# Machine Learning Approach for Maximizing Thermoelectric Properties of BiCuSeO and Discovering New Doping Element

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}of 0.93, compared to the original model (R

^{2}of 0.57). The model was validated and used to predict the ZT of the unknown doped BiCuSeO compounds. The predicted result was logically justified based on the thermoelectric principle. It means that the ML model can guide the experiments to improve the thermoelectric properties of BiCuSeO and can be extended to other materials.

## 1. Introduction

_{i}is the regression coefficient automatically calculated by an ML algorithm, and x

_{i}is the feature or descriptor for representing the character of materials. Even though there are many ways to generate the features, Magpie is the software that originates features for material science by using physical properties. They are operated with mathematics requiring only chemical formula [10]. Furthermore, the features have the potential to build an ML model with advantages in a comfortable and quick method for searching new candidate materials [11,12]. With many advantages, ML has the potential to be a new approach to accelerate the discovery of thermoelectric material with high performance.

#### Related Work

_{x}Bi

_{2}Te

_{2.85+y}Se

_{0.15}system with ML [14]. The correlation between microstructure and thermoelectric properties was investigated with the principal component analysis (PCA) and the regression algorithm. Furthermore, apart from predicting the properties of new materials, ML could design the experimental conditions to obtain a high ZT value. Hou et al. presented an effective way to find the optimal chemical composition of the Al

_{2}Fe

_{3}Si

_{3}thermoelectric compound [15]. With the Bayesian Optimization (BO) algorithm, ML can be applied to the experiment effectively. The power factor can be improved by about 40% compared to the sample with the initial Al/Si ratio of 0.9. Moreover, the author claimed that the framework of this study could be extended to the extrinsic doping of Al

_{2}Fe

_{3}Si

_{3}. These related works can be summarized in Table 1.

_{2}Se

_{2})

^{2−}layers alternatively stacked by the insulating (Bi

_{2}O

_{3})

^{2+}layers. Due to distinct functionalities and the weak bonding between these two layers, BiCuSeO showed outstanding thermoelectric properties and outperformed most thermoelectric oxides [25]. Therefore, intense research interest is focusing on BiCuSeO to lift the thermoelectric performance and ZT even higher. The most common approach to enhance ZT is by extrinsic doping some elements into the BiCuSeO structure to lower thermal conductivity, increase carrier concentration, and optimize electrical transport properties [25,26,27]. Nevertheless, since there are numerous available dopants, tedious experiments are required. Therefore, ML could be a wise choice to address the issue by providing guidance for appropriate effective doping of BiCuSeO.

## 2. Materials and Methods

_{i}is the regression coefficient automatically calculated by an ML algorithm, and x

_{i}is the features or descriptors for representing the character of materials. The algorithm which showed the best performance was selected.

^{2}) and (2) the root mean squared error (RMSE). The R

^{2}was determined by:

_{1-x}A

_{x}CuSeO, where A is the dopant and x was set to 0.02). To discover a candidate to maximize the ZT value, the dopant (element A) was not in the original datasets and could possibly be done by experiments. Converting the materials into the numerical feature vectors benefits thermoelectric material researchers to build the ML model and discover new candidate material with the only chemical formula.

## 3. Results and Discussions

^{2}), and (2) the root mean squared error (RMSE). R

^{2}accounts for how well the model can capture the correlation between the features and the ZT value, whereas RMSE is used to evaluate the model accuracy regarding the error from prediction. The perfect fit would result in the R

^{2}of 1 and RMSE of 0.

^{2}of 0.57 and the RMSE of 0.13 from the test set. The R

^{2}value is relatively low, implying that the model is not very accurate. The model inaccuracy lies in the original data from the experiment database. The reported ZT values of the pristine BiCuSeO from several research groups varied significantly. For example, Farooq et al. reported the ZT of 0.25 [29], but Yang et al. reported the ZT of 0.42 [30] for the same compound (BiCuSeO). These points are explicitly shown in Figure 2, where the orange squares line up horizontally at the ‘predicted ZT’ around 0.3. The discrepancy was due to the experimental details, such as processing parameters, microstructures, etc., which strongly affect the ML performance because the ML models were trained with the features that were extracted from chemical formulas only. The variations from experimental parameters were not included in the ML model, resulting in the model’s inaccuracy.

