Preisach modeling of imprint on hafnium zirconium oxide ferroelectric capacitors

Abstract

Imprint, the preferential orientation of the polarization of a ferroelectric device subjected to elevated temperatures, is a primary reliability concern afflicting data retention in ferroelectric RAM. In this paper, we demonstrate Preisach-based hysteresis modeling, which can be used to predict imprint behavior in ferroelectric thin films. A method was developed for capturing imprint in the context of a Preisach model and a numerical approach for evaluating the Preisach distribution was expanded upon. Interpolation and curve fitting were used to make predictions of the Preisach distributions of imprinted ferroelectric hafnium zirconium oxide devices after short-duration bakes at 23-260 °C and long-term bakes at 85 and 125 °C. In the case of long-term bakes, imprint-induced coercive shifts were modeled as shifts in the derivative of the top and bottom hysteretic polarization curves. The shift in the curves is modeled by fitting experimental data to a commonly used empirically logarithmic relationship reported in the literature. Simulations give remanent polarizations and coercive fields within <5.0 μC/cm2 and 0.1 V, respectively, of the raw data average.