Self-assembly and properties of domain walls in BiFeO₃ layers grown via molecular-beam epitaxy

The control of topological textures within the lattice, charge, and spin order parameters of multiferroic materials offers the possibility to realize emergent behaviors that transcend the functionality of any spatially uniform host material. Indeed, ferroelectric domain walls are already employed in various applications spanning nonlinear optics,^1,2 nanoelectronics,³ and nonvolatile memories.^4,5

Epitaxial layers of the room-temperature multiferroic BiFeO₃ are a well-established material platform for hosting domain walls with functional properties.⁶ To date, the overwhelming majority of BiFeO₃ films are produced using far-from-equilibrium growth techniques incorporating ion irradiation during film growth, including magnetron sputter deposition⁷ and pulsed-laser deposition.⁸ When uncontrolled, ions spawn unintended defects impacting domain wall morphology and properties.^9,10 Molecular-beam epitaxy, in contrast, provides an alternative synthesis approach which employs thermalized molecular fluxes.¹¹ Near-equilibrium growth regimes free from the bombardment of energetic ions¹² are expected to engender subtler defect profiles,¹³ desirable for the fabrication of nonlinear optical elements as well as for understanding leakage mechanisms in nonvolatile ferroelectric-based memories.

In this letter, we employ molecular-beam epitaxy^11,14 to grow commensurately strained BiFeO₃/SrRuO₃/DyScO₃(110)_o epitaxial heterostructures (the o subscript designates orthorhombic indices in the nonstandard Pbnm setting) and demonstrate the self-assembly of ferroelectric BiFeO₃ domain walls with unprecedentedly long-range order. The walls exhibit the combination of enhanced conductivity and electrical rectification. We anticipate that the results discussed here may prove useful for improving the fabrication of nonlinear optical and nanoelectronic devices.

BiFeO₃/SrRuO₃/DyScO₃(110)_o heterostructures are grown without breaking vacuum in a Veeco GEN10 molecular-beam epitaxy system with a chamber base pressure of 1 × 10⁻⁸ Torr using deposition conditions summarized in Table I. For SrRuO₃ growths, ruthenium is supplied in abundance with a ruthenium-to-strontium flux ratio of J_Ru/J_Sr > 2. At a growth temperature of 780°, the excess ruthenium oxidizes forming volatile RuO_x species which continuously desorb from the growth surface resulting in single-phase SrRuO₃ layers.¹⁵ BiFeO₃ is grown in an oxidant comprised chiefly of ozone (and 20% oxygen). This approach, which represents an evolution of increasing oxidation environments,^14,16–20 helps to suppress the formation of oxygen vacancies, responsible for engendering mobile electrons²¹ and ensures the oxidation of bismuth.¹⁴ Additionally, high bismuth-to-iron flux ratios (J_Bi/J_Fe ∼ 16) are employed to compensate the loss of volatile BiO_x species at the high homologous growth temperature utilized (Ts ∼ 650); the desorption of bismuth oxides during BiFeO₃ deposition is analogous to that of ruthenium oxides during SrRuO₃ growth. Although multiple films were grown and all findings presented here (and in the supplementary material) are obtained from a single film, for which Rutherford back scattering spectrometry results yield a film bismuth-to-iron molar ratio equal to 0.98 ± 0.07. The deposition of stoichiometric layers, containing equal concentrations of bismuth and iron, combined with long diffusion lengths for surface adatoms promote films with long-ranged crystallographic and ferroic order.

The structural perfection of BiFeO₃ layers deposited on SrRuO₃-coated DyScO₃(110) substrates is established using the combination of x-ray diffraction (XRD), atomic force microscopy (AFM), and scanning transmission electron microscopy (STEM). An XRD θ−2θ scan (see Fig. S1 of the supplementary material) collected between 10 ≤ 2θ ≤ 110° using Cu K_α1 radiation (wavelength λ = 0.154 06 nm) exhibits only 00l_p film and hh0_o substrate reflections (the p subscript refers to pseudocubic indices); the absence of additional reflections evince a phase-pure single crystalline film.

