Variability Analysis in a 3-D Multi-Granular Hf$_x$Zr$_{1-x}$O$_2$ Ferroelectric Capacitor

TL;DR

This study uses simulation techniques to analyze how grain structure and dielectric content affect the variability of remnant polarization in 3-D ferroelectric capacitors, revealing significant impacts on hysteresis behavior.

Contribution

It introduces a novel simulation approach coupling PVD and TCAD to study variability in multi-granular ferroelectric capacitors, highlighting the effects of grain profile and dielectric content.

Findings

Linear profile grains show more hysteresis variability.

Dielectric grains increase hysteresis variability.

Higher dielectric content reduces hysteresis retentivity.

Abstract

A simulation-based study of variability of remnant polarization $\left (P_r \right)$ in a multi-granular 3-D ultra-thin ferroelectric (FE) capacitor is presented in this paper. The Poisson Voronoi Tessellation Diagram (PVD) is used for the nucleation of grains in the FE region, which corresponds to the physical growth mechanism. The PVD algorithm implemented in MATLAB is coupled with TCAD simulations, to trace the ferroelectric hysteresis loop. It is found that the grains which have linear profile of $P_r$ show larger variability in the FE hysteresis loop, compared to the grains, which follow the Gaussian distribution of $P_r$. Additionally, the impact of dielectric content in the FE grains is analyzed. It is seen that the dielectric grains cause very large amount of variability in the FE hysteresis loop. An increase in the dielectric grains also leads to a loss in the retentivity of the hysteresis loop.