Nanometer-Sized Crystalline Clusters of IGZO Films Determined from the Grazing Incidence X-ray Scattering and Anomalous X-ray Scattering Data Combined with Reverse Monte Carlo Simulations

Abstract

Grazing incidence X-ray scattering measurements have been carried out on c-axis aligned crystalline-indium gallium zinc oxide (CAAC-IGZO) film and nanocrystalline category-indium gallium zinc oxide (NC-IGZO) film and the following results were obtained: (1) the characteristic layered structure of the IGZO crystal did not hold its shape and the X-ray scattering profile showed only a relatively sharp first peak at the wave vector (Q) = 21.8 for CAAC film and 23.1 nm⁻¹ for NC film, respectively, and additional weak broad peaks were observed at a higher angle. (2) In the case of the CAAC film, tiny peaks were observed at Q = 7 and 14 nm⁻¹, corresponding to the positions of the 003 and 006 reflections, respectively, of the IGZO crystal. Such tiny peaks were not detected in the case of NC film but the asymmetry of the first peak at the low angle side was clearly observed. (3) These structural features implied that more than three polyhedral units, such as InO_x (x = 4–6), GaO_y (y = 4–6), and ZnO_z (z = 4–6), were likely to coexist. It is appropriate to call this structural feature as cluster-1. (4) A composite-type structure formed by combining these polyhedral units is also likely to exist and leads to middle-range ordering. This structure is called cluster-2. The size of such cluster-2 has been estimated to be 2.2 nm for CAAC film and 1.8 nm for NC film using the measured pair distribution function. To gain insights into the structural features of IGZO films, realistic atomic-scale models were obtained to fit not only the ordinary interference function of grazing incidence X-ray scattering but also the environmental interference function of the anomalous X-ray scattering (AXS) with Zn-absorption edge using reverse Monte Carlo (RMC) simulation. (5) The resultant models indicated the complex and irregular atomic arrangements of two types of IGZO films, which are well characterized by nanometer-sized crystalline clusters. This characteristic feature may be referred to as crystalline–cluster–composite (triple C) structure.

1. Introduction

Indium gallium zinc oxide (IGZO) thin films, which are a quaternary system of In, Ga, Zn, and O, are widely used for electronic devices, such as energy-saving displays for smartphones and tablets. Hosono et al.^1–4) published several reports based on the amorphous IGZO films. On the other hand, a new type of IGZO film has been reported, which is crystalline rather than amorphous, based on cross-sectional transmission electron microscopy (TEM). The c-axis is preferentially aligned perpendicular to the film surface but no orientation has yet been confirmed for the a–b plane. Clear grain boundaries have also not been detected. This new IGZO film is called c-axis-aligned crystalline (CAAC) IGZO film.⁵⁾ Depending on the deposition conditions, the crystalline nature is less noticeable; in this case, the IGZO film is assigned to the nanocrystalline category (NC) film⁶⁾ because discrete spots suggesting crystalline features can be observed while applying nano-beam electron diffraction. This result contrasts the halo diffraction pattern, which usually represents the non-crystalline systems. Thus, crystalline features are likely to be essential for the characterization of the structure of both CAAC and NC films, although their periodicity shows a further reduction. Based on these new results, Sharp Co. Ltd. started the commercial mass production of IGZO-FTE in 2012. The growing technological importance of IGZO films has led to an increase in the need to understand their properties, especially the origin of the discrete spots detected in both CAAC and NC films and if NC film is analogous to amorphous IGZO.^7–9) Therefore, quantitative structural analysis of CAAC and NC films is strongly required.

This study aims to report the structural features of two IGZO films that are determined using grazing incidence X-ray scattering and anomalous X-ray scattering (AXS) data combined with reverse Monte Carlo (RMC) simulations. Based on data processing including AXS measurements, the fine structures of both amorphous and crystalline materials could be obtained at various states.^10,11) Thus, this approach prompts us to apply a rather complex structure, including both polyhedral units and middle-range ordering, to the existing multi-component (In–Ga–Zn–O) system.

2. Experimental Procedures

2.1 Preparation of IGZO thin films

Samples of IGZO thin film were deposited on a silica glass substrate through DC sputtering using a polycrystalline InGaZnO₄ target prepared from In₂O₃, Ga₂O₃, and ZnO with approximately the same proportions. The film deposition was carried out by SEL Co. Ltd. The conditions for the sample preparation and thickness and density of the resultant films obtained by X-ray reflectivity measurements, including the critical angle, are listed in Table 1. Note that a structural study was performed by cutting out a sample with dimension 30 × 40 mm from a large deposited plate.

Table 1 Sample preparation conditions (*) Deposition condition: 100 nm × 5 steps (+); Deposition condition: 111 nm × 9 steps. The density was estimated from the critical angle of the X-ray reflectivity measurement.

2.2 Grazing incidence X-ray scattering measurements

Grazing incidence X-ray scattering measurements on the films were carried out using a multipurpose, fully automatic X-ray diffractometer at 40 kV and 30 mA and a scintillation counter (RIGAKU-SmartLab). The incident X-ray beam produced from a fine-focused copper, sealed X-ray tube was monochromatized and collimated by a Goebel mirror. In this method, the monochromatic X-rays are incident on a sample surface at glancing angles of less than one degree. Based on the preliminary experiments, the X-ray scattering intensity pattern from a single thin film was obtained using the out-of-plane mode and setting the incident angle and the slit width to 0.5° and 0.20 mm, respectively. To evaluate the density of the thin film, a critical-angle measurement was performed with the same diffractometer. In this case, the incident X-rays were monochromatized and collimated by a channel-cut Ge (110) crystal with an angular resolution of ∼0.0033°.

