves, are normally designed on the basis of the conformal mapping technique and the use of the traditional formula for electric field in the capacitor gap: E=U∕s. U is applied voltage and s is the width of the gap. The important characteristic of the planar capacitor is its tunability defined as n=C(0)∕C(U). The dependence of the tunability on the ferroelectric film thickness (hf) has been experimentally investigated. The saturation or feebly marked maximum on the dependence of n on hf was observed. The appearance of the maximum can be explained using the corrected formula for the field in the gap: E≅U∕(s+hf). The formula was earlier theoretically developed on the basis of minimization of the free energy accumulated in the planar capacitor and using the Ginzburg–Devonshire equation for the nonlinear polarization of the ferroelectric film. The result should be considered as a correction of the model of a planar capacitor based on the conformal mapping technique.