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 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.