The X-ray scattering intensity I_mes(Q) measured on a sample as a function of the scattering angle 2θ in arbitrary units may be expressed with the following equation:¹²⁾   

\begin{equation} I_{\textit{mes}}(Q) = \mathit{PAC}[I_{\textit{coh}}(Q) + I_{\textit{inc}}(Q)], \end{equation} (1)

where P is the polarization factor, A is the absorption factor, C is the apparatus factor, and I_coh(Q) and I_inc(Q) are the coherent and incoherent scattering intensities in electron units, respectively. We also used the wave vector Q = 4π sin θ/λ based on the wavelength λ. After making corrections for P, A, and C, the coherent scattering intensity I_coh(Q) can be estimated using the normalization process to convert the measured law data into electron units. The Krogh–Moe–Norman method is the most frequently used for such a normalization process.¹²⁾ The reduced interference function Qi(Q) can then be given as:   

\begin{equation} Qi(Q) = Q[I_{\textit{coh}}(Q) - \langle f^{2}\rangle]/\langle f\rangle^{2}. \end{equation} (2)

If the atomic scattering factor for atom j and its atomic fraction are given by f_j and c_j, the average atomic scattering factor and its mean-square value are expressed as $\langle f \rangle = \sum_{j = 1}^{n}c_{j}f_{j} $ and $\langle f^{2} \rangle = \sum_{j = 1}^{n}c_{j}f_{j}^{2} $, respectively. Here, the brackets denote the statistical average. The radial distribution function (RDF) 4πr²ρ(r) of a substance of interest can be obtained with the following Fourier transformation:¹²⁾   

\begin{align} 4\pi r^{2}\rho (r)& = 4\pi r^{2}\rho_{\text{o}}g(r) \\ &= 4\pi r^{2}\rho_{\text{o}} + \frac{2r}{\pi}\int_{0}^{\infty}Qi(Q)\sin QrdQ \end{align} (3)

where ρ(r), ρ_o, and g(r) are the radial density function, average number density, and pair distribution function, respectively.

It may be noteworthy that the reliable structural information for systems of less noticeable crystalline nature can be obtained, because the truncating effect is not so serious, when the experimental data are available in the wave vector region up to about Q = 80 nm⁻¹ and the ghosts arising mainly from the truncating effect are relatively easy to trace, as their positions are functions of the upper limit of Fourier integration of eq. (3).¹²⁾

2.3 Anomalous X-ray scattering (AXS) measurements

The AXS measurements were carried out at a beamline (7C station) of the Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Japan. The sample was mounted on a double-axis goniometer (KOZU RST6K/KHI-4) that was placed vertically to eliminate the polarization effect. The intensity of the incident beam was monitored by a nitrogen gas flow-type ion chamber placed in front of the sample. The scattered intensities were obtained by a portable intrinsic Ge solid state detector (IGRET, EG&G Ortec, USA). The measured intensity was then converted to intensity in counts per photon by dividing the total number of estimated photons by the total monitor counts. Other details of the AXS measurements are almost identical to those described in the previous studies.^13,14)

Since IGZO is a quaternary system of In–Ga–Zn–O, the measured scattering intensity only provides average information of 4 × (4 + 1)/2 = 10 partial pair correlations. The results are not sufficient to allow definite structural characterization. Therefore, the use of AXS measurements with two energies close to the absorption edge of one of the constituent elements is a useful way to solve such difficulties by permitting the environmental structure around a specific element in a system of interest. For example, when choosing two energies close to the Zn-K absorption edge and simply subtracting the intensities, the resultant energy variation certainly provides the environmental structural function around Zn in the IGZO film. The second structural data of IGZO films, involving the four pairs Zn–O, Zn–Zn, Zn–Ga, and Zn–In, can be obtained because the contributions from the pairs unassociated with Zn (none Zn pairs) are unchanged in such an energy region.

If the energy of the incident X-ray is close to the absorption edge relevant to K- or L-shell electrons of element A in the system, the total atomic scattering factor becomes complex, indicating the distinct energy dependence due to the anomalous dispersion effect, which can be expressed by:¹⁵⁾   

\begin{equation} f_{\text{A}}(Q,E) = f_{\text{A}}^{\circ}(Q) + f'_{\text{A}}(E) + if''_{\text{A}}(E) \end{equation} (4)

where $f_{\text{A}}^{\circ }(Q)$ corresponds to the scattering factor of the atom at the energy sufficiently far from the absorption edge and $f'_{\text{A}}(E)$ and $f''_{\text{A}}(E)$ are the real and imaginary parts of the anomalous dispersion terms, respectively.

