Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors

Abstract

In this paper, we present a simulation analysis for coplanar-plate capacitors made on ferroelectric thin films. The ${\hbox{Ba}}_{0.5}{\hbox{Sr}}_{0.5} {\hbox{TiO}} _{3}$ films with thicknesses in the 100-nm range were prepared on alumina substrates and their dielectric properties were evaluated in the kilohertz and gigahertz frequency ranges. The permittivity values ranged from 750 to 1250, depending on the thickness of the film and the measurement frequency. Simulations were performed with the help of three commercially available Maxwell's equation solvers based on the most commonly used numerical methods, designed in planar 3-D and full 3-D software. The basics of the numerical methods are described and the simulated capacitance is compared to the experimentally determined values. The variations are ascribed to the different approaches used for the simulation of the thin films with high permittivity values in the individual Maxwell's equation solvers, which led to errors in the computation. Problems that are specific to each method are described, and optimized approaches for the simulation of structures made on thin films are presented.