Reduced dimensional ferroelectric domains and their characterization techniques

INTRODUCTION

Ferroelectricity is one of the most major physical phenomena that is applicable to electronic devices because of its sustainable polarity without an external electric field and its switchability by external stimuli^[1] [Figure 1A]. These properties of ferroelectric materials make them highly suitable for applications in non-volatile memories, information storage devices such as FeRAM (Ferroelectric Random Access Memory) and FeFET (Ferroelectric Field Effect Transistor). To apply ferroelectric materials in devices effectively, it is crucial to understand the structure and properties of the polarization they exhibit. This involves investigating the polarization mechanisms, which explain how polarization occurs, and the switching dynamics that control polarization. Depending on the desired form of the component, the properties of ferroelectric materials should be tuned and designed accordingly. Particularly, with the trend toward miniaturization in the device industry, the downsizing of ferroelectric materials has become increasingly important. Simultaneously, various techniques, such as transmission electron microscopy^[2,3] (TEM), for analyzing the structure and characteristics of miniaturized ferroelectric materials are being developed and integrated to meet these demands [Figure 1B]. For example, high-angle annular dark-field scanning TEM (HAADF-STEM) can directly show the breaking of inversion symmetry and polarization in materials at the atomic scale, as illustrated in Figure 1C.

Figure 1. Ferroelectric characteristic and its domain structure. (A) A schematic of a typical ferroelectric P-E hysteresis loop. Based on the polarization direction, two distinct binary digits can be differentiated. (B) Dark-field TEM image showing ferroelectric domains with 180° domain walls in Pb(Zr,Ti)O₃ thin film. (C) HAADF-STEM image overlaid with its polarization angle map and corresponding Pb(Zr,Ti)O₃ structure. Color wheel means the orientation of the polarization at each unit cell. Reproduced with permission^[3]. Copyright 2012, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim.

In this paper, we aim to provide a brief overview and classification of oxide-based ferroelectrics, particularly focusing on their unique characteristics and the various mechanisms underpinning their extensive research. We will discuss why oxide-based ferroelectrics have been predominantly studied and what potential benefits can be expected from them. Subsequently, we will delve into various research endeavors related to the scaling of ferroelectrics, primarily considering aspects related to thickness and width. Lastly, we review techniques for analyzing the properties of ferroelectrics and explore their applications in research.

FERROELECTRIC MATERIALS

The pioneering research into ferroelectric phenomena began with the hysteresis measurements of Rochelle Salt in 1921^[4]. Subsequently, in 1941, ferroelectricity was discovered in the oxide perovskite material called BaTiO₃, which sparked expectations that ferroelectricity could manifest in simple structures. This led to the active exploration and discovery of new ferroelectric materials in perovskite oxides such as Pb(Zr,Ti)O₃^[5] and LiNbO₃^[6]. A brief history of representative oxide-based ferroelectrics is summarized in Table 1. Alongside the discovery of these materials, research on non-volatile memory based on ferroelectrics began in the 1950s^[7], capitalizing on the characteristic of ferroelectric polarization states representing binary states. FeRAM and FeFET^[8], two significant developments in this field, were proposed in 1952 and 1963, respectively, garnering considerable attention in the academic community. However, they faced limitations, such as endurance, retention, scalability (with device thickness typically above 100 nm), and compatibility issues in thin-film performance.

As a result, there have been research efforts to synthesize ferroelectric materials as thin films with the aim of creating small electronic devices. Around the same time, there were significant efforts to create thin films of superconductors such as YBa₂Cu₃O₇, leading to advancements in the technology to epitaxially deposit them in a single crystal form^[9,10]. This progress allowed for the control of ferroelectricity coupled with lattice structures through epitaxial control. The development of thin films of layered ferroelectrics, such as SrBi₂Ta₂O₉, aimed to address endurance issues^[11]. Research has also been conducted on very thin ferroelectric films such as PbTiO₃^[12] and BiFeO₃^[13]. Additionally, as the thickness of thin films has gradually reduced, studies related to the manifestation of ferroelectric properties in non-ferroelectric materials, such as SrTiO₃, have begun to emerge^[14].

In recent years, a significant breakthrough occurred in the field of ferroelectric research with the discovery that HfO₂, which had been widely used as a high-k (permittivity) gate insulator in the semiconductor industry, exhibited robust ferroelectric properties when doped with silicon^[15]. This discovery, made in 2011, led to an explosion of research related to inducing ferroelectricity in HfO₂ through doping with elements such as Zr and Y^[16-18]. The introduction of this new paradigm in ferroelectric research, driven by the discovery of new materials, has sparked a multitude of studies aimed at realizing ferroelectricity at even smaller thicknesses and applying it to highly dense memory devices.

Two-dimensional (2D) ferroelectric materials, being inherently thin, offer significant advantages in terms of scaling. Active research is being conducted on quasi-2D materials using oxide membranes such as BiFeO₃^[19] and CsBiNb₂O₇^[20]. The most well-known 2D materials include transition metal dichalcogenides such as MoS₂^[21], with numerous reports of ferroelectricity in materials such as SnTe^[22], In₂Se₃^[23], and CuInP₂S₆^[24,25]. These 2D materials possess stable surfaces free of dangling bonds and are less affected by substrates, which is advantageous. Most 2D ferroelectrics exhibit Curie temperatures above room temperature and have varied electronic bandgaps, making them suitable for practical applications^[26]. A prime example is SnTe, which can exhibit in-plane ferroelectricity down to a one-unit-cell limit at low temperatures^[27]. In addition, CuInP₂S₆, a room-temperature ferroelectric with a layered structure, exhibits out-of-plane ferroelectric polarization due to the off-centering of Cu and In ions from the center of sulfur octahedra, with polarization observed even in layers as thin as 4 nm^[24].

As materials have become miniaturized, there has been a growing need for a better understanding of ferroelectricity within these materials. Consequently, research into techniques for characterizing such ferroelectricity has seen significant advancements. The ferroelectric properties in thin films often exhibit notable differences from those in bulk materials, which has spurred further investigations.

FERROELECTRIC MECHANISM

The foundation for the development of new ferroelectric materials begins with a structural understanding of the underlying mechanisms responsible for ferroelectricity. Ferroelectricity typically arises from the breaking of inversion symmetry in ionic crystal structures^[3]. It can be explained through various mechanisms, including proper ferroelectricity, often associated with displacive mechanisms, order-disorder mechanisms, and anisotropic lone-pair effects. For instance, the tetragonal phase of BaTiO₃ occurs at temperatures below the Curie temperature of 120 °C^[27]. In this material, the tetragonal lattice structure is established with Ba ions as the reference points, and displacements of Ti⁴⁺ ions and oxygen octahedra give rise to ferroelectricity^[28] [Figure 1]. Almost concurrently, an order-disorder type ferroelectric model was proposed for BaTiO₃, which, in reality, exhibits mixed characteristics^[29-31]. According to the order-disorder model for BaTiO₃, the disorder in the paraelectric phase is related to the positioning of Ti ions. This characteristic of BaTiO₃ is well-illustrated through Raman spectroscopy, where the high-temperature Raman spectra show two broadbands at 260 and 530 cm^-1, indicating the disorder of Ti ions^[32,33]. In general, the order-disorder mechanism involves electric dipoles aligning in one direction as the temperature drops below the Curie point (T_C), thereby acquiring ferroelectric properties. This mechanism is well-known in materials such as KH₂PO₄^[34] and NaNO₂^[35].