The AXS measurements are usually carried out at two energies (E₁ and E₂, where E_abs > E₂ > E₁) on the lower energy side of the absorption edge of a specific element A in the system of interest because of particular near-edge phenomena, such as XANES, XAFS, and extremely intense fluorescent radiation above the edge. Under such conditions, the differential interference function around A, $Q\Delta i_{\text{A}}(Q,E_{1},E_{2})$, may be given as follows:   

\begin{equation} Q\Delta i_{\text{A}}(Q,E_{1},E_{2}) = \frac{Q\{(I_{\text{eu}}(Q,E_{1}) - \langle f^{2}(Q,E_{1})\rangle) - (I_{\text{eu}}(Q,E_{2}) - \langle f^{2}(Q,E_{2})\rangle)\}}{W(Q,E_{1},E_{2})} \end{equation} (5)

  

\begin{equation} W(Q,E_{1},E_{2}) = \sum\nolimits_{j=1}^{N}c_{j}\Re[f_{j}(Q,E_{1}) + f_{j}(Q,E_{2})], \end{equation} (6)

where $\Re [f_{j}(Q,E_{1}) + f_{j}(Q,E_{2})]$ denotes the real part of the values in the brackets. The Fourier transform of $Q\Delta i_{\text{A}}(Q,E_{1},E_{2})$ provides the environmental RDF around A, $4\pi r^{2}\rho _{A}(r)$, in the system:   

\begin{align} 4\pi r^{2}\rho_{A}(r)&\equiv 4\pi r^{2}\sum_{j=1}^{N}\frac{\Re [f_{j}(Q,E_{1}) + f_{j}(Q,E_{2})]}{W(Q)} \rho _{\text{A}j}(r)\\ & = 4\pi r^{2}\rho_{\text{o}} + \frac{2r}{\pi c_{\text{A}}[f'_{\text{A}}(E_{1}) - f'_{\text{A}}(E_{2})]}\\ &\quad \times \int_{0}^{\infty}Q\Delta i_{\text{A}}(Q,E_{1},E_{2})\sin (Qr)\mathrm{d}Q \end{align} (7)

This AXS method certainly promises a new powerful tool for determining the environmental RDF, as a function of the distance, around a specific element of the multi-component system. It may also be worth mentioning that the area A_Aj under the peak for an A–j pair in the environmental RDF for A directly corresponds to the coordination number N_Aj for the atom j around A:   

\begin{equation} A_{\text{A}j} = \int_{a}^{b}4\pi r^{2}\rho_{\text{A}}(r)\mathrm{d}r = \frac{\Re [f_{j}(Q,E_{1}) + f_{j}(Q,E_{2})]}{W(Q)}N_{Aj} \end{equation} (8)

2.4 Reverse Monte Carlo (RMC) simulation

One of the main purposes of this work is to obtain a realistic atomic-scale model for IGZO films, which reproduces both the ordinary interference function of grazing incidence X-ray scattering and the environmental interference function of AXS using the Zn-K absorption edge. For this purpose, we used RMC simulation originally proposed by McGeevy and Pusztai in 1988.¹⁶⁾ The computer performance and usability have rapidly improved over the past 30 years. Thus, RMC analysis is widely used to analyze amorphous materials, such as liquid alloys and molten salts, and crystalline materials, such as ferrite and oxyhydrooxide.¹⁵⁾ The RMC algorithm employed in this work is essentially identical to that proposed by McGeevy and Pusztai.¹⁶⁾ Some additional details are provided below.

(1) If N particles are arranged in a volume V, their number density should coincide with the experimental density value listed in Table 1. For example, we used a configuration of a total of 5040 atoms, whereby 2160 atoms represent In, Ga, and Zn by 720 atoms each and remaining 2880 atoms of O(oxygen) in the supercell consisting of a = 3.36 nm, b = 3.54 nm, and c = 5.32 nm (volume = 63.28 nm³) under ordinary periodic boundary conditions. The initial atomic configuration was set similar to the structural unit found in homologous-type IGZO or spinel-type crystals. The structural units of bcc- and fcc-type and dense random packing models are often used for liquid alloys. The following procedure was used to determine if the initial atomic configuration is suitable.

(2) Under ordinary periodic boundary conditions in which the cell is surrounded by the images of itself, partial pair distribution functions, g_ij(r), are calculated and their Fourier transform provides the interference functions of the respective pairs as a function of the wave vector. By considering the so-called weighting factors for each atomic pair expressed by the atomic scattering factor of a constituent element and its fraction, we can easily estimate the interference function to directly compare experimental interference function data. It is worth mentioning that the environmental interference function around Zn in IGZO films can also be obtained by using the four pairs Zn–O, Zn–In, Zn–Ga, and Zn–Zn.

(3) Since the first simulated results usually show certain differences from the experimental data, a new configuration is then generated by the random movement of one particle and the interference functions are computed using the procedure described in the second step. The simulated results and measured structural data are then compared again. Such an iterative process is carried out until reasonable convergence can be achieved using the following statistic of χ²:^10,16)   

\begin{align} \chi^{2}& = \sum_{m=1}^{n}\frac{\{i(Q_{m}) - i^{c}(Q_{m})\}^{2}}{\sigma^{2}(Q_{m})}\\ &\quad + \sum_{\alpha}\sum_{m=1}^{n}\frac{\{\Delta i_{\alpha}(Q_{m}) - \Delta i_{\alpha}^{c}(Q_{m})\}^{2}}{\sigma_{\alpha }^{2}(Q_{m})}, \end{align} (9)

where i^c(Q_m) and Δi_α^c(Q_m) are the calculated interference function and its difference for the α component measured at Q_m, respectively, and σ(Q_m) and σ_α(Q_m) are the estimates of the experimental error. If $\chi ^{2}{}_{\text{new}} \prec \chi ^{2}{}_{\text{old}}$, the new configuration is accepted. However, in the $\chi ^{2}{}_{\text{new}} \succ \chi ^{2}{}_{\text{old}}$ case, the calculation returns to the old configuration. A new configuration is then generated by the random movement of another particle.

