Sub-nm2 ferroelectric domains via charged 180 degree walls in ZrO2

TL;DR

This work demonstrates sub-nm2 ferroelectric domains in ZrO$_2$ thin films created by densely packed head-to-head and tail-to-tail charged 180° domain walls. The walls arise and persist due to flat longitudinal optical phonon bands and bound-charge compensation by interstitial oxygen, yielding wall cores with Pbcm-like and P4_2/nmc-like structures and walls predicted to be conducting with ultralow motion barriers. First-principles calculations link the observed structures to low band gradients $E_g$ and specific zone-boundary modes, while experiments using plan-view ABF-STEM and 4D-STEM DPC imaging resolve the vertical dipole rearrangements and wall cores. The results reveal two-dimensional independence of coexisting HH/TT domains within 2D polar sheets, enabling ultracompact, reconfigurable domain-wall nanoelectronics and offering a platform to explore antipolar ordering and novel ferroelectric-antiferroelectric phenomena in fluorite oxides.

Abstract

Flat phonon bands in fluorite ferroelectrics (HfO2 or ZrO2) shrink polar domains laterally to an irreducible half-unit-cell width (0.27 nm) within which the vertical arrangement of dipoles is expected to remain uniform. We report on the direct observation of nonuniform and nearly discrete vertical arrangements of dipoles in ZrO2 thin films consisting of closely spaced head-to-head (HH) and tail-to-tail (TT) charged 180 degree walls, each exhibiting a distinct bulk-like structure. These charged domain walls (CDWs) further compress the irreducibly narrow, laterally stacked domains vertically to a thickness of 1-2.75 nm, yielding in-plane domains with sub-nm2 footprints-among the smallest ever reported for any ferroelectric material. The HH and TT walls form due to their flat longitudinal optical (LO) polar bands and are electrostatically stabilized by bound-charge compensation via interstitial oxygen atoms, which act as natural structural defects at the HH walls. Moreover, these walls are predicted to be conducting and to exhibit ultralow propagation barriers, with HH walls (1.6 meV) being far more mobile than TT walls (22.3 meV), indicating strong potential for low-voltage, domain-wall-based nanoelectronics.

Figures (20)

• Figure 1: Observation of charged 180° domain-walls and antipolar ordering in ZrO$_2$.(a) Plan-view ABF-STEM image of a [100]-oriented grain in a 10-nm-thick ZrO$_2$ film, revealing polar planes laterally separated by nonpolar layers. Each polar plane hosts a series of alternating, vertical HH and TT domains, separated by HH and TT charged 180° domain walls. The length of the dipole vectors represents the displacement of OII atoms from the centrosymmetric position of the respective surrounding Zr cage. The tetragonal $P4_2/nmc$ phase is regarded as the reference for determining the polarization direction. Note that atomic columns appear with dark contrast in the ABF-STEM image. (b) The corresponding down- and up-polarized domains, are denoted by blue and red colors, respectively. The smallest and largest HH–TT domain-wall center-to-center distances are 2 and 5.5 unit cells (uc), respectively. For the (c) HH and (d) TT wall configurations, the atomic model, reconstructed atomic-potential map from DPC-STEM imaging, experimental ABF-STEM images, simulated ABF-STEM images, and oxygen-column intensity profiles are shown.
• Figure 2: Flat LO polar bands at the HH and TT domain walls in ZrO$_2$.(a) and (b) Experimental ABF-STEM images for HH and TT domain wall configurations, featuring $Pbcm$- and $P4_2/nmc$-like core structures, respectively. Phonon band dispersions along the CDWs direction ($z$ direction) are plotted for (c)$Pbcm$ and (d)$P4_2/nmc$ phases of ZrO$_2$. The eigenvectors corresponding to the LO polar modes at $\Gamma$-point and their respective band-connected modes at $Z$-point are visualized (①-④) by black/blue arrows. The blue arrows denote the displacements of the back-plane atoms in ③ and ④. The ⓧ and $.$ show the displacements of oxygen atoms along –$x$ and $x$ directions, respectively. (e) DFT-optimized ZrO$_2$ HH-TT configuration and the related off-center displacements of OII atoms.
• Figure 3: Projected density of states (PDOS) and HH/TT domain-wall dynamics.(a) Unit-cell-by-unit-cell PDOS for a fully optimized HH–TT domain-wall system, highlighting hole-doped (p-type) metallic behavior at both TT and HH walls, particularly at the latter, due mainly to the interstitial oxygen atoms. The black and red lines show the PDOS for Zr and O atoms, respectively. (b) Translation of the TT domain wall by one unit cell with respect to the initial structure in panel (a), while the HH wall remains stationary. (c) Propagation of the HH wall with respect to the structure in panel (b), while the TT wall remains stationary. (d) and (e) The corresponding energy barriers and minimum-energy paths (MEP) for the motions of the TT and HH walls, respectively.
• Figure 4: Antipolar ordering via strongly charged 180° domain walls. Schematic plan‐view of a ZrO$_2$ film featuring self-organized, two-dimensional, irreducibly narrow, lateral polar layers (red-blue sheets) isolated by nonpolar planes (purple sheets). Each single polar layers contains a series of closely spaced, charged 180° domain walls alternating between HH and TT configurations, leading to vertical domains (red or blue) within each polar layer. The TT CDWs are laterally aligned in the adjacent polar sheets. The relaxed atomic model and schematic polarization profile for a selected region (dashed outline) of a polar sheet are shown on the right.
• Figure S1: Electrical characterization of ZrO2 MFS sample.(a) Overview of the Al/TiN/ZrO2/SiO2/p+ Si thin film heterostructure. (b) HRTEM image of the thin film heterostructure. c P-V loop obtained from the heterostructure confirming the ferroelectricity of the device.