Insights into Ferroelectric BaTiO₃: Revealing Fundamental and Functional Aspects through Electron Spectroscopy

Abstract

X-ray absorption (XAS) and photoelectron spectroscopy (XPS or PES or ESCA—electronic structure for chemical analysis) are widely used techniques that allow to access the full electronic structure of the surfaces and buried interfaces offering complementary information on both the occupied (valence) and empty (conduction) states. XAS technique relies on measuring the signal corresponding to dipole-allowed transition, hence shines-up the unoccupied states’ investigation, which differs from XPS, where electrons are ejected from occupied states into the continuum, probing the occupied density of states. In the following, our purpose is to illustrate some of the potentials of XPS and XAS techniques by presenting some of the work where they were employed to study and describe bulk and interfacial phenomena in BaTiO3 systems.

1. Introduction

A multiphase material with at least one dimension on the nanometric scale is called a nanocomposite. These materials can be categorized as ceramic, metal, or polymer matrix nanocomposite materials based on their matrix group [1]. New materials with unique functions and multifunctionalities are eagerly wanted as the need for performance and complexity in electrical and optical systems grows [2]. When compared to conventional single-phase films, nanocomposite thin-film materials and nanoparticles are seen to be among the most promising possibilities due to their advantages in size and physical property tunability [3, 4, 5]. Three primary forms of nanostructures are found in nanocomposite thin-film materials: multilayers, nanoparticles-in-matrix, and vertically aligned nanocomposites (VANs). Every structure of a nanocomposite offers benefits for the coupling of materials. For instance, there are a lot of functionalizable surface regions in the nanoparticles-in-matrix structure [6, 7]. It has been shown that multilayer structures can be employed in optical applications, primarily as meta-materials [8]. The capacity of VANs, a recently created nanocomposite structure, to produce ordered, regulated structures in a single step makes them particularly interesting. VANs exhibit a vertical link between two phases with respect to the distribution and size of nanopillar characteristics. It has been shown that these organized VAN structures can be used to modify optical, electrical, magnetic, and superconducting characteristics [9]. Many novel VAN systems, such as BaTiO₃ (BTO)-Au, BTO-Fe, and BTO-Co, combine metals with oxide materials in addition to the most well-known oxide-oxide VANs [10]. These novel oxide-metal VANs have demonstrated improved and/or novel physical properties, particularly at room temperature, such as magnetic anisotropy, optical anisotropy, magneto-optical coupling, enhanced second harmonic generation (i.e., nonlinearity), and plasmonic resonance, by incorporating metals rather than oxides [5, 9]. Other promising applications of BTO systems such as non-volatile memory storage devices and nonlinear optics in ferroelectric capacitors, are based on the ferroelectric properties [11, 12]. Since a metallic electrode is typically used to drive a ferroelectric system, the metal-ferroelectric contact becomes a crucial problem in device physics. Single-domain ferroelectric states with polarization perpendicular to the film are stabilized by the semiconducting nature of ferroelectric thin films, which can be as thin as 100 nm [13]. The electronic bands are bending toward lower binding energies near surfaces for an inwardly oriented polarization and toward higher binding energies for an outwardly oriented polarization [14]. As a result, X-ray photoelectron spectroscopy (XPS) research becomes a valuable tool to investigate the ferroelectric state and to extract crucial information on the band bending [15, 16] close to the surfaces and their corresponding interfaces with different electrodes. It has been demonstrated that core levels shift rigidly with respect to the vacuum level and with the valence band maximum, following the band alignment direction [14, 17, 18]. Because valence band (VB) photoemission decreases the photoexcitation cross section by orders of magnitude when compared to core levels, VB study utilizing soft X-ray photoemission is known to be often difficult. Furthermore, the higher density of states at the metal’s Fermi level and the resulting attenuation of the semiconductor’s VB signal by the top metal could obscure the valence band maximum [19]. The XPS approach allows one to deduce the band alignment in semiconductors close to the contact region with a metal placed on its surface by examining the core-level shifts. In the following, we will explore Au-Fe-BTO and Co-BTO nanocomposite system prepared by using a non-equilibrium processing technique, in order to assess the miscibility of Fe and Au throughout the pillar production process in a BTO matrix [10, 20]. Furthermore, spectroscopic methods will be used to present some new studies on the interactions of metal/BTO materials [17, 21, 22].

