Understanding structures at the nano and atomic scales is essential for managing the properties of thin films. The optoelectronic and mechanical properties of thin films are strongly affected by their structural characteristics, including the film thickness and shape, and the size of the embedded nanostructures. Crystalline properties, such as crystallinity, domain size, and domain orientations, as well as chemical compositions, are fundamental information for controlling the physical and chemical behaviors of thin-film systems. In a thin-film system, the role of the surface and interface is important for understanding the changes in material properties. Recently, it has become necessary to understand the changes in materials under in situ operando conditions according to external environmental stimuli such as heat treatment, electric bias, pressure, and electromagnetic wave irradiation. Because changes in the crystalline and material properties of thin films must be closely monitored, X-rays have become a powerful tool to non-invasively measure these changes at the atomic scale.

X-rays,which are electromagnetic waves of several keV, interact with the scattering or absorption of electrons in an atom. The energy of X-rays is as high as a few tens of keV, corresponding to the binding energies of the k-shell electrons of the elements. Therefore, we can simply assume that, if not in resonance, all the electrons are free electrons. However, the scattering length of an electron is too small (~10⁻¹⁵ m, Thomson scattering length) to observe the scattering signals, unless collective scattering, such as diffraction or weak scattering signals under high-flux X-rays are present.

The wavelength of X-rays is a few Å, which is the order of magnitude of atom-atom distances in a unit cell of the crystal structure. Therefore, we can observe a strong Bragg X-ray scattering signal for a crystalline film composed of periodically ordered atoms. That is, the collective elastic scattering intensities (Bragg signals) of X-rays are a function of the correlation lengths of the electron densities. Figure 1(a) shows a schematic diagram of X-ray scattering divided into two regimes, small and wide-angle, by the scattering angle 2θ. We can investigate the momentum transfer Q by measuring the X-rays scattered by a sample, where Q is a function of the inverse lengths constituting the scattering system, as shown in Fig. 1(b). Figure 1(b) shows a schematic representation of the relationship between the scattering angle and the size of the material system, this includes, in the smallangle regime, inter-nano structures such as sizes and distributions of nanoparticles or thin film thickness, and in the wide-angle regime, inter-atomic structures such as lattice parameters of a unit cell.

Figure 1. (a) Schematic view of X-ray scattering. The wavevectors of the incident and scattered X-rays are ${\overrightarrow{k}}_i$ and ${\overrightarrow{k}}_f$, respectively. In most cases, elastic scattering occurs while keeping the magnitude of the scattering wavevector equal to that of the incidence wave vector, as shown in the inset figure. Momentum transfer of X-rays is defined as $\overrightarrow{Q}$ = ${\overrightarrow{k}}_f$ − ${\overrightarrow{k}}_i$ , and if two wavevectors exist in the x-z plane (scattering plane), $\overrightarrow{Q}$ = $2{\overrightarrow{k}}_z$. Actually, $\overrightarrow{Q}$ is the wavevector transfer since the momentum of photon is defined as $\hslash \overrightarrow{k}$, however we can ignore the constant $\hslash$ and consider the wavevector transfer as the momentum transfer (as a physical quantity). (b) Scattering angle related to correlated lengths of scatterers such as nano-structures and atomic structures.

The X-ray intensity from a lab source is not sufficient for obtaining scattering signals from thin films because of the relatively small scattering volume. In addition, the X-ray energies should be varied for elemental-sensitive scattering or fluorescence signals of thin films. Various in situ and operando experiments are crucial for understanding the device’s performance in real situations. Synchrotron (SR) Xrays are very bright and collimated within a few tens of microns, enabling numerous types of in situ experiments with high resolutions in reciprocal space and time. For elemental discrimination, we could easily tune the SR X-ray energies for anomalous X-ray scattering and X-ray absorption experiments.

In this study, we focus on the basic information for SR X-ray experiments of thin-film systems: X-ray reflectivity-Total reflection X-ray fluorescence (XRR-TXRF), grazing incidence wide-angle X-ray scattering (GIWAXS), and 3-dimensional reciprocal space mapping (3D RSM). X-ray signals near the critical angle are important because we can obtain depth-dependent information on thin-film systems. Therefore, we introduce TXRF combined with X-ray reflectivity, which is a powerful method for thin-film characterization [1–4]. GIWAXS is also a key analysis technique for obtaining crystalline features within thin films [5–7]. In addition, 3D RSM of a Bragg signal is briefly presented, which can show phenomena related to defects such as grain boundaries in thin-film systems [8–10].