(4) The change in the partial pair distribution functions of g_ij(r) is calculated and Δi^c(Q) and χ² are again obtained from this new i^c(Q). If the new χ² value is smaller than the old one, the new configuration is accepted; otherwise, it is accepted only with a probability less than unity. This iteration process is made until χ² shows reasonable convergence.

To quickly achieve reasonable convergence, some regulations for specific atom pairs and local ordering units and their geometrical linkage are sometimes introduced. However, only the regulation that the partial pair distribution functions of g_ij(r) are equal to zero for all values below the atomic diameter was used in this work. Since the measured scattering intensity corresponds to the average information of ten partial pair correlations in a quaternary system, it is quite natural that the structural parameters with both necessary and sufficient conditions are hardly obtained from a single structural function alone. Therefore, the AXS measurements can provide an additional structural function for the sample of interest and are quite effective for RMC simulations.

3. Results and Discussion

3.1 Characteristic X-ray scattering patterns

Figure 1 shows the X-ray scattering intensities as a function of the scattering angle of the NC film measured by changing the glancing angle of the incident X-ray beam using the out-of-plane mode. If the glancing angle is 2.0°, a broad peak attributed to a silica glass substrate is detected at 2θ = 21°. On the other hand, the scattering intensity can be obtained from the thin film alone as long as the glancing angle is set to <1.0°. Based on these results, highly accurate measurements were carried out for both CAAC and NC films to reduce the experimental error, under the condition of keeping the glancing angle at 0.5°. The X-ray scattering intensity in electron units can be obtained by normalization after correction for air and Compton scattering. The results are shown in Fig. 2 as a function of the wave vector Q together with the calculated data for polycrystalline IGZO.

Fig. 1

X-ray scattering intensity patterns of the NC film measured in out-of-plane mode at changing angles of the incident X-ray beam.

Fig. 2

X-ray scattering intensity in electron units as a function of the wave vector Q obtained from highly accurate measurements on CAAC and NC films while maintaining the glancing angle at 0.5° applying air scattering. Data for polycrystalline IGZO are also shown for comparison.

It should be noted that the height of the first peak of the CAAC film is twice that of the NC film and two tiny broad peaks appear at Q = 7.0 and 14.0 nm⁻¹, which correspond to the 003 and 006 reflections of the IGZO crystal ($R\bar{3}$ a = 0.330 nm, c = 2.610 nm),¹⁷⁾ respectively. These results directly imply that the CAAC has a long-range order in comparison with that of the NC film. The position of the shoulder at the lower angle side of the first peak of the NC film is coincident to the fist peak position of the CAAC film such that a part of the structural components of the CAAC film may also exist in the NC film within the first-order approximation. Nevertheless, we suggest that the most important points of the experimental results in Fig. 2 are the notable size reduction and the decomposition of the particular layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs in the IGZO crystal. The basic X-ray scattering intensity patterns of the CAAC and NC films clearly differ from that of ultrafine crystalline particles. The X-ray scattering intensity pattern can be explained by the Bragg peaks with distinct peak broadening associated with ultrafine zinc-ferrite crystalline particles with diameters in the order of 4 nm.¹⁸⁾

The RDFs were computed using Fourier transformation of the structure function in electron units,¹²⁾ and the results are illustrated in Fig. 3(a). As mentioned previously, the RDFs of IGZO film only provide average information on ten partial correlations with weighting factors of the respective atomic pairs. It should also be noted that the more the atomic number increases, the more strongly will the X-rays scatter. For example, the weighting factor of the In–In pair is 1.05 and contrasts with that of the In–O pair of 0.26 such that the area under the peak of the RDF for the In–In single pair is four times as large as that of the In–O single pair. Considering that almost 60% of the weighting factors of the IGZO film are attributed to the metal–metal pairs, the RDFs in Fig. 3(a) mainly provide information about the distributions of metal–metal (cation–cation) pairs. The peak at ∼0.2 nm in the RDFs corresponds to the correlations of three pairs, that is, In–O (0.218 nm, 6 oxygens), Ga–O (0.202 nm, 5 oxygens), and Zn–O (0.202 nm, 5 oxygens) in the IGZO crystal. Here, the values given in round parentheses are the distance and oxygen coordination number, respectively. Thus, it is very difficult to separate these three superimposed pair correlations from the RDF data. Nevertheless, Fig. 3(a) shows that the following useful structural information can be obtained from the distances of the second and third peaks and the oscillating behavior representing deviations from the average number density:

Fig. 3

Radial distribution function (RDF) and PDF for CAAC and NC films computed from the measured intensity data shown in Fig. 2 by using Fourier transformation. (a) RDF; (b) PDF.

(1) The CAAC film shows a relatively distinct metal–metal correlation in comparison with the NC film.

(2) The RDF of the CAAC film indicates correlations at distances of 0.36, 0.50, and 0.68 nm. These values coincide, more or less, with the distance of the In–M pairs between the InO₆ and (Zn,Ga)O₅ slabs (0.358 and 0.487 nm) and distance of the M–M pairs (0.661 and 0.660 nm) in the IGZO crystal.

