A Liouville Model for Polycrystalline Ferroelectrics Emphasizing Kinetic Integrity and Deployability in Circuits with Charge and Current Constraints

In this paper, we propose a compact Liouville model, which invokes the Liouville formula into Landau theory to account for the polycrystalline ferroelectrics, and experimentally verifies its predictive capability in dynamic behaviors of the circuits incorporating Zr-doped HfO2 ferroelectric capacitor (FeCap). The kinetic parameters of the model can be determined unambiguously by the frequency response to the area of saturated hysteresis (FRASH) loop, which enables reliable predictions on the dynamical behaviors. The deployability of circuits under charge and current constraints are experimentally validated in the conjunction of FeCap and MOSFET, as well as in the reconfigurable combinational circuit including two field-effect transistors and one FeCap, respectively. As the results, all the experimental data can be well reproduced by the model, which supports it to be a versatile and compatible modeling tool for the ferroelectric circuits.