A DFT+$U$+$V$ study of pristine and oxygen-deficient HfO${}_2$ with self-consistent Hubbard parameters

Abstract

HfO${}_2$-based ferroelectrics have emerged as promising materials for advanced nanoelectronics, with their robust polarization and silicon compatibility making them ideal for high-density, non-volatile memory applications. Oxygen vacancies, particularly in positively charged states, are suggested to profoundly impact the polymorphism kinetics and phase stability of hafnia, thereby affecting its ferroelectric behavior. The electronic structures of pristine and oxygen-deficient hafnia polymorph have been extensively studied using density functional theory, primarily employing (semi-)local exchange-correlation functionals. However, these methods often underestimate band gaps and may not accurately capture the localized nature of $d$-electrons. In this work, we investigate hafnia in various phases using DFT + $U$ + $V$, with onsite $U$ and intersite $V$ Hubbard parameters computed self-consistently via the pseudohybrid Hubbard density functional, ACBN0, and its extended version eACBN0. We find that the self-consistent DFT + $U$ method provides comparable accuracy to the computationally more expensive Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional in predicting relative thermodynamic stability, band gaps, and density of states. Furthermore, it is a cost-effective approach for estimating the formation energies of oxygen vacancies. Additionally, we demonstrate that environmentally dependent Hubbard parameters serve as useful indicators for analyzing bond strengths and electronic structures in real space.

References in corpus (17)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• The GW method
• The Origin of Ferroelectricity in Hf${}_x$ Zr${}_{1-x}$ O${}_2$: A Computational Investigation and a Surface Energy Model
• Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach
• Pathways Towards Ferroelectricity in Hafnia
• Self-consistent hybrid functional for condensed systems
• Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations
• Extended DFT+U+V method with on-site and inter-site electronic interactions
• Structural Polymorphism Kinetics Promoted by Charged Oxygen Vacancies in HfO${}_2$
• CoFFEE: Corrections For Formation Energy and Eigenvalues for charged defect simulations
• Efficient First-Principles Approach with a Pseudohybrid Density Functional for Extended Hubbard Interactions
• Ab initio study of lattice dynamics of group IV semiconductors using pseudohybrid functionals for extended Hubbard interactions
• Onsite and intersite electronic correlations in the Hubbard model for halide perovskites
• Linear-response calculation of the effective Coulomb interaction between closed-shell localized electrons: Cu, Zn, and ZnO
• Effects of self-consistent extended Hubbard interactions and spin-orbit couplings on energy bands of semiconductors and topological insulators