2. Co-BaTiO₃ and Au-Fe-BaTiO₃ nanocomposite thin films

Ferroelectricity, ferroelasticity, and ferromagnetism are three functionalities, often cross-coupled in multiferroic materials [23]. These materials would exhibit electric polarization in the presence of an external magnetic field, and they would become magnetized in the presence of an external electric field. In the subsequent section, we showcase a metal-ceramic composite film, wherein uniformly dispersed Co particles, with an average size of 70 nm, are embedded in an insulating BaTiO₃ matrix [10]. Co was chosen due to its large saturation magnetostriction, small magnetic coercivity for a strong magnetoelectric coupling, and compatibility with Co-doped diluted magnetic semiconductor thin films, such as Co-doped ZnO, for potential applications to spintronic devices [10]. Co-dispersed BTO matrix composite films were fabricated on single crystalline (001) SrTiO₃ (STO) substrate using RF magnetron sputtering. A SrRuO₃ (SRO) bottom electrode layer was epitaxially formed over STO substrate by pulsed laser deposition for dielectric and magnetoelectric studies. Firstly, a 100-nm-thick BTO layer was deposited over SRO/STO to prevent potential electrical leakages. Then, a 400 nm-thick BTO-Co composite layer was grown. The X-ray diffraction showed a tetragonal BTO film (P4mm) with BTO-Co nanocomposite film grown on STO. The reciprocal space maps showed that the BTO matrix in the composite film is compressively strained in both in-plane and out-of-plane directions due to the scattered Co particles. The Fourier transform of the EXAFS function $\mathit{\chi }\left(\mathit{k}\right)$ into real space yielded the radial distribution function, which shows that the particles generated in the BTO matrix are metallic Co clusters. Atomic-scale images from high-resolution transmission electron microscopy showed that the BTO matrix encircles the Co particle closely, meeting the need for a strain-mediated magnetoelectric coupling. A well-defined ferroelectric hysteresis with low electrical leakage was shown by the polarization-electric field curve. At E = 0, the spontaneous polarization was about 10 ∼ μC/cm². The BTO-Co composite film’s in-plane magnetization-field hysteresis loop envisaged that the Co particles in the BTO matrix are ferromagnetic, with a remanent magnetization of about 70 emu/cm³. Large magnetodielectric effects of the BTO-Co film at room temperature were demonstrated by the marked shift in the relative dielectric permittivity. The close atomic-scale binding between the two constituent phases of the BTO-Co film was suggested to be responsible for the improved strain-mediated magnetoelectric coupling of the film.

On the other study, BTO was epitaxially grown as the matrix material on STO by pulsed laser deposition in the three-phase Au-Fe-BTO nanocomposite system. [10, 17, 20]. In the designs, Fe and Au were chosen to combine ferromagnetic Fe and plasmonic Au [6, 24]. Due to their biocompatibility and capacity to combine plasmonic and magnetic features, bimetallic nanoparticles of alloyed Au-Fe have garnered attention [6, 24]. Au and Fe are immiscible at equilibrium and do not alloy at any temperature, but the phase-separated Au-Fe nanoparticles became homogenous at higher Au: Fe ratios. [6, 24]. The deposition rate was used to control the thin-film’s growth kinetics in order to produce three-phase nanocomposite thin films with adjustable material and structural characteristics, lower laser frequencies resulted in less in number larger pillar dimensions [25]. The chosen laser frequency was 2, 5, and 10 Hz. The 2 Hz sample exhibited notable phase separation between the Au and Fe metallic phases in the BTO matrix due to slow deposition rate, which caused the Au to diffuse toward the top of the thin film, while the Fe diffused toward the bottom of the film [20]. On the other hand, the 5 and 10 Hz samples present a well-mixed, evenly distributed Au and Fe phases, with an average diameter of the Au and Fe nanoparticles of 18.7 nm for 5 Hz sample and 11.1 nm for the 10 Hz one. As the deposition rate increases, so did the amount of Au in the nanoparticles.

The increase of the deposition rate leads to a shift in the Au and Fe peaks to higher 2θ values and a broadening of the peaks in the X-ray diffraction θ-2θ pattern. Since both metallic phases are vertically connected in the BTO matrix, increasing 2θ values and wider peaks suggest that portions of the metal lattices may be under compressive out-of-plane strain. There was a peak splitting between the alloy peak and the Au peak when the Au: Fe ratio was less than 50% [26]. The percentage of Fe in the thin-film materials rose due to the higher deposition frequency; consequently, the metals’ compressive strain increased and the lattice parameter generally decreased. Additionally, there were minor variations in the BTO (002) peaks, suggesting that the metal nanostructures incorporated within may have an impact on the BTO matrix’s crystallinity.

Increased deposition rates resulted in thin-film materials that exhibit significantly greater variations in their in-plane and out-of-plane directions’ magnetic behavior or magnetic anisotropy. In the 2 Hz sample, the fully separated particles exhibited the smallest anisotropic magnetic response with the highest response at room temperature due to the nanocomposite’s spherically formed Fe nanoparticles. Anisotropy increased with increasing deposition rate. At low temperatures, the out-of-plane magnetic saturation also rose as the deposition rate decreased. Anisotropic magnetic behavior changed as a result of the increased Au content and alloying because the alloyed nanoparticles’ more rod-like form revealed greater shape anisotropy.

Due to the higher concentration of Au in the alloy and more vertically aligned Au-Fe nanostructures in the 5 Hz sample compared to the 2 and 10 Hz samples, the 5 Hz sample exhibits broad hyperbolic behavior. The hyperbolic wavelength appears to have been moved downward by the alloyed nanostructures; however, each film only exhibits hyperbolic behavior in the infrared. The lowest magnetic and optical anisotropy and distinct Au and Fe nanoparticles in the matrix are observed in the 2 Hz sample. In contrast, the 5 and 10 Hz samples produce higher magnetic and optical anisotropy and far more evenly alloyed Au-Fe nanostructures in the BTO matrix.

