Structures and electronic properties of domain walls in BiFeO3 thin films

Abstract Domain walls (DWs) in ferroelectrics are atomically sharp and can be created, erased, and reconfigured within the same physical volume of ferroelectric matrix by external electric fields. They possess a myriad of novel properties and functionalities that are absent in the bulk of the domains, and thus could become an essential element in next-generation nanodevices based on ferroelectrics. The knowledge about the structure and properties of ferroelectric DWs not only advances the fundamental understanding of ferroelectrics, but also provides guidance for the design of ferroelectric-based devices. In this article, we provide a review of structures and properties of DWs in one of the most widely studied ferroelectric systems, BiFeO3 thin films. We correlate their conductivity and photovoltaic properties to the atomic-scale structure and dynamic behaviors of DWs.


INTRODUCTION
Since the discovery of ferroelectricity in BaTiO 3 in the mid 1940s [1], ferroelectric oxides have become a prototypical example of functional materials, attracting considerable interest both in fundamental research and device engineering. The spontaneous polarization in a ferroelectric can be reversed through the application of an external electric field that is greater than the coercive field, a behavior similar to the reorientation of magnetic moments under an applied magnetic field for ferromagnetic materials. Due to such switchability and the small size of ferroelectric domains, which can be as small as a few nanometers [2], ferroelectric materials can be utilized in an important class of high-density and non-volatile memories. Ferroelectric memories have a number of advantages, such as low power consumption, fast writing speed, and high cyclability, which, in most cases, is superior to the performance of other non-volatile devices [3].
The domain wall (DW) is an important element of ferroelectric materials. It is a quasi-2D boundary separating domains that differ in the orientation of spontaneous polarizations. The DW types are distinguished by the rotation angles of polarization between neighboring domains, e.g. 71 • , 109 • , and 180 • in BiFeO 3 . DWs appear as the material is cooled below the Curie temperature (T C ) [4]. This occurs as a result of symmetry breaking in the crystal structure during the phase transition, and the domain pattern that forms is governed by minimization of the free energy of the boundaries [5,6]. This free energy is related to electrostatic energy and elastic energy, which can be affected by several factors. Polarization bound charges and free charges [7][8][9][10] affect electrostatic energy, misfit strain contributes to elastic energy [10], and defects [11][12][13][14] affect both electrostatic and elastic energy. Variation of these factors can lead to the stabilization of a number of unique DW structures, either ordered or disordered. Over the past few years, there has been continuously increasing evidence showing that DWs can exhibit novel properties, including enhanced conductivity [15][16][17][18][19], photovoltages [20][21][22][23][24][25][26] and current rectification [27], all of which make DWs appealing for applications as active elements in future nanodevices.

REVIEW
In this review, we summarize the recent progress on the experimental study of DW structures and properties in one of the most widely studied ferroelectric systems, BiFeO 3 . We will first illustrate the microstructure of 71 • , 109 • and 180 • DWs in BiFeO 3 thin films, and the engineering methods used to produce ordered DW patterns, including boundary-condition engineering and defect engineering. The microstructures and atomic structures of DWs are revealed by a combination of piezoresponse force microscopy (PFM), aberration-corrected atomic-resolution scanning transmission electron microscopy (STEM), and in situ transmission electron microscopy (TEM). This is followed by a discussion on the properties of the DWs including DW conductivity and DW photovoltaics. The studies on DW conductivity include those findings from uncharged and charged DWs, and the formation of charged domain walls (CDWs) controlled by an external electric field. We will then show that characterization of the microstructure can provide us with a fundamental understanding of the properties at the macro scale and associated structural mechanisms. Finally, we will discuss the new possibilities brought by the recent advancement of electron microscopy techniques including high-energy-resolution electron energy loss spectroscopy (EELS) and multi-dimensional imaging, on the study of the electronic structure, charge and their interplay at the ferroelectric DWs and ferroelectric materials in general.