(3) Note that these three correlations are the new information that is obtained in this work because they cannot be obtained by XAFS analysis,¹⁹⁾ which is one of the powerful techniques used to determine the first nearest-neighbor correlation.

Figure 3(b) shows the so-called pair distribution function (PDF), g(r) = ρ(r)/ρ_o, of the CAAC and NC films. The PDF data are sometimes used to estimate the cluster size (or the certain ordering region) by assuming that the range of r_s, where the deviation from ρ_o (ordering region) disappears, may be defined as a value of r_s beyond which g(r) = 1 ± 0.005. The value of ±0.005 is considered to be a reasonable choice for the error at a larger distance. In other words, this approach suggests that the r_s value must become large if the crystalline feature becomes distinct.¹²⁾ Note that the concept of RDF can be extended to crystalline and non-crystalline materials and imperfect gases.¹²⁾

Based on the PDF results of Fig. 3(b), both the CAAC and NC films converge at the average number density value at a distance beyond 2 nm. This indicates that the size of the clusters in these two films is ∼2 nm. In addition, the oscillating behavior of the PDF for the CAAC film in Fig. 3(b) continues at a slightly longer distance compared with the NC film. Thus, the cluster size was estimated by assuming that that the size might be equal to the distance at which the deviation from the average number density disappears. The cluster size is 2.2 nm for CAAC film and 1.8 nm for NC film, respectively. These values are consistent with the size of the deposited pellets (1.92 nm for CAAC film and 1.44 nm for NC film) obtained by high-resolution electron microscopy;⁹⁾ the deposited pellets are aligned parallel to the substrate surface.

3.2 Characteristic features of differential intensity patterns by AXS

The present AXS measurements were carried out for CAAC and NC films using the X-rays with two energies, 300 and 25 eV, below the Zn-K edge (9.659 keV). Taking account of the absorption coefficients of both films at these energies, the measurements were carried out under the condition of keeping the glancing angle at 0.3°. After making corrections for absorption and Compton scattering, the measured intensity data were normalized and the differential intensity patterns mainly arising from the energy variation of ∼8% in the real part of the anomalous dispersion term of Zn were obtained.

The AXS results for NC and CAAC films are illustrated in Fig. 4, where the dotted line and solid line denote the coherent scattering intensity data in electron units measured at 25 and 300 eV below the Zn-K absorption edge, respectively, and each differential intensity pattern obtained by the AXS measurements is illustrated by the small dotted line in the bottom. The differential intensity pattern for Zn provides the environmental structural function around Zn for both IGZO films because the contribution from non-Zn pairs is automatically eliminated when determining the difference between the data obtained at 25 and 300 eV below the absorption edge. Note that the small peak at the lower angle side of the first peak and oscillating behavior of CAAC film in the differential intensity pattern differ from those of the average structural data given by both the dotted and solid lines. The Fourier transform of the differential intensity pattern allows us to obtain the environmental RDF around Zn, 4πr²ρ_A(r), defined by eq. (7). The results are illustrated in Fig. 5.

Fig. 4

AXS results for (a) NC film, (b) CAAC film. The dotted line and solid line denote the coherent scattering intensity data in electron units measured at 25 eV and 300 eV below the Zn-K absorption edge (9.659 keV), respectively. The small dotted line in the bottom shows the differential intensity pattern for Zn.

Fig. 5

Environmental radial distribution function around Zn (Zn-RDF) for the CAAC and NC films by AXS with Zn-K absorption edge.

The interpretation of Zn-RDF in Fig. 5 is rather simple when comparing it with the average RDF in Fig. 3 involving correlations of ten atomic pairs. Nevertheless, it is not so easy to obtain accurate structural information from Zn-RDF alone because the weighting factors for Zn-RDF are Zn–O (0.32), Zn–Ga (1.48), Zn–In (2.50), and Zn–Zn (1.11) and the weighting factor of the Zn–In pair is 7.8 times larger than that of the Zn–O pair. Therefore, the main structural information of Zn-RDF in Fig. 5 should be again considered for the metal–metal correlations around Zn in IGZO films. Thus, for example, the metal–metal correlations of the CAAC film are relatively distinct in comparison with those of NC film and a peak shift of the Zn-RDF for CAAC film to the longer distances is observed. The Zn-RDF of CAAC film illustrated by the dotted line again indicates correlations at distances of 0.36, 0.50 and 0.68 nm. (see Fig. 3(a)). This is newly obtained information based on the present AXS measurements, implying a distinct Zn–In pair correlation, similar to that found in IGZO crystals, rather than correlations of Zn–Zn and Zn–Ga pairs.

The peak detected at ∼0.2 nm of the Zn-RDFs corresponds to the correlation of the Zn–O pair (0.202 nm, 5 oxygens) in the IGZO crystal. The Zn-RDFs provide information about the Zn–O distance, 0.207 nm, and oxygen coordination number, 3.2, for NC film and of Zn–O distance, 0.210 nm and oxygen coordination number, 5.8, for CAAC film, respectively. These results coincide with the crystal case (0.202 nm, 5 oxygens). However, it should be noted that the uncertainties of the computation are ±0.03 nm for the Zn–O distance and ±0.6 for the oxygen coordination number. These uncertainties are mainly attributed to the small weighting factor of the Zn–O pair compared with those of other metal–metal pairs.

