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Rintaro Minami, Eiji Kita, Chiharu Mitsumata, Hideto Yanagihara

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[Estimation of valence state and growth rate using principal component analysis of plasma emission in reactive sputtering deposition](https://mdr.nims.go.jp/datasets/57dea07d-6ef9-4877-b490-9af0806ab49c)

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ARTICLEEstimation of valence state and growth rate using principalcomponent analysis of plasma emission in reactive sputteringdepositionRintaro Minamia, Eiji Kitaa, Chiharu Mitsumataa,b, and Hideto Yanagiharaa, ba Department of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, JapanbTsukuba Research Center for Energy Materials Science (TREMS), University of Tsukuba,Tsukuba, Ibaraki 305-8573, JapanARTICLE HISTORYCompiled July 24, 2025ABSTRACTReactive sputtering is a complex process in which the valence state of the depositedmaterial and the deposition rate are highly sensitive to growth conditions. Reli-able monitoring is essential for achieving reproducible and high-quality thin filmgrowth; however, practical methods remain limited. In this study, we developed areal-time analysis method that combines broad-range plasma emission spectroscopywith principal component analysis (PCA). The results demonstrate that the valencestate and deposition rate of iron oxide thin films can be accurately predicted usingthe first and second principal components. This approach offers a promising tool forreal-time prediction and control of the deposition process.KEYWORDSmachine learning; principal component analysis (PCA); reactive magnetronsputtering; plasma emission spectrum; Mössbauer spectroscopy.1. IntroductionThin films of various ceramic compounds, such as oxides and nitrides, are importantfunctional materials. Among the many methods for growing such films, magnetronsputtering is a widely used physical vapor deposition (PVD) techniques both in ba-sic research and industrial applications. Reactive magnetron sputtering enables thegrowth of a wide range of fascinating oxides and nitrides with diverse compositionsand relatively high throughput by controlling the amount of reactive gas such as oxy-gen or nitrogen. In practice, reactive sputtering is used to produce various functionalmaterials, including TiO2 [1,2] for photocatalytic and photoelectrochemical applica-tions, TiN and Si3N4 [3] for protective coatings, aluminum-doped zinc oxide(AZO) asan alternative to indium tin oxide(ITO) for transparent electrodes [4], and Cu2O [5]and ZnO [6] for solar cell applications.A major practical issue in reactive sputtering is the hysteresis observed in the re-lationship between deposition rate and reactive gas flow. This phenomenon arisesCONTACT Chiharu Mitsumata Email: mitsumata.chiharu.fp@u.tsukuba.ac.jp, and Hideto YanagiharaEmail: hideto.yanagihara.fm@u.tsukuba.ac.jpbecause the target surface transitions between metallic and compound (oxidized or ni-trided) states as the reactive gas flow increases or decreases. However, this transitionstrongly depends on the prior state of the target surface. The sputtering process inthe metallic state is referred to as the metallic mode, whereas the sputtering in thecompound state is known as the compound mode, or more specifically, the oxide ornitride mode when using oxygen or nitrogen, respectively.This difference in oxidation or nitridation state of the target surface causes hys-teresis in the deposition rate, which has been observed both experimentally [7–12]and theoretically.[13,14] As a results, even under nominally identical deposition con-ditions, the deposition rate and composition ratio of sputtered thin films can vary,making real-time process control challenging.In PVD processes, including sputtering, a quartz crystal microbalance is often usedto monitor film thickness in real time. This device estimates mass by measuring changesin oscillation frequency caused by accumulating film [15]. However, in reactive sput-tering, oxidation and nitridation reactions are highly sensitive to minor environmentalfluctuations within the chamber, making accurate real-time film thickness estimationdifficult. Empirically, the color of plasma emission during reactive sputtering appearsto strongly depend on the amount of reactive gas introduced. This suggests the emis-sion spectrum contains comprehensive information about the ionization states of inertgases, reactive gases, and target species.In fact, plasma emission analysis has been considered a cost-effective and control-lable method for monitoring reactive sputtering, based on techniques developed forconventional non-reactive sputtering.