_{0.99}Cd

_{0.01}CuSeO of 0.25 and 0.43 [29], while Yang reported the ZT of BiCuSeO and Bi

_{0.98}Pb

_{0.02}CuSeO of 0.42 and 0.66 [30]. By normalizing, the ‘experimental ZT

_{normalized}’ of Farooq’s BiCuSeO and Bi

_{0.8}Cd

_{0.2}CuSeO became 1.0 and 1.72, whereas ‘experimental ZT

_{normalized}’ of Yang’s BiCuSeO and BiCu

_{0.8}Zn

_{0.2}SeO were 1.0 and 1.57. The normalization can be determined as $Z{T}_{normalized}=\frac{Z{T}_{doped}}{Z{T}_{undoped}}\text{}$. In other words, by using this process, the ‘experimental ZT

_{normalized}’ of the pristine BiCuSeO from any publication was turned into unity. The ‘experimental ZT

_{normalized}’ of the doped BiCuSeO thus indicated the ratio of improvement between the doped BiCuSeO and the pristine BiCuSeO. The ML model was then reconstructed such that the ZT was only related to the chemical formulas, and other experimental dependent variables were eliminated.

^{2}of 0.78 and RMSE of 1.48 for the test set. The R

^{2}of 0.78 in Figure 3 is larger than the R

^{2}of 0.57 in Figure 2, indicating the improvement of the model’s accuracy. However, the higher RMSE (1.48) in Figure 3 compared to Figure 2 (RMSE = 0.13) does not mean that its prediction’s error is worse. In fact, it is incorrect to compare the RMSE between the two figures because the data ranges are not the same. The scales in both axes in Figure 2 range between 0 and 1.2, whereas Figure 3 ranges from 0 to 20.0. Hence, it is expected that the RMSE in Figure 3 tends to be higher.

^{2}for the ML model in Figure 3 is relatively high, there are still outliers that deviated from the ideal line, for instance, the orange square and the blue circle on the right of the figure, leading to the reduction of R

^{2}. This situation occurred even when the selected features in the model were already optimized. Therefore, we tried improving our ML model further by analyzing the original datasets. We found that the outliers and inaccuracy of the model could be from the different doping sites in the BiCuSeO compound. In general, doping elements in BiCuSeO is done by substituting atoms at different sites, written in a chemical formula Bi

_{1-x}A

_{x}Cu

_{1-y}B

_{y}Se

_{1-z}C

_{z}O

_{1-w}D

_{w}, where A, B, C, and D are dopants. Sometimes, dual dopings were done at one or more sites. The purpose of doping in each site is different, such as lowering thermal conductivity, bandgap engineering, and tuning electrical transport properties [17]. We assumed that our ML model could not capture the pattern from the data including all variations. Therefore, we analyzed the data and grouped the datasets into a few sub-groups. The major sub-group (145datasets) was the BiCuSeO compound doped at the Bi site (Figure 1), for instance, Bi

_{0.98}K

_{0.02}CuSeO [31]. This group is vital from the thermoelectric perspective. The BiCuSeO structure consists of two layers: the conducting (Cu

_{2}Se

_{2})

^{2−}layers and the insulating (Bi

_{2}O

_{3})

^{2+}layers. The electrical transport pathway is mainly limited to the Cu

_{2}Se

_{2}layers, whereas the Bi

_{2}O

_{2}layers behave as a charge reservoir [32]. Thus, doping at the Bi site provides extra charge carriers for thermoelectric power factor tuning without interrupting the carrier transport. Therefore, the ML was reconstructed based on these datasets.

^{2}was considerably increased to 0.89, with the RMSE of 0.40, indicating the improvement of the model’s accuracy. However, decreasing the amount of data and using many features (154 features) could lead to overfitting, which means the model shows high performance on the training dataset but low performance on the test set [33]. To address the issue, we exported the features or descriptors representing the material characteristics from our ML model and ranked them according to their importance to the model. There were a total of 154 generated features, but the first 30 important features are shown in Figure 5. We then optimized the ML model by including only the important features. We have tried including the first 3, the first 6, the first 9… and so on important features in the model. The best-performance model was obtained when the first 12 important features (as highlighted in Figure 5) were used. Figure 6 shows the results from such a model, with the R

^{2}of 0.93 and the RMSE of 0.33 for the test set, an improvement in accuracy from the model in Figure 4. If one compared the model in Figure 6 to the primitive model in Figure 2, the accuracy performance increased >63%. However, before bringing the model to use, the generalization of the model was carried out via Leave One Out Cross Validation (LOOCV). This method is appropriate, particularly for small-size datasets [5]. The validation resulted in the RMSE of 0.71 for the training dataset, which means that the predicted ZT

_{normalized}values from the model have an error of ±0.71.

^{2}), whereas the electronic configuration of Na is 1s

^{2}2s

^{2}2p

^{6}3s

^{1}resulting in the NUnfilled of 1. In the case of the BiCuSeO compound, the NUnfilled of Bi, Cu, Se, and O is 3, 1, 2, and 2, respectively, and hence, the min_NUnfilled of BiCuSeO is 1, according to the minimum NUnfilled of Cu. For the doped compound, such as Bi

_{0.94}Mg

_{0.03}Pb

_{0.03}CuSeO, the min_NUnfilled of this compound is 0 because the NUnfilled of Mg equals 0. By using Pearson correlation analysis, it was found that the lower the min_NUnfilled, the higher the ZT

_{normalized}. The lowest min_NUnfilled (0) was found in the BiCuSeO doped with, for example, Mg, Ca, Sr, Ba. These elements are divalent ions (Mg

^{2+}, Ca

^{2+}, Sr

^{2+}, Ba

^{2+}). When they were substituted for Bi

^{3+}, an extra +1 charge was generated for charge neutralization. This extra charge increased the carrier concentration of the BiCuSeO system, leading to optimization of power factors [17,34,35]. Therefore, it is reasonable for min_NUnfilled to be the most important feature for our ML model.

_{normalized}of the doped BiCuSeO at Bi-site (Bi

_{1-x}A

_{x}CuSeO, where A is the dopant and x = 0.02). We selected some elements that were not already in the model datasets, and such elements could be synthesized experimentally. Figure 7 shows the predicted ZT

_{normalized}value for some candidate materials. The highest ZT

_{normalized}belongs to the Si-doped compound, which is reasonably justified. It was reported that doping light elements at the Bi-site in BiCuSeO could promote carrier mobility from the decreased carrier scattering [36]. Since Si can be considered as a light element, doping Si for Bi is likely to promote carrier mobility and increase ZT. Moreover, the DFT simulation of the Si doping at Bi-site showed the increased electrical conductivity, with a slight decrease in the Seebeck coefficient, from the modified electronic band near the Femi level, resulting in a large power factor. On the other hand, the Cl-doped compound exhibited the lowest ZT

_{normalized}value from the model. This result is understandable. The previous experiment reported that doping Cl at Se-site negatively affected the ZT value, by increasing both electrical resistivity and thermal conductivity [37]. Thus, Cl is unlikely to be a good candidate for doping in BiCuSeO.