One of the merits of the AXS method is to obtain the environmental structural function around a specific element in the multi-component system. However, frequent difficulties occur associated with a quaternary case such as IGZO, particularly in estimating information directly from the environmental RDF data. This contrasts the binary or ternary cases. Therefore, the realistic atomic-scale models were obtained in this work by fitting not only the ordinary interference functions (Fig. 2) but also the environmental interference functions of Zn-AXS (Fig. 4) by applying RMC simulations.

The following point may also be given. Atomic-scale structure of IGZO crystal is known to be characterized by the particular layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs where the positions of Zn and Ga do not be distinguished. Considering these facts in mind, the essential points on the present IGZO films could be obtained with sufficient reliability from two independent structural functions. It has also been demonstrated in other examples, such as iron-oxyhydroides including Cr, Cu and Ni and (AgBr)-(Ag₂O)-(GeO₂) superionic conductors,^10,11)

3.3 Analysis by RMC simulations

The following simulation trials were carried out to check whether the RMC results reproduce the fundamental features of the structural function such as the first peak positions of the structural functions at Q = 21.8 and 23.1 nm⁻¹ for CAAC film and NC film, respectively, and the asymmetry of the first peak at its low-angle side, which was clearly observed for NC film.

(1) The initial atomic configuration (initial model) was tested to analyze the structure of both the CAAC and NC films by RMC simulation. Although there are several crystal structures in which the ratio between the metallic cation and oxygen anion is 0.75, one of the characteristic features of trigonal InGaZnO₄ or crystals is the densely close-packing of oxygen, whereas metals of relatively smaller size occupy the positions equivalent to the vacant space produced by oxygens.^20,21) Considering these facts, the atomic arrangements found in trigonal InGaZnO₄ or cubic spinel-type MgAl₂O₄ were tested for the initial model.

(2) For example, based on trigonal InGaZnO₄, we defined the initial model consisting of an arrangement of a total of 1260 atoms, where 540 atoms represent 180 atoms of In and 360 atoms without difference between Ga and Zn and remaining 720 atoms of O (oxygen) in the supercell consisting of a = 2.14 nm, b = 3.06 nm, and c = 2.81 nm (volume = 18.40 nm³). This initial model well-reproduced the first peak position and asymmetry of the first peak at its low-angle side for NC film.

(3) Based on the cubic spinel-type structure, we defined the initial model consisting of an arrangement of a total of 1512 atoms, where 648 atoms represent 216 atoms of In and 432 atoms without difference between Ga and Zn and remaining 864 atoms O in the supercell consisting of a = b = c = 2.67 nm (volume = 19.03 nm³). This initial model did not well-reproduce the first peak position and asymmetry of the first peak at its low-angle side for NC film.

(4) Based on trigonal InGaZnO₄ employed in the first step, further RMC simulations were carried out by changing the number density corresponding to the NC film up to that of the CAAC film. In this case, we observed a shift in the first peak position from Q = 23.1 nm⁻¹ for NC film toward a smaller Q value, 21.8 nm⁻¹, for CAAC film during the simulation step. However, the convergence was insufficient. Therefore, the structural difference between CAAC and NC films cannot be explained by the density difference alone.

(A) RMC results for NC film

Based on the results of the simulation trials, we used the initial model for RMC of the NC film, as shown in Fig. 6(a). The image shows that several polyhedral units, such as an octahedron and trigonal dipyramid, are involved in this initial model and six or five oxygen atoms surround the metal atoms of In, Ga, or Zn in each polyhedral unit. The initial model for NC film was set based on the arrangement of a total of 5040 atoms, where 2160 atoms represent In, Ga, and Zn by 720 each and remaining 2880 atoms of O in the supercell consisting of a = 3.42 nm, b = 3.56 nm, and c = 5.41 nm (volume = 65.87 nm³). This corresponds to the number density of 76.51 atoms/nm³. Note that this number density value is 0.96 times smaller than that of the CAAC film (see next section: 79.56 atoms/nm³) and agrees with the ratio of the macroscopic density values of these two films, i.e., 0.95 = 5.7/6.0 Mg/m³.

Fig. 6

Initial model for the RMC of IGZO films used in this work. Several polyhedral units are involved in this initial model. (a) NC film, (b) CAAC film. [cross-hatch pattern denotes polyhedral units around In (white), Ga (light gray), and Zn (dark gray), respectively.]

Based on this initial model and the random movement of one particle to generate a new configuration with the computer, the iteration process was repeatedly carried out until the statistic parameter χ² defined by eq. (9) showed reasonable convergence and therewith reproduced both the ordinary interference function of grazing incidence X-ray scattering and the environmental interference function of AXS with the Zn-K absorption edge.

Note that the iteration process in this work was sometimes stopped and the reproduction of the experimental structural functions is far from complete due to considerable differences beyond the experimental uncertainty. This is the case because the present IGZO film has a really high density and the random movement of one particle to generate a new configuration in the computer is not sufficient to achieve reasonable convergence. In such case, we additionally introduced the swap process in which some metal atoms in the layered structure exchange their positions. The additional iteration process led to a reasonable convergence. This contrasts the cases of ordinary RMC simulations for liquid alloys and molten salts with a relatively low number density.

The RMC results for NC film are shown in Fig. 7(a), where the solid line denotes the experimental results and the dotted line represents the simulated results. As shown in Fig. 7(a), the simulated results well-reproduce the experimental data of the ordinary interference function and environmental interference function of AXS with Zn-K absorption edge. This includes the asymmetry of the first peak at its low-angle side clearly observed for NC film, although such an asymmetry feature is not included in the Qi(Q) expression. Thus, the results of Fig. 7(a) imply that the realistic atomic-scale model can be used to characterize the structure of NC film.