Another example, BiFeO₃, exhibits ferroelectricity due to the presence of Bi³⁺ with 6s² lone pairs^[36]. Pb(Zr,Ti)O₃ encompasses characteristics of both cases mentioned above, and it has a large remnant polarization of about 82 μC/cm^2[37]. It exhibits ferroelectricity through the relative displacements of oxygen octahedra and Ti⁴⁺/Zr⁴⁺ ions, in addition to the presence of 6s² lone pairs from Pb^2+[38]. In the case of typical displacive ferroelectricity, materials often face competition between polar distortion and BO₆ octahedral rotation, influenced by the Goldschmidt tolerance factor. As a result, among the numerous perovskite materials, those with ferroelectric properties remained relatively undiscovered or less well-known^[39].

On the other hand, improper ferroelectricity has been discovered in recent years and found to result from polarization-coupled geometric distortion of polyhedral^[40,41] or magnetic ordering^[42] as in hexagonal-YMnO₃, layered perovskite such as Ca₃Ti₂O_7, and orthorhombic-TbMnO₃ materials. Strong hybridization between the transition metal and oxygen ions is not necessary in improper ferroelectricity, so non-d⁰ transition metal can be introduced, allowing magnetoelectric coupling^[43]. Boracite is an example of improper ferroelectric and has attracted interest due to its multiferroic properties^[44,45]. It has a complex structure denoted as M₃B₇O₁₃X (where M is a divalent metal and X is a halogen). Using Mg₃B₇O₁₃Cl as an example, the material transitions from a cubic phase at high temperatures to an orthorhombic phase through structural shearing as the temperature decreases, leading to a ferroelectric transition^[46,47]. The spontaneous polarization is about 1 μC/cm². Boracite can have six different domain states, each separated by straight boundaries. It can simultaneously possess charge-neutral 180° and charged 90° domain walls, making it a promising material for electronic applications^[48,49].

More specifically, within the category of improper ferroelectrics, there exists a type known as hybrid improper ferroelectrics^[41]. In this case, polarization arises from a complex distortion pattern that involves more than two nonpolar lattice modes with different symmetries. An example of a hybrid improper ferroelectric is the layered perovskite Ca₃Mn₂O₇, in which polarization is manifested through a combination of octahedral rotation mode and tilt mode. In addition, the reversal of polarization can be achieved by distortion in just one of these modes, either rotation or tilt. In the case of interfacial engineered materials, such as ferroelectric PbTiO₃ and paraelectric SrTiO₃ superlattices, improper ferroelectricity can emerge due to a unique type of atomic rearrangement^[50]. First-principle calculations indicate that the ground state is not purely ferroelectric; rather, it predominantly involves the antiferrodistortive rotation of oxygen atoms. Polarization can arise from the coupling of two in-phase and out-of-phase octahedral rotational modes. Notably, these materials exhibit a very large dielectric constant that remains unaffected by temperature changes.

As illustrated in Figure 2, hexagonal YMnO₃, unlike the typical perovskite structure, has a B-site Mn with a two-dimensionally networked MnO₅ polyhedra structure^[51]. These MnO₅ triangular bipyramids can geometrically buckle to induce inversion symmetry breaking. Similarly, layered perovskites have BO₆ octahedra that are two-dimensionally networked such as YMnO₃, aligned in-plane^[52]. The way these octahedra rotate determines the ferroelectric polarization, and the polarization expressed as layer-resolved polarization is present in-plane. Structures such as Ruddlesden-Popper A_n+1B_nO_3n+1, Aurivillius Bi₂O₂(A_n-1B_nO_3n+1), and Dion-Jacobson A′(A_n-1B_nO_3n+1) belong to the layered perovskite structure^[53] [Figure 2B].

Figure 2. Improper ferroelectric structure with geometric distortion. (A) Hexagonal YMnO₃ structure with centrosymmetric non-polar (left), down-polar (middle), and up-polar (right). Distortion of MnO₅ triangular bipyramids is indicated with arrows. (B) Ruddlesden-Popper Sr₃Zr₂O₇ layered structures showing polar and anti-polar characteristics. ZrO₆ octahedral rotations determine the polarity of the structure. Reproduced with permission^[52]. Copyright 2018, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim.

In this way, oxygen octahedra and perovskite structures can also play a role in inducing ferroelectricity. The control of perovskite structures is achieved in thin films through factors such as strain and octahedral network connectivity^[54,55]. Several studies have investigated the relationship between ferroelectric materials and oxygen octahedral structures^[56,57]. BiFeO₃ has diverse domain structures and exhibits various phase transitions in response to factors such as pressure, temperature, and strain^[58-61]. It primarily adopts the rhombohedral R3c space group with an a^-a^-a^- oxygen octahedral tilt in Glazer notation^[62]. The octahedral structure can be altered in various ways through the interfacial connectivity^[63,64], resulting in transition between ferroelectricity and antiferroelectricity, and fine-tuned domain spacing^[56]. There have also been reports of ferroelectricity induced by variations in the oxygen octahedral structure in materials such as CaTiO₃^[65]. Similar to most perovskite materials, CaTiO₃ adopts the Pnma space group, and it exhibits paraelectric properties due to the stable a^-b⁺a^- oxygen octahedral rotations, as shown in Figure 3A^[66]. It has been shown that local ferroelectricity can emerge at the ferroelastic twin boundaries between antiferroelectric domains in CaTiO₃^[67,68]; also, ferroelectricity can be induced by the suppression of octahedral distortion when subjected to strong tensile strain^[69]. Furthermore, through density functional theory (DFT) calculations, it has been validated that when the oxygen octahedra adopt forms such as a^-a^-a^- or a⁺a⁺c^-, a polar structure can be stabilized, and it realized through the interface engineering^[70] [Figure 3B]. This highlights the significant impact that the oxygen octahedral structure can have on the ferroelectric properties of materials.

Figure 3. Hidden ferroelectricity of CaTiO₃ and oxygen octahedra pattern engineering. (A) Annular bright field (ABF)-STEM and piezoresponse force microscopy (PFM) analysis of paraelectric CaTiO₃ on (001) LaAlO₃. Corresponding oxygen octahedral rotation mapping and polarization mapping results coincident with the non-polar structure. (B) ABF-STEM and PFM analysis of ferroelectric CaTiO₃ on (111) LaAlO₃. Corresponding oxygen octahedral rotation mapping, and polarization mapping results coincident with the polar structure. Reproduced with permission^[70]. Copyright 2020, The Authors, published by Springer Nature.

The delicate rotation of oxygen polyhedral is one of the key parameters to dominate the ferroelectricity in oxides. Brownmillerite structure (ABO_2.5, A,B = transition metals), as shown in Figure 4A, similar to perovskite structure (ABO₃), has the well-ordered oxygen vacancy channels, leading to the presence of oxygen tetrahedra^[71,72]. Brownmillerite has a regularly repeating pattern of oxygen octahedral and tetrahedral layers due to oxygen coordination^[73]. In the case of SrFeO_2.5, a representative brownmillerite structural material, the oxygen octahedral FeO₆ layers are centrosymmetric, similar to the cubic phase of SrFeO₃, resulting in a non-polar structure^[74,75]. However, the oxygen tetrahedral FeO₄ layers can undergo non-centrosymmetric distortions, leading to ferroelectric properties^[76-78]. Interestingly, the oxygen tetrahedra collectively rotate to the left or right in a chain-like manner while also exhibiting displacement. This combined behavior results in ferroelectricity. Theoretically, it has been reported that in SrCoO_2.5, depending on the arrangement of the oxygen tetrahedral layer, the Pmc21 space group can be stabilized, leading to the emergence of a ferroelectric state^[79]. Furthermore, in the I2bm space group, it has been calculated that the tetrahedral chain rotates in one direction, resulting in a polarization of approximately 6.38 μC/cm^2[77]. Experimentally, in SrFeO_2.5, ferroelectricity has been demonstrated through P-E measurements, second harmonic generation (SHG), piezoresponse force microscopy (PFM), and various other techniques^[78] [Figure 4B]. Additionally, the ferromagnetic properties associated with tetrahedral rotation have been observed, confirming its status as a multiferroic material. In the material Bi₂SiO₅, ferroelectricity is induced similarly by the rotation of silicate tetrahedral chains, but there is a difference in that the apical oxygen is fixed in brownmillerite structures such as SrFeO_2.5^[80,81].

Figure 4. Novel ferroelectricity in brownmillerite structure. (A) Atomic structural features of perovskite and brownmillerite. Tetrahedral chain of brownmillerite can be distorted up and downward. (B) Experimental measurements in brownmillerite SrFeO_2.5 thin film. Polarization and junction current as a function of electric field (left) and PFM measurements (right). Reproduced with permission^[78]. Copyright 2019, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim.

Fluorite HfO₂ has a variety of polymorph structures, and depending on the structure, the material can exhibit ferroelectricity. Under ambient temperature and pressure conditions, the monoclinic structure with a non-polar P2₁/c space group is stable in bulk form^[82], while it is known to stabilize the metastable non-polar P4₂/nmc tetragonal phase and the polar Pca2₁ orthorhombic phase in thin films^[17,83,84]. There are many attempts to stabilize this orthorhombic phase through doping or strain. It is known that Si:HfO₂ thin film has a polar orthorhombic structure, which initially nucleates as a metastable tetragonal phase at high temperatures. Depending on the presence or absence of capping during sample cooling, it either becomes a monoclinic phase or stabilizes as a polar orthorhombic phase^[16]. In cases where TiN electrode capping is present, mechanical shearing is confined, leading to the manifestation of the orthorhombic structure. This orthorhombic Pca2₁ structure has a unique configuration that divides into polar and non-polar layers, gaining attention as a structure that can be ultimately scaled from the perspective of ferroelectric domains and domain walls^[85].

FERROELECTRIC DOMAINS

After understanding the structural mechanisms that induce ferroelectricity, when we examine actual ferroelectric material inside, we find the same polarity regions called ferroelectric domains. These domains are separated by interfaces known as domain walls. When polarization is aligned in a single direction, it becomes electrically unstable, prompting the formation of domains to compensate for this instability. In other words, ferroelectric domains result from the interplay between wall energy and depolarization fields induced by surface bound charges from ferroelectric polarization^[86]. Ferroelectric domains vary depending on the electrical and mechanical boundary conditions, such as crystallographic orientation, strain, and local defect^[87-91]. For instance, in the case of tetragonal proper ferroelectrics such as Pb(Zr,Ti)O₃ and BaTiO₃, they have polarization in the <001> direction, resulting in domains of 90 and 180 degrees. In contrast, the domains of BiFeO₃ have a rhombohedral structure with polarization in the <111> direction, allowing for domains of 71, 109, and 180 degrees^[92]. Due to these various angular domains, the vortex nanodomain pattern of BiFeO_3, as shown in Figure 5A, has been reported on a TbScO₃ substrate^[93]. The formation of these domains is driven by localized electrostatic forces, especially at the interface where the 109° domain walls end. Such domains can be switched using an electric field, enabling various applications of ferroelectric materials. Depending on the domain structure, the interaction between domains can either facilitate or hinder switching, potentially influencing parameters such as remnant polarization^[94]. In terms of the coercive field, this parameter is related to the effectiveness of domain switching under an electric field^[95]. Thus, these parameters can vary depending on the domain structure. For example, HfO₂ possesses a high coercive field, which can be interpreted as a result of the nearly eliminated interactions between domains^[85]. Therefore, understanding the domain formations and observing domain motions are essential for the design of practical electronic devices.

Figure 5. Various types of ferroelectric domains. (A) TEM images of vortex shape nanodomain structure of BiFeO₃ thin film. Reproduced with permission^[93]. Copyright 2011, American Chemical Society (B) Atomic scale STEM image of small size of domains in improper ferroelectric, YMnO₃. Reproduced with permission^[96]. Copyright 2013, The Authors, published by Springer Nature.

Besides, domain walls themselves can present radically different properties from neighboring domains, opening an alternative route towards unusual functionalities with enormous application potential. Because it plays the role of a boundary connecting two domains, lattice distortion is strong^[2,96,97], and accordingly, a strain-related driving force arises, making it easy for charged defects to accumulate^[98,99]. In the case of BiFeO₃ sample grown on DyScO₃ substrates with higher deposition rates and with higher oxygen pressure, the 71° domain wall shows small lattice distortion and relatively low conductivity, whereas the 109° and 180° domain walls exhibit significant lattice distortion and high conductivity. In the case of BiFeO₃ grown on SrRuO₃-buffered SrTiO₃ substrates, the conductive nature of a 71° domain wall is also achieved due to oxygen vacancies lowering the Schottky barrier at the domain wall^[100]. In addition, when the polarization directions of adjacent domains meet at the domain wall in a tail-to-tail or head-to-head configuration, the charge accumulation results in high metallic conductivity^[101-103]. BiFeO₃ shows p-type conduction through the appearance of Fe⁴⁺ and bismuth vacancies at the domain wall^[98]. Similarly, in Pb(Zr,Ti)O₃, the accumulation of Ti³⁺ at the domain walls enables n-type conduction. In the layered ferroelectric (Ca,Sr)₃Ti₂O₇, most of the polarization is aligned in-plane, leading to predominant head-to-head and tail-to-tail configurations and resulting in numerous charged walls^[104]. Not only does the domain wall affect conductivity, but it also facilitates the accumulation of oxygen vacancies. This can effectively lower the local energy bandgap, enhance the photocurrent^[105], or produce a depolarization field, leading to an increased electromechanical response and, consequently, improved piezoelectric properties^[106]. Attempts have been made to utilize the conducting domain wall of LiNbO₃ in memristors^[107]. These phenomena have triggered efforts to apply domain boundaries in electronic devices for diverse purposes. A SrRuO₃/BiFeO₃/SrRuO₃ film was fabricated with a tail-to-tail polarization configuration, inducing in-plane charged domain walls^[108]. Using electric field cycling, they demonstrated the ability to create, erase, and move these charged domain walls, revealing memristive characteristics.

