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Abstract
Electronic grade ZnGa2O4 epitaxial thin films were grown on c-plane sapphire substrates by metal-organic chemical vapor deposition and investigated using spectroscopic ellipsometry. Their thickness, roughness and optical properties were determined using a Multiple Sample Analysis based approach by the regression analysis of optical model and measured data. These samples were then compared to samples which had undergone ion etching, and it was observed that etching time up to four minutes had no discernible impact on its optical properties. Line shape analysis of resulting absorption coefficient dispersion revealed that ZnGa2O4exhibited both direct and indirect interband transitions. The modified Cody formalism was employed to determine their optical bandgaps. These values were found to be in good agreement with values obtained using other popular bandgap extrapolation procedures.
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1. Introduction
Wide bandgap (${\textrm{E}_\textrm{g}}$) semiconductors have many advantages in electronic device applications including power devices, 5G communication, quick chargers, deep ultraviolet (DUV) optoelectronics, and Industry 4.0 technologies because of their ultra-high breakdown electric field, control of the electrical conductivity, chemical stability, and temperature insensitivity. While most parts of power devices are fabricated using Si ( = 1.1 eV), the third-generation semiconductors such as GaN (${\textrm{E}_\textrm{g}}$ = 3.4 eV) and SiC (${\textrm{E}_\textrm{g}}$= 3.2 eV) are rapidly rising in demand, thanks to applications towards the development of small area, high frequency switching, high power density, and low energy consumption. Although GaN and SiC power devices are attracting substantial attention from major manufacturers, they still suffer from drawbacks such as high cost and high melting points (2220 °C and 2730 °C for GaN and SiC, respectively). For instance, SiC is an extremely hard material which is difficult to cut, grind and polish. It has a slow growth rate, requires extremely high working pressures for bulk production and consumes very high energy to be melted from ingots [1]. Owing to these drawbacks, Gallium oxide ($\textrm{G}{\textrm{a}_2}{\textrm{O}_3}$) is becoming more attractive amongst wide bandgap semiconductors. This is thanks to its high Baliga’s Figure of Merit (BFOM) and critical breakdown field [2–5], which make it suitable for next generation power device applications. It is also suitable for DUV photodetectors (PDs) thanks to its low conductivity and photocurrent [6,7]. On the other hand, ternary wide bandgap semiconductors such as Zinc gallate ($\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$) presents a bandgap of about 4.6-5.2 eV and has outstanding optical and electrical properties. This material can therefore be regarded as a propitious candidate for high power devices, and DUV PDs [8–10].
Several works on synthesis of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}\; $ thin films by sputtering, hydrothermal, spin coating, sol-gel and pulsed laser deposition process have been published. However, the above deposition technologies always resulted in nanostructured, amorphous or polycrystalline films, which makes it difficult to be used in power device applications. Very high quality $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ films have been obtained using metal-organic chemical vapor deposition (MOCVD) by varying parameters such as reaction gas flow rate, working pressure and temperature. High quality $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ epitaxial films have been applied to transistors for power electronics and phototransistor applications. Schottky type $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}\; $ based DUV PDs have been demonstrated to exhibit excellent optoelectronic properties (discussed in our previous research [11–13]). However, the fundamental physical properties of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ have still not been widely investigated.
Spectroscopic ellipsometry (SE) has positioned itself as one of the most popular characterization techniques for determination of optical properties of thin films, bulk materials, interfaces, and even heterostructures and quantum wells. It is considered more precise and accurate than irradiance (intensity) based reflection or transmission measurements [14] thanks to the fact that it measures a ratio quantity rather than the intensity of probing radiation, thereby making it insensitive to intensity fluctuations. SE data can also numerically account for surface roughness, overlayers and effects due to strain, temperature, pressure, etc. by assuming model parameters as functions of the dependent characteristics. Advantages of SE include the ability to penetrate entire sample stacks to probe underlying layers and fast, precise data acquisition over multiple wavelengths. In addition to determination of optical constants, it allows for complete non-destructive depth profiling of film systems in material science, solid state physics, semiconductors, chemistry, display technologies, optical coatings, data storage, real time monitoring of processes, etc [15,16]. Further advancements and applications of SE have been summarized in several reviews [17,18].
While it is usually straightforward to analyze spectroscopic ellipsometry data when the films are either opaque or transparent, it often becomes difficult to find a unique solution for films which are semi-transparent. Several methods could be employed to alleviate this problem [19] such as measurement over multiple angles of incidence, optical constants parameterization, additional information from transmission measurements [20], Arwin – Aspnes method [21], interference enhancement [22], and multiple sample analysis (MSA) [22]. In the latter approach two or more samples are analyzed simultaneously to determine a unique solution to the complex dielectric function, assuming their optical constants remain identical over a certain thickness range.