Fig. 7

RMC results of this work. The data were obtained to reproduce two structural functions determined by independent measurements. (a) NC film, (b) CAAC film. The solid and dotted lines denote the experimental and computed data, respectively.

(B) RMC results for CAAC film

The essential points of the RMC simulation process for CAAC film are similar to that for NC film, although a density of 6.0 Mg/m³ must be taken into account for computation. We used the initial model for RMC of CAAC film, as shown in Fig. 6(b). The initial model for CAAC film was set by the arrangements of a total of 3360 atoms, where 1440 atoms represent In, Ga, and Zn by 480 each and remaining 1920 atoms O in the supercell consisting of a = 3.36 nm, b = 3.54 nm, and c = 3.55 nm (volume = 42.23 nm³). This corresponds to a number density of 79.56 atoms/nm³. This number density value is 1.04 times larger than that of the NC film (76.51 atoms/nm³) and agrees with the ratio of the macroscopic density values of these two films, 1.05 = 6.0/5.7 Mg/m³.

Based on the initial model for NC film shown in the previous section, further RMC simulations were carried out by changing the number density corresponding to the NC film up to that of the CAAC film. However, we could reproduce the difference in the first peak position between NC film and CAAC film with Q = 23.1 and 21.8 nm⁻¹, respectively. Consequently, the structural difference between CAAC and NC films cannot be explained by the density difference alone.

The RMC results for CAAC film are shown in Fig. 7(b), where the solid line denotes the experimental results and dotted line represents the simulated results. As shown in Fig. 7(b), the simulated results reproduce the experimental interference function data. Thus, the results of Fig. 7(b) are considered to be at least in a sense of the necessary condition at best and the realistic atomic-scale model can likely be used to characterize the CAAC film structure. The RMC results for CAAC film indicate that the coincidence between the experimental and simulated results is not in the same order of magnitude in comparison with that for the NC film (Fig. 7(a)). With respect to this, better results may be obtained when the preferred orientation of the c-axis, perpendicular to the substrate surface, detected for CAAC film by high-resolution electron microscopy (TEM) is quantitatively taken into account for further simulations. Nevertheless, the main purpose of this work was to obtain the essential and specific structural features of CAAC and NC films. Therefore, we rather compare the realistic atomic-model of CAAC film with that of NC film (see Fig. 7) because they reproduce the two independent structural functions well.

(C) Characteristic features of the models for CAAC and NC films obtained by RMC

Figure 8 shows the sectional view of the atomic positions in the middle-range order obtained from a representative RMC-generated atomic configuration for the CAAC and NC films. Here, the realistic atomic-scale model is visualized using polyhedral units, i.e., cross-hatch pattern (InO_x, x = 4, 5, and 6), white (GaO_y, y = 4, 5, and 6), and light gray (ZnO_z, z = 4, 5, and 6), respectively. The following point is suggested with respect to the coordination of the polyhedral unit of InO_x marked by the cross-hatch pattern. The XAFS results for IGZO film¹⁹⁾ indicate that the distance of In–O is 0.211 nm, i.e., 3% less than that for the crystal (0.218 nm). Therefore, there is a high probability that the octahedral atomic arrangement of InO₆ well-recognized in the IGZO crystal changes toward smaller units, such as that of InO₅ or InO₄, both for the CAAC and NC films. This is consistent with the RMC results.

Fig. 8

Sectional view of the atomic positions in the MRO obtained from a representative RMC-generated atomic configuration. (a) NC film, (b) CAAC film [cross-hatch pattern (InO_x, x = 4–6), white (GaO_y, y = 4–6), and light gray (ZnO_z, z = 4–6), respectively]. The residual layered structure closely related to cluster-2 is shown as white ellipse.

As shown in Section 3.1, the structural functions of both the ordinary X-rays and AXS with Zn-absorption edge show a notable size reduction and decomposition of the layered structure clearly recognized in the IGZO crystal. Such characteristic structural features covering the middle-range order are visualized in Fig. 8. Remember that a clear grain boundary was not observed in the CAAC and NC films and the basic features of their scattering intensity profile can be expressed by more than one broad maximum followed by a relatively sharp first peak and a sharp Bragg peak is not included. These experimental facts prompt us to assume an appreciable size reduction and decomposition of the layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs in the IGZO crystal. The notable size reduction and decomposition of the layered structure detected in both the CAAC and NC films are certainly not identical to that of silica glass, where the density reduction from crystal (2.65 Mg/m³) to glass (2.21 Mg/m³) is 16.6%. For example, the density reduction from crystal (6.35 Mg/m³) to CAAC film (6.0 Mg/m³) is only 5%. Therefore, it is likely to assume that connecting atomic arrangements forming the middle-range order (MRO) continue to exist in the structures of CAAC and NC films and this MRO is mixed with the short-range order defined by polyhedral units and represented by InO₅, GaO₅, and ZnO₅. Such structural features are more or less associated with the layered structure formed by InO₆ and (Zn,Ga)O₅ slabs in the IGZO crystal. For convenience, the residual layered structure of both the CAAC and NC films is shown by a white ellipse in Fig. 8. Figure 9 shows the same sectional view as that of Fig. 8 for NC film (a), and CAAC film (b), but in this figure we do not distinguish the local atomic coordination using three different symbols. This change clarifies the residual layered structure, particularly in the side model as can be readily seen from Fig. 9.

