Modeling ferroelectric capacitor switching with asymmetric nonperiodic input signals and arbitrary initial conditions

The switching behavior of ferroelectric capacitors experiencing arbitrary time-dependent electric fields and arbitrary initial conditions is investigated both theoretically and experimentally. A general approach for modeling incomplete dipole switching in ferroelectric capacitors is used to derive equations describing the electrical behavior of a simple characterization circuit with arbitrary initial conditions and arbitrary time-dependent applied voltages. The equations include four experimentally determined parameters: the remanent and spontaneous polarizations, the coercive field, and the ferroelectric dielectric constant. Once these model parameters are determined from a single high-frequency sinusoidal hysteresis loop, model predictions are made with no adjustable parameters. The circuit behavior for both sinusoidal and trapezoidal input signals is computed, including asymmetric and nonperiodic signals as well as several different initial conditions. The accuracy of the model predictions is quantitatively verified with experimental data. The approach is also utilized to model the switching behavior of a ferroelectric capacitor containing a sheet of space charge. It is found that hysteresis loop distortions resulting from ionizing radiation resemble those caused by a sheet of space charge. This quantitative modeling capability facilitates the optimization of the design of ferroelectric memory circuits by minimizing the amount of required electrical testing and characterization. It can also be used to facilitate the identification and understanding of degradation mechanisms occurring in ferroelectric thin films.