DW STRUCTURES AND BOUNDARY-CONDITION ENGINEERING OF DW PATTERNS
BiFeO 3 bulk material has a rhombohedral structure consisting of two pseudocubic (P) perovskite unit cells connected along the body diagonal with the two oxygen octahedra rotated clockwise and counterclockwise around the axis by 13.8 • [28]. BiFeO 3 thin films with misfit strain less than 4.5% [29] exhibit a monoclinically distorted structure that is similar to the bulk rhombohedral phase, and are thus referred to as 'rhombohedral-like (R-like)' structures [30], as shown in Fig. 1a [31]. In pseudocubic unit cells of the R-like structure, the oxygen octahedra and the central Fe cation are displaced from their respective positions at the face and body centers, giving rise to a large spontaneous polarization (∼100 μC cm −2 ) along the < 111> P (subscripts P denote pseudocubic indices) directions, and resulting in four different ferroelastic variants (r 1 -r 4 ) (Fig. 1b) [32]. Rotations between polarization variants in the R-like BiFeO 3 can be 71 • (ferroelastic-ferroelectric), 109 • (ferroelastic-ferroelectric), or 180 • (ferroelectric), yielding three types of domain walls. When the misfit strain is larger than 4.5%, the BiFeO 3 unit cell will transform into a 'tetragonal-like (T-like)' structure [30], as shown in Fig. 1a. In such a structure, the Fe atom is coordinated by five oxygen atoms and displaced from the body center, resulting in a giant polarization of ∼ 150 μC/cm 2 [33].
In ferroelectric and ferroelastic thin films, patterns of DWs depend strongly on the boundary conditions at the surfaces or interfaces. First, the lattice mismatch between the film and substrate leads to a biaxial-strain mechanical boundary condition [37,[43][44][45], which can be altered by choosing substrates spanning a wide range of lattice parameters [29,32,[46][47][48]. Second, the electrical boundary condition is critically dependent on free charge compensation at the interfaces and can be tailored by choosing substrates or epitaxial buffer layers with different conductivities [49][50][51]. Additional restrictions on the boundary condition can be made by changing the vicinality or atomic termination of the substrates [52,53]    substrate in 2011 [32]. The cross-sectional TEM image and the corresponding schematic in Fig. 2 show the existence of triangle domains at the BiFeO 3 /TbScO 3 interface where the 109 • DWs terminate. Polarization mapping at the triangle domain reveals the formation of a 'mirrored pair' of inclined 180 • DWs, resulting in a closure vortex structure with polarization rotating around the 109 • and 180 • DW intersection point. Such a structure is formed due to the existence of bound charge density waves, i.e. alternate positive and negative bound charges at the interfaces, which produce a non-uniform depolarization field (Fig. 2c) favoring the vortex formation. According to our experimental results shown in Fig. 2d, vortex arrays can also be realized at both BiFeO 3 /SrTiO 3 and the BiFeO 3 /TbScO 3 interfaces in a BiFeO 3 /SrTiO 3 /BiFeO 3 heterostructure grown on the (110) TbScO 3 substrate. Vortex structures were also discovered recently in PdTiO 3 thin films [60][61][62] and PdTiO 3 /SrTiO 3 superlattices [36]. The periodicity of the vortices can be tuned by growing the PbTiO 3 films with different thicknesses [60]. In ultrathin PbTiO 3 layers embedded in the PbTiO 3 /SrTiO 3 superlattices, longrange ordered vortex-antivortex arrays were found to exhibit a nearly continuous polarization rotation [36]. It is interesting to note that as the thickness of the BiFeO 3 layer decreases, the vortices at the bottom and top interfaces of each BiFeO 3 layer will move closer to each other. As a result, one can expect to observe an array of new vortices (formed by the merging of the abovementioned vortices located at the bottom and top interfaces) in each BiFeO 3 layer of the BiFeO 3 /SrTiO 3 or BiFeO 3 /TbScO 3 superlattices, similar to the vortex arrays observed in the PbTiO 3 /SrTiO 3 superlattices.

