Accurate compact nonlinear dynamical model for a volatile ferroelectric ZrO2 capacitor

We have measured the dynamical response of ZrO2 capacitors to applied triangular voltage waveforms with varying frequencies and amplitudes to determine the voltage and charge on the devices as a function of time. We have fit our experimental results to a Landau–Khalatnikov dynamical equation with a sixth order Landau–Ginzburg–Devonshire polynomial to represent the static charge-voltage behavior, and obtained coefficients of determination R2 > 0.99 for the fits. Analysis of the resulting quantitative model reveals an extremely small range of negative differential capacitance <16 mV. The hysteresis loops in the dynamical charge-voltage curves are found to result primarily from energy loss during the ferroelectric transitions, as represented by a frequency-dependent series resistance in the model.