2-1. Reflectivity

X-ray reflectivity does not measure atoms individually but rather measures the overall electron density distribution of a film in the vertical direction. X-rays are reflected from the interfaces of different electron densities, and the reflection follows Snell’s law. Therefore, X-ray reflectivity is a function of electron density along the surface normal direction expressed in Eq. (1), and it provides information on the film thickness, density, and roughness of the surface and interfaces of a film [11]. Because the X-ray wavelength is of a few Å, the reflectivity can vary with changes in thickness and roughness on the Å scale, allowing high spatial resolution analysis of atomic structures. In Eq. (1), q_z and ρ(z) are the momentum transfer and 1-dimensional electron density along the surface normal direction, respectively.

Figure 2 shows the schematic and simulated reflectivity patterns when X-rays are incident on a thick substrate at angles as low as θ ~ 0.1 − 5°. As shown in Fig. 2(a), reflection, refraction, and absorption occur at the interface between two different media, similar to other electromagnetic waves. These phenomena are described by the refractive index (n) of the medium, which is less than one in the X-ray domain. The refractive index is expressed in Eq. (2), where δ is phaserelated and β is the absorption-related term. Equations (3) and (4) show the relationship of two terms (δ, β) and the atomic form factors of consisting elements of a thin film, where λ is the incident X-ray wavelength, r_e = 2.82 × 10⁻¹⁵ m is the Thomson scattering length, ρ_e is the electron density, $f_j^0$ is the j-th atomic form factor at 2θ = 0, $f_j^{\text{'}}(E)$ is the j-th anomalous atomic form factor, Z is the atomic number, $f_j^{\text{'}\text{'}}(E)$ is the imaginary part of the atomic form factor, and µ is the linear absorption coefficient. The refractive index, n, is related to the scattering length density (SLD), as shown in Eq. (5) [11].

Figure 2. (a) X-ray reflection, refraction, and absorption when X-rays of wavevector ${\overrightarrow{k}}_i$ incident on the surface of a thick substrate. n₀ and n₁ are refractive indices of air and substrate, respectively, and σ is the surface roughness of the substrate. Reflection occurs when θ_i = θ_f, and refraction follows Snell’s law as explained in the text. Additionally, photoelectrons (PE), fluorescence (FL), and heat are generated when incident X-rays are absorbed by the medium. (b) Calculated (left) X-ray reflectivity patterns and (right) SLD (scattering length density) profiles of a thick LaAlO₃ substrate. The X-ray energy was set to 10 keV and the roughness of the surface was set to 0 (black) and 3 Å (red). (c) Reflection of a single slab. n₀, n₁ and n_∞ are refractive indices of air, slab, and substrate, respectively. σ₁ and σ_∞ are roughness between air and slab, and between slab and substrate, respectively. (d) Calculated X-ray reflectivity patterns of SrTiO₃(10 nm)/LaAlO₃ systems. Two films have surface roughness with σ₁ = 3 and 7 Å, and all σ_∞ are fixed at 3 Å. And two X-ray energies are considered to see the anomalous effect on δ (density-related value) of SrTiO₃ film. One at 10 keV (black, red) and the other at 16.2 keV (blue), slightly above the Sr K absorption edge. (Left) Calculated reflectivity patterns and (right) SLD profiles. In SLD profiles, * indicates LaAlO₃. All reflectivity patterns were calculated using the Refnx program [13].

From Snell’s law [Eq. (6)] and the boundary conditions, the Fresnel equation for X-ray reflectivity (r) and transmittivity (t, refraction) are derived as shown in Eq. (7), where n0 is the refractive index in vacuum, n1 is the refractive index of medium 1, θ_i is the incident angle, and θt is the refracted angle in radians [12]. The absorption of X-rays near resonant conditions is greatly increased, resulting in energetic photoelectrons, heat, and characteristic fluorescence. However, characteristic fluorescence is usually negligible under non-resonant conditions. We measure the reflectivity of a flat sample during specular reflection, which is when the angles of the incidence and the reflection of the X-rays are kept the same, as shown in Fig. 1(a) inset. Specular reflection is different from diffuse scattering, which is caused when electron density fluctuations deviate from the average z position of an interface.