Figure 1(a) highlights diffracted intensity oscillations²² near DyScO₃ 110_o, which result from the interference of x-rays reflected at BiFeO₃ and SrRuO₃ interfaces. Measured intensities are accurately reproduced by simulations^23,24 based on a heterostructure with atomically sharp interfaces, pseudocubic out-of-plane lattice parameters a_⊥ of 0.3991 (BiFeO₃), 0.3942 (SrRuO₃), and 0.3939 nm (DyScO₃), film thicknesses of 217 (BiFeO₃) and 23 nm (SrRuO₃), and a thickness-limited film out-of-plane mosaic coherence. The in-plane mosaic coherence length, ∼2 μm, is determined²⁵ from the full-width-at-half-maximum (FWMH) value of the BiFeO₃ 001_p reflection (0.012° = 43 arcsec), measured along [001]_o using ω-rocking curve scans [Fig. 1(a), insert]. The FWHM value measured for the BiFeO₃ reflection is the same as that for the underlying DyScO₃ and demonstrates that the film structural perfection is limited by the intrinsic mosaicity of the substrate.

From lattice-resolution STEM images obtained along the $11¯0o$ zone axis near BiFeO₃/SrRuO₃ [Fig. 1(c)] and SrRuO₃/DyScO₃ [Fig. 1(d)], we find atomically abrupt heterostructure interfaces with commensurate pseudo cube-on-cube crystallographic stacking: BiFeO₃(001)[100]_p ∥ SrRuO₃(001)[100]_p ∥ DyScO₃(110)[001]_o.

AFM height images, including Fig. 1(b), evince smooth surfaces (0.2 nm root-mean-square height fluctuations) over macroscopic distances (≳20 μm) with motifs including unit-cell-tall (0.4 nm) step-edges oriented parallel to BiFeO₃ [110]_p and DyScO₃ $[11¯1]o$⁠, 260-nm-wide $[11¯1]o$-oriented terraces (0.09° miscut), and shallow islands (areal density ≲10⁶ cm⁻²). The latter, through analyses of in situ reflection high-energy electron diffraction (RHEED) patterns (see Fig. S2 of the supplementary material), are determined to form during the layer-by-layer growth of SrRuO₃.

To investigate the breaking of cubic symmetries and the emergence of topological features within BiFeO₃, we perform XRD reciprocal space maps (RSM), lateral (LPFM), and vertical (VPFM) piezoforce microscopy (PFM), and bright-field transmission electron microscopy (BF-TEM).⁵³ RSM analyses carried out about film peaks reveal that the BiFeO₃ 103_p and 113_p family of reflections are split into doublets and triplets [Fig. 2(a)], consistent with monoclinically distorted pseudocubic unit cells that have been sheared along $110p$⁠.²⁶ The descent in symmetry from the cubic perovskite to the monoclinic structure is accompanied by polar $111p$ cation displacements and antiferrodistortive a⁻a⁻a⁻ antiphase FeO₆ octahedral rotations.²⁷ The symmetry-breaking process engenders four structural and eight ferroelectric variants, represented by $rψ±$⁠, in which the subscript ψ identifies the azimuthal orientation of the in-plane polarization component and the superscript ± selects the out-of-plane component. Analyzing the intensity variation of the 103_p and 113_p family of peaks [see Fig. 2(a)] reveals that the BiFeO₃ layer consists primarily of two structural variants, $r+45○$ and $r−45○$⁠, which develop due to the orthorhombic symmetry of the DyScO₃ substrate.²⁸ The volume fraction occupied by the dominant vs secondary structural variants is estimated from ratios of RSM peak integrals to be ≳0.99. These findings are corroborated by PFM analyses [e.g., Fig. 2(b)], which exhibit a two-level contrast.

To determine the out-of-plane polarization orientation, ferroelectric domains are locally poled by applying ±15 V tip biases to a conductive probe while rastering it across the sample surface. Plan-view VPFM images (see Fig. S3 of the supplementary material) demonstrate that in regions where the tip is negatively biased, changes in contrast are observed due to the polarization being poled toward the tip. That the out-of-plane polarization component of as-deposited layers is homogeneously aligned toward the substrate is consistent with the A-site termination of our SrRuO₃ electrode, which encourages the BiFeO₃ polarization to orient in such a way that a depolarization field develops to counteract a built-in field associated with the valence states of each perovskite layer.²⁹ 