DEFECT ENGINEERING
While boundary-condition engineering has demonstrated tremendous success in control of DW patterns in ferroelectric thin films, one major limitation of such a method has been that once the variable at the boundary condition is set, such as the choice of substrate, further modification to control or alter DW patterns during material synthesis becomes difficult. This reduces the parameter space for creating more complex structures with ordered DW patterns and thus imposes restrictions on the functionalities of the system. On the other hand, defects in ferroelectric oxides can also have a remarkable impact on ferroelectric domain structures.
Commonly observed defects such as dislocations and vacancies can interact with domains and DWs to pin polarization configurations. The recent work by Li et al. [31,40,41] and others [35] reported a strong electrostatic driving force provided by charged impurity defects, another type of common defect with a structure different from the host material. Their results suggested the possibility of using engineered impurity defects in combination with suitable interface boundary conditions to control domain formation and create complex DW structures.  during the synthesis of a BiFeO 3 film, which can induce a novel mixed-phase 'head-to-head' polarization structure [31]. In Fig. 3   charged defects in the BiFeO 3 matrix to configure special DW patterns that are not favorable in natural boundary conditions [40]. By slightly changing the substrate temperature during the film growth, an array of linear charged Fe-rich defects can be introduced into the BiFeO 3 film at a constant level that is 110-130 nm above the interface (Fig. 3 case 2). The interaction between the charged defects and the polarization lead to a reconfigured DW pattern in the BiFeO 3 film. As shown in Fig. 3

Circle-like defects
In addition to the planar and linear defects, Li et al. found that circle-like defects, named nonstoichiometric nanoregions (NSNRs), can stabilize hedgehog or antihedgehog nanodomains [41]. The circle-like defects were deliberately introduced by changing the substrate temperature during the film growth, similar to the previous example. The stabilized hedgehog/antihedgehog domains can be coupled with polarization rotations, which results in polarization vortices. The hedgehog and antihedgehog domains are shown in Fig. 3  The black curve reveals that DW has activated conduction while the red curve shows that the domain region has less conduction. They then specifically studied 109 • DW conductivity in 2010 [16]. They used 100-nm-thick 10% La-doped BiFeO 3 thin film, in which La doping allows coherent 109 • domain growth [55], with an SrRuO 3 bottom electrode grown on (110) o DyScO 3 substrate. PFM and c-AFM results ( Fig. 4d and e) indicate an ordered 109 • stripe domain structure and corresponding local conductivity at the DWs. The I-V curves (Fig. 4g) are measured by using AFM tip stepping perpendicular to the 109 • DW with the same load. The I-V curves increase linearly at low voltage and transit to large curvature at higher voltage. Such phenomena were explained by the oxygen vacancy activation in an electric field as shown schematically in Fig. 4f, where enhanced conductivity at the wall is caused by changes in the local bandgap [55].  Fig. 4h and i) show that most of the DWs observed are 71 • DWs with enhanced conduction. The I-V curves (Fig. 4j) are measured in constant polarization regions and in regions containing a 71 • domain wall. The DW I-V curve shape (in red in Fig. 4j) reveals a Schottky emission mechanism with the majority of carriers provided by oxygen vacancies. The observed conductivity at 71 • DWs here is different from the previous study by Seidel et al., where the 71 • DW conductivity is not found in BiFeO 3 films that were grown on DyScO 3 substrates at higher deposition rates and with higher oxygen pressure [15]. Such differences indicate that the material synthesis conditions are critical for the conductive nature of different types of DWs.

Charged domain wall
In ferroelectrics, most DWs are charge-neutral as a result of 'head-to-tail' polarization configurations, such as in the previous examples. The electrostatic energy of uncharged DWs is usually minimized but they only have low conductivity that is thermally activated [57]. In contrast, DWs with polarization discontinuity carry net bound charge and are referred to as charged domain walls (CDWs). They are electrically active and can possess much higher conductivity than the charge-neutral DWs. There are two types of CDWs in ferroelectrics. One is formed where the original charge-neutral DW is bent by external applied fields of internal defect pinning effects. Such CDWs have conductivities of ∼ 10-10 3 times as high as those of bulk domains [7] but tend to reduce to an uncharged state when the applied field is removed or the pinning effects are thermally overcome [63]. The other type is directly formed by 'head-to-head' or 'tail-to-tail' polarization configuration and can be stabilized by free charge carrier compensation without applied fields or defect pinning [64][65][66]. These CDWs can have very high conductivity up to 10 9 times that of the bulk domains and result in an insulating-to-metallic transition [64,67]. Furthermore, the net bound charges can produce a depolarization field that results in an increased electromechanical response and thus better piezoelectric properties [68].