Figure 2(b) shows the calculated reflectivity of a thick LaAlO₃ substrate and the SLD with a roughness of σ = 0 Å (black line) and σ = 3 Å (red) [13]. As previously mentioned, the refractive index n of the medium is less than 1 in the X-ray domain and the n of air (vacuum) is 1. Therefore, X-rays can be reflected at a certain angle when they are incident on the surface of a material from the air at a certain incident angle, defined as the critical angle θ_c. The critical angle is a function of the electron density of the medium and is approximated as θ_c = $\sqrt{2\delta }$. The surface roughness lowers the overall intensities of the reflectivity pattern with $q_z^{-4}$ dependence on σ = 0, as shown in Fig. 2(b) left. The SLD changed from abrupt to continuous at the interface as the roughness increased from 0 to 3 Å in Fig. 2(b) right.

In the caseof a single slab, X-rays were reflected at the surface and interface, and two reflected X-rays interfered with each other, as shown in Fig. 2(c). As a result of the interference, the Kiessig fringe, which is the oscillation of the intensity with respect to the scattering angle, appeared in the X-ray reflectivity data, and the oscillation period was determined by the slab thickness. The reflectance of a single slab is expressed by Eq. (8), where r₀₁ and r_1∞ are the reflectivity amplitudes at the top surface of the slab and the interface between the slab and the thick substrate, respectively. The phase term p² is expressed by exp(q₁d), where q₁ is the wave vector transfer in the slab and d is the thickness of the slab [12].

Figure 2(d) shows the calculated reflectivity patterns and corresponding SLD profiles of the SrTiO₃(10 nm)/LaAlO₃ systems under three different conditions. The first two cases show different surface roughness values, and the last case shows different X-ray energies. The film thickness can be obtained in the kinematic approximation region, that is, $q>3q_c$, using the relation $\Delta q=2\pi /d$.

To understand the effect of surface roughness, we assumed two films with different surface roughness of 3 and 7 Å and assumed an X-ray reflectivity measurement of 10 keV. The data show that the intensity decreased significantly as q increased on a rougher surface than on a flat surface. For the 3 Å surface roughness case, we assumed that the X-ray reflectivity measurement of 16.2 keV was comparable with the 10 keV data. The 16.2 keV X-ray reflectivity measurement was slightly higher than the Sr K absorption edge at 16.10 keV. As shown in the blue curve of Fig. 2(d) left, the oscillation amplitude increases at 16.2 KeV compared with the black data of 10 keV. This increased amplitude is the resonant effect of the X-rays at 16.2 KeV caused by the Sr atoms. The amplitude of the oscillation is proportional to the difference in the electron density between the slab and substrate. In addition, the resonant effect also increased the oscillation amplitude, as shown in the 16.2 keV data in Fig. 2(d) left. Therefore, elementdependent information was obtained by tuning the X-ray energy to the X-ray reflectivity measurements.

All layered film systems can be modeled as homogeneous N layers using Parratt’s approach, as shown in Fig. 3(a). In this model, we assume N homogenous layers with two boundary conditions: air and an infinitely thick substrate layer [14]. The reflectivity can be calculated recursively from the reflection amplitude of the previous layer, starting with the reflectivity of the N-th layer directly above the thick substrate, where no multiple scattering in the substrate, the (N + 1)-th layer, is assumed. This approach counts all refractions and scattering in each layer of the medium, resulting in multiple scattering events. Consequently, this method provided a reliable solution for fitting the critical angle. Reflectivity is the square of X-rays, that is, electromagnetic waves, and phase information cannot be obtained from the reflectivity data. Therefore, various solutions are possible in a one-dimensional electron density distribution. Moreover, to obtain the correct solution, it is necessary to specify parameters within a certain range before starting the data fitting using Parrat’s formula.