In the improper ferroelectric YMnO₃, the ferroelectric domain is interestingly coupled with magnetic order^[109], making its domain structure different from conventional ferroelectrics. YMnO₃ can exhibit six distinct domain patterns^[96,110,111] [Figure 5B]. Structural distortions at domain walls, accompanied by Y ion movements, manifest as antiphase boundaries combined with ferroelectric domain walls. Considering a domain labeled as α as the baseline structure, α, β, and γ domains exhibit antiphase boundary relationships. With polarization directions denoted as + or -, a total of six possible domains can emerge from a single point, forming a cloverleaf pattern. These domains appear periodically as α, β, γ and can be defined as either clockwise or anti-clockwise vortex directions based on their order. While enhanced conductivity observed in domain walls of materials such as BiFeO₃ and Pb(Zr,Ti)O₃ was not evident in YMnO₃’s conductive atomic force microscopy (c-AFM) results^[110], there are findings of domain wall conductivity due to vacancy ordering in oxygen-deficient situations^[112]. However, the domain orientation in YMnO₃ can vary, being either in-plane or out-of-plane^[113]. Depending on how domain walls meet, they can exhibit characteristics of charged domain walls in the case of tail-to-tail longitudinal domain walls or uncharged domain walls when forming antiparallel transverse domain walls^[51,114].

In Y-doped HfO₂ single crystals, the structure stabilizes from monoclinic to orthorhombic based on the yttrium doping concentration^[115]. With about 12% doping, a stable ferroelectric domain with 90° and 180° domains was imaged. However, in thin films, a mix of various structures such as monoclinic, orthorhombic, and tetragonal is commonly observed, intertwined in small-sized grains with varied orientations, necessitating atomic scale analysis using STEM. HfO₂ thin film is known for its wake-up effect, where the structure changes and domains align under an electric field, enhancing its ferroelectric properties^[116]. For instance, in a Gd-doped HfO₂ film, the monoclinic, orthorhombic, and tetragonal structures coexist as nanosized grains^[117] [Figure 6A and B]. The 90° domain boundaries of the orthorhombic structure are displayed similarly to those in Figure 6C; however, after field cycling, switching occurs at the 90° domain wall. Similarly, in Hf_0.5Zr_0.5O₂, both uncharged and negatively charged types of 90° domain walls were identified, and it was revealed through field-cycling that a 90° domain wall transforms into a 180° domain wall. This was used to explain the origin of the wake-up effect. Computational studies on the domain forms of HfO₂ ferroelectric orthorhombic structure revealed various domain wall formations depending on polarization orientation and lattice matching. Notably, a specific 180° domain wall energy showed a negative value of about 21.3 mJ/m², indicating stabilization of an anti-polar domain^[118]. These findings pave the way for future studies on ultranarrow domains that maintain polarization at a half-unit cell width and on scaled-down ferroelectrics^[85].

Figure 6. Polymorphic domain structure of HfO₂. (A) Monoclinic atomic structures with three different directions. (B) Orthorhombic atomic structures with three different directions. (C) HAADF-STEM images show intermixed monoclinic and orthorhombic, and tetragonal structure with a few nanometer scales. Reproduced with permission^[117]. Copyright 2018, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim.

Beyond the domain walls in ferroelectrics, exotic topological domain structures have become a significant research focus^[119]. As the dimensions of ferroelectrics decrease, the influence of boundaries such as interfaces and surfaces increases, leading to the formation of structures such as flux-closure domains^[120], polar vortices^[121], skyrmions^[122], merons^[123], and hopfions^[124] [Figure 7A]. These structures, studied extensively in magnetic materials, pose a challenge in ferroelectrics due to the strong coupling between the lattice and polarization. This coupling causes an energy penalty for polarization rotation against the crystallographically permitted directions, making the creation of exotic topological structures more challenging than in magnetic materials. However, advancements in theoretical studies and experimental characterization methods have spurred research into various topological structures. Theoretical studies on new topological polar vortices in reduced dimensions, such as nanodots and nanorods, have led to numerous investigations^[125,126]. For instance, when PbTiO₃/SrTiO₃ multilayer films are grown under tensile strain on GdScO₃, flux-closure domains form, as shown in Figure 7B, with their periodicity varying with the thickness of the PbTiO₃ film^[120]. These structures emerge as a result of the interplay between elastic energy, electrostatic energy, and polarization gradient energy. In superlattice PbTiO₃/SrTiO₃ on DyScO₃, for example, the formation of polar vortices is driven by competition among the epitaxial constraint-induced elastic energy in PbTiO₃ on DyScO₃^[121], the significant polar discontinuity between PbTiO₃ and SrTiO₃ causing electrostatic energy, and the gradient energy required for changes in polarization direction and magnitude. Factors such as the periodicity of the superlattice and strain play a crucial role in this competition. For periodicity shorter than ten unit cells, conventional a₁ and a₂ domains form, whereas longer periodicities lead to the formation of flux-closure domains. In addition, on TiO₂-terminated SrTiO₃ substrate, which imposes compressive strain as opposed to the tensile strain of DyScO₃, polar skyrmions can be obtained. When a 5 nm PbTiO₃ film is grown on SmScO₃ substrate under tensile strain, polar merons, which are akin to half-formed skyrmions, are observed. These exotic topological structures hold potential for applications in advanced memory devices and nanoelectronics.

Figure 7. Exotic topological ferroelectric domains. (A) Representative examples of topological structures. Each arrow indicates the direction of polarization. Reproduced with permission^[119]. Copyright 2020, Wiley-VCH Gmbh. (B) Atomic scale STEM image of flux-closure domains in PbTiO₃/SrTiO₃ multilayer films. Reproduced with permission. Yellow arrows represent the directions of polarization. Reproduced with permission^[120]. Copyright 2015, American Association for the Advancement of Science.

FILM THICKNESS SCALING

In thin films, the characteristics of the material can differ significantly from bulk due to the size effect, notably effects caused by strain, interfaces, etc. Consequently, the form of domains can change, and the overall characteristics of the thin film can be entirely different. For example, strained BaTiO₃ thin films grown on DyScO₃ and GdScO₃ substrates lead to enhanced ferroelectric properties^[127]. Ferroelectric transition temperature is almost 500 °C higher, and a remnant polarization is at least 250% higher than bulk BaTiO₃ single crystal. In thin films of paraelectric SrTiO₃, ferroelectricity can be realized at a thickness of fewer than 12 unit cells due to polar nanoregions induced by antisite defects^[14], as shown in Figure 8. For another paraelectric CaTiO₃, when thin film growth is induced in the (111) direction, ferroelectric structural characteristics appear up to about 9 nm, and beyond that, the original Pnma phase paraelectric characteristics appear^[128].

Figure 8. Emergence of ferroelectricity in ultrathin films of otherwise non-ferroelectric SrTiO₃. (A) Schematics illustrating the effect of polar nanoregions based on thickness. In thicker films, polar nanoregions are not effectively aligned, whereas in thinner films, they align well. (B) Inverted ABF-STEM image and corresponding polarization mapping. Polar nanoregions are well visualized. Reproduced with permission^[14]. Copyright 2015, American Association for the Advancement of Science.

With the advancement of various thin film synthesis methods such as pulsed laser deposition (PLD), molecular beam epitaxy (MBE), and atomic layer deposition (ALD), it became possible to deposit ferroelectric materials very thinly, enabling the development of miniaturized ferroelectric materials with newly induced ferroelectric properties. However, ferroelectricity in thin films does not always appear favorably^[129]. In terms of a dead layer, a parasitic low permittivity layer associated with the boundary between ferroelectric and electrode, it is thought to cause a collapse in the permittivity of thin film capacitor structures. This limits the effective use and integration of high permittivity materials. While the dead layer is an inherent feature at the dielectric-metal interface, it can be engineered out in certain cases, particularly where interface bonding is weak. For SrTiO₃ single crystals, theoretical analyses have confirmed the presence of a dead layer, predicting strong intrinsic suppression of permittivity^[130]. Experimentally, when lamellae of SrTiO₃ single crystals, created using a focused ion beam (FIB), are formed into capacitor structures with Pt electrodes, a significant inherent suppression of permittivity is observed, despite SrTiO₃ remaining intact up to the interface^[131]. However, in specific systems, this dead layer can be eliminated. For example, in BaTiO₃ single crystals made into lamellae and constructed into an Au/BaTiO₃/Au structure, there are no indications of permittivity suppression in thin films as thin as 75 nm^[132]. This indicates the possibility of engineering out the dead layer by controlling defects and strain. Theoretical calculations have revealed the potential existence of a negative dead layer in ferroelectric capacitors, especially when proper interface termination is established^[133]. This understanding not only confirms the existence of strong intrinsic effects even with perfect interfaces but also emphasizes that with an appropriate choice of electrode material, interface bonding effects can enhance the dielectric response, overcoming the material's limitations. This understanding confirms strong intrinsic effects even in perfect interfaces and highlights the importance of selecting suitable electrode materials, thereby overcoming the inherent limitations of the materials.

Also, ferroelectric materials inherently have a size effect, where ferroelectricity decreases as the critical thickness is approached. This phenomenon has been a significant topic of discussion. In reality, the limit of critical thickness exists due to factors such as defects and interface effects within materials. As the film becomes thinner, the effect of the depolarization field increases^[134], and with increased interface, issues arise from oxygen vacancy and charge injection at the interface between metal electrodes and ferroelectrics, leading to fatigue after cycling, reducing endurance. In recent years, many studies on thin films have been conducted to overcome the limitations of critical thickness. Several materials and their critical thickness and polarization characteristics are introduced. It has been confirmed that a (001) oriented BaTiO₃ thin film between two metallic SrRuO₃ electrodes shows ferroelectricity down to a thickness of about six unit cells^[134]. The disappearance of ferroelectric instability is due to a depolarizing electrostatic field, which arises from dipoles at the ferroelectric-metal interfaces. It is also evident that the softness of the SrRuO₃ lattice plays a pivotal role in screening the ferroelectric polarization in BaTiO₃. The critical thickness for ferroelectricity is further reduced to 1.2 nm^[135]. For Pb(Zr,Ti)O₃, a critical thickness as thin as that of BaTiO₃ has been reported^[12]. In PbTiO₃ thin films with a stripe domain pattern, a study revealed the correlation between the reduction in film thickness and the decrease in Curie temperature^[136]. Based on these findings and subsequent calculations, it was predicted that films as thin as two unit cells could be formed at lower temperatures. Using synchrotron X-ray, it has been demonstrated that at room temperature, the ferroelectric critical thickness can be reduced to as little as three unit cells, about 1.2 nm^[12]. There was even a subsequent report suggesting an absence of critical thickness altogether^[137]. Through STEM analysis, films grown on SrTiO₃ with a SrRuO₃ electrode showed a remnant polarization of 22 μC/cm² down to a two unit cells thickness. In contrast, films grown on SrTiO₃ without a SrRuO₃ electrode exhibited a reduced polarization of 16 μC/cm² at a mere 1.5 unit cells (0.6 nm) thickness, as shown in Figure 9. In the case of BiFeO₃, although the bulk is rhombohedral, thin films can stabilize in a tetragonal structure due to strain^[138]. Several reports showed that ferroelectricity appeared in such thin films in a tetragonal phase^[139]. When transformed to a tetrahedral-like structure on a La_0.7Sr_0.3MnO₃ bottom electrode, strong out-of-plane polarization was reported to appear even at a thickness of 1.2 nm due to the accumulation of oxygen vacancies at the interface. Furthermore, at room temperature, tetragonal phase BiFeO₃ on an SrRuO₃ electrode was reported to have robust out-of-plane spontaneous polarization even at one unit cell thickness^[140]. Although very thin, compared to bulk, the polarization characteristics themselves were significantly degraded, so this trade-off needs to be addressed.

Figure 9. Thickness-dependent ferroelectricity in Pb(Zr,Ti)O₃ on a SrTiO₃ substrate. ABF images from regions with thicknesses of 6.5, 4, and 1.5 unit cells. Displacements and polarizations consider both the cation and oxygen. While polarization is suppressed in thin film, it remains stable. Reproduced with permission^[137]. Copyright 2017, The Authors, published by Springer Nature.

For the improper ferroelectric YMnO₃, it was reported through calculations that there might be no critical thickness^[141]. The intrinsic bulk polarization is 8.7 μC/cm², smaller than conventional proper ferroelectrics, but in films, it is slightly smaller at 6.5 μC/cm². It is known that it can have a single domain without electrodes or external fields, unlike proper ferroelectrics in terms of free energy. This polar state has been experimentally proven through STEM and SHG, and it was maintained even at a thickness of three unit cells, about 10 nm^[142]. At a very low temperature of 20 K, it was confirmed that hexagonal YbFeO₃ had no critical thickness limit up to three unit cells^[143]. Especially through the fitting of depolarization effects, it was proven that the spontaneous polarization was maintained even as the thickness became very thin. In layered bismuth oxide Sm-substituted Bi₆O₉, ferroelectric properties were found even at a thickness of less than one nanometer at room temperature^[144]. In particular, it was confirmed that the remnant polarization has a high value of 17 μC/cm², even at a reduced thickness [Figure 10].

Figure 10. Ferroelectricity in layered bismuth oxide. The HAADF-STEM image shows a well-grown film with a thickness of one nanometer. Despite the film being reduced by 1 nm in thickness, the remnant polarization remains high. Reproduced with permission^[144]. Copyright 2023, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.

HfO₂ shows promise for polarization-driven memories and ferroelectric-based transistors because of their compatibility with complementary-metal-oxide-semiconductor technology. When ferroelectricity was first reported in Si:HfO₂ thin films with a thickness of 10 nm, it was expected that they would exhibit high ferroelectricity even at thin thicknesses^[16]. In the case of Hf_0.5Zr_0.5O₂ grown on the metallic pyrochlore Pb₂Ir₂O₇, the polar orthorhombic phase stabilizes at thicknesses below 30 nm, and ferroelectric characteristics were confirmed even at 5 nm^[145]. Near the interface, the orthorhombic phase remains stable, while in thicker films, the upper portion transitions into a non-polar monoclinic phase with a finger-like shape. A 10 nm thick Y:HfO₂ grown in the (111) direction was reported to have a very large polarization value of 64 μC/cm^2[146]. When oriented in the (111) direction, the Pca2₁ orthorhombic phase becomes stable, exhibiting minor rhombohedral distortion, which highlights the significance of structural limitations in maintaining the ferroelectric phase. Ferroelectricity was confirmed in Hf_0.5Zr_0.5O₂ grown by ALD, even at an incredibly thin thickness of 1 nm^[147]. From a structural perspective, as the material's size decreases, it undergoes structural distortion and shifts towards higher symmetry. Unlike conventional perovskite structures that transition to non-polar, the fluorite-structured Hf_0.5Zr_0.5O₂ exhibits a high-symmetry polar orthorhombic phase rather than a non-polar monoclinic one. As a result, ferroelectricity increases with decreasing size. Similarly, ZrO₂, possessing the same fluorite structure, typically remains stable in the antiferroelectric tetragonal phase^[148]. However, when its thickness is reduced to 2 nm or less, it transitions to the ferroelectric Pca2₁ orthorhombic structure. Notably, ferroelectric properties persist even at a unit cell thickness as thin as five angstroms.

FERROELECTRIC DOMAIN WIDTH SCALING

For high-density integration, it becomes extremely important to not only reduce the thickness of the ferroelectric thin film but also downsize the width of the domain, which serves as an information unit. In terms of domain size, it is classically described by the Landau-Lifshitz-Kittel’s law concerning ferroic domains^[149-151]. This law was theoretically proposed based on a straightforward stripe-patterned domain. As the domain's vertical dimension area grows, the energy of the domain wall also increases. Consequently, when the thickness increases, the formation of a domain wall is avoided, leading to a larger domain size. Moreover, when the domain's volume energy decreases, its formation becomes more stable. This relationship can be mathematically represented by the square root dependence on the domain size's thickness. Initially, this law was introduced to describe the domain of ferromagnetism. However, Mitsui and Furuichi later extended it to the ferroelectric Rochelle salt 180° domain structure^[86]. In the case of single crystal BaTiO₃, lamellae were created using a FIB to observe domain changes according to thickness^[152]. This approach demonstrated, through direct STEM observation, that the law governing these changes applies well from the millimeter scale down to the nanometer scale. In addition, within a single lamella, it was observed that a sharp thickness gradient leads to a strong bifurcation. In the context of thin films, the relationship is direct: an increase in film thickness results in a larger domain size, while a decrease leads to a smaller domain size. In PbTiO₃ thin films, a nanoscale 180° stripe domain pattern was confirmed as a satellite pattern in X-ray scattering^[136]. It was observed that as the thickness reduced to 1.6 nm, the periodicity of these domains decreased to as small as 3.7 nm. Also, this has been observed in Pb(Zr,Ti)O₃ films, where changes in the size of the stripe pattern's a-domain with respect to thickness were confirmed using PFM and TEM. The critical thickness for forming a stripe pattern was found to be around 60 nm, and the domain width was constrained to approximately 10 nm at that thickness^[153].

Another issue causing small-sized domains is the thickness of the ferroelectric domain wall. Ferroelectricity naturally creates domains with Ising-, Bloch-, or Neel-type domain walls to prevent sudden polarity shifts, which can often weaken the magnitude and confined size of ferroelectricity [Figure 11A]. Neel-like domain walls have been observed in Pb(Zr,Ti)O₃ single crystals and thin films, while Bloch-type domain walls were observed in LiTaO₃ single crystals^[154-156]. In such domain walls, to change the aspect of polarization, the size must either diminish or the polarization must decrease through rotation, as shown in Figure 11B. Consequently, the thickness of the domain wall is large, and the domain size is limited. Moreover, because ferroelectricity is influenced by the soft phonon mode, which represents a collective movement of atom displacements, the switching scale of individual domains is inherently restricted^[85].

Figure 11. Scaling of domain wall width in PbTiO₃ and HfO₂. (A) Calculation results of the finite thickness of the domain alongside the destabilized one unit cell-width domain. (B) HAADF-STEM images of Neel-like domain wall in Pb(Zr,Ti)O₃. Reproduced with permission^[155]. Copyright 2016, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim. (C) Calculation results of zero-width domain wall and stabilized on unit cell-width domain. (D) ABF-STEM image of the unit cell-width domains in HfO₂. (A and C) Reproduced with permission^[85]. Copyright 2020, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. (D) Reproduced with permission^[15]. Copyright 2022, The Authors, published by Springer Nature.

For the improper ferroelectric hexagonal ErMnO₃, the situation is somewhat similar. At specific local domain wall points, very thin domains with a thickness of one unit-cell have been observed, which was attributed to strong electrostatic attractive interactions^[157]. However, this was not a commonly observed feature. Due to the coexistence of the general antiphase boundary and the ferroelectric domain wall, there are limitations to the wall width. In ErMnO₃, the thickness of the ferroelectric domain wall is around a few nanometers, with observations showing a gradual switch in polarization^[158,159].

Pca2₁ orthorhombic HfO₂ has garnered significant attention due to its remarkably fine domains and walls with a half-unit cell width^[85] [Figure 11C]. The domain formation in HfO₂ stems from the alternating arrangement of ferroelectric and spacer layers, leading to a flattened phonon dispersion. As a result, HfO₂ can switch via the creation of zero-width domain walls, contrasting the diffused domain walls observed in prototypical ferroelectric PbTiO₃. Analysis of STEM images for PbTiO₃ reveals these diffused domain walls, where a reduction in the strength of polarization is noticeable over a domain wall area spanning 1~3 nm, accompanied by lattice distortion^[155]. In contrast, the half-unit cell domain width of HfO₂ was directly verified in Hf_0.5Zr_0.5O₂ films grown between TiN electrodes using STEM [Figure 11D]. Polarization in HfO₂ manifests solely within the polar layers, with the movement of oxygen in the Hf lattice confirming this polarization. In the as-grown state, domains with unidirectionally aligned polarization are visible on the left of Figure 11D, while those with alternately aligned polarization appear on the right of Figure 11D. Unique oxygen displacement configurations, such as down-up-up-down-up, have been observed, and these structural attributes vividly depict the zero-width domain wall characteristics^[15].

Another example of ultrafine domains is CsBiNb₂O₇^[20] [Figure 12A]. This material, with its layered Dion-Jacobson phase, can be exfoliated in a quasi-two-dimensional manner due to the weak bonding between layers. The in-plane polarization, aligned in the layer direction in the bulk crystal state, can exhibit unit cell-sized domains. This characteristic is attributed to the Cs ion weakening the bond between the NbO₆ octahedra layers, resulting in reduced domain wall energy. In HfO₂, the polar and spacer layers have different oxygen coordination numbers, three and four, respectively, and each layer exhibits very weak coupling, preventing lattice vibrations from propagating. Likewise, layered perovskites show weak couplings between oxygen polyhedra across each layer, suggesting a possible origin for layer-resolved ferroelectricity. Bi₂TeO₅ is another example where unit cell-wide domains form due to weakened connections between oxygen polyhedra^[160] [Figure 12B]. Bi₂TeO₅ has a layered structure primarily consisting of pyramidal BiO₅ pentahedra. When a domain boundary forms, an additional BiO₆ octahedron intercalates as a buffer layer between the adjacent polar BiO₅ layers, reducing domain wall energy. These examples illustrate that weakened connectivity in the oxygen polyhedral network is a key factor in inducing unit cell-wide ferroelectric domains.

Figure 12. Unit cell-width ferroelectricity in various materials. (A) HAADF-STEM image and atomic structure of layered CsBiNb₂O₇. Displacements of Bi ions are indicated by arrows. Reproduced with permission^[20]. Copyright 2021, American Physical Society. (B) PFM and HAADF-STEM images accompanied by the atomic structure. When domain walls form, BiO₆ octahedra emerge. Reproduced with permission^[160]. Copyright 2022, The Authors, published by Springer Nature.

The brownmillerite material is of interest when examining unit cell-wide domains. What makes it unique is its structure: it alternates between oxygen octahedra and oxygen tetrahedra, with a distinctive arrangement of oxygen vacancy channels^[161]. Interestingly, only the oxygen tetrahedra exhibit ferroelectric properties in brownmillerite, whereas the oxygen octahedra remain non-polar^[162]. This alternating structure, with non-polar regions disrupting the continuity of polar regions, is a trait also seen in other materials such as HfO₂, CsBiNb₂O₇, and Bi₂TeO₅. Specific types of brownmillerite, namely CaFeO_2.5 and SrFeO_2.5, have unique structures: the former is anti-polar, and the latter is polar. If these polarizations were to intermix, they might display a random polarization pattern akin to the sequence observed in HfO₂.