[7,10,16–22]. Previous studies have primarily fo-cused on specific emission lines associated with atoms in the chamber. However, theintensities of these lines result from complex interactions involving emission and ab-sorption by various species in the process environment. Moreover, determining whichwavelengths should be monitored remains fundamentally unclear, with no assurancethat monitoring only a specific line will adequately capture phenomena such as hys-teresis in deposition rate due to changes in reactive gas flow. Therefore, we analyzethe entire emission spectrum, by incorporating all available wavelength informationrather than focusing on individual lines.Among various analytical methods, we selected principal component analysis (PCA)for its ability to clearly reveal the relationship between dependent (analysis results)and independent (input data) variables, thereby facilitating interpretation. PCA hasalready been applied in several pioneering studies in materials science, particularly inplasma-based processes. [23–25]It was used to explore relationships between emissionspectra and material properties. In contrast, to this earlier research, this study aimsto extract information about the growing film to enable real-time process control.A suitable prototype compound for this purpose must satisfy two criteria: (1) thevalence (oxidation) state should be controllable by adjusting the oxygen flow, and(2) a clear transition between metallic and compound modes should be reflected inmeasurable physical properties and/or the growth rate. The growth of spinel-typeiron oxide thin films by the reactive magnetron sputtering satisfies both criteria. Byadjusting the oxygen gas flow rate (φ), either Fe3O4 (containing mixed-valence Fe2+and Fe3+) or γ-Fe2O3 (comprising Fe3+ only) can be selectively grown [26], withcorresponding differences in growth rate and valence state. In this study we appliedPCA to plasma emission spectra measured during deposition, aiming to predict boththe valence state and the growth rate of iron oxide thin films. Additionally, we used thePCA results and plasma spectra to derive a physical interpretation of the depositionprocess.2This article is organized as follows: Section 2 outlines the fabrication method foriron oxide thin films. Section 3 describes the evaluation of valence state and depositionrate. Section 4 presents the PCA results. Finally, Section 5 summarizes the findingsof the study.2. MethodSpinel-type iron oxide thin films were grown using reactive RF magnetron sputteringby introducing O2 gas into an Ar base gas during film growth. The process temperaturewas 300◦C. Single crystal MgO (001) substrates were used. A 15 sccm Ar gas flow wasmaintained, while O2 flow was varied from 0.0 to 1.5 sccm as a growth parameter. Thetotal gas pressure was kept between 1.60 and 1.65 Pa. The RF sputtering power wasset to 100 W. After the substrates were heated at 300◦C for 1 hour, pre-sputtering wasperformed for 10 minutes in a 15 sccm Ar flow. Sputtering deposition was then carriedout by introducing O2 gas as a reactive component. Films with thicknesses typicallyranging from 30 to 60 nm were grown for various physical property measurements.Because the reactive sputtering process often exhibits hysteresis between the metal-lic and the oxide modes, careful control of the target surface state whether metallicor oxidized is essential for ensuring experimental reproducibility. To address this, weconducted film growth experiments using two different deposition procedures, refferedas the ascending process(AP) and descending process(DP) as described in Tables 1.As shown in Fig. 1, plasma emissions characteristic of the reactive RF magnetronsputtering process during the fabrication of iron oxide samples were observed usinga Czerny-Turner-type spectrometer (Thorlabs CCS220). The emissions were collectedthrough a quartz-glass viewport via an optical fiber[27].The viewport is located roughly50 cm away from the cathode. The spectrum data were integrated and normalized toover one minute.To characterize the lattice constants and film thicknesses of the grown films, X-ray diffraction (XRD) and X-ray reflectivity (XRR) measurements were performedusing Co-Kα radiation. The valence state of the iron oxide films was investigated byconversion electron Mössbauer spectroscopy (CEMS) (see Appendix A). All charac-terizations were conducted at room