Figure 3. (a) Parratt’s approach. n_j is the refractive index of the j-th layer, where n₀ is for air and n_N+1 is for the thick substrate. The first calculation starts at the interface between the N-th layer and substrate, where a multiple scattering within the substrate can be assumed to be zero due to its sufficient thickness. From the Fresnel reflectivity (R_N) and transmittivity (T_N) at z=Z_N where the interface between the N-th layer and the substrate lies, finally

Figure 3(b) shows the calculated reflectivity and corresponding SLD of a Pt(50 Å)/Ni(50 Å) bilayer on a c-cut sapphire substrate. There are complicated oscillations originating from bilayer structures, and it is easy to recognize that the shortest period of oscillation corresponds to the total film thickness of the bilayer, which is approximately 100 Å. Before a reflectivity fit, a robust estimation of the layer thicknesses is possible by obtaining a Fourier transform of the normalized reflectivity.

Tran et al. [1] measured anomalous X-ray reflectivity patterns to understand the alloying mechanism of PtNi bilayers during thermal annealing. They prepared PtNi bilayers on a c-cut sapphire substrate by e-beam evaporation and then measured reflectivity data at X-ray energies near the Ni K absorption edge to enhance signals from Ni atoms in the film. As the temperature increased, the Ni atoms in the bottom Ni layers moved toward the Pt layer, forming an intermediate alloying layer.

X-ray evanescent waves were formed under the condition of total external reflection. X-rays traveled along the surface and penetrated the medium, and the X-ray penetration depth ξ was determined by the angles of incidence and total external reflection, as described in Eq. (9). Figure 4(a) shows the evanescent wave at θ ≤ θ_c, and the penetration depth is defined as the position at which the evanescent wave intensity became 1/3 of the intensity at the surface. The penetration depth increases from a few to thousands of nanometers with respect to the incident angles, as shown in Fig. 4(b), then we can investigate depth-dependent crystalline properties and compositional information. Figure 4(c) shows a schematic diagram of the TXRF setup. At incident X-rays slightly higher than the absorption edge of the element to be probed, the fluorescence signals of the element were enhanced, and the signal was proportional to the intensity of the penetrated evanescent wave.

Surface segregation of cations has been an important issue for solid oxide fuel cell cathode materials at operating temperatures. In 2016, Yu et al. [3] investigated Sr segregation in strontium-doped lanthanum cobalt ferrite films with various Sr contents using TXRF. They prepared two types of samples, as-deposited and post-annealed, to observe Sr segregation after annealing. Consequently, Sr segregation was observed in the surface region (~ 10 nm) after post-annealing, and Sr segregation occurred as the Sr content increased in the films [3].

2-2. GIWAXS

Investigating GIWAXS is valuable for observing the crystalline properties of polycrystalline thin films. In GIWAXS, the X-ray incident angle is small and close to the critical angle, and widely scattered Xrays are measured using a two-dimensional (2D) detector. It is a powerful method, especially for organic materials or very thin films, because the scattering volume increases owing to the long optical path of X-rays at a small grazing incident angle. Using the same analogy as TXRF, we can investigate the depth-dependent crystal structure by changing the X-ray incident angle. Figure 5 depicts a general scheme of the GIWAXS setup: the incident angles of the X-ray are set within 0.5θ_c ≤ θ ≤ 3θ_c and the sample-to-detector distance (SDD) is close to approximately 300 mm to measure the scattering signal over wide angles. It is worth noting that high collimation with a few hundreds of micron-sized beams is necessary because the illumination area increases significantly at the grazing angle, and fine tuning of the incident angles is important to determine the penetration depth of X-rays. As shown in Fig. 5, the detector pixels assigned to y and z in real space can be converted into q values in the reciprocal space of q_y (or q_∥) and q_z, respectively.