3. X-ray photoemission spectroscopy

Photoelectron spectroscopy is a technique, which has the ability to derive the chemical compositions of the studied material by detecting the signatures of all atomic species (with the exception of hydrogen). It also gives information on the chemical state of the constituents within a given system via the XPS chemical shifts [27], details of the local environment, and localization of emitting species. The surface sensitivity of this method owes to the relatively low value of the inelastic mean free path of the photoelectrons escaping from the sample [28]. The range for the inelastic means free path (λ) as function on the photoelectron kinetic energy (KE) is $\sim 4-5\AA$ for $\mathrm{KE}\sim 40-60\mathrm{eV}$ to $\sim 15-20\AA$ for $\mathrm{KE}\sim 1.2-1.5\mathrm{keV}$. The photoemitted intensity decays to $1/e$ of the initial value [18]:

$$I\left(E\right)=I_0\left(E\right)exp\left[-\frac{d}{\lambda \left(E\right)}\right]$$E1

with d the overlayer thickness, $I_0$ photoemission intensity for electrons of kinetic energy E. Therefore, $\sim 95\%$ of the photoemission signal comes from a layer with depth equal to $\sim 3\lambda \cong 1.5-6\mathit{nm}$ from the sample surface, with a dependence on the kinetic energy following a universal curve [29] with a minimum around $\sim 100\mathrm{eV}$.

The XPS method originates from the photoelectric effect applied to atomic inner shells (Figure 1). The principle of this technique [18] resides in a photon absorption with hν energy by an atom on an electronic shell characterized by a specific binding energy (BE) [27], resulting in a photoelectron emission with kinetic energy (KE) given by [18]:

Figure 1.

(a) A sketch of a photoelectron spectrometer X-ray radiation ionizes the sample, and the kinetic energies of the ejected electrons are recorded by the energy analyzer; (b) basic principle of an X-ray photoelectron spectroscopy; (c) origin of XPS core levels with different binding energies for a thin film deposited on a substrate.

$$E_k=\mathit{hv}–E_b-\mathrm{\Phi }$$E2

where $\mathit{hv}$ is the energy of incoming radiation, $E_b$ is the binding energy of the electron, and $\mathrm{\Phi }$ is the work function of electrons from the solid material ($2–7\mathrm{eV}$ [18]) equal with the difference between the vacuum level and the Fermi energy (Figure 1b).

The peaks of emitted photoelectrons, which give information about the BE/KE of all atoms from the sample, are the key physical parameters connected with:

1. The charge state of the atom by the so-called “chemical shift” with respect to its neutral phase (e.g., a positively ionized species displays higher binding energies than the same atomic species in a neutral state because it requires more energy than from a neutral [17, 30, 31] – see Figure 1c). These shifts help in differentiating the nature of the compounds formed in the sample when using comparing for examples with values included in various databases, such as NIST database. As can be seen in Figure 1c), the binding energies may further rely upon other factors such as the surface or bulk character of the emitting atoms, the interplay of the emitting atoms from a layer with the substrate atoms, or the appearance of the defects. These contributions reflect on the XPS spectrum, and they can be separated by “deconvolution” of the total signal. Additionally, comparing the line intensity rising from different atomic species, normalized by “atomic sensitivity factors” [32] is helpful in identifying the nature of chemical composition of a sample [14].

2. The electronic correlations within the atomic shells capable of generating shake-up/down satellites.

3. Elemental analysis and chemical compositions obtained by the comparison of the intensities corrected with “atomic sensitivity factors” possible due to atomic specific binding energies [14, 33, 34, 35].

Some conditions must be considered when an XPS analysis is performed: ultra-high vacuum (UHV) compatibility (not appropriate for example for biological matter) and cleanness of its surface, otherwise the electrons of interest from the material are attenuated by the contamination layer. For a deeper investigating of the atomic composition and chemical states, one can use cycles of ion sputtering to remove layers from the sample surface. Furthermore, XPS acquisitions at oblique emission increase the surface sensitivity, with a new $\lambda =\lambda \mathit{\text{cosθ}}$, where θ is the off-normal angle ($\theta =0$ for normal emission).

4. Photoemission studies of BaTiO₃ interfaces

The essential characteristic of photoemission spectroscopy resides in the element selectivity and depth sensitivity of core levels. These features are useful in determining stoichiometry, intermixing, and the presence of defects and impurities, which give critical information on the physical properties of heterostructures. Moreover, photoelectron spectroscopy is a powerful tool in probing the electronic signature of the buried interfaces, along with their evolution during film growth.

In addition to the chemical sensitivity, in the case of very thin interfaces of only a few lattice constants, photoemission experiments are better suited than transport measurements because they overcome high leakage currents, granting direct access of the interface electronic structure.

As an example, we consider the case of a thin ferroelectric BaTiO₃ (BTO) layer on top of La_0.6Sr_0.4MnO₃ (LSMO) [17], which leads to a hole-depleted state in the LSMO electrode in contact with the ferroelectric (FE). This state is seen in X-ray photoelectron spectroscopy through distinct energy separation between the bulk and interface regions of both Sr. 3d and La 3d surface core-level components (see Figure 2). More exactly, the interface component (Figure 2 green curve) features significantly smaller shift toward higher binding energies compared to the bulk component. This behavior is due to better screening of the electron core interaction in the FE-induced electron-enriched (hole depleted) interface state.

Figure 2.

Sr. 3d XPS spectra recorded on the two samples at normal incidence and at 60° (a) on bare LSMO and (b) on BTO-covered LSMO. La 3d XPS spectra recorded on the two samples at normal incidence and at 60° (c) on bare LSMO and (d) on BTO-covered LSMO. Reproduced with permission from ref. [17]. Copyright © 15 mar 2023 RNP/24/MAR/077036.

In Figure 3(a, b) one can observe the presence of oxygen vacancies near the BTO surface given by the smaller component at lower binding energies (Ti³⁺) [37]. The ratio between Ti⁴⁺ atoms and the reduced Ti³⁺ species, of about 0.1, represents a measure of the n-type doping in the ferroelectric layer [37], while the increase of the Ti³⁺/Ti⁴⁺ ratio in surface-sensitive measurements indicates that the oxygen vacancies accumulate rather at the surface, not at the interface. This is expected behavior for thin FE films with the direction of the polarization pointing downwards, toward the interface [21, 22, 38]. The higher binding energy component in Ba 3d assigned to surface-related emission points out the undercoordinated surface Ba atoms [39]. Other studies [40, 41, 42] also confirmed the screening charges pulled toward the interface from the ferromagnetic layer, resulting in hole depletion when the ferroelectric polarization points toward the interface and hole accumulation when ferroelectric polarization points away from the interface. These features reflect in the modulation of the electroresistance depending on the ferroelectric polarization direction [40] with applications in random access memories based on FE/FM tunnel junctions. Furthermore, depletion or accumulation of holes induced at the BTO/LSMO interface leads to changes in the orbital order when the FE polarization of the top layer is out of plane [17].

Figure 3.

XPS spectra of BTO recorded in the (a) Ti 2p and (b) Ba 3d spectral regions. Top spectra are recorded at normal incidence, and bottom ones are recorded with the samples tilted at 60° in order to separate the surface and bulk contributions. Spectra were fitted using Voigt profiles [36] with different inelastic background terms for each of the components characterized by the convolution of Gaussian and Lorentzian functions. This fitting procedure developed in IGOR software is ideal for performing curve fittings of the XPS experimental data and allows finding the parameters of interest with accuracy. Reproduced with permission from ref. [17]. Copyright © 15 mar 2023 RNP/24/MAR/077036.

Another important aspect in designing devices is understanding the mechanism of metal/FE interface formation. In this sense, Popescu and coworkers studied the impact on ferroelectricity and band alignment of Au grown on BTO (Figure 4) [21]. One can see the polarization signature in photoemission as shifts toward lower binding energies (LBE) for inwards orientation and as shifts with respect the Fermi level of the metal toward higher binding energies (HBE) for the other case. This shift also applies for valence band maximum [14, 17, 19]. So, besides extracting such signatures close to the surfaces, XPS method gives information about their corresponding interfaces with different electrodes. The shift toward HBE upon Au deposition indicates the stabilization of a polarization state pointing away from the surface (P⁺) [43]. When increasing Au thickness becomes observable a deviation from the expected stoichiometry ($r=O/\mathit{Ti}=3$) (Figure 4g) due to the oxygen vacancies in BTO (the release of mobile charges of 2e⁻/unit cell) [44]. The evolution of r with Au thickness also expresses the contribution of the intrinsic charge carriers when the depolarization field inside the ferroelectric BTO compensates.

Figure 4.

A sketch of Au/BTO system (a,b); Ba 3d (c) and Ti 2p (d) XPS spectra after successive Au deposition on BTO. Red symbols are experimental data, black lines are fits, and green and blue lines are individual components. (e) Ba 3d5/2 and (f) Ti 2p3/2 BE variations of different XPS components resulted from the fit of spectra recorded in (c,d) as function on the Au nominal thickness; (g) O/Ti ratio after successive Au deposition. Reproduced with permission from ref. [21]. Copyright © 15 mar 2023 5,750,091,203,508.

A similar study, on Cu/BTO system [22] revealed a rather intrinsic than extrinsic (as in the case of Au/BTO) compensation mechanism, until a $30\AA$ coverage, suggesting the accumulation of negative charges close to the interface and the transfer of free charges from BTO to the Cu clusters (Figure 5). At larger thicknesses, when the ratio of O/Ti recovers going up to oxygen excess (100 Å Cu), the compensation process becomes extrinsic as well. The outcome is that the screening of the out-of-plane ferroelectricity depends on positive charges (holes and ionized donors) leading to a p-self-doped regime [19].

Figure 5.

(a) Ba 3d and (b) Ti 2p XPS spectra after successive Cu deposition on BTO substrate. Red symbols represent the experimental data, black lines are the fits, and green and blue lines represent individual components. (c) Valence band maximum obtained with monochromatized Al K_α source when Cu is deposited. The red line represents the annealed surface prior metal deposition used to extract the Fermi level and to estimate the VBM (see the inset); (d) Cu 2p; evolution of binding energy of (e) Ba 3d_5/2, (f) Ti 2p_3/2, (g) Cu 2p components resulted from the fit of spectra recorded in (a), (b) and (d) as function on the Cu nominal thickness. (h) O/Ti ratio after successive Cu deposition. Reproduced with permission from ref. [22]. Copyright © 18 mar 2023 5,751,960,216,102.

Another illustration of XPS capabilities relates to the indication of the domain termination, as was the case of Bocirnea and co study [38]. For Ni/BTO some coexistence of BO₂ - and AO-terminated domains were observed. In addition, the XPS can also provide useful hints about the band bending in systems, which induce certain polarization states (Figure 6) [14, 21, 22].

Figure 6.