In this work we have studied excellent quality $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin films and determined its optical properties in terms of complex refractive index and dielectric function as a function of wavelength and photon energy, respectively, using MSA. Estimates of the optical bandgap of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ are also presented. One batch of samples was grown for different time durations to obtain different thicknesses using a bottom-up approach. Two other batches of samples having the same initial thickness were etched for different times to obtain different thicknesses from a top-down approach. Samples from both the bottom-up and top-down approaches were analyzed using MSA and their optical properties were compared. It is observed that the etched samples showed a small increase in surface roughness but exhibited similar optical properties as the unetched samples. This makes a case for the optical stability of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}\; $ material, making it a viable choice for semiconductor devices where applicable. This study also corroborates the feasibility of using MSA for determination of a unique solution to optical constants and structural parameters of a thin film as the complex refractive index, thickness and roughness determined using MSA are found to be almost identical to the parameters when determined individually.
2. Experimental
$\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ epitaxial thin films were grown on c-plane sapphire substrates by MOCVD where Diethylzinc (DEZn), Triethylgallium (TEGa) and oxygen were used as Zn, Ga and ${\textrm{O}_2}$ precursors, and the flow rates of precursors were maintained at 90, 100 and 700 sccm, respectively. Due to the small lattice mismatch between sapphire and $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$, it is chosen as the substrate for growth of high quality single crystalline $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin films. The growth temperature and working pressure were maintained at 720 $^\circ $C and 25 torr, while the growth time was varied to achieve different thicknesses for samples 1(a-c). The as deposited films were etched by Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE) for samples 2a-3d. The $\textrm{BC}{\textrm{l}_3}$ and $\textrm{C}{\textrm{l}_2}$ flows for ICP-RIE were maintained at 15 sccm under chamber pressure of 1 mTorr, while the DC and RF bias were set to 250 W and 50 W, respectively. Nine such $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin film samples were examined with their growth / etching durations tabulated in Table 1. The samples 1a, 1b and 1c were grown with identical growth conditions for a growth time of 20, 30 and 40 minutes, respectively, to obtain films with three different thicknesses (nominally 70, 110 and 150 nm, respectively) but with identical crystal structure and optical properties. Samples 2a and 2b were grown to have the same initial film thickness (≈ 80 nm). The films were then etched using ion bombardment for a period of 1 and 4 minutes, respectively, to obtain different final thicknesses. Similarly, samples 3a, 3b, 3c and 3d were grown with the same initial film thickness (≈ 120 nm), and etched for 1, 2, 3 and 4 minutes, respectively, to obtain four different final film thicknesses. Both etched sample groups were grown with identical growth conditions before etching and are assumed to share an identical crystal structure and hence identical optical properties.
Table 1. Growth and etching parameters for the studied samples
$\mathrm{\theta }/2\mathrm{\theta }$ scan x-ray diffraction (XRD) and x-ray rocking curve (XRC) measurements were performed using a PANalytical Empyrean x-ray diffractometer (Malvern Panalytical, Almelo, The Netherlands). A parabolic multilayer mirror followed by a 2-bounce Ge (220) monochromator producing Cu $\textrm{K}{\mathrm{\alpha }_1}$ radiation with a divergence of 54 arcsec (0.015$^\circ $) was used as primary optics and a 0.27$^\circ $ parallel plate collimator was used as secondary optics. A 45 kV generator voltage and 40 mA tube current were used for the Cu X-ray source to study the film crystal structure.
All samples were measured with a Mueller matrix spectroscopic ellipsometer and analyzed using the CompleteEase (CE) software package, respectively, both from J. A. Woollam Co., Inc. (Lincoln, NE, USA). The measurements were made over a spectral range of 210-1690 nm (0.7–5.9 eV), at four angles of incidence ranging from 45$^\circ $ to 75$^\circ $ in steps of 10$^\circ $. From model fitting of the ellipsometric data (described in detail in the modelling section below) optical properties in terms of complex refractive index $N(\lambda )= n(\lambda )+ ik(\lambda )$, dielectric function (relative permittivity) ${\varepsilon _r}(E )= {\varepsilon _1}(E )+ i{\varepsilon _2}(E )$, and absorption coefficient $\alpha (\lambda )$ were obtained. Here, n refers to refractive index and k to extinction coefficient. The optical properties are presented as a function of wavelength, $\lambda $, or photon energy, $E.$ The optical data was also used to estimate the band gap values of the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$. In addition, the fitting resulted in film thicknesses and surface roughness values.