The preferred orientations with respect to the azimuthal angles can be observed using GIWAXS, as shown in Fig. 6. The left two-column images show the schematic view of GIWAXS for a Debye ring of a Bragg peak and the corresponding crystal domain orientations. For randomly oriented crystal domains, the color of the Debye ring was uniform, indicating that the Bragg peak intensities did not change along the circle. If the preferred orientations of the domains existed with a random distribution, there were bright spots in the Debye ring, indicating the preferential ordering of crystals. Finally, only one spot was shown for the crystal domains perfectly aligned along one azimuthal angle, as shown at the bottom of Fig. 6(a). As shown in the schematic, the Debye ring had some width along $q_r(=\sqrt{q_y^2+q_z^2})$ because of the broadened illumination area of the incident X-rays. The right column images show the (100) Debye rings of Cs-rich (FA,MA) Pb(I,Br)₃ perovskite films with additives. In this case, the X-ray incident angle was slightly smaller than the critical angles of the films, indicating that the X-ray signals originated mainly from the surface region of the film. The analysis results of the 2D data were in good agreement with the characteristics of the (100) crystal domain orientations, as previously described.

Yoon et al. [5] investigated the effect of the alkyl chain length of various alkylamine ligands (AALs) on the preferred orientations of organometallic perovskite films in depth by measuring GIWAXS at different X-ray incident angles. Figure 7 shows the azimuthal line profiles of the (100) Debye rings in the GIWAXS patterns of the Cs-rich (FA,MA)Pb(I, Br)3 with BA, OA, OAm, and without AALs. They concluded that longer AALs were effective for the alignment of the (100) domains along the surface normal direction. The longer alkyl chain AALs mole-cule effect was more clearly observed in the surface region than in the bulk region, which seemed to be related to the movement of AAL molecules to the surface region during solvent evaporation.

2-3. 3D RSM

A material system is defined by the atomic density distribution of its elements. The atomic density distribution can be simply assumed to be the electron density distribution when considering the interaction between the matter and X-rays. The X-ray scattering intensity is the Fourier transform of the autocorrelation function of electron density in real space, which is a function of 2π/r (r, correlation length) in reciprocal space. For crystal structures, which are a set of unit cells, strong Bragg diffraction occurs when the Laue condition, a selection rule determined by the space group for the crystal, is met. Typically, we measured the one-dimensional (1D) pattern around the Bragg diffraction signal by scanning along the arc of the Edwald sphere using a point detector, as shown in Fig. 8(a). From a 1D sectioned pattern of a 3D Bragg signal in reciprocal space, it is possible to obtain limited information in the scanned direction, such as peak width, diffuse elongation along only the scanned direction, and approximated integrated diffraction.

2D RSM is a decisive method for evaluating the strained status of the film by the substrate. 2D RSM is generally measured using a point detector, but it is very time consuming, especially if it is very thin or has low crystallinity. Recently, 2D X-ray detectors with high spatial and time resolutions, as well as a wide dynamic range in intensity, have become possible, opening the door to 3D visualization of reciprocal spaces. Figure 8(b) shows the schematic of the 3D RSM setup. A 3D RSM can be obtained by obtaining 2D scattering images rocking the incident angle around the Bragg angle with a fixed 2D detector at the scattering angle to be measured.

By analyzing the 3D RSM of a Bragg peak, it is possible to investigate crystal domains along specific directions such as in-plane axes compared to those of substrates, anisotropic diffuse signals due to thermal vibrations, and 3D defect distributions. Ha et el. investigated the role of defects in the metal-insulator transition (MIT) of VO₂ thin films grown on c-cut sapphire substrates using 3D RSM at various temperatures [8]. They confirmed diffuse peaks originating from rutile-like defects separating the monoclinic ordered domains and their behavior in reciprocal space during heating near MIT. The analysis of 3D scattering signals provided two pre-transition states in the structural phase transition near MIT, where two different signals from monoclinic ordering and planar rutile-like defects were treated separately in a 3D reciprocal space.

In this study, we introduced SR-based X-ray experiments with brief explanations of thin-film characterization. Highly bright, collimated, and energy-tunable SR X-rays provided various X-ray techniques, such as XRR, TXRF, GIWAXS, and 3D RSM, with high spatial and time resolution. In addition, in situ real-time changes in films were observed using SR X-rays under external stimuli, such as heat, pressure, mechanical stress, electrical bias, and electromagnetic irradiation. Owing to these advantages, the application field of SR X-rays is increasing, allowing the development of new materials and elucidating the mechanisms of physical and chemical changes in materials.

The authors declare no conflicts of interest.