(a) Represents the band bending at an ideal ferroelectric surface with outwards (↑) polarization; (b) the similar case, for a ferroelectric with inwards (↓) polarization; (c) the way such polarization may be detected as distinct components in X-ray photoelectron spectroscopy. ${\mathrm{E}}_{\mathrm{CBm}}$ represents the energy of the conduction band minimum, ${\mathrm{E}}_{\mathrm{VBM}}$ the energy of the valence band maximum, ${\mathrm{E}}_{\mathrm{F}}$ the Fermi energy, ${\mathrm{\Phi }}_{\mathrm{FS}}$ the work function of the ferroelectric semiconductor, $\mathrm{P}$ the polarization (positive when pointing outwards), $\mathrm{\delta }$ the depth where one may find the polarization charge sheet, $\mathrm{\epsilon }$is the permittivity of the ferroelectric, and e the elementary charge. Reproduced with permission from ref. [14]. Copyright © 18 mar 2023 5,751,960,231,506.

5. Angle-resolved XPS – ARPES

Another variant of the photoemission spectroscopy technique is angle-resolved XPS (ARPES), which offers direct access to the electronic properties of a system (Figure 7). Measuring the kinetic energy and the emission angle distributions of the emitted photoelectrons, ARPES provide useful information about the carrier density at the Fermi level, and it can map the electronic band structure. Additionally, it gives information on the spectral function of a system and the topology of the reciprocal space. The hemispherical analyzers conventionally used in ARPES measurements can operate in the angle-resolved mode producing energy-momentum data along an extended cut in k-space within a single measurement. The manipulator allows a precise orientation of the sample at an arbitrary position and angle (polar angle $\phi$, tilt $\psi$, and azimuth $\theta$). Due to the small escape depth of the photoelectrons produces by ordinary UV light source, ARPES technique is limited to surfaces. A loss of 2–3 orders of magnitude in photoexcitation cross section appears when probing deeper into the bulk with soft or hard X-ray radiation, which can be overcome only by the use of high-brilliance X-ray sources such as in synchrotron radiation facilities. The ARPES mechanism can be, in a first approximation, described by a “one-step” process, where a “vertical” excitation of the electron from the valence band occurs with momentum conservation. Hence, the electrons excitation at constant wave number in the first Brillouin zone can be mapped via their energy-momentum (E–k) dispersion relations of the valence electrons.

Figure 7.

A sketch of angular resolved photoelectron spectroscopy; the incident beam with photon energy $\mathrm{hv}$ excites photoelectrons from a finite-size spot on the surface of the sample with the possibility of varying the angle. {x,y,z}&{x’,y’,z’} — Orthonormal positively orientated coordinate systems for the intrinsic coordinate system of the sample and for the laboratory coordinate system. The analyzer detects only electrons with momenta ${\mathrm{P}}_{\mathrm{e}-}=\left\{0,\text{ksinη},\text{kcosη}\right\}$ with $\mathrm{\eta }$ the analyzer angle between the electron momentum and analyzer axis and $\mathrm{k}=\sqrt{2{\mathrm{m}}_0{\mathrm{E}}_{\mathrm{k}}}/\mathrm{\hslash }$ the acceptance angle.

The equation that connects the wave vector of the photoelectrons in the vacuum k and their kinetic energy is [18]:

$$\mathrm{\hslash }\mathit{k}\mathbf{=}\left({\mathrm{\hslash }\mathit{k}}_{\mathbf{\parallel }},{\mathrm{\hslash }\mathit{k}}_{\mathbf{\perp }}\right)\mathbf{=}\left(\sqrt{2m_0{E}_k}\mathbf{·}\mathit{\text{sinθ}},\sqrt{2m_0{E}_k}·\mathit{\text{cosθ}}\right)$$E3

where $\mathit{k}=\sqrt{2m_0{E}_k}/\mathrm{\hslash }$, $m_0$ is the electron rest mass, ${\mathit{k}}_{\mathit{\parallel }}\mathit{,}{\mathit{k}}_{\mathit{\perp }}$ represent the surface parallel and normal components, $\theta$ is the electron takeoff angle with regard to the surface normal direction.

Considering the photoelectrons in the solid as free electrons (for an excitation energy $\mathit{hv}–E_b>10\mathrm{eV}$), the energy-momentum dispersion relation becomes [18]:

$$\mathit{hv}–E_b-\left(U-\mathrm{\Phi }\right)=\frac{{\left(\mathrm{\hslash }\left|\mathit{k}\right|\right)}^2}{2m^{\ast }}$$E4

where $U$ is internal potential which correlate with the bottom energy of the pseudo-parabolic dispersion regarding the vacuum level, $\mathit{k}$ and $m^{\ast }$ are the momentum and the effective mass of a photoelectron inside the sample [45].

We are interested in $\mathit{k}$, which preserves the initial state electron wave vector [18]:

$$\mathrm{\hslash }\mathit{k}=\left({\mathrm{\hslash }\mathit{k}}_{\parallel },{\mathrm{\hslash }\mathit{k}}_{\perp }\right)=\left({\mathrm{\hslash }\mathit{k}}_{\parallel },\sqrt{{\left({\mathrm{\hslash }\mathit{k}}_{\perp }\right)}^{\mathbf{2}}+\mathit{U}}\right)$$E5

The surface parallel component of the momentum can be directly determined from the ARPES spectra at different $\theta$ angles [18]:

$${\mathit{k}}_{\mathbf{\parallel }}\mathbf{=}\frac{\sqrt{2m_0{E}_k}}{\mathrm{\hslash }}\mathbf{\times }\mathit{\text{sinθ}}\approx 5\sqrt{E_k}\mathit{\text{sinθ}}\left[{\mathit{nm}}^{-1}\right]$$E6

$${\mathit{k}}_{\mathbf{\perp }}\mathbf{=}\frac{\sqrt{2m_0{E}_k+U}}{\mathrm{\hslash }}\mathbf{,}\theta =0$$E7