3. Theory
3.1 Ellipsometry and modelling
The foundation of analysis of ellipsometric data lies with the Fresnel reflection and transmission equations for polarized light. A ratio $\rho $ of complex valued Fresnel reflection coefficients is used to define the standard ellipsometric parameters, $\mathrm{\psi }$ and $\Delta $, expressed as,
A three-layer optical model was established for the analysis of the measured ellipsometric data. Figure 1 illustrates the optical model consisting of a semi-infinite $\textrm{A}{\textrm{l}_2}{\textrm{O}_3}$ substrate, the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin film, a roughness layer and air (void) as the ambient. The optical constants of a bare $\textrm{A}{\textrm{l}_2}{\textrm{O}_3}$ substrate with an unpolished backside were obtained using a Tauc-Lorentz oscillator model. The optical properties of the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin films were modelled using a Herzinger–Johs (HJ) parameterized semiconductor (PSemi) oscillator function-based model [24,25]. A highly flexible functional shape with Kramers-Kronig consistent properties makes it applicable to a wide range of materials with both direct and indirect bandgaps [26,27], as it allows for an accurate description of dielectric function around the fundamental band edge [28,29]. This amongst other benefits make the HJ formalism a good choice for the description of dielectric function of crystalline samples [30–32]. The overlayer employed to represent surface roughness in the samples was modelled as a 50/50 mixture of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ and ambient (air) using the Bruggeman Effective Medium Approximation (EMA) [33,34] with thickness as the only regression parameter. Several reports comparing surface roughness values obtained using EMA and root-mean-square roughness obtained using atomic force microscopy have been published. It has been shown that there is a linear correlation between the two values [35,36], irrespective of window sizes [37–39] and hence surface roughness can be described effectively using EMA. Film thickness, surface roughness and optical properties of the samples were then determined by fitting the optical model to the experimental data. A Levenberg-Marquardt multivariate regression algorithm was used to minimize the mean squared error (MSE) between the measured and modeled data [40,41]. MSA approach [19,42] was employed to further improve the accuracy of determined optical properties. This approach is based on the underlying assumption that films grown with the same process conditions would possess identical crystallographic and hence optical properties, over a range of different film thicknesses. Thus, measurements were made at multiple angles of incidence and data regression was done with one optical model for all datasets simultaneously, to obtain a unique solution of the dielectric function with minimal correlation.
Fig. 1. Optical model description of sample with bottom, middle and top layer blocks representing substrate, thin film and film surface roughness, respectively.
3.2 Optical bandgap
The electronic bandgap energy, ${E_g}$ can be determined by analyzing the spectral dependence of the absorption coefficient, $\alpha = 4\pi k/\lambda $ and taking the ${\alpha ^2}$ asymptote on the horizontal energy axis. Depending on the type of interband transitions allowed within the material, ${E_g}$ can then be related to $\alpha $ by [43],
In this study, we define the optical bandgap (using the same notation ${E_g}$) as the energy above which the square of absorption coefficient (${\alpha ^2}$) increases linearly with increasing photon energy ($E$) [32]. This corresponds to the energy of photons that make vertical transitions from the upper valence band to the Fermi surface in the conduction band. Even though absorption can be approximated by means of a square root dependence with non-parabolic conduction bands, it serves only as an indicative of the electronic bandgap, not the actual difference between conduction band minimum and valence band maximum of the material. Difference in optical and electronic bandgaps arises as a result of bandgap renormalization due to a variety of reasons including doping, transition broadening, exciton absorptions, phonon interactions, impurities, defects, and choice of growth parameters [30,32]. The overall linearity of a plot of ${\alpha ^2}$ vs E for our samples was analyzed based on Eq. (2) to determine allowed interband transitions exhibited by the material. Several formalisms [17,45–57] have been used and scrutinized in the literature over the choice of correct methodology to determine bandgap energy, with Tauc [58] and Cody [59] formalisms serving as the most popular choices.
Herein, we use the modified Cody formalism according to,
4. Results and analysis
Figure 2 shows θ/2θ-scan XRD measurements for the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin films grown on c-plane sapphire substrate for samples 1a, 1b and 1c. Except for Al2O3 0006 peak located at 41.7$^\circ $, only $2$ peaks for 111, 222 and 333 spinel $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ are observed at 18.5$^\circ $, 37.5$^\circ $ and 57.5$^\circ $ (Fig. 2(a)), respectively, indicating that the films are highly oriented with growth along <111 > direction. The result is consistent with our previous transmission electron microscopy study [11] that the films grown under an optimal condition by MOCVD are epitaxially on the sapphire substrate. In addition, the XRC measurement for 222 peaks show a full width half maximum value of 0.04$^\circ $, 0.03$^\circ $ and 0.06$^\circ $ for samples 1a, 1b and 1c, respectively (Fig. 2(b)). From XRD data it was concluded that the as-deposited epitaxial thin films are single phase with a high crystal quality.
The experimental and modelled data at four angles of incidence for ellipsometric parameters $\mathrm{\psi }$ and $\Delta $ of unetched sample 1a of sample group 1 are shown in Fig. 3 (ψ and $\Delta $ of samples 1b and 1c are presented in [Supplementary data 1, Figure S1]). The shape parameters of the HJ oscillator used to model the experimental data were fixed, while the amplitude, broadening and central energy parameters were allowed to be determined from the regression analysis. The thickness and roughness values were also allowed to vary during the fitting process, while the optical properties were assumed to be similar in accordance with the MSA approach. A remarkably low MSE value of 2.1 was obtained after the regression analysis, and no significant correlation was observed between the fitting parameters. Consequently, one HJ oscillator was deemed sufficient to obtain a very good fit between the measured data and model. The resulting thickness and roughness values are tabulated in Table 2.
Table 2. Obtained structural parameters from the regression fits
Similar MSA was employed on sample group 2 and sample group 3, and good fits (MSE = 2.5 and 2.6, respectively) with no strong correlation were obtained in both cases [Supplementary data, Figure S2 and Figure S3]. The resulting thickness and roughness values for the three groups are tabulated in Table 2 (Group MSA). In order to confirm the accuracy of these values, a fit parameter uniqueness plot for each MSA group. Different values of thickness and roughness were compared against obtained MSE and it was determined that the resulting values after regression were unique and accurate. These results are presented in Figure S4 in Supplementary data.
It was observed that optical constants obtained from the MSA of group 2 were almost identical to the optical constants obtained from the MSA of group 3, indicating that the etching process had no discernible impact on the optical properties of the two groups of samples. Also, the amplitude, broadening and central energy fit parameters between the three MSA groups did not show discernible change. However, the roughness values for etched samples (group 2 and 3) were relatively higher than the unetched samples (group 1), indicating possible surface degradation as a result of the ion bombardment.
Furthermore, the optical constants for the etched samples were found to be similar to the optical constants determined for the unetched samples, suggesting that the current model description was applicable to multiple samples. To corroborate this hypothesis, a combined MSA was performed across all samples (group 1–3) using the same HJ oscillator - based optical model. The amplitude, broadening and central energy parameters of the HJ oscillator as well as the thickness and roughness values of the films were chosen as fit parameters to be determined by the software. A good fit was obtained between the optical model and measured optical data with MSE = 2.7 and no strong correlation between fit parameters, thereby proving the robustness of the applied optical model. Also, a very good agreement was observed between the thickness and roughness values determined using individual and combined MSA approaches, these are summarized in Table 2 (Combined MSA columns). When comparing the resulting optical constants of each sample, it was concluded that all $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ films exhibited almost identical optical properties. This shows that an etching time of 1-4 minutes had no discernible impact on the optical properties of $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ thin films thereby showing growth of repeatable, good quality films is a possibility. Figure 4 shows optical data obtained from the combined MSA. The refractive index, extinction coefficient and absorption coefficient are plotted vs wavelength in Figs. 4(a) and 4(b), respectively, while the dielectric function and absorption coefficient vs photon energy is plotted in Figs. 4(c) and 4(d). The $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ is seen to be transparent from about 300 nm up to the measurement limit 1690 nm and the absorption onset is seen to occur near 250 nm or 4.96 eV (tabulated data for optical constants is presented in Supplementary data, Data File 1, Ref. [62]).
Fig. 4. Optical constants from the combined MSA. (a) Complex refractive index $N(\lambda )= n(\lambda )+ ik(\lambda )$, (b) Absorption coefficient $\alpha (\lambda )$, (c) dielectric function ${\varepsilon _r}(E )= {\varepsilon _1}(E )+ i{\varepsilon _2}(E )$ and (d) Absorption coefficient $\alpha (E )$.
A more detailed analysis of the absorption onset and optical bandgap was made by analyzing the absorption data in Fig. 4(d), according to the formalisms described in the optical bandgap section. The variations of ${\alpha ^2}$ vs E and ${\alpha ^{1/2}}$ vs E are presented in Fig. 5, which indicate the presence of both direct and indirect allowed interband transitions in the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ films. When comparing the two plots, ${\alpha ^{1/2}}$ versus E exhibits a longer band tail around the onset of absorption and occurs at a comparatively lower photon energy while ${\alpha ^2}$ versus E exhibits a steeper slope around the band edge at a comparatively higher photon energy. These are characteristic features designating indirect and direct allowed transitions, respectively, and have been discussed for many materials [28,44,49,63].
