基于DFT+$U$+$V$的纯HfO₂和氧缺陷HfO₂的研究
A DFT+$U$+$V$ study of pristine and oxygen-deficient HfO$_2$ with self-consistent Hubbard parameters
AI总结：
本研究通过DFT+$U$+$V$方法探讨HfO₂的电子结构，揭示自洽Hubbard参数对预测热力学稳定性、带隙和氧空位形成能的重要性。
摘要：
以HfO₂为基础的铁电材料已逐渐成为先进纳米电子器件的有前景材料，其坚固的极化和与硅的兼容性使其成为高密度、非易失性存储器应用的理想选择。氧空位，特别是正电荷状态的空位，被认为深刻影响hafnia的多形动力学和相稳定性，从而影响其铁电行为。纯态和氧缺陷的hafnia多形的电子结构已广泛使用密度泛函理论研究，主要采用（半）本地交换相关泛函。然而，这些方法往往低估了带隙，并可能无法准确捕捉d电子的局域性质。在本工作中，我们利用DFT + $U$ + $V$研究了hafnia的不同相态，其中 onsite $U$和intersite $V$的Hubbard参数通过伪混合Hubbard密度泛函ACBN0及其扩展版本eACBN0自洽计算。我们发现，自洽的DFT + $U$方法在预测相对热力学稳定性、带隙和密度态方面与计算成本更高的Heyd-Scuseria-Ernzerhof（HSE）混合密度泛函具有可比的准确性。此外，它是一种经济有效的估算氧空位形成能的方法。此外，我们证明了环境依赖的Hubbard参数在分析真实空间中的键强和电子结构方面是有用的指示器。
英文摘要：
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.
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