Charged domain wall attached to a triangle nanodomain
CDWs attached to triangle domains in BiFeO 3 film were reported by Li et al. [56]. They studied a 20-nmthick BiFeO 3 film on a (110) o TbScO 3 substrate. The triangle domain structure, shown schematically in Fig. 5a, consists of vertical and inclined boundaries that are 109 • and 180 • DWs, respectively. The 71 • CDW above the triangle domain shown in Fig. 5b region 1 is not a linear boundary but an area with gradual polarization rotations (Fig. 5c). Figure 5d shows a large a ⊥ /a ratio at the 71 • CDW, which indicates the formation of T-like structure at the CDW and a reduction of the electrostatic energy compared to that of a linear 'head-to-head' CDW. Also, the T-like 71 • CDW region and the surrounding R-like regions result in both positive and compensating negative bound charges, which reduce the electrostatic energy even further.

Charged domain wall in a nanoisland
Ma et al. studied CDWs that form in square BiFeO 3 nanoislands. The film is grown on a 2-nm-thick (La, Sr)MnO 3 bottom electrode on (001) LaAlO 3 substrate [69]. As shown in Fig. 6a, their film is composed of a self-assembled, high-density array of square nanoislands. The low-magnification HAADF STEM image (Fig. 6b) shows that the nanoislands are 200 nm in length and 40 nm thick and grow from the 20-nm-thick BiFeO 3 matrix. High-magnification HAADF STEM images show clear boundaries between the R-like nanoislands and the T-like matrix. The in-plane polarization projection, measured with PFM ( Fig. 6c), revealed that each nanoisland has four quadrants that have polarizations all pointing toward the island center. The out-of-plane polarization projection gives polarization pointing downward in the as-grown film. The dark-field TEM image show strong contrast between the left and right regions (Fig. 6g), suggesting different polarization directions. High-magnification HAADF STEM images of regions h, i, and j, highlighted in the lowmagnification TEM image, each show different polarization states. Region h has polarization along the body diagonal towards the lower-right center and region j points to the lower-left center. Region i shows a 71 • 'head-to-head' CDW with 3-5 nm width. Together, these results confirm that the nanoislands contain center-convergent quaddomains formed with 71 • CDWs. As shown in Fig. 6e and f, enhanced conductance with a cross-shape is observed by using c-AFM. Under 1.5 V, the 'head-to-head' CDW gives a maximum current of 2 pA. After the quad-domains are switched to form a 'tail-to-tail' CDW, the maximum current measured reaches 2 × 10 3 pA. Such a huge difference between the two types of CDWs results from a difference in their interaction with the bottom electrode's free charge carriers. The free carriers in La 0.7 Sr 0.3 MnO 3 are p-type, which cannot interact with the positively charged 'head-to-head' DW but will accumulate at the negatively charged 'tail-to-tail' DW, resulting in very low conductance at 'head-tohead' CDWs and enhanced conductance at 'tail-totail' CDWs. The I-V curves show diode-type conductance, indicating a large current flow for forward bias, which results from the holes moving from the BiFeO 3 valence band to the tip. There is no obvious current detected for reverse bias since not enough holes can move to the BiFeO 3 valence band from the tip.

Regular thin film
BiFeO 3 domains can be easily switched by an external electric field, accompanied by DW creation or annihilation. The switching process shown in