A limited number of ARPES measurements on BTO are available [46]. One of them was performed by Stefan Muff and coworkers [47]. They have shown the metallic states with a two-dimensional nature [48] that comes from the in-gap state (Figure 8) are attributed to the partially occupied Ti 3d states, split in the Ti 3d_xz and Ti 3d_yz orbitals due to the straind induced by the epitaxial growth, resulting in TiO₆ octahedral distortions [49]. The Fermi surface around the $\overline{\mathrm{\Gamma }}$ points feature spectral weight, elongated along both $\overline{\mathrm{\Gamma X}}$ directions (Figure 8a, d). On BTO no clear bulk dispersion can be noticed [46] as a direct consequence of the electric field present in the bulk of the film. Muff et al. suggested that the absence of energy dispersion of the states around the Fermi level relates to the Wannier-Stark localization (WSL) effect [47]. When growing 3 uc of STO on top of BTO (Figure 9d, e, f), ARPES display states similar to pure BTO (Figure 9a, b, c), used as an indication of the preserved ferroelectricity. A WSL character is present through stripes extending over several surface Brillouin zones on the Fermi surface. For larger STO film thickness, the electric field reduces, the smearing is smaller, and polaron replicas appear in the shallow electron pocket (Figure 9f) [50]. WSL is not visible when the surface has 5-uc of STO (Figure 9g, h, i). The electronic structure becomes similar with the one present in bulk STO, the electric field of BTO decay to a value that no longer influences the electronic properties at the sample surface. Then, the two-dimensional electron gas (2DEG) is a combination of d_xy states with small effective mass, m_eff and d_xz, and d_yz states with large m_eff (Figure 9h, i) [51].

Figure 8.

(a)–(c) constant energy surfaces of 20 uc of BTO grown on STO measured with hν = 80 eV for E_b = E_F (a), E_b = 150 meV (b), and E_b = 300 meV (c). (d)–(f) same as (a)–(c) for 20 uc BTO on KTO. (g)–(j) different ferroelectric domain configurations of the films and the corresponding WSL states for in-plane polarizations along ⟨100⟩ (g) and ⟨010⟩ (h) and out-of-plane polarization along ⟨001⟩ (i). (j) Combined WSL sta+tes from the three configurations with equal weight. Reproduced with permission from ref. [47]. Copyright © 15 mar 2023 RNP/24/MAR/077038.

Figure 9.

(a), (d), (g) Fermi surface, (b), (e), (h) band map at k_y = 0 Å⁻¹, and (c), (f), (i) two-dimensional curvature measured at hν = 82 eV. (a)–(c) for the 20-uc BTO film, (d)–(f) for a 3-uc STO film on top of 20 uc of BTO, and (g)–(i) for a 5-uc STO film on top of 20 uc of BTO. The arrows in (f) indicate the polaron replica. Reproduced with permission from ref. [47]. Copyright © 15 mar 2023 RNP/24/MAR/077038.

6. X-ray absorption spectroscopy (XAS: EXAFS and XANES)

As we have already pointed out in the XPS section, X-ray light with energy ranging from ∼500 to 500 keV (wavelengths from ∼25 to 0.25 $\AA$) is absorbed by the matter through photoelectric effect (see Figure 1b and Figure 10a). The binding energy of the participant’s electronic core level must be less than the incident X-ray energy so that the electron can be ejected with a finite kinetic energy. Basically, the X-ray is absorbed by an electron with certain binding energy, which is ejected from the atom and the resulting core hole is filled by an electron from another core level or from the valence band, accompanied by fluorescence or Auger electron emission. Unlike in the photoemission process, in the XAS technique, the resulting fluorescence or Auger electrons are measured.

Figure 10.

(a) The photoelectric effect, where a core-level electron is promoted out of the atom after an X-ray absorption; (b) decay of the excited state in the case of an X-ray fluorescence; (c) decay of the excited state for an auger effect; (d) X-ray absorption measurements where an incident beam of monochromatic X-ray source of intensity I₀ passes through a sample of thickness x and transmits a beam with intensity I (i.e. transmission mode) (i), fluorescence mode (ii) and electron yield (iii).

The most important parameter, when dealing with X-ray Absorption Spectroscopy (XAS), is the absorption coefficient $\mu$ given by Beer-Lambert law [52]:

$$I=I_0{e}^{-\mathit{\mu x}}$$E8

where I is the intensity transmitted through the sample, $I_0$ is the X-ray intensity incident on a sample, x is the sample thickness, $\mu \approx \frac{\rho Z^4}{A{E}^3}$ provide the probability that x-rays will be absorbed, $\rho$ is the sample density, Z is the atomic number, A is the atomic mass, and E is X-ray energy.