## 4. Conclusions

^{2}of 0.57. We then improved the model’s accuracy by normalizing the experimental ZT of the doped BiCuSeO with the pristine BiCuSeO. The modified ML model showed improved accuracy with an R

^{2}of 0.78. Furthermore, we selected the data for the BiCuSeO doped at Bi-site only and reconstructed the model. The R

^{2}increased to 0.89, indicating the enhanced model’s accuracy. Last but not least, only 12 important features were used in the model, which resulted in the increased R

^{2}to 0.93 and the RMSE of 0.33. Furthermore, the most important feature, min_NUnfilled, was discussed and correlated to the physical parameters of materials. The model predicted the substantial ZT improvement for the Si-doped BiCuSeO material, which is scientifically sound from the thermoelectric principle. Therefore, the ML model of this work can provide a guideline for experimental researchers for improving the thermoelectric properties of BiCuSeO and can be extended to other thermoelectric materials.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The crystal structure of BiCuSeO consists of conducting (Cu

_{2}Se

_{2})

^{2−}layer and insulating (Bi

_{2}O

_{3})

^{2+}layer. It also shows the dopant substituted at the Bi site.

**Figure 2.**The plot of the Predicted ZT versus the Experimental ZT from the ML model using ET regressor. The total datasets of 264 datasets were used, resulting in the R

^{2}of 0.57 and the RMSE of 0.13.

**Figure 3.**The plot of the Predicted ZT

_{normalized}versus the Experimental ZT

_{normalized}from the ML model using RF regressor. The total datasets of 264 datasets were used, resulting in the R

^{2}of 0.78 and the RMSE of 1.48.

**Figure 4.**The plot of the Predicted ZT

_{normalized}versus the Experimental ZT

_{normalized}from the ML model using ET regressor. The total dataset of 145 datasets was used, resulting in the R

^{2}of 0.89 and the RMSE of 0.40.

**Figure 5.**Exported features from the ML model, ranked according to their importance. The first 12 features are: 1. min_NUnfilled = minimum of total number of unfilled valence orbitals of the elements in the material (Bi

_{1-x}A

_{x}CuSeO), 2. range_SpaceGroupNumber = range of space group of T= 0 K ground state structure of the elements, 3. max_ SpaceGroupNumber = maximum of space group of T = 0 K ground state structure of the elements, 4. dev_Row = deviation of row on periodic table of the elements, 5. sum_NfValence = summation of number of filled f valence orbitals of the elements, 6. dev_NValence = deviation of total number of valence electrons of the elements, 7. min_Electronegativity = minimum of Pauling electronegativity of the elements, 8. avg_NfValence = average of number of filled f valence orbitals of the elements, 9. range_Electronegativity = range of Pauling electronegativity of the elements, 10. range_NUnfilled = range of total number of unfilled valence orbitals of the elements, 11. sum_GSvolume_pa = DFT volume per atom of T = 0 K ground state, 12. max_NpUnfilled = maximum of number of unfilled p valence orbitals of the elements.

**Figure 6.**The plot of the Predicted ZT

_{normalized}versus the Experimental ZT

_{normalized}from the ML model using ET regressor. The total dataset of 145 datasets was used with the first 12 important features, resulting in the R

^{2}of 0.93 and the RMSE of 0.33.

**Figure 7.**Predicted ZT

_{normalized}values for the selected Bi

_{0.98}A

_{0.02}CuSeO compounds, where A is the dopant shown in the y-axis.

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**MDPI and ACS Style**

Parse, N.; Pongkitivanichkul, C.; Pinitsoontorn, S.
Machine Learning Approach for Maximizing Thermoelectric Properties of BiCuSeO and Discovering New Doping Element. *Energies* **2022**, *15*, 779.
https://doi.org/10.3390/en15030779

**AMA Style**

Parse N, Pongkitivanichkul C, Pinitsoontorn S.
Machine Learning Approach for Maximizing Thermoelectric Properties of BiCuSeO and Discovering New Doping Element. *Energies*. 2022; 15(3):779.
https://doi.org/10.3390/en15030779

**Chicago/Turabian Style**

Parse, Nuttawat, Chakrit Pongkitivanichkul, and Supree Pinitsoontorn.
2022. "Machine Learning Approach for Maximizing Thermoelectric Properties of BiCuSeO and Discovering New Doping Element" *Energies* 15, no. 3: 779.
https://doi.org/10.3390/en15030779