Rare-earth (RE) ion-doped phosphors have attracted much attention in applications such as solar cells [1] [2] [3], photocatalysts [4], and white Light-Emitting Diodes (W-LEDs) [5] [6], displays and temperature sensing [7], because they exhibit sharp and intense luminescence in the visible and near-infrared wavelength regions. Since the 4f inner-shell transition of rare-earth ions is generally prohibited, host materials that relax the selection rule are candidates for utilizing the luminescence phenomenon derived from this transition [8]. Of these, rutile and anatase types of titanium oxide (TiO₂) thin films are the most likely candidates. In our group’s previous research [9] [10] [11] [12] [13], we found that the best way to increase the luminescence derived from RE ions is to add them to anatase TiO₂ (A-TiO₂), and when Sm³⁺ or Nd³⁺ ions are added to TiO₂, they replace the Ti sites and are incorporated into the TiO₂ matrix. According to a detailed X-ray absorption fine structure (XAFS) analysis, the difference in luminescence is explained by the change in the ligand structure of the REs when added to the rutile and anatase crystal lattices. When adding to the rutile, the distances between the surrounding six oxygen ions are equal, but when adding to anatase, the sample showed strong luminescence because the six-fold oxygen ions are distinguished by four oxygen ions (O₄) and two oxygen ions (O₂). The difference in distance between these two types of oxygen ions and RE ions is large, which enhances luminescence. Based on the Judd-Ofelt theory [14] [15], the ligand structure surrounding the REs determines the spontaneous emission rate of the REs, which may be interpreted as an increase in the spontaneous emission rate due to the low symmetry induced in anatase. In addition, since the branching rate of anatase luminescence varies little between samples, it may be closely related to the increase in the population of low-symmetry ligand structures that enhance or induce this luminescence. We know that symmetry that maximizes luminescence can be obtained by annealing Sm-doped TiO₂ formed on a Si (100) substrate at 700˚C - 800˚C in an oxygen atmosphere. However, with this information, it is necessary to repeat the experiment again to find the optimum parameters when the board is changed. In addition, there is still a degree of freedom in selecting the board, so it is not sufficient information for establishing new measures. In this study, we aim to propose a strategy to produce materials with high luminescence intensity from XRD data. For this purpose, we used LASSO regression one of the machine learning algorithms [16], to predict the integrated luminescence intensity using the experimentally obtained XRD patterns as explanatory variables.

Sm-doped TiO₂ thin films were deposited on Si (100) substrate by laser ablation using a YAG laser (λ = 355 nm, 1 W/cm²). The crystal structure of TiO₂ can be selected between anatase and rutile forms by carefully manipulating the oxygen partial pressure during the ablation [12], and the single phase anatase thin films were fabricated in 1.5 × 10⁻² Torr. These samples were annealed in a vacuum or oxygen atmosphere for 10 to 60 min at 400˚C to 900˚C, for a total of 72 samples. XRD patterns of these samples were then acquired at 0.01 rad intervals. A He-Cd laser (λ = 325 nm) was used to measure the fluorescence intensity from the samples. If the spectrum of the XRD pattern is used as an input as it is, the explanatory variables exceed the prepared 72 samples and the risk of overfitting increases, so the number of explanatory variables should be reduced. For this reason, the peak positions and full width at half maximum (FWHM) data that commonly appeared in all the samples are shown in Table 1 were extracted from

the XRD patterns and used as explanatory variables. The integrated intensity of the luminescence of the 4 G 5 / 2 → 6 H J / 2 (J = 5, 7, 9, 11) inner shell transitions originating from Sm³⁺, which was commonly observed in all samples, was calculated and the sum of them was used as the objective variable. These variables were tied together to construct a prediction model by LASSO regression. In LASSO model, the importance of each explanatory variable is expressed by the weight of that variable. These weights are chosen to minimize the following equation:

∑ i = 1 N ( y i − β 0 − ∑ j = 1 K β j x j ) + α ∑ j = 1 K | β j | (1)

where N is the number of samples, K is the number of explanatory variables, y_i is the true value of sample i, β₀ is the intercept, β_j is the weight of the j-th explanatory variable, and α is the tuning parameter.

