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 a clear understanding of the domain interactions, domain density, nucleation, domain wall motion, negative capacitance effects, and other multi-domain characteristics. All these crucial attributes strongly depend on the coupling between neighboring domains in HZO which is quantified by gradient energy coefficient (g). Furthermore, HZO has unique orientation-dependent lateral multidomain configurations, which plays a key role for directional dependence of g. To develop an in-depth understanding of these effects, there is a need for a thorough analysis of g in HZO, including its orientation and strain-dependence. In this work, we analyze the energetics of multidomain configurations, domain growth mechanism and gradient energy coefficients of HZO corresponding to lateral domain walls using first-principle Density Functional Theory (DFT) calculations. The dependence of g on domain width and strain is also analyzed to provide a comprehensive understanding of this crucial parameter. Our results indicate that one lateral direction exhibits the following characteristics: (i) 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 is much sensitive to strain. In contrast, in the other lateral direction, the following attributes are observed: (i) 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 shows negligible sensitivity to strain (up to the 1% strain limit considered in this work).