CHARACTERIZATION TECHNIQUES FOR FERROELECTRICS

Beyond the measurements of polarization-electric field or polarization-voltage hysteresis, which validate fundamental traits of ferroelectrics such as spontaneous and remnant polarization and the coercive field, there is a need to study the structural features and switching behaviors of ferroelectric domains for their integration into electronic devices. Microscopy-based imaging methods are predominantly used to evaluate these characteristics. At its simplest, domains are visualized using an optical microscope that employs polarized light. This approach is non-destructive and primarily captures domain patterns that are a micrometer in size or larger. As the trend moves towards smaller electronic devices, the spotlight has turned to techniques such as X-ray imaging, scanning probe microscopy (SPM) imaging with nanometer-scale probes, and TEM imaging on the unit cell level^[163-166]. Every method brings its unique strengths and challenges, and often, a combination of techniques is employed to elucidate ferroelectric properties. This review seeks to delve into the TEM imaging approach, focusing on the detailed examination of miniaturized domains and their related atomic structures. In this section, we will discuss the TEM imaging method, emphasizing a detailed exploration of miniaturized domains and recent advancements in the atomic-level structures.

Before discussing the TEM imaging approach, it is worth noting that PFM is a powerful tool for investigating the domain dynamics of ferroelectrics^[167]. The principle of PFM involves using the piezoresponse force, which acts between the scanning probe and the surface of the sample while scanning the surface with the probe^[168]. The contrast of the domain is due to the converse piezoelectric effect induced by AC voltage, resulting in a topographic image. PFM allows for nondestructive visualization and control of ferroelectric domains, not only sensing with the probe but also directly applying bias to facilitate domain switching, making it an excellent method for observing domain wall motion^[169]. The resolution in PFM is determined by the size of the scanning probe's apex, with recent advancements achieving imaging resolution down to about 10 nm from the micrometer level. Advanced PFM offers a range of versatile modes, such as switching spectroscopy PFM that captures local hysteresis loops at individual points^[170], Stroboscopic PFM for nanosecond time resolution^[171], resonance-enhanced PFM to boost measurement sensitivity^[172], along with dual AC resonance tracking PFM^[173], and band-excitation PFM^[174].

To analyze the precise atomic structure of ferroelectrics, TEM serves as a powerful observation tool enabling atomic scale examination with the use of a short-wavelength electron beam. The transmitted beam interferes with the ultra-thin specimen, generating phase information about the periodic crystal structure. Crystallographic information and chemical composition can be characterized using TEM. In addition, TEM is suitable for identifying the domain structure over a relatively large area, spanning a few square micrometers. In particular, dark-field TEM images, which select specific diffraction spots, show a strong bright contrast for the selected region under a two-beam condition. Because diffraction spots can violate Friedel’s law based on the polarity of the structure, ferroelectric domains are distinctly visualized by intensity in dark-field TEM. Furthermore, TEM operates in real-time mode, enabling in situ imaging under conditions such as the application of an electric field or heating, and it also offers the advantage of visualizing defects in materials and polymorphic structures^[175].

Using in situ holders, a conductive nanoprobe is precisely positioned to contact the specimen through a piezo-driven manipulator^[176]. The ferroelectric switching process can be observed in situ with this nanoprobe, as demonstrated in a Pb(Zr,Ti)O₃ thin film^[177,178]. The intrinsic electric fields, established at the interfaces between the ferroelectric and electrode, dictate the nucleation sites and growth rates of the ferroelectric domains, as well as the orientation and mobility of domain walls. Meanwhile, dislocations exert only a mild pinning force on the movement of domain walls. In a capacitor configuration using a Pb(Zr,Ti)O₃ film between Ni and SrRuO₃ electrode, a ferroelectric hysteresis graph resembling the typical P-E hysteresis is derived from the switched area-electric field curve^[179]. In a study concerning Pb(Mg_1/3Nb_2/3)O₃-0.38PbTiO₃ (PMN-PT), the influence of electric field on ferroelectricity was explored based on the thickness of the TEM sample^[180]. The results demonstrated that, for thicker samples, the 90-degree domain switches to 180 degrees when subjected to electric biasing. In contrast, thinner samples maintained the 90° domain [Figure 13]. Given that TEM samples need to be exceptionally thin to permit electron beam transmission, their characteristics, when thin, are distinct from those of thicker counterparts, providing a clear insight into domain behavior at a reduced scale.

Figure 13. Thickness dependence of ferroelectric/ferroelastic domain switching under electric biasing. (A) Dark-field TEM images of thick TEM samples under the electric field. Yellow regions indicate the 180° domain switched regions. (B) Dark-field TEM images of thin TEM samples under the electric field. Pink regions indicate the 90° domain switched regions. Reproduced with permission^[180]. Copyright 2020, The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.

Although most research has been focused on studies using conductive nanoprobes, recent experiments have been conducted using micro-electromechanical systems (MEMS) devices to apply electric biasing locally and stably^[181,182]. Ferroelectric thin film samples are usually prepared by creating a lamella using FIB and then transferring the sample^[181,183]. Through the design of the sample's electrode, the electrical path can be constructed as desired, either in-plane or out-of-plane^{[182,184,185]}. In PMN-PT single crystal, electrical biasing experiments were conducted using a MEMS chip. During the 280 electrical cycles, c-domain formation was observed, and charge accumulation was also monitored using TEM. The accumulation of charge led to the formation of frozen domains and shed light on ferroelectric degradation^[185]. As another example, in situ electrical biasing experiments were conducted on an (La,Sr)MnO₃/Hf_0.5Zr_0.5O₂/(La,Sr)MnO₃ capacitor at the atomic scale. Direct observation confirmed the reversibility of oxygen vacancy migration at the oxygen-reactive electrode, and it was revealed that the vacancy migration is intertwined with ferroelectric switching^[184]. When in situ bright field (BF)-STEM imaging was performed at a field of 300 kV/cm, lateral creeping of the domain wall in Pt/Pb(Zr,Ti)O₃/(La,Sr)MnO₃ was observed as an image contrast^[186]. In addition, another example, as shown in Figure 14, includes direct observations at the atomic scale using Fe ion displacements of BiFeO₃ ferroelectric domain switching when an electric field was applied^[187].

Figure 14. In situ BF-STEM image at the wall location together with Fe-displacement vectors superimposed on the color map of the Fe-displacement rotation angle. The sequence of applied voltages is numbered. Reproduced with permission^[187]. Copyright 2022, The Authors, published by American Chemical Society.

Atomic scale imaging methods, such as negative spherical aberration imaging (NCSI) and STEM, provide a detailed view of structures such as unit cell-wide domain at the atomic level^[188]. These techniques allow for a precise analysis of even the nanosized domains such as flux-closure domains^[189,190] and their domain walls^[154]. Through the analysis of ionic displacement and distortion at the atomic level, we gain a deeper insight into the structures. Unlike TEM, which analyzes phase information, these methods provide imaging of precise atomic structures, making them suitable for analyzing unique features in thin films, such as the polar nanoregions^[191,192] in relaxor ferroelectric properties or distinct domain forms such as polar vortexes^{[121,193,194]}. They are adopted for unveiling hidden information. Electric polarization could be determined by ionic displacements in the images, and structural features such as tetragonality and relative tilt and rotation angles are simultaneously characterized at the unit cell level^[195].

