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

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 multidomain 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 multidomain effects, there is a need for a thorough analysis of g. In this work, the energetics of multidomain configurations and domain growth mechanism corresponding to lateral domain walls (DWs) 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 V m3 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 V m3 C-1, and iii) g increases (reduces) with compressive (tensile) strain. Gradient energy coefficient (g) in hafnium zirconium oxide (HZO) plays a key role in dictating the functionality of ferroelectric devices. In this work, the authors explore the most energetically favorable domain walls (DWs) in HZO using first-principles calculations, discuss their anisotropic properties in the two lateral directions, describe their dynamics, calculate g parameters, and predict their response to strain.image