A model for the hysteresis loop's simulation of ferroelectric capacitors

A phenomenological physical model is derived for description of the P-E hysteresis behavior and simulated ferroelectric capacitor. The polarization of ferroelectric capacitors experiencing arbitrary conditions can be well depicted if we know the switching ferroelectric dipole polarization Pd with respect to the electric field E. In the model the differential equations dP(d)/dE = C * P-s + P-d/2 * P-s-P-d/2 and theta P-sat/theta E are introduced to depict the saturated and unsaturated conditions of the switching ferroelectric dipole polarization respectively, where C = 1/EcPs In P-s + Pr/P-s - P-r and P-r, P-s, E-c taken as positive quantities, are the remanent polarization, spontaneous polarization, coercive field, and P-sat is the value of the polarization on the saturated hysteresis loop at the field of interest, Omega is a positive function less than orequal to one,which is defined in the model by Omega = exp(-vertical bar P-d - P-sat(-) - P-sat(+)vertical bar)/P-sat(-) - P-sat(+) where alpha = + for increasing fields and alpha = - for decreasing fields. All the parameters are physically based and can be easily extracted from measured data. Our experimental data and literature's experimental date show relevant agreement with the model for both saturated and minor loops and any arbitrary conditions.