Searching for Hidden Perovskite Materials for Photovoltaic Systems

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Searching for hidden perovskite materials for photovoltaic systems by combining data science and first principle calculations Keisuke Takahashi, Lauren Takahashi, Itsuki Miyazato, and Yuzuru Tanaka ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01479 • Publication Date (Web): 07 Jan 2018 Downloaded from http://pubs.acs.org on January 7, 2018

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Searching for hidden perovskite materials for photovoltaic systems by combining data science and first principle calculations Keisuke Takahashi,∗,† Lauren Takahashi,¶ Itsuki Miyazato,‡ and Yuzuru Tanaka† Center for Materials research by Information Integration (CMI2 ),National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan, Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan, and Freelance Researcher, Central Ward, Sapporo 064, Japan E-mail: [email protected]

∗

To whom correspondence should be addressed Center for Materials research by Information Integration (CMI2 ),National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan ‡ Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan ¶ Freelance Researcher, Central Ward, Sapporo 064, Japan †

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Abstract Undiscovered perovskite materials for applications in capturing solar lights are explored through the implementation of data science. In particular, 15,000 perovskite materials data is analyzed where visualization of the data reveals hidden trends and clustering of data. Random forest classification within machine learning is used in order to predict the band gap of perovskite materials where 18 physical descriptors are revealed to determine the band gap. With trained random forest, 9,328 perovskite materials with potential for applications in solar cell materials are predicted. The selected Li and Na based perovskite materials within predicted 9,328 perovskite materials are evaluated with first principle calculations where 11 undiscovered Li(Na) based perovskite materials fall into the ideal band gap and formation energy ranges for solar cell applications. Thus, the implementation of data science accelerates the discovery of hidden perovskite materials and the approach can be applied to the materials science in general for searching undiscovered materials.

Keywords Perovskite, Photovoltaic, Machine learning, Density functional theory, Band gap, Random forest Materials informatics is on the brink of changing the dynamics of how materials are discovered. 1–3 At its core, material informatics is essential for accelerating the discovery of materials and uses data science to link hidden trends and periodicities within materials data to material properties. Such trends and periodicities, often referred to as descriptors, can be linked to materials properties within multi-dimensional space through the implementation of machine learning. 4 If the machine is able to determine the relation between data trends and properties, one can then consider it possible to design materials directly from the desired materials properties. 5,6 There have been several successful cases of discovering hidden materials through the use of materials informatics where undiscovered ternary oxide 2


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compounds and materials with low thermal conductivity are found. 7,8 These are but a few examples showing that introducing data science within materials science can accelerate the process of discovering materials. Perovskite materials have garnered much attention due to having ideal band gaps for capturing solar light, leading to the design of photovoltaic systems. 9–12 A tremendous amount of potential element combinations can be considered within perovskite structures, suggesting that there should still be hidden and undiscovered perovskite materials useful for solar light capturing. 13,14 High throughput first principle calculations have previously been used to screen for potential perovskite materials for solar light capturing, but such calculations are found to leave unexplored spaces of perovskite materials due to the limitation of heavy computational times. 13–16 Through utilizing high throughput first principle calculations, approximately 19,000 perovskite oxides, oxynitrides, oxysulfides, oxyfluorides, and, oxyfluoronitrides are explored and store as data although only few of calculated perovskite materials fall into the potential solar cells applications. 16,17 If machine learning is able to reveal the descriptors determining the band gap within perovskite materials data, then rapid prediction of perovskite materials for applications in solar light capturing can be considered to be achievable in principle. Thus, trends and periodicities hidden within the data of 19,000 perovskite materials are sought after and hidden perovskite materials for applications in capturing solar light are explored through the use of materials informatics. Material data consisting of 15,000 perovskite materials generated by high throughput first principle calculations are explored. 16,17 Machine learning is implemented in order to uncover hidden trends and periodicities linking to the band gap of the perovskite materials. In particular, random forest classification within scikit–learn is implemented for the machine learning process. 18 Within the random forest, the number of trees is set to 10. Cross validation is implemented to evaluate the accuracy of the trained machine where the data set is randomly organized into 80% trained data and 20% test data and the average score is taken by 10 randomly split trained and test data. Note the seed for the random forest is fixed at

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the highest average score in cross validation. The first principle calculations within grid based projector augmented wave (GPAW) method is implemented in order to evaluate the band gap and thermal stability of predicted perovskite materials. 19 In particular, atomic models in a (1x1x1) unit cell of predicted perovskite materials are constructed within periodic boundary conditions and 10x10x10 special k points of the Brillouin zone sampling is applied. 20 The structural optimization and the formation energy of perovskite materials are calculated using the exchange correlation of Perdew–Burke–Ernzerhof (PBE) with spin polarization calculations. 21 The exchange correlation of GLLB-sc is implemented for calculating the band gap as the bandgaps of the database have also been calculated using the GLLB-sc exchange correlation and are shown to calculate band gap comparible to band gap reported in experiments. 16,22 The formation energy of perovskite materials (ABC2 D) is calculated as Equation 1:

Eb = E[ABC 2 D] − E[A] − E[B] − 2E[C] − E[D]).

(1)

In addition, E[A], E[B], E[C], and E[D] represent the free energy of bulk A, B, C, and D per atom, respectively. Note that negative formation energy indicates an exothermic reaction.

Figure 1: Atomic model of perovskite materials, ABC2 (C1,C2)D. Atomic color code; Blue:A, Green:B, Yellow: C, Red:D. Data analysis and visualization are performed in order to reveal hidden trends and periodicities within the perovskite material data. In particular, data of 15,000 perovskite mate-

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Figure 2: Data visualization of (a) bandgap (eV) and element D in ABC2 D with corresponding total atomic orbital of ABC2 D, and (b) electronegativity of A and B in ABC2 D with corresponding formation energy. rials consisting of ABC2 (C1,C2)D as shown in Figure 1 is selected out of 19,000 perovskite materials data. 17 In general, information from the periodic table can often be recognized as descriptors for predicting the materials properties. 2,4 Therefore, the data of 15,000 perovskite materials is organized by adding corresponding information from the periodic table such as electronegativity and atomic orbitals. In addition, the materials data is converted into numerical variables where element names are converted to atomic numbers and atomic orