Direction-Dependent Lateral Domain Walls in Ferroelectric Hafnium Zirconium Oxide and their Gradient Energy Coefficients: A First Principles Study

TL;DR

This study uses first-principles calculations to analyze the energetics and gradient energy coefficients of lateral domain walls in ferroelectric HZO, revealing orientation-dependent behaviors and strain effects on domain growth.

Contribution

It provides the first detailed quantification of gradient energy coefficients for different lateral domain walls in HZO, highlighting their orientation-dependent properties and strain responses.

Findings

One lateral direction has ultra-sharp domain walls with negative g.

The other lateral direction has gradual domain walls with positive g.

g varies with compressive and tensile strain in opposite ways for the two directions.

Abstract

To understand and harness the physical mechanisms of ferroelectric Hafnium Zirconium Oxide (HZO)-based devices, there is a need for clear understanding of domain interactions, their dynamics, negative capacitance effects, and other multi-domain characteristics. These crucial attributes depend on the coupling between neighboring domains quantified by the gradient energy coefficient (g). Furthermore, HZO has unique orientation-dependent lateral multidomain configurations. To develop an in-depth understanding of multi-domain effects, there is a need for thorough analysis of g. In this work, the energetics of multidomain configurations and domain growth mechanism corresponding to lateral domain walls of HZO are analyzed and gradient energy coefficients are quantified using first-principles Density Functional Theory calculations. These results indicate that one lateral direction exhibits the following characteristics: i) DW is ultra-sharp and domain growth occurs unit-cell-by-unit-cell, ii) the value of g is negative and in the order of $10^{-12} Vm^{3}C^{-1}$, and iii) g reduces (increases) with compressive (tensile) strain. In contrast, in the other lateral direction, the following attributes are observed: i) DW is gradual and domain growth occurs in quanta of half-unit-cell, ii) g is positive and in the order of $10^{-10} Vm^{3}C^{-1}$, and iii) g increases (reduces) with compressive (tensile) strain.