The emerging ferroelectric technology needs a reliable model for the simulation of the ferroelectric capacitors. This model would play a crucial role in designing new ferroelectric nonvolatile memories. As a main requirement, such a model must allow the calculation of the polarization variations for an arbitrary voltage applied to the ferroelectric. However, in spite of the large efforts made in modeling, most of the existing solutions fail to satisfy the above requirement or lack a minimal physical background. To address these problems, we developed a model based on a ferroelectric interpretation of the Preisach theory of hysteresis. In this articles, we try to elucidate how this theory, initially developed for ferromagnetic particles, can be adapted to the ferroelectric materials, despite the many differences between the two. Because the Preisach theory assumes a distribution of the coercitive voltages, we try to clarify its physical meaning in the case of the ferroelectric materials and propose a methodology to determine this distribution experimentally. To facilitate the implementation of the model, the experimental results are then fitted by an analytic function and the whole bidimensional distribution is calculated using a linear approximation. To evaluate the validity of the model, we performed simulations using the Spectre® circuit simulator and the results are in very good agreement with the measurements for the saturated hysteresis loops. The differences existing for the partial loops are mainly due to the linear approximation used for the Preisach distribution. This model can be successfully used for the design of the real memories.

Bartic, A. T., Wouters, D. J., Maes, H. E., Rickes, J. T., & Waser, R. M. (2001). Preisach model for the simulation of ferroelectric capacitors. Journal of Applied Physics, 89(6), 3420–3425.