Writing and erasing charged domain walls
With the understanding of the CDW formation and fundamental mechanisms, Crassous et al. reported a technique to easily write and erase CDWs in 45-nmthick La-doped BiFeO 3 thin films with an SrRuO 3 bottom electrode on (110) o DyScO 3 substrate using PFM [9]. As the tip is moving along the BiFeO 3 surface, it creates a trailing field [71] that controls the in-plane polarization direction while the perpendicular electric field between the tip and bottom electrode controls the out-of-plane polarization direction, as shown in Fig. 8. Two 3 × 3 μm 2 regions were initially written into a monodomain with different trailing fields to demonstrate CDW writing. The writing process is initiated by applying an electric field to pull the out-of-plane polarization up combined with the trailing field to control the in-plane polarization direction. Domains 1, 2 and 3 are written first with the trailing field oriented along the [001] o direction and then domains 4, 5 and 6 are written with the trailing field along the opposite direction, so that domains 1-3 are polarized right and domains 4-6 are polarized left. The in-plane PFM results show 'head-to-head' CDWs at the 1/6, 2/5 and 3/4 interfaces, and 'tail-to-tail' CDWs at the 6/2 and 5/3 interfaces. The c-AFM mapping shows a current of ∼ 1.7 nA at the 'head-to-head' CDW with a 2.5 V bias applied. No conductance is detected at the 'tailto-tail' CDW. Interestingly, such observations are totally different from the nanoisland CDW results reported by Ma et al. Crassous et al. believe that this is because the positive bound charges at the 'head-tohead' CDW are screened by the electrons from the tip and result in the creation of a conductive state. The 'tail-to-tail' CDW, on the other hand, has negative bound charges at the wall that cannot be compensated by the free electrons from the tip and therefore tend to minimize its charged density by forming zigzag DWs. Also, in Crassous et al.'s case, SrRuO 3 bottom electrodes (n-type) are used, providing mobile electrons to screen the positive bound charges at the 'head-to-head' CDWs, while Ma et al. used (La, Sr)MnO 3 , which provides mobile holes, resulting in conducting 'tail-to-tail' CDWs as mentioned in section 'Charged domain wall in a nanoisland'.
The manipulation of CDWs through scanning probe microscopy (such as PFM) only allows access to the domain structure from the surface. Due to the requirement of free charge compensation, however, some CDWs present at the top surface of  Fig. 9a, the left configuration is stable without CDW because the 109 • and 180 • DWs are far away from each other and therefore have very weak electrostatic interaction. Once the CDW has been written, the system is still stable since the bound charge close to the interface can be compensated by free carriers from the bottom electrode, reducing the electrostatic energy. The process was induced by applying an external electric field. The 109 • and 180 • DWs start to move as the bias reaches 1.7 V. While the bias is increasing, the two domains move toward each other and intersect, which eventually results in a shrinkage of the triangular domain and the formation of a CDW. The corresponding I-V curve in Fig. 9c reveals that the film has no conductivity below 3.5 V when there is no CDW, but passes 640 nA at 5.5 V once the CDW has formed. Such results give rise to the correlation between the enhanced conductance and the existence of CDW.

DOMAIN WALL PHOTOVOLTAICS
While the conventional light-to-electrical energy conversion process is achieved by using a p-n junction or a heterojunction [72,73] to separate electrons and holes, Yang et al. developed a new model for charge separation and photovoltage generation using BiFeO 3 ferroelectric DW modification under white light, yielding photovoltage significantly higher than the bandgap [20]. BiFeO 3 has a direct bandgap of ∼ 2.67 eV [74] with open-circuit voltage V oc E g . The photovoltaic nanodevices are fabricated by defining two 500-μm-long platinum electrodes separated by 200 μm, on top of a100nm-thick BiFeO 3 film; the electrodes can be either parallel or perpendicular to the DWs (Fig. 10a, b). Figure 10c, d shows the measured I-V curves of 71 • DWs with both electrode configurations under no illumination and saturation illumination with white light. In the parallel configuration, V oc is measured as 16 V with an in-plane short-circuit current density of ∼ 1.2 × 10 −4 A cm −2 . The perpendicular configuration, on the other hand, shows large photoconductivity but no V oc . A drop in potential was measured across all types of DWs, with 180 • DWs showing the largest drop, followed by 109 • and then 71 • DWs. They believe that such phenomena can be explained by the schematic band structure model in Fig. 10e depicting both the domains and DWs in dark conditions. The drop in potential across the DW creates an electric field that will provide an enhanced electronhole pair separation process when illuminated. The separated electrons and holes build up on either side of the DWs and sum up over a large scale, leading to the large V oc . In contrast, if the light is incident inside the domain, the excited charge is localized and tightly bound due to the weak built-in electrical field, resulting in a quick recombination and no photovoltaic effect.
This model, however, has been challenged by Bhatnagar et al.'s work with a measurement combing photoelectric AFM and PFM at the DWs and inside domains on 100 nm-thick (001) P BiFeO 3 thin films grown on (110) o TbScO 3 substrate [22]. They studied the BiFeO 3 photovoltaic effect on both 71 • and 109 • DWs, and the experimental set up is similar to the schematics in Fig. 11a   which is larger than the BiFeO 3 bandgap. For 71 • DWs, the I-V curves of both parallel and perpendicular geometries show significant V oc of −7.6 V and − 6.6 V, respectively. Both groups' results show a V oc larger than the BiFeO 3 bandgap, but Bhatnagar et al.'s work claims that the DWs, due to their relatively high intrinsic conductivity, work as resistors with lower resistance rather than working to separate charges as mentioned in Yang et al.'s model. The relationship between V oc and the conductivity can be expressed by the following equation: [75][76][77] where J ph is the photocurrent, σ d is the dark conductivity, σ ph is the photoconductivity, and L is the distance between the electrodes. Only the dark conductivity and the photoconductivity affect V oc , since J ph is uniformly generated across the whole film by shift currents [78], and L is constant. In Fig. 11b, the total effective conductivity (σ d + σ ph ) has contributions from both the domains and the DWs, which can be modeled as either a parallel or serial circuit. The perpendicular geometry gives lower V oc since it has parallel conductivity mode and results in higher conductivity. Also, the 109 • DW has higher conductivity than that of the 71 • DW, which results in smaller V oc for the 109 • DW than that of 71 • DWs, in all cases. CDWs [23], which is a follow-up work to section 'Charged domain wall in a nanoisland'. They used a similar square BiFeO 3 nanoisland with either 'head-to-head' or 'tail-to-tail' CDWs configurations as shown in Fig. 6c and d, repectively, and photoassisted AFM to measure the photoresponse behavior [79]. As the 1.4 V bias voltage is applied, the nanoisland with 'head-to-head' CDWs shows ∼ 0.2 pA dark current, and 23 pA photocurrent when irradiated with a 405 nm laser, giving a photo-to-dark current on-off ratio of 11,500%. In contrast, 'tailto-tail' CDWs show 0.69 nA dark current and 1.1 nA photocurrent, with a much lower on-off ratio of 159%. The measurements at the domains without/with laser illumination show negligible signal.

