Structure of $180^\circ$ ferroelectric domain walls in $\mathrm{HfO_2}$ and $\mathrm{ZrO_2}$

TL;DR

This study uses density functional theory to analyze the structure, energy, and polarization of 180° ferroelectric domain walls in HfO2 and ZrO2, enhancing understanding of experimental TEM observations.

Contribution

It introduces detailed models of ferroelectric domain walls in HfO2 and ZrO2, linking domain width to energy and polarization, and offers methods to interpret TEM data despite missing oxygen atom positions.

Findings

Domain wall energy depends on domain width.

Polarization directions can be inferred from Hf atom positions.

Models improve interpretation of TEM observations.

Abstract

We report two series of structures representing two types of $180^\circ$ ferroelectric domain walls in $\mathrm{HfO_2}$ and $\mathrm{ZrO_2}$. We model the domain structures with different width by density functional theory calculations. The results reveal the dependency of domain wall energy and polarization on domain width. We show how the directions of polarization of ferroelectric domains can be determined from experimentally observed Hf atoms, despite the fact that the knowledge about the positions of O atoms is missing. The two series of structures thus provide more thorough interpretation and hence deeper understanding of experimental observations by transmission electron microscopy.