temperature. The following sections present theresults of these analyses.3. Experimental Results3.1. Determination of lattice constants and valence stateThe XRD results for all fabricated thin film samples could be categorized into tworepresentative patterns, as shown in Fig. 2. These patterns correspond to samplesgrown by the DP process at oxygen flow rates of 0.5 sccm and 1.5 sccm, respectively.The results qualitatively agree with previous report [26], indicating that Fe3O4 tendsto form at lower oxygen flow rates, whereas γ-Fe2O3 is more likely to form underhigher oxygen flow conditions.The results of CEMS experiments and analyses are summarized in Appendix A.Representative CEMS spectra are shown in Fig. A1. The oxygen flow dependenceof both lattice constants and valence states is summarized in Figs. 3(a) and 3(b),respectively. The data indicate that Fe3O4 is obtained at the oxygen flow rate of30.3 − 0.9 sccm in the AP and 0.3 − 0.8 sccm in the DP. In contrast, γ-Fe2O3 isobtained at 1.0 − 1.5 sccm in the AP and at 0.9-1.5 sccm in the DP. Notably, at anoxygen flow rate of 0.9 sccm, significant differences in lattice constants were observedbetween the two processes, indicating the hysteresis region of the reactive sputteringprocess.3.2. Determination of growth rateFilm thickness was measured using XRR method. Fig. 4 shows the calculated growthrates based on film thickness and deposition time at each oxygen flow rate, along withthe iron flux rate. As with the valence states and lattice constants, clear hysteresis ap-pears near φ =0.9 sccm.This demonstrates that typical characteristics of the reactivesputtering process also appear in this oxide system.[7] The iron flux rate representsthe number of iron atoms deposited per square meter per second. At φ = 0.9 sccm,although the oxygen flow rates were identical, noticeable differences in growth rateswere observed between the AP and the DP, consistent with differences in lattice con-stants and valence states. The hysteresis gap is largest at this point, indicating thatit corresponds to the transition region discussed in the previous section.4. Analysis and Discussion4.1. Dimensional reduction with PCAAs shown in Fig. 5, the plasma emission spectra observed during deposition exhibitnumerous peaks, and their intensities depend strongly on the deposition conditions.Machine learning was applied to the spectral data to systematically analyze spectralchanges under different sputtering conditions. Since spectral data are functions ofwavelength, they form high-dimensional vectors. Thus, PCA was used for dimension-ality reduction and feature extraction.PCA leverages data variance as a feature, and can be implemented using either cen-tralization (focusing on the mean), or standardization (focusing on variance). Sincethe intensity of plasma emission spectra varies significantly depending on the elementor ion species, only centralization was applied in this study. Plasma emission spectrawere integrated over a 10-minute period from the onset of deposition. The measureddata were preprocessed by normalizing each spectrum to its maximum intensity. Ad-ditionally, to address the spectrometer’s dynamic range limitations, intensities below1/300th of the maximum were set to 0 as noise.The contribution rates of the principal components indicating the proportion ofvariance retained from the original data, were calculated. The first principal com-ponent(PC1) retained 65.5%, PC2 retained 31.2%, PC3 retained 1.5%, and PC4 re-tained 0.6% of the total variance. The contribution rate dropped significantly fromPC3 onward. The cumulative contribution rate for PC1 and PC2 reached 96.7%, in-dicating that these two components retained sufficient information. Thus, the original3,648-dimensional data (corresponding to the number of wavelengths) were effectivelyreduced to two dimensions for subsequent analysis.44.2. Prediction of valence state and growth rateAn analysis of the valence states of iron oxide thin films under varying oxygen flowrates, as a function of principal component scores, is shown in Fig. 6. Each sampleis plotted according to its oxygen flow rate and whether it followed the AP or DP.A linear boundary (PC2 = 2.308 × PC1) separating Fe3O4 and γ-Fe2O3 regions wasdetermined using a simple perceptron algorithm, as indicated by the dashed line.Samples on the left side of the boundary corresponds to γ−Fe2O3 and those on theright side to Fe3O4. The symbols ”+” and ”×” denote the centroid positions of eachgroup, which serve as reference data derived from machine learning.Deposition rates (from Fig. 4) were then plotted against PC1 and PC2. Assuminga linear relationship, multiple regression fitting was performed, and the results areshown in Fig 7. Although hysteresis was observed around an oxygen flow rate of 0.9sccm, the regression yield a high correlation coefficient (R2 = 0.89). Figures 6 and7 demonstrate that plasma emission spectra can be used to predict deposition ratesregardless of the iron oxide phase.In general, the sputtering deposition rate strongly influenced by input power, withhigher power resulting in faster deposition. Under high-power plasma conditions, spec-tral line intensities increase, making them useful for controlling deposition rates. How-ever, in this study, spectral data were standardized by maximum intensity, meaningthat absolute intensity-values were not used. PCA axes are derived from the eigenvec-tors of the variance-covariance matrix of the data, meaning PCA scores are influencednot only by specific wavelengths but also by the distribution of relative intensities. Thesuccessful correlation between PCA scores and deposition rates in this study suggeststhat relative rather than absolute intensity was dominant facotr. These findings high-light the importance of feature extraction using machine learning for emission-basedprocess control in reactive sputtering.4.3. PCA LoadingsThis section explains the physical significance of the first and second principal compo-nents used to estimate valence and deposition rate in the previous section. The prin-cipal component loadings represent the elements of the eigenvectors of the variance-covariance matrix of the original data and those indicate the correlation coefficientsbetween the data vectors and the principal component axes. Larger absolute valuesof the loadings signify a greater contribution from the spectral data at a given wave-length to the corresponding principal component axis. Principal component analysisis a linear mapping of the spatial coordinates representing the data distribution. Thecontribution to the principal component scores from each wavelength can increase ordecrease depending on the loadings. As a result, the scores extract characteristic shapeinformation embedded in the spectral data. The loadings control the degree to whichdata at specific wavelength increase or decrease the principal component scores. Forinstance, in two-dimensional space as shown in Fig.6, positive and negative loadingson the PC1 axis correspond to rightward and leftward shifts, respectively, while thoseon the PC2 axis correspond to upward and downward shifts. The magnitude andsign of the loadings at each wavelength determine the location of a sample in PCAspace. Figure 8 shows, the loadings of the first and second principal components acrossall measured wavelengths. These loadings represent the contributions of all samples,including both Fe3O4 and γ-Fe2O3.The wavelengths corresponding to emissions from elements in the material system5are compared with the principal component loadings in Fig.9. The elements includedare Fe I, Fe II, and Ar, and the emission wavelengths from the NIST database [28] wereused as references. The measured wavelengths were grouped into regions (a) through(d) based on differences in emission intensity from each ion. In the short-wavelengthregion, primarily Fe I emissions were observed, though some emissions did not alignwith notable features in the loadings ( Fig. 9(a)). In Fig. 9(b), contributions fromboth Fe I and Fe II are present; notably, Fe II around 510 nm and Fe I around 517nm contribute independently. However, estimating the valence state in this region isdifficult, as the PC1 loadings are positive and the PC2 loadings are negative. Dur-ing deposition, emission spectrum was more intense at wavelengths above 700 nm,as shown in Fig.5. In Figs. 9(c) and 9(d), the dominant emissions originate fromAr, indicating that changes in plasma conditions influenced the principal componentloadings in these regions. While these emissions do not directly originate from thedeposited material, plasma-state variations during deposition may have affected ma-terial valence. For example, the most notable spectral differences between Fig.5(a)and (b) are in the 750 nm and 840 nm regions. Here, the PC1 loading is positive andthe PC2 loading is negative. Consequently, the emission intensity in this wavelengthrange tends to increase when the principal component scores are located in the lowerright region of Fig 6. This analysis demonstrates that comparing spectra with