When the X-ray photon excites a core electron into unoccupied states in the sample (the incident X-ray has an energy equal to that of the binding energy of a core-level electron), there is an abrupt increase in the absorption (called absorption edge comparable with the promotion of this core level to the continuum). The coefficient $\mu \left(E\right)$ is important for XAS measurements, at and above the energy of a known core level of a specific atomic species. One can choose, which element to probe adjusting the X-ray energy to an appropriate absorption edge, which makes XAS an element-specific technique. This feature can be fully explored in combination with variable X-ray sources supplied by X-ray synchrotrons. The core levels electrons have well-defined binding energies, and the absorption edge energies are documented. The absorption spectrum of a material accommodates plenty of information about the electronic structure because the energy of the core-level electron depends on the existence of core-level spin-orbit coupling, atomic number, and the ionic or valence state of the atom [53, 54]. Usually, the absorption edges are indicated by letters (K, L, M, N, O, P) for the transitions from the levels with the atomic quantum number n (n = 1, 2, 3, 4, 5, 6). The electron transition is characterized by nl_s (l = s, p, d, f, g is the orbital quantum number, and s is the spin quantum number). A XAS spectrum contains different information connected to the dominant electronic contributions: the pre-edge region [55] corresponding to orbital hybridization between states of distinct orbital character, the edge or near-edge region employed in X-ray near-edge absorption spectroscopy [56] (XANES, particularly at K and L edges), and the extended energy range above the absorption edge used in extended X-ray absorption fine-structure (EXAFS) spectroscopy.

The edge energies differ as a function of the atomic number (∼Z²) and X-ray energies between 5 and 35 keV can probe almost all the elements. Both K and L edges can be handled in the hard X-ray regime, while M edges of heavy elements and L edges of transition metals are probed in the soft X-ray regime. When the absorption takes place, the atom is considered to be in an excited state having a core electron level empty and a generated photoelectron. In femtoseconds, the excited state will decay without altering the X-ray absorption process through two mechanisms: X-ray fluorescence (Figure 10b) and Auger effect (Figure 10c). In the first case, an X-ray with known energy is emitted when a higher energy electron core-level electron occupies the deeper core hole. The emitted fluorescence energies are used to identify the atoms in a sample and the concentrations. Auger effect appears when an electron drops from a higher electron level and a second electron is emitted, sometimes out of the sample. Both mechanisms offer information about the absorption coefficient μ. For energies >2 keV X-ray fluorescence is expected, and for lower energies Auger process prevails.

XAFS can be measured in either transmission $\left(\mu \left(E\right)x=ln\frac{I_0}{I}\right)$ (Figure 10d(i)) [57] or fluorescence/Auger emission $\left(\mu \left(E\right)\propto \frac{I_f}{I_0}\right)$ geometries (Figure 10d(ii)/(iii)), with $I_f$ is the monitored intensity of a fluorescence line/electron emission linked with the absorption process.

For the EXAFS the oscillations well above the absorption edge are important, which characterize the EXAFS fine-structure function $\chi \left(E\right)$ [58].

$$\chi \left(E\right)=\frac{\mu \left(E\right)x-{\mu }_0\left(E\right)x}{∆{\mu }_0\left(E\right)x}=\frac{\mu \left(E\right)-{\mu }_0\left(E\right)}{∆{\mu }_0\left(E\right)}$$E9

with $\mu \left(E\right)$ the measured absorption coefficient, ${\mu }_0\left(E\right)$ the absorption of an isolated atom, and $∆{\mu }_0\left(E\right)$ the measured jump in the absorption $\mu \left(E\right)$ at $E_0$ energy threshold (Figure 11).

Figure 11.

(a) Transitions that contribute to XAS edges; (b) example of Ni K absorption edge, with the three regions of the XAS data.

A better way to work in EXAFS is to consider the wave nature of the photoelectron originated in the absorption process, transforming the X-ray energy to k, the wave number of the photoelectron. It has the dimensions of 1/distance and is represented by $k=\sqrt{2m\left(E-E_0\right)}/\mathrm{\hslash }$, with $E_0$ the absorption edge energy and $m$ the electron mass. This leads to the EXAFS equation [58]:

$$\chi \left(k\right)=-S_0^2\sum _j\frac{N_j}{k{R}_j^2}{f}_j\left(k\right){\mathrm{e}}^{-2k^2{\sigma }_j^2}{\mathrm{e}}^{-\frac{2R_j}{\lambda \left(k\right)}}sin\left[2k{R}_j+{\varphi }_j\left(k\right)\right]$$E10

where $\chi \left(k\right)$ represents the oscillations as a function of photoelectron wave number, $S_0^2$ is an attenuation factor for EXAFS oscillations when considering the multiparticle effects, j is the number of the coordination layers around the absorbing atom, N_j is the number of neighboring atoms, R_j is the distance to the neighboring atom, with the mean square deviation ${\sigma }_j^2={⟨R_j-⟨R_j⟩⟩}^2$ of R_j (the distance to the neighboring atom) is the disorder in the neighbor distance, f_j(k) and ϕ_j(k) represents the scattering properties of the atoms neighboring the excited atom, and λ(k) the mean free path of electron between two inelastic collisions. Knowing the scattering amplitude f_j(k) and phase-shift ϕ_j(k), the EXAFS equation allows one to determine N_j, R_j, ${\sigma }_j^2$. Additionally, EXAFS is sensitive to the atomic species of the neighboring atom due to the Z dependence of the scattering factors.

The polarization of the electromagnetic wave may also influence the absorption process. When the circularly polarized light is used, the scattering process responds to the spin state of the core electron and to the presence of spin-asymmetries in the valence band (ferromagnetism). In the case of linearly polarized light, the response is connected with the asymmetric distributions in the electron charge density (anti/ferromagnetism and ferroelectricity). There are three ways of measuring XAS (Figure 10d):

• Direct measurements: Measuring the light transmitted across a specimen (Figure 10d(i)) [59].