Between regions of uniform polarization are domain walls, two-dimensional topological field excitations that emerge when the potential energy describing the order parameter consists of deep valleys and disconnected ground states.³⁰ Plan-view LPFM [Fig. 2(b)], cross-sectional VPFM [Fig. 2(c)], and cross-sectional BF-TEM micrographs [Figs. 2(d) and 2(e)] show that the domain walls in our as-grown BiFeO₃ layers self-assemble into a periodic quasi-one-dimensional stripe array along DyScO₃ [001]_o with inter-wall separations measuring 145 ± 2 nm. The walls are found to be inclined ∼45° relative to the surface normal [Figs. 2(c)–2(e)], in agreement with geometric considerations for 71° walls (the wall type is labeled based on the angle formed between polarization vectors in adjacent domains) residing on {110}_p planes.^31,32 In previous work, it was shown that the inclination angle and the wall type can be controlled by changing boundary conditions²⁸ and film thicknesses;³³ similarly, the wall orientation can be tuned through the application of biaxial in-plane strain^34,35 from $100p$ for 1.5% ≲ m ≲ 0.3% to $110p$ for m ≈ 3.6%, in which m is the lattice mismatch between the BiFeO₃ film and the underlying substrate.^35–39 

The stripe domains are occasionally seen to terminate within the film, giving rise to one-dimensional topological defects analogous to dislocations [the dotted circle in Fig. 2(b)]. Despite the one defect that we observe in a ≳ 20 μm field of view, the structural perfection of the pattern realized here represents the most well-ordered self-assembled array of ferroelastic domain walls produced to date.^{33,35,36,40–46}

The electrical properties of the BiFeO₃/SrRuO₃/DyScO₃(110)_o heterostructure are investigated using conductive AFM (c-AFM), by grounding the bottom SrRuO₃ electrode and rastering a biased tip in contact with the sample surface while recording through-layer currents. Typical results, shown in Figs. 3(a)–3(d), establish that no current flows for biases V_b ≤ 1 V (detectable current limit ∼1pA). In the 2 ≤ V_b ≤ 3 V regime, the current is preferentially emitted at domain walls, where the conductivity is two to ten times higher than at domains [see the current histogram in Fig. 3(e)]. At a bias of V_b = 4 V, the corresponding electric field across the film, 180 kV/cm, exceeds the coercive field of bismuth ferrite, ∼170 kV/cm.⁴⁴ As a consequence, c-AFM images acquired under these conditions, including Fig. 3(d), contain contributions from both resistive and displacement currents as a result of domains being locally poled.

Macroscopic current-voltage I(V) measurements, obtained by integrating the c-AFM measurements over a 5 × 5 μm² area, Fig. 3(f), highlight the existence of rectifying behavior, agreeing with previous reports.^9,10 The enhanced conduction at 71° domain walls can be understood to result from a combination of effects which include a reduction in the BiFeO₃ conduction band energy and an accumulation of intrinsic defects,^10,47 including double-donor²¹ oxygen vacancy states, near the walls. The asymmetric response, which produces the rectifying behavior, is attributed to the combination of dissimilar emission barrier heights across the film/electrode and film/tip interface as well as to the presence of an out-of-plane film polarization which breaks up/down symmetry.⁴⁸ For the measurement conditions employed, Joule heating is estimated^49,51,52 to cause a temperature rise of only ∼0.03 K; for reference, electric fields are expected to trigger breakdown in perovskite oxides only above ∼2000 kV/cm,⁵⁰ five to ten times larger than the largest values applied here.

The ability to produce ordered walls with well-ordered periodicity, as demonstrated here, could have immediate technological implications. For example, domain walls are already lithographically introduced into commercial nonlinear crystals to help satisfy momentum conservation in three-photon interactions. These processes, which include sum frequency generation and parametric down conversion, are essential for up-converting laser frequencies as well as entangling photons for quantum computation. Being able to produce arrays of walls which self-assemble into high-fidelity patterns could provide a bottom-up alternative for the fabrication of such nonlinear optical elements. Additionally, the perfection of the patterns realized here reflects an intrinsically low concentration of defects. The realization of films with low defect density are necessary to produce energy efficient memories with ferroic orders that can be easily switched at low coercive fields without wall pinning. Finally, the 71° domain walls are shown to simultaneously exhibit enhanced conductivity and electrical rectification—attributes which are desirable for emerging nanoelectronic applications, including domain wall memories.⁴ 

Additional film characterization, including XRD θ−2θ, RHEED, and VPFM, is provided in the supplementary material.

This work was supported in part by the Semiconductor Research Corporation (SRC) as nCORE task No. 2758.003 and NSF under the E2CDA (ECCS 1740286) and MRI (Grant No. 1338010) programs. This work made use of the Cornell Center for Materials Research (CCMR) Shared Facilities, which are supported through the NSF MRSEC program (Grant No. DMR-1719875). Substrate preparation was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NSF (Grant No. ECCS-1542081).