A PHYSICAL MODEL FOR THE ELECTRICAL HYSTERESIS OF THIN-FILM FERROELECTRIC CAPACITORS

A mathematical model for the electrical hysteresis of ferroelectric thin-film capacitors based on the Landau free energy theory is presented. The hysteresis of a single ferroelectric crystallite is derived from free energy considerations. The hysteresis of a polycrystalline material is obtained by accounting for the spatial distribution and the structural phase of the crystallites. The hysteresis functions for the tetragonal and rhombohedral phases are derived. The model is a true expression of the polarization of a ferroelectric material based on physical principles, not a curve-fitting algorithm. The electrical history of the ferroelectric is explicit in the calculation of the polarization. It is therefore capable of simulating complex behavior such as arbitrary waveforms and sub-hysteresis loops.