• Measuring the intensity of secondary electrons—electron yield (Figure 10d(ii)), where the bulk of the signal comes from secondary electrons generated from de-excitation of high energy Auger electrons (Figure 10c).

• Measuring the intensity of photons emitted in the atomic transition to the ground state—fluorescence yield—Figure 10d(iii) probing a volume associated with the extinction length of the fluorescence X-rays in the material.

Most of the XAS studies for ABO₃ perovskites were on the TiO₆ octahedra responsible for their ferroelectric properties. The Ti K-edge XANES preserves certain features sensitive to the local symmetry and structural distortions [60]. Even if XANES of A-atoms is less informative, it was used to validate structure models, especially for solid solutions [61, 62, 63]. It is convenient as a reference point because it forms the sub-lattice that influences the unit cell of the perovskites.

In 1997, Ravel and co [64] presented XAFS data showing that the phase transition of BTO is predominant of the order-disorder type. They used XAFS to determine the local atomic configurations of BTO in a temperature range that covers all four structural and ferroelectric phases (rhombohedral, orthorhombic, tetragonal, and cubic). Temperature-dependent titanium K-edge XANES measurements were made on powder BTO samples in the fluorescence geometry using synchrotron radiation. The barium EXAFS results and XANES spectra indicate that the local displacement of the titanium atom in BTO is in a rhombohedral direction at all temperatures, and the order-disorder model explains the dominant nature of the local structure all through its phase transitions.

When depositing Fe on BTO, Radaelli et al. [42] indicated by XAS measurements the existence of an interfacial-oxidized iron layer corresponding to Fe atoms in chemical interaction with BTO. They focused on L₃ edge for higher intensity and a less critical background subtraction and found two components for Fe, corresponding to Fe metallic (707.4 eV) and oxidized Fe (Fe^m+ state at ∼709 eV). The obtained dichroic signal in correspondence of the L₃ Fe edge indicated a ferromagnetic (FM) order in the ultrathin Fe layer capped with 1 nm of Co. In Co–L_2,3 (Fe–L_2,3) spectra taken at room temperature on Au/Co/Fe/BTO capacitors with lower Co thickness (∼0.1 nm), Co is observed in stabilizing a non-oxidized and FM ultrathin Fe layer on BTO surface. When no capping Co is added, Fe islands of ∼2ML act as superparamagnetic particles presenting no remanent net magnetization at room temperature. From the XAS Fe–L_2,3 spectra taken at room temperature on Au/Co/Fe/BTO capacitors after polarizing BTO with V⁺ = +5 V (E = 170 kV cm⁻¹) (P_up), the presence of some net magnetization in the FeO_x layer is indicated. The dichroic signal of FeO_x suppresses for P_dn that induces the transition of FeO_x into either a nonmagnetic or an antiferromagnetic state and confirms the remanent magnetization of the FeO_x in P_up case. The validation of the relationship between the magnetic switching and dielectric polarization is given by XAS measurements after the samples depolarization, and it shows as negligible differences of XMCD between P_up and P_dn. XMCD confirmed that the magnetization of the interfacial FeO_x can be electrically switched on and off by switching the polarization of BTO. The average unmodified XAS line shape upon polarization reversal supports the appearance of the magnetization switching at FeO_x layer without notable modifications of the oxidation state within the Fe film. This was a new magnetoelectric coupling mechanism, where only the magnetic ordering of interfacial Fe atoms is affected, while “bulk” metallic Fe atoms maintain their FM behavior.

A study focused on the local structure of the A atom in ABO₃ perovskites was conducted by Anspoksa et al. [65]. They used the combination of reverse Monte Carlo and evolutionary algorithm [66] to reconstruct the structure of BTO using the Ba K-edge EXAFS spectra acquired in a wide temperature range covering the most interesting structural phases. They showed that BTO has strong Ba-Ti correlations, with A ion playing an active role in formation of ferroelectric and other ferroic phases.

7. Conclusions

The full electronic structure of the surfaces and buried interfaces can be accessed using widely used techniques, such as X-ray absorption and photoelectron spectroscopy, which provide complementary information on both the occupied and empty states. Unlike XPS, which probes the occupied density of states by ejecting electrons from occupied states into the continuum, XAS relies on measuring the signal corresponding to dipole-allowed transition, hence shining light on the exploration of unoccupied states. We explored some of the results obtained by using XPS and XAS techniques to analyze and characterize interfacial processes in BaTiO₃ systems, highlighting their potential in disclosing the fundamental electronic structure and the functionality of BTO-based nanocomposites. Specifically, we concentrated on the nanocomposites studies with a metal-ceramic type composite film Co-BTO, and we showed how a three-phase system composed of BTO with two immiscible metals, Au and Fe can be well-mixed resulting in Au-Fe alloy pillars. Using x-ray photoelectron spectroscopy, the effects of the bonding mechanism and band alignment in a ferroelectric BTO/LSMO heterostructure were also envisaged, followed by a comprehensive study of metal/BTO interfaces.

Acknowledgments

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P1-1.1-TE-2021-0136, within PNCDI III and Core Program - Component Project 2 No. PN23080202, funded by the Romanian Ministry of Research, Innovation and Digitization. The fee for open access publication was supported from the project 35PFE, funded by the Romanian Ministry of Research, Innovation and Digitization.