Ferroelastic Charged Domains in Ferroelectric BiFeO3 Nanoneedles

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Charged domain walls (CDWs) in ferroelectrics have attracted interest in nanoelectronics due to their higher conductivity in comparison to neutral domain walls [1]. However, the study of CDWs is challenging due to their inherent instability. Typically, charged compensation mechanisms such as oxygen vacancies are required to offset the instability caused by an accumulation of bound charge at the CDWs [2, 3]. Therefore, finding other stability mechanisms for CDWs can facilitate the study of the fundamental physics of CDWs and prompt further integration of CDWs in devices. In this work, ferroelectric BiFeO3 (BFO) nano-needles are studied using an aberration corrected scanning transmission electron microscope (AC-STEM). The BFO needles are milled from a 200nm BFO film on a (110)-oriented TbScO3 substrate using a Ga ion sourced focused ion beam (FIB) by implementing an annular milling method [4] as shown in Fig 1a. A milled BFO needle sample used for experiment is shown in Fig 1b. Through AC-STEM, high-angle annular dark field (HAADF) and 4D-STEM datasets were acquired for a tilt series of high-symmetry zone axis shown in Fig 1(c,d,e). From the collected HAADF data along the low-order projections in the BFO needle, unit cell polarization analysis in Fig 2(a,b,c) revealed a stabilized tail-to-tail CDW (T-T CDW) residing at the needle tip and other CDWs at the bulk of the sample. The polarization in BFO is conventionally defined by the displacement of the Fe central cation from its centrosymmetric position in respect to four neighboring Bi atoms. From the polarization analysis, the polarization direction demonstrates an isotropic nature of the ferroelectric domains when viewed from the (100) and (010) projections. In addition, a polarization rotation toward the needle surface is observed. This polarization rotation is necessary for the T-T CDW formation, as such finding the cause of the rotation can hint into other possible stability mechanisms for CDWs. To explain the polarization rotation toward the surface observed in the BFO needle, the needle geometry of the sample was considered. A needle geometry would provide a significant degree of surface curvature compared to planar thin films. The surface curvature was measured by calculating the curvature from the radius of curvature along the needle surface. Through this analysis, the asymmetry in the surface curvature could influence the direction of the polarization toward a particular direction. A correlation between the surface curvature and the upward polarization domain at the tip region was defined where the polarization tends to point toward the surface region with greater curvature. Therefore, surface curvature can influence the directionality of the domains by potentially changing the distribution of fields. The effect of varying surface curvature can also be observed by the differences in lattice parameters in the surface region where an expansion in the out-of-plane lattice parameter is correlated with a higher surface curvature. Varying curvature can play a role in the strain distribution in the needle sample and as a result influence the stability and formation of CDWs. In addition, phase field simulations were conducted to study the polarization domains given a nano-needle geometry. In the simulations, the post-FIB fabricated needle dimensions were considered in the simulation model to generate a 3D input model shown in Fig 3(a,b). From the simulation results, CDWS are observed throughout the needle sample. The simulated domains demonstrate a tendency to have a net directionality of the polarization orientation. In Fig 3(c,d), the average polarization in the simulated BFO needle demonstrates the formation of CDWs in the needle sample. The formation of CDWs in the nano needle can act to decrease the depolarization energy by potentially providing conductive channels to redistribute charges. This effect is magnified because of the 3D surface from a needle geometry where a greater amount of bound charge should reside at the surface compared planar thin films. Overall, the geometric considerations of a nanoneedle sample were considered to help describe CDWs formation and stability in BFO. The interplay between strain and charge was highlighted as contributing toward formation and stability of CDWs by two geometrical factors of a needle sample: surface curvature and high surface to volume ratio. Surface curvature influenced the distribution of strain where the surface to volume ratio influenced the distribution of charge. As such, CDWs can form in BFO nano-needles to compensate for high surface charge and surface curvature can be a mechanism for CDWs stabilization. The interplay between the studied geometrical factors in stabilizing conventionally unstable CDWs demonstrates the importance of sample geometry on preferred domain states in ferroelectrics. This study gives insight into the influence of sample geometry engineering on domain formation and prompts further study in other nanostructures on the formation and stability of ferroelectric domains. (a) Schematic of a planar thin film of BFO on a TSO substrate fabricated into a BFO nanoneedle. The arrows in BFO thin film represent 109 deg. ferroelectric domains. (b) HAADF image of BFO nano needle. (c,d,e) HAADF images of the tilt series of high-symmetry projections. Needle sample is tilted +/- 45 deg. from (110) projection. Inset images show the pseudocubic unit cell structure for their corresponding projection. Scale bar = 2nm. (a,b,c) Maps of averaged polarization at the BFO nano-needle tip along the three high-symmetry projections (100), (110) and (010). Scale bar = 2nm. (a) Phase field input model for based on the FIB fabricated BFO nanoneedle. (b) 3D phase field model. (c,d) Phase field calculated unit cell averaged polarization mapping of a BFO nano-needle. Two charged domain walls are observed on the left and right side of the simulated nano needle.

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