Figure 1 shows the integrated PL intensity of the fluorescence from

4 G 5 / 2 → 6 H J / 2 (J = 5, 7, 9, 11) obtained from the PL measurement, normalized by the maximum value obtained in this experiment. The horizontal axis represents the temperature of the heat treatment applied to the material after film formation, and the vertical axis represents the time at which the temperature was maintained. Figure 1(a) shows the integrated luminescence intensity when the heat treatment was performed in an oxygen atmosphere. Figure 1(b) shows the integrated luminescence intensity when the heat treatment was performed in a vacuum, and the results are similar to those in Figure 1(a), but the integrated luminescence intensity is generally lower. Considering the relationship

between (a) and (b) in Figure 1, it can be inferred that the presence or absence of oxygen defects plays a role. It is known that energy is exchanged between rare-earth ions in rare-earth doped phosphors, and the energy used for luminescence is lost with the increase of oxygen defects [17] [18], resulting in a decrease in the overall fluorescence intensity.

Figure 2 shows the lattice constants of the a- and c- axes calculated from the XRD patterns using the Bragg equation. In this figure, a sample without annealing (As-depo in Figure 2) is prepared for comparison, and the average values of the lattice constants are plotted because the changes in the lattice constants were small at the same annealing temperature. From this figure, it can be seen that the annealing causes an overall decrease in the lattice constant compared to As-depo, and the decrease tends to increase with increasing annealing temperature.

As shown in Figure 3, the peak shifts and standard deviation of FWHM at the crystal plane were observed for all samples. Each point is derived from all the samples, which indicates that the peak shift varies from 0.02 rad to 0.07 rad among the samples. In contrast to the variation of the peak shift, the variation of the FWHM between samples is almost negligible.

Figure 4 shows the prediction results of the LASSO regression using the explanatory variables (Table 1) extracted from the XRD pattern. The coefficient of determination R² and the mean squared error (MSE) of this model were obtained to be 0.76 and 0.03, respectively. The closer the coefficient of determination is to 1, the better the fit of the model is, and the closer the MSE is to 0, the better the prediction is and with less error.

As shown in Figure 5, the importance of each explanatory variable estimated from the LASSO regression, excluding the explanatory variables that became zero because the LASSO regression sets parameters with low importance to zero. It

can be seen that the most important explanatory variables are P(200), F(200), P(101), P(103), and F(101) in that order. These important factors can be attributed to the incorporation of Sm into the matrix of TiO₂, which generates internal stresses [19], and furthermore, the incorporation of Sm changes the lattice constant as explained by Vegard’s rule. Since the results of Figure 2 show that the a- and c- axes change with increasing annealing temperature, it is considered that the increase in annealing temperature is proportional to the amount of Sm incorporated into the matrix of TiO₂. In this way, since the luminescence intensity is maximized at around 700˚C, it may be said that the internal stress generated by the Sm cells incorporated at around 700˚C created the local structure that maximizes the luminescence.

In this research investigation, the integrated luminescence of Sm-doped TiO₂ deposited on Si (100) substate in the visible light region is predicted by using XRD data. Since the raw XRD pattern has many data, we extracted the peak positions and half-widths of the peaks derived from TiO₂ and used these as explanatory variables. Using these explanatory variables and luminescence data, a model to predict the integrated luminescence intensity was constructed using LASSO regression, one of the machine learning algorithms. The model was able to predict the integrated luminescence intensity with high accuracy. It was found that P(200), F(200), P(101), P(103), and F(101) are important factors in this model. The background of this model is the incorporation of Sm into the matrix of TiO₂, which may express the relationship between the internal stresses generated by the incorporation and the local structure around Sm.

The authors would like to thank the member of Zhao laboratory for their experiment help and involvement in this study.

The authors declare no conflicts of interest regarding the publication of this paper.

Tamamoto, Y., Murayama, M. and Zhao, X.W. (2022) Optimization of Crystal Structure Based on Experimentally Obtained XRD Patterns for Fluorescence of Sm³⁺-Doped TiO₂ Thin Films by Machine Learning. Optics and Photonics Journal, 12, 147-155. https://doi.org/10.4236/opj.2022.126011