The physical origin of inhomogeneous field within HfO₂-based ferroelectric capacitor

In this work, the origins of the inhomogeneous field within the HfO2-based ferroelectric (FE) capacitor are investigated. We propose a model to simulate the relationship between the reversed polarization and the applied pulses with different amplitudes and durations. The electric field distribution is considered to be influenced by the ferroelectric layer thickness (t(FE)) and the built-in field (E-b). Then, the distribution parameters of both two physical factors and the Merz law, which define the switching dynamics, could be obtained by fitting the experimental results. Comparing with the results of high-resolution transmission electron microscope and first-order reversal curve measurements, it can be reasonably concluded that the physical origin of the inhomogeneous field in HfO2-based ferroelectrics is the random distribution of t(FE) and E-b. This work improves the understanding of the switching dynamics by providing the origins of the inhomogeneous field in an FE film.