machinelearning results is effective for material identification. However, a more direct methodfor estimating material valence remains necessary.4.4. Inverse transformation from PCA coordinatesThis section considers the real-time control of the film deposition process throughemission spectrum analysis. In PCA, it is necessary to construct a variance-covariancematrix that includes data collected during film deposition. However, the accumulationof training data reduces computational speed, making real-time control impractical.To address this, a parallel method combining immediate spectral analysis and high-precision machine learning was developed.First, we describe the mathematical operations required for the inverse transforma-tion. As is well known, PCA is a linear transformation of position vectors in orthogonalspace. Let D be the matrix of centered spectral data for all samples. The transforma-tion that maximizes the variance in D is given by,P = DU (1)where U is the matrix whose columns are the normalized eigenvectors of DTD, and DTdenotes the transposed matrix of the data array. This transformation maps the originalplasma emission spectra D to the principal component space P . The components ofthe eigenvectors u that make up U correspond to the PCA loadings described earlier.Since the loadings indicate how much wavelength contributes to a principal componentspectrum based on how much each wavelength contributes to a principal component,the inverse transformation of the Eq.(1) reconstructs the spectrum based on featuresextracted by PCA. The inverse transformation is defined as,Drev = PUT (2)where P is the scattered data from each sample. When interpolated data points pare used, the spectrum reconstructed from prinipal component features is given by6drev = pUT , which is the feature vector. Because the original matrix D was mean-centered, drev must be adjusted by adding back the mean spectral intensity to compareit with actual measured spectra.In this study, the first and second principal components retain 96.7% of the vari-ance in the original data. Therefore, the emission spectra were reconstructed usingonly these two components. As shown in Fig.6, the centroid positions of each ironoxide thin film in principal component space were used to compute average emissionspectra. Figure. 5(c) and (d) show the results of the inverse transformation of the cen-troids (PC1,PC2), which characterize the deposition processes of Fe3O4 and γ-Fe2O3,respectively. These reconstructed spectra, derived via machine learning, serve as rep-resentative emission profiles for identifying the emitting plasma during deposition.Note that the spectral difference between Fig. 5(c) and (d) tends to resemble the PC1loadings (not shown here).Figure 10 presents the cosine similarity between these reconstructed spectra andexperimentally measured spectra obtained during iron oxide thin film deposition. Thespectra from all measured samples were used to calculate the similarity to the sim-ulated Fe3O4 and γ-Fe2O3 spectra. Similarity to Fe3O4 is plotted on the horizontalaxis, and similarity to γ-Fe2O3 is on the vertical axis. Based on the results, spectrafalling below the dashed line are identified as Fe3O4, whereas those above are identifiedas γ-Fe2O3. These classifications are consistent with Mössbauer spectroscopy results(Table A1), where circles correspond to γ-Fe2O3 and triangles to Fe3O4, confirmingthe validity of classification using cosine similarity. Accordingly, the valence of theoxide film can be determined in real time during deposition using pretrained machinelearning model. For instance, this enables evaluation of whether the oxygen flow rateis excessive or insufficient, providing feedback on process parameters. However, as il-lustrated in Fig.10, this approach does not yet support linear-scale control of processparameters in real time. We consider linear-scale process control to be a future issueto be addressed in a separate study.5. SummaryWe addressed the inherent complexity of the reactive sputtering process for iron oxidefilm growth, where the valence state and deposition rate of thin films are highly sensi-tive to deposition conditions. A real-time diagnostic method was developed, combiningplasma emission spectroscopy over a broad wavelength range with PCA.The analysis revealed that the valence state and deposition rate of iron oxide thinfilms can be accurately predicted using only the first and second principal componentsderived from the emission spectra. This approach remained effective even under