On the Evaluation of Remnant Polarization in 3D Cylindrical Hafnia-Based Ferroelectric Capacitors

In this study, we establish a phase field model for the 3D cylindrical hafnia-based ferroelectric capacitors (FeCAPs) to capture the ferroelectric (FE) characteristics of the crosssection. Based on this, we show how the remnant polarization (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P_{\mathrm{r}}$</tex>) can be evaluated with minimum error. We further carry out an in-depth analysis on how geometric factors influence the FeCAP performance. Our results indicate that cylindrical FeCAPs with a smaller inner radius exhibit lower <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P_{\mathrm{r}}$</tex> due to intensified depolarization field. With increasing inner radius, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P_{\mathrm{r}}$</tex> of cylindrical FeCAP approaches that of planar FeCAP. This model provides a valuable tool for assessing memory capacity and optimizing the structure of 3D FeRAMs.