Analysis of absorption spectra based on the modified Cody formalism according to [Eq. (3)] was applied and the intercept of linear extrapolation was used to estimate ${E_g}$ (presented in Fig. 6(a)). As a comparison, estimates were also derived using the Cody, Tauc and modified Tauc formalisms [Supplementary data, Figure S5]. In addition, the ${E_g}$ values were compared with linearly extrapolated value of the onset of absorption (${\alpha ^2}$ and ${\alpha ^{1/2}}$ for direct and indirect ${E_g}$, respectively) as well as the central energy parameter of HJ oscillator. While it has proven difficult to determine a unique / unanimously accepted methodology for the estimation of ${E_g}$, we believe that in many cases the choice of methodology would not significantly affect the value or overall trend of the obtained ${E_g}$. This is the case for films with high purity and crystal quality and can be observed for the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ in this study. To determine a precise estimation of ${E_g}$, three overlapping regions of linearity were chosen in the plot according to [Eq. (3)] to make the linear extrapolations (presented in Fig. 6(b)). The arithmetic mean of these extrapolated values was then chosen to represent final ${E_g}$ for our samples, while the standard deviation between these values was chosen as uncertainty.
Fig. 6. (a) Bandgap estimation using Modified Cody formalism [Eq. (3)] with (b) Weightage considerations shown for direct ${E_g}$ estimation.
The mean ${E_g}$ extracted according to [Eq. (3)] and the HJ oscillator Eo1 value are tabulated in Table 3 and are found to be identical to the ${E_g}$ values obtained from other formalisms (note that HJ oscillator only reports direct allowed transitions). Hence, it was concluded that the $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ samples in this study exhibited a direct ${E_g}$ of 5.07 ± 0.015 eV and an indirect ${E_g}$ of 4.72 ± 0.015 eV. These values were found close to the range of experimental ${E_g}$. values presented in [9]. A summary of previously reported work in terms of synthesis techniques, optical constants obtained, and characterization techniques implemented can be found in an earlier publication [64]. It is also evident that while all techniques yield a similar value of ${E_g}$, [Eq. (3)] provides the most linear region for the linear extrapolation and determination of ${E_g}$, therefore, the use of [Eq. (3)] for estimation of ${E_g}$ for crystalline semiconducting materials is preferred in this study.
Table 3. Mean optical bandgaps from different techniques in eV
5. Conclusion
High quality $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ epitaxial thin films were grown on c-plane sapphire substrates by MOCVD and their thickness, roughness and optical properties were determined using SE and the MSA approach. It was observed that optical properties of samples which were ion etched for 1-4 minutes remained similar to optical properties of unetched samples. Line shape analysis of the absorption coefficient dispersion revealed that $\textrm{ZnG}{\textrm{a}_2}{\textrm{O}_4}$ exhibited both direct and indirect interband transitions. A modified Cody formalism was chosen to determine their optical bandgaps, resulting in a direct bandgap of 5.07 ± 0.015 eV and an indirect bandgap of 4.72 ± 0.015 eV. These values were compared to other popular bandgap extrapolation techniques and were found to be consistent with each other.
Funding
Vetenskapsrådet (2018-04198); Stiftelsen för Strategisk Forskning (2009-00971); STINT foundation (MG2019-8485); Wafer Works Corporation and Ministry of Science and Technology (109-2221-E-009-143-MY3, 109-2622-E-009-033, 109-2634-F-009-028, 109-2224-E-009-002, 110-2218-E-A49-020-MBK, 110-2622-8-009-018-SB, 110-2224-E-A49-003, 111-2923-E-A49-003-MY3); MAtek (2021-T-006).
Acknowledgments
Credit authorship contribution statement: Conceptualization, S.B., C.-L.H., R.-H.H., and K.J.; methodology, S.B., C.-L.H., R.-H.H., and K.J.; resources, S.B., C.-L.H., R.-H.H., J.B. and K.J.; data curation, S.B.; writing—original draft preparation, S.B.; writing—review and editing, C.-L.H., J.B., R.-H.H., R.M., J.P.C. and K.J.; project administration, C.-L.H., R.-H.H. and K.J.; funding acquisition, J.B., R.H.H. and K.J. All authors have contributed to the writing and agreed to the published version of the manuscript.
Disclosures
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. The optical constants obtained after analyzing the data are available in Data File 1, Ref. [62].
Supplemental document
See Supplement 1 for supporting content.
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