SUMMARY AND PROSPECTS
Here, we have reviewed the current status of BiFeO 3 DW microstructures and their conductive and photovoltaic properties. The uncharged DWs show enhanced conductance with measured current in the pA range, while the later reported CDWs have conductances of four orders of magnitude higher than the uncharged DWs. The ferroelectric switching process in CDWs opens up a way to directly manipulate their formation and motion, forming the building blocks for reconfigurable nanoelectronic devices based on writing and erasing CDWs. The role of DWs in producing photovoltaic properties is important: running parallel to the collecting electrodes provides a high open-circuit voltage larger than the BiFeO 3 bandgap. Many other DW properties and mechanisms are, however, still unclear and need to be explored, such as stresspolarization bound charge coupling, electron-hole pair dynamics, defect engineering with larger impurity defect dimensions, and switching processes with higher spatial resolution. To achieve this, additional characterization with TEM works is necessary.
Because of the high spatial resolution and flexibility for housing in situ probes, TEM has been used for studies on the atomic structure, dynamics and electronic structure of ferroelectric materials, especially heterogeneous structures such as interfaces and DWs. While unsettled mechanisms, such as point defect and oxygen vacancy dynamics, represent new challenges for characterization, the emergence of new imaging techniques may bring new possibilities to these studies. The advanced 4D STEM technique including charge density mapping may provide atomic-level local charge and electric field distribution at the DWs, giving rise to better understanding of bound charge coupling and electron-hole pair dynamics. The crosssectional c-AFM imaging technique [40,80] plus cross-sectional STEM provides both macro-and micro-level information that can be applied to large defect dimension studies. Vibrational microscopy and high-energy-resolution EELS, which can detect oxygen vacancies and electronic structures on the atomic scale, may help to provide more information on and better explanations for many current problems. For DW switching, only low-magnification TEM images have been available thus far because most in situ sample holders are limited to a single tilt axis, making it impossible to accurately align the microscope onto the crystal's zone axis, a requirement for atomic resolution imaging. The new double tilt in situ TEM holder developed by Mingjie Xu et al. [81] opens up a possible path to tilt the sample to the zone axis, enabling the acquisition of high-magnification atomic-scale switching images. This may help improve our understanding of DW formation and the interaction with surrounding defects during the process.