Session D56: Understanding Ferroelectricity in Hafnia Through Modeling and Simulations

Multi-order parameter coupling and phase identification in hafnia

Ferroelectric hafnia exhibits excellent size scalability and silicon compatibility, which makes it promising for future ferroelectric nanoscale computing devices. Unlike conventional ferroelectrics such as perovskites, whose ferroelectric phase transitions are described by a single polar order parameter, hafnia has a wide variety of phases, with complicated phase transitions involving multiple order parameters. From a theoretical perspective, this makes it difficult to understand the underlying reason(s) for hafnia’s unique properties and behavior. From an experimental perspective, this variety also complicates phase identification, characterization, and development of prototype devices. Here, we describe first-principles simulations and Landau-Ginzburg-Devonshire modeling to show that the multi-order parameter nature of hafnia is the key to understanding its unique phase transitions, domain wall structures and polarization switching behaviors. Due to the presence of multiple order parameters, domain walls of different configurations could be formed, and each of them shows distinct switching mechanisms. Moreover, the existence of non-polar order parameters also suggests the existence of special domain walls where the sign of polarization is preserved across it. These domain walls are topological defects that could commonly exists in hafnia thin-film and have distinct properties. Finally, infrared spectrum, electronic band structure and exciton absorption simulations are performed to help experimental phase identification. These works deepen our theoretical understanding of ferroelectric hafnia, suggest possible ways to enable easier polarization switching and lower coercive field, and provide guidance for experimental characterization.

 

This work was conducted in collaboration with Songsong Zhou, Jiahao Zhang, Von Braun Nascimento, and Atanu Samanta. We benefited from advice from Jon Ihlefeld. This material is based upon work supported by the USDOE, Office of Science, Office of Basic Energy Sciences EFRC program, Award Number DE-SC00211118.  Computational support was provided by the NERSC, a U.S. Department of Energy, Office of Science User Facility located at LBNL, operated under Contract No. DE-AC02-05CH11231.   

Theoretical discussion of the exotic intrinsic properties of hafnia ferroelectrics

Hafnia ferroelectrics hold great promise for the development of nano-devices that may take advantage of their permanent and switchable electric polarization. Hence, their technological interest has made them a focus of attention. But that is not all: surprisingly, these materials are proving to constitute a ferroelectric class of their own, displaying many intrinsic behaviors that seem genuinely unprecedented and certainly lay outside the "standard model" of soft-mode ferroelectricity in perovskite oxides. In this talk I will present first-principles results to discuss and explain some of those intriguing properties. In particular, I will discuss the evidence for (im)proper ferroelectricity -- and a possible soft-mode behavior -- in these compounds. I will also address the question of whether hafnia should be consider a triaxial, biaxial or uniaxial ferroelectric, explaining how the last option may be sufficient (and convenient) to account for the behavior of many woken-up samples. I will then show that, within such a uniaxial picture, it is possible to identify a centrosymmetric reference phase that yields a straightforward description of all the known low-energy polyrmorphs of these materials, evidencing how they are structurally connected. Finally, I will discuss the piezoelectric response of hafnia ferroelectrics, emphasizing the various unique features it presents (e.g., sign tunability). Time permitting, I will summarize other recent results of my group, e.g., on hafnia-based superlattices.   

Origin of Zero-Energy-Cost Domain Walls beyond the Flat Phonon Bands

Although we report our purely DFT paper on the zero-energy-cost domain walls in HfO2 [1], still the flat polar phonon band is not the entire origin of the zero-energy-cost domain wall. This is because other phonons modes except the polar mode included in this compound are not energetically flat at all. Finally, we discover that a new-type phonon-phonon coupling can successfully explain the zero-energy-cost domain walls in this fluorite-type ferroelectric. I will talk about the origin by introducing the new coupling mechanism that uniquely exists in this commercial ferroelectric.

 [1] Scale-free ferroelectricity induced by flat phonon bands in HfO2, H.-J.Lee et al., Science 369, 1343 (2020).   

Polarization of Ferroelectric Hafnia: Up or Down?

HfO₂-based ferroelectrics have attracted huge interest in the past ten years due to their good compatibility with CMOS technology and stable ferroelectricity at the nanometer scale. It has been unambiguously demonstrated that the intrinsic ferroelectricity in doped hafnia films is associated with the orthorhombic structural phase of the Pca2₁ space group [1]. However, the polarization switching mechanism remained ambiguous. Here, using a state-of-the-art solid-state generalized variable cell nudged elastic band (VCNEB) method, we predict that the most energetically favorable switching pathway in ferroelectric hafnia involves three-fold O atoms passing across the nominal unit cell boundaries bounded by the Hf atomic planes [2]. This finding is at odds with the commonly accepted polarization switching mechanism, where the displacement of the O atoms is limited by the nominal unit cell boundaries. Our results have significant implications for the understanding of ferroelectricity in HfO₂-based ferroelectrics, including (1) the assignment of polarization orientation to different ferroelectric domains, (2) domain-wall motion under an applied electric field, (3) the measurable magnitude of ferroelectric polarization, and (4) the longitudinal piezoelectric coefficient. These results are important for the interpretation of experimental data on HfO₂-based ferroelectrics and may be relevant to a broad range of ferroelectrics where the ionic polar displacements from the relevant centrosymmetric phase are large.   

 

Y. Yun at al., Nature Mater. 21, 903 (2022).

Y. Wu et al., Phys. Rev. Lett. 131, 226802 (2023).     

Understanding Ferroelectricity in Hafnia Through Modeling and Simulations

Ferroelectric hafnium and zirconium oxides have undergone rapid scientific development over the past decade, bringing them to the forefront of very low-power electronic systems. Simulations are playing an increasingly important role in understanding and guiding experimental work to maximize the potential application of these materials in low-power devices and sensors, and to address technical limitations that still hinder their use.

Numerous first-principles simulation studies have investigated the structural properties and free energy of the polar orthorhombic Pca21 phase (standard ferroelectric phase) and the possible appearance of competing polar phases, which are reviewed here. However, the functional properties need to be simulated in larger and transient systems than the unit cells, but at the same high accuracy level. This is possible through the development of machine-learned potentials, in which considerable progress has been made, and the results of which are presented here. Simulations at the grain size scale allow the study of size effects in polycrystalline hafnium and zirconium oxide materials and of real piezoelectric and pyroelectric effects. Furthermore, they allow the exploration of the energy landscape as a function of temperature, size effect, and electric field. The simulated results compare well with the experiment. Other simulations describing larger spatial and temporal scales are kinetic Monte Carlo simulations of correlated electron and charged defect motions in the ferroelectric capacitor, based on calculated diffusion coefficients and defect levels. This approach allows us to address the existing reliability problems in the devices.

R. Ganser, S. Bongarz, A. von Mach, L. Azevedo Antunes, A. Kersch, Phys. Rev. Applied 18, 054066 (2022) https://doi.org/10.1103/PhysRevApplied.18.054066

P. D. Lomenzo, L. Collins, R. Ganser, B. Xu, R. Guido, A. Gruverman, A. Kersch, T. Mikolajick, U. Schroeder, Advanced Functional Materials, 2303636 (2023), https://doi.org/10.1002/adfm.202303636