Modeling of charge switching in ferroelectric capacitors

To simulate charge switching in ferroelectric capacitors, a pair of exponential growth and decay currents is mapped to the process of polarization reversal. This is based on the fact that these exponential currents [i.e., i = I(m) e(t/tau) (t < or = 0) and i = I(m) e(-t/tau) (t > or = 0)], are completely specified by two constants I(m) and tau and each accommodates an integral charge Q = I(m) x tau. Equating this charge to the remanent spontaneous polarization allows for the modeling of switching current. For practical circuit simulations for charge switching, this modeling of switching current is simplified to an exponential decay current whose integral charge is set equal to the total reversed spontaneous polarization. This is because an exponential decay current can be conveniently implemented by charging a series resistor and capacitor (RC) circuit with a pulse-voltage source. The voltage transitions of the pulse source are associated with the polarization reversal and can be controlled with a noninverting Schmitt trigger that toggles at the positive and negative coercive voltages of a ferroelectric capacitor. The final circuit model incorporates such electrical and geometrical parameters as capacitance, remanent spontaneous polarization, coercive field, electrode area, and film thickness of a ferroelectric, thin-film capacitor.