Fig. 9

The same sectional view as in Fig. 8 for (a) NC film, (b) CAAC film, but the local atomic coordination is not distinguished by three different symbols. This change clarifies the residual layered structure, particularly in the side model.

The results of both Fig. 8 and Fig. 9 provide the characteristic structural features of the CAAC and NC films, which could be visualized for the first time. They can be summarized as follows:

(1) The basic structural feature of both CAAC and NC films can be represented by a mixture of polyhedral units (referred to as cluster-1) such as InO_x (x = 4–6), GaO_y (y = 4–6), and ZnO_z (z = 4–6), although considerable size reduction and decomposition of the layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs in the IGZO crystal were observed.

(2) A composite-type structural feature (referred to as cluster-2) produced by combining the polyhedral units likely exists in both CAAC and NC films and leads to MRO. Cluster-2 of the CAAC film is larger than that of the NC film.

(3) Note that cluster-2 is considered to be associated with the layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs in the IGZO crystal, although some metal atoms of In, Ga, and Zn in the layered structure exchange their positions. In other words, the IGZO films may be characterized by a composite-type structure in which a mixture of polyhedral units (cluster-1) and combinations produce cluster-2. The structural difference between the CAAC and NC films might be mainly due to the size of cluster-2. The characteristic features of the composite-type structure of the CAAC film are responsible for the first peak position of the structural function at Q = 21.8 nm⁻¹. On the contrary, characteristic features of the composite-type structure of the NC lead to the first peak position of the structural function at Q = 23.1 nm⁻¹ and to asymmetry of the first peak.

(4) Figure 10 shows the correlations of the metal–metal pairs in IGZO films as a function of the distance obtained from the RMC models shown in Fig. 9. With respect to the NC film, the oscillating behavior of the cation–cation (M–M) pair is similar to that of the In–M pair. Therefore, in the structural formation, Zn(Ga) is considered to play the same role as that of In. On the contrary, the oscillating behavior of the In–M pair in the CAAC film indicates a unique feature with the correlation distance of 0.49, 0.56, and 0.62 nm. This implies that In and Zn(Ga) play different roles in the structural formation of the CAAC film, corresponding to the nature of the layered structure of the IGZO crystal.

Fig. 10

Correlations of metal–metal pairs in IGZO films as a function of the distance obtained from the RMC models in this work. (a) NC film, (b) CAAC film.

Based on these results, the structure of both the CAAC and NC films can be characterized by complex and irregular atomic arrangements of nanometer-sized crystalline clusters. This is considered to be the best explanation for the structure of the deposited IGZO film. The complex and irregular atomic arrangements of nanometer-sized crystalline clusters contribute to the resilience against atomic rearrangement. The structure of the CAAC and NC films is more stable and can maintain the atomic arrangements relevant for the atoms at a relatively high density value. This extends the film deposition conditions. Such features are promising for the production of a large square film in areas with good homogeneity and higher density. These features also benefit the production of IGZO films with sufficient reliability for device fabrication in microelectronics.

4. Concluding Remarks

In this study, we observed that, with respect to the X-ray scattering intensity profile, the height of the first peak of the CAAC film was twice as that of the NC film and small peaks were observed at Q = 7 and 14 nm⁻¹, which correspond to the 003 and 006 reflections of the IGZO crystal, respectively. On the contrary, an NC film shows a shoulder at the lower wave vector side of the first peak and its position coincides with that of the first peak position of the CAAC film. The most important experimental results are the appreciable size reduction and decomposition of the layered structure formed by the InO₆ and (Zn,Ga)O₅ slabs that were clearly detected in the IGZO crystal. The basic X-ray scattering intensity pattern for the CAAC and NC films clearly differs from that of the ultrafine crystalline particles such as zinc ferrite with diameters in the order of 4 nm.¹⁸⁾ Realistic atomic-scale models were obtained in this work so as to fit both the ordinary and environmental interference functions of Zn-AXS by applying RMC simulations. One of the most important RMC simulation results is the determination of the basic structural features of both CAAC and NC films, which are well-characterized by nanometer-sized crystalline clusters. A more specific illustration of the complex and irregular atomic arrangements in these films can be represented by a mixture of polyhedral units (referred to as cluster-1) and complex and irregular atomic arrangements (referred to as cluster-2) produced by combining some of the polyhedral units. The latter certainly leads to MRO. The size of cluster-2 was estimated to be 2.2 nm for CAAC film and 1.8 nm for NC film. This agrees with the crystalline nanometer-sized features, which were well-recognized by high-resolution electron microscopy.⁹⁾ The characteristic structural features found in both CAAC and NC films can be referred to as crystalline–cluster–composite (triple C) structure. It can also be concluded that the structural features of both CAAC and NC films are classified on the basis of a boundary region between amorphous and crystalline phases in crystallography.²²⁾

Acknowledgements

The authors express their gratitude to the staff of the Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Japan, for the kind help with the AXS measurements (Proposal No. 2017G191). One of the authors (YW) is grateful to Dr. Shunpei Yamazaki, the president of SEL Co. Ltd., and Mr. Yoichi Kurosawa, SEL staff member, for the preparation of the IGZO films named CAAC and NC.

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