In general, HAADF-STEM and annular BF (ABF)-STEM images are the widely adopted imaging modes in STEM. HAADF-STEM is a robust imaging mode that displays the atomic number or Z-contrast of materials. The background of these images is dark, and thermally diffused scattered electron signals appear bright. It has been reported that the intensity of HAADF-STEM images is proportional to roughly 1.4~2 times the atomic number. However, it is challenging to observe light elements, such as oxygen, due to their low thermal diffuse scattering effect. ABF-STEM was introduced in a smaller annular form to address the difficulty HAADF-STEM has in detecting light elements. It has been revealed that ABF-STEM can image elements as light as hydrogen^[196]. However, there are still challenges in imaging lighter elements due to issues such as aberration, defocus, tilt, and sample thickness.

eABF-STEM (enhanced ABF-STEM) is a newly developed technique designed for the sensitive visualization of light elements, offering improvements over the traditional ABF-STEM^[197]. This method combines the advantages of both ABF-STEM and BF-STEM [Figure 15]. A BF-STEM image is generated from the scattered electron signal, where light elements appear bright and heavy elements appear dark. This is because heavy elements scatter farther from the center, while light elements scatter less. Although BF-STEM is effective for detecting light elements, it can be challenging to accurately interpret atomic columns since intermediate weight elements are ambiguously displayed. In contrast, ABF-STEM displays dark signals at atomic columns against a bright background, making atomic columns intuitively recognizable. However, a drawback of ABF-STEM is the difficulty in observing light elements, as the incoherent effective source size diminishes the ABF-STEM signal. eABF-STEM is obtained by subtracting BF detector signals from ABF detector signals. While the overall signal intensity is reduced compared to ABF-STEM, the intensity difference between light and heavy elements increases, significantly enhancing the visibility of light elements. When eABF-STEM is utilized in ferroelectric materials, it is frequently used to demonstrate the relationship between the oxygen octahedra and ferroelectricity^[198]. There has been a revelation using eABF-STEM about the gradual change in the oxygen octahedral tilt due to interface strain in the ferroelectric Bi_0.5Na_0.5TiO₃ thin film, and its association with the ferroelectric displacement of the Ti ion^[199].

Figure 15. Four different STEM imaging modes. (A) STEM images of the LaAlO₃ with intensity profiles. Reproduced with permission^[197]. Copyright 2013, Elsevier B.V. (B) Comparison between ABF- and eABF-STEM images of CaTiO₃ thin film.

Moreover, advanced electron microscopy techniques, such as differential phase contrast (DPC) and 4D-STEM imaging using pixelated detectors, are being rapidly developed^[200-203]. These techniques not only allow for the direct mapping of the internal electric field within materials but also enable imaging at higher resolutions^[204]. DPC determines the phase shifts caused by interactions between the electron beam and the sample, enabling the detection of both electric and magnetic fields, as shown in Figure 16. Especially after it was revealed that atomic resolution could be achieved, there were expectations that the measurement of polarization would become possible^[205]. Indeed, this capability was demonstrated in the material BiFeO₃, where the distribution of the electric field and the nature of polarization due to doping could be analyzed^[200]. Research has been published illuminating the flexoelectric effect related electrical polarization mapping^[201] and the non-Ising electric field distribution in ferroelectric domain walls^[206] using DPC. In addition, a recent study highlighted the DPC in real-time to observe the atomic switching of ferroelectric wurtzite Al_0.94B_0.06N induced by an electron beam^[207].

Figure 16. DPC-TEM measurements of electric fields. (A) Schematic representation of the basic principle of the DPC technique. (B) Vector plot of the atomic electric field in Ca-doped BiFeO₃. Reproduced with permission^[200]. Copyright 2018, American Chemical Society. (C) Electric fields at the polar domain walls. Reproduced with permission^[201]. Copyright 2020, The Authors, published by Springer Nature Limited.

The ferroelectric polarization can be observed over a large scale, but it can also manifest in very local structures. To analyze the subtle details visible in TEM images, software-based analysis techniques, such as deep learning, are being extensively researched alongside the development of TEM hardware^[70,208]. Software-based techniques for atomic position analysis have been extensively studied to analyze factors such as polarization, relative displacement, distortion of the octahedra, and the lattice's tetragonality^[209-212] [Figure 17]. The atomic positions can be determined using 2D quadratic fitting, Gaussian fitting, or the center of mass methods. Recently, techniques such as segmentation through k-means clustering based on unsupervised learning are also used to find atomic positions^[208]. To extract precise peaks, the signal-to-noise ratio is improved using the Wiener filter in the frequency domain, especially for periodic images^[213]. Advanced techniques such as nonlocal means denoising^[214] and block matching and three-dimensional filtering (BM3D)^[215,216] have also been employed. Currently, a significant portion of image analysis through peak detection has been automated, and the processing speed has greatly improved, alleviating many challenges in the structural analysis of ferroelectrics^[208].

Figure 17. Example of machine learning-based STEM image analysis flowchart. Entire workflow of precise atomic peak analysis in parallelly acquired HAADF-STEM and ABF-STEM images of SrTiO₃. Preprocessing steps reduce noise and enhance the peak contrast, and segmentation steps achieve the coordinate information of atomic columns. Reproduced with permission^[208]. Copyright 2022, The Authors, published by Springer Nature.

One of the strengths of deep learning-based analysis is that it allows for objective data analysis, eliminating human subjectivity; also, it is capable of processing vast amounts of data swiftly and efficiently. An example of applying deep learning to TEM research is its use in analyzing STEM images to understand the structure of the oxygen octahedra^[70]. This research identified the a^-b⁺a^- and a^-a^-a^- octahedral tilt structures in CaTiO₃ and linked them to ferroelectricity. Since STEM images are two-dimensional, they contain very subtle 3D structural information, which was meticulously analyzed. In addition, in a study involving polycrystalline Hf_0.5Zr_0.5O₂, deep learning was used on 4D-STEM data^[217]. This revealed that it was possible to distinguish between the centrosymmetric monoclinic P2₁/c, tetragonal P4₂/nmc phase, and the orthorhombic Pca2₁ phase with ferroelectric polarization in the TEM samples, disregarding factors such as thickness, tilt, and rotation. Similarly, an automated workflow using the ResNet 18 convolutional neural network technique was reported for classifying the monoclinic and orthorhombic phases in HZO to identify ferroelectric domains^[218].

CONCLUSIONS

As the demand for advanced devices in the rapidly evolving information technology and artificial intelligence industries increases, pioneering a new class of miniaturized, high-functioning materials becomes a paramount research priority. With advancements now reaching the ultimate limits of materials, such as the unit cell or atomic levels, this review sheds light on various ferroelectric materials. These materials are examined from both structural and domain perspectives, which are critical to ferroelectric research. We introduced the characteristics manifested in reduced structures. In particular, we highlighted the importance of the oxygen polyhedral structure as the cornerstone of oxide ferroelectric miniaturization. Moreover, we discuss the progressive advancements in sophisticated microscopy techniques vital for characterizing these miniaturized materials. In the future, it seems imperative to achieve breakthroughs that utilize atomic structures at the unit cell scale. Moving forward, there is a need to elucidate still-unknown challenges in operating unit cell-based devices stably and integrating them into real-world applications.