typicalreactive sputtering conditions exhibiting hysteresis with respect to the reactive gas flowrate, including in the transition region. These findings demonstrate that even complexprocesses in reactive sputtering can be effectively interpreted and predicted throughmultivariate analysis of plasma emissions.This approach not only enhances the physical understanding of the sputtering pro-cess but also offers a practical solution for real-time process monitoring and control.Future work will focus on extending this method to other material systems and inte-grating it with feedback control mechanisms for fully automated deposition processes.7AcknowledgementsMössbauer studies were performed at the Tandem Accelerator Complex, Universityof Tsukuba (UTTAC), and the Organization for Open Facility Initiatives, Universityof Tsukuba. This work was supported by the Japan Society for the Promotion ofScience (JSPS) KAKENHI (22H04966, 23K26535, and 24H00408), and in part, by theAdvanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM)of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) ofJapan (grant number JPMXP1224BA0008).References[1] Lindgren T, Mwabora JM, Avendaño E, et al. Photoelectrochemical and opti-cal properties of Nitrogen doped Titanium dioxide films prepared by reactiveDC magnetron sputtering. The Journal of Physical Chemistry B. 2003 Jun;107(24):5709–5716. Available from: https://doi.org/10.1021/jp027345j.[2] Takeda S, Suzuki S, Odaka H, et al. Photocatalytic TiO2 thin film deposited ontoglass by DC magnetron sputtering. Thin Solid Films. 2001;392(2):338–344. 3rdInternational Conference on Coatings on Glass (ICCG); Available from: https://www.sciencedirect.com/science/article/pii/S0040609001010549.[3] Chen YH, Lee KW, Chiou WA, et al. 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Plasma emission spectra were collectedby a spectrometer through a quartz-glass viewport via an optical fiber.11Figure 2. Typical XRD patterns around the MgO(004) peak. Green circles and yellow triangles representresults at oxygen flow rates of 0.5 sccm and 1.5 sccm, respectively.12Figure 3. O2 flow dependence of (a) lattice constants and (b) valence ratios from CEMS for reactively sput-tered iron oxide thin films. Solid circles and triangles correspond to samples from the AP and DP, respectively.13Figure 4. Growth characteristics of the iron oxide thin films. Black circles represent AP results, and redtriangles represent DP results. (a) Deposition rate at each oxygen flow rate. (b) Iron flux rate at each oxygenflow rate. The fitting curves are visual guides.14Figure 5. Plasma emission spectra observed during the fabrication of iron oxide samples using the AP(wavelength range: 200-1000 nm). (a) Spectrum at an oxygen flow rate of 0.3 sccm. (b) Spectrum at an oxygenflow rate of 1.5 sccm. (c) PCA-inverse-transformed spectrum at the centroid of Fe3O4. (d) PCA-inverse-transformed spectrum at the centroid of γ-Fe2O3.15Figure 6. Iron oxide samples plotted in principal component space using the first and second principalcomponents. Circles represent samples from the AP; triangles represent those from the DP. The symbols ”+”and ”×” indicate centroid positions for γ−Fe2O3 and Fe3O4, respectively. The dashed line is the perceptronderived boundary separating the two compounds.16Figure 7. Prediction of growth rate using the first and second principal components. A multiple regressionanalysis was performed to derive a first-order polynomial for predicting growth rate. The growth rate z [Å/s] isexpressed using PC1 (x) and PC2 (y) as z = 0.34− 0.30x− 0.23y, shown by the dashed line. Circles representγ-Fe2O3 thin films, whereas triangles represent Fe3O4 thin films.17Figure 8. Principal component loadings at each wavelength (wavelength range: 200− 1000nm) for (a) PC1and (b) PC2.18Figure 9. Comparison of principal component loadings and emission wavelengths of Fe I (neutral Fe atoms),Fe II (Fe+ ions), and Ar. Short-wavelength regions: (a) 410−450nm, (b) 500−525nm. Long-wavelength regions:(c) 720− 800nm, (d) 800− 880nm.19Figure 10. Cosine similarity between the plasma emission spectra measured during iron oxide thin filmfabrication and the simulated spectra obtained by inverse transformation from the centroids in Fig. 6.20Table 1. Deposition procedures for AP and DP. The pre-sputtering steps PS1 and PS1-1 remove surfaceoxides from the target. PS1-2 forms a sufficiently thick oxide layer on the target surface. PS2 stabilizes thesurface oxide under steady-state conditions at a predetermined oxygen flow rate.Process step O2 flow rate (sccm) Duration (min)PS1 0.0 10.0AP PS2 Set value 10.0Film growth Set value Appropriate timePS1-1 0.0 10.0DP PS1-2 2.0 10.0PS2 Set value 5.0Film growth Set value Appropriate time21Appendix A. Valence state determinationTo evaluate the valence states of the fabricated iron oxide thin films, conversion elec-tron Mössbauer spectroscopy (CEMS) was used. While traditional Mössbauer spec-troscopy counts transmitted γ-rays, the CEMS technique [29] measures internal con-version electrons ejected following the resonant absorption of γ-rays. With a maximumescape depth of about 100 nm, this method is well-suited for thin film measurements,and was used for measurements of iron oxide thin films [26]. A conventional CEMScounter was employed, and spectra recorded at room temperature were analyzed usingcommercially available fitting software (MossWinn 4.0). Mössbauer parameters of hy-perfine fields (Hhf), isomer shifts (δ) and subspectral area ratios were extracted fromthe fits. Figure A1 shows the CEMS spectra recorded at room temperature and theirfitted results for iron oxide samples fabricated under the Ascending Process.(1) Oxygen Flow Rate: 0.3 sccm The spectrum in Fig. A1 (a) consists of twosextets with internal magnetic fields of approximately 500 kOe and 450 kOe.These values along with the isomer shifts, correspond to the A and B sites ofthe spinel structure of Fe3O4 [30]. Confirming its presence of Fe3O4 in the thinfilm [31].(2) Oxygen Flow Rate: 1.5 sccm The spectrum in Fig. A1 (b) is characterizedby a single sextet around 500 kOe, indicating the presence of γ-Fe2O3[30]. Thisoxide contains only Fe3+ ions and shows nearly identical magnetic fields andisomer shifts for both A and B sites, making it difficult to distinguish betweenthem. The absence of spectral peaks near 450 kOe confirms that the film consistssolely of γ-Fe2O3 [32].For other samples, the spectra could be categorized as either Fe3O4 as in Fig. A1(a) or γ-Fe2O3 as in Fig. A1(b), and the corresponding fitting parameters are listedin Table A1. The ratios of Fe2.5+ and Fe3+ were evaluated from the fit results and areshown in Fig. 3 (b). In Fe3O4, the A sites are occupied by Fe3+, whereas the B sitesare occupied by equal amounts of Fe2+ and Fe3+, namely Fe2.5+ . The Fe2+/Fe3+ ratioin Fe3O4 samples was estimated from the area ratio of A and B sites.Based on Table A1 and Fig. 3, the results are summarized as follows:• In the Ascending Process, Fe3O4 is formed at oxygen flow rates of 0.3 – 0.9sccm, and γ-Fe2O3 is formed at 1.0 – 1.5 sccm.• In the Descending Process, Fe3O4 is formed at oxygen flow rates of 0.3 – 0.8sccm, and γ-Fe2O3 is formed at 0.9 – 1.5 sccm.Notably, at an oxygen flow rate of 0.9 sccm, the lattice constants and valence statesdiffer depending on the deposition process. At low oxygen flow rates, Fe is sputteredfrom the target in metallic form (metal mode) and reacts with oxygen on the substrateto form Fe3O4, which has a lower oxidation state. At high flow rates, the target surfacebecomes oxidized (compound mode), and oxidized iron is sputtered and further reactswith oxygen on the substrate, resulting in γ-Fe2O3 with a higher oxidation state.22Figure A1. Representative CEMS spectra for iron oxide samples. The circles represent experimental data,and the red lines indicate fitted results. (a) Spectrum of the sample grown at an oxygen flow rate of 0.3sccm. The green and blue lines correspond to the fitted components for the A site (Fe3+) and B site (Fe2.5+),respectively. (b) Spectrum of the sample grown at an oxygen flow rate of 1.5 sccm, fitted assuming a singlevalence state of Fe3+.23Table A1. Mössbauer fitting parameters for reactively sputtered Fe oxide thin filmsAscending Process Descending ProcessO2 flow Hhf (kOe) δ* (mm/s) Area (%) Hhf (kOe) δ* (mm/s) Area (%)(sccm) A B A B A B A B A B A B0.3 505 466 0.43 0.66 56.4 43.6 505 467 0.40 0.68 51.6 48.50.5 503 464 0.41 0.66 52.7 47.3 503 466 0.36 0.64 44.8 55.20.7 503 465 0.36 0.67 47.0 53.0 490 459 0.28 0.66 35.2 64.80.8 491 460 0.26 0.64 33.3 66.7 496 464 0.30 0.66 49.9 50.10.9 496 464 0.36 0.67 57.9 42.1 507 0.31 1001.0 501 0.38 100 501 0.26 1001.1 514 0.35 100 505 0.36 1001.5 501 0.38 100 501 0.38 100*δ : Isomer shift relative to α-Fe.24 Introduction Method Experimental Results Determination of lattice constants and valence state Determination of growth rate Analysis and Discussion Dimensional reduction with PCA Prediction of valence state and growth rate PCA Loadings Inverse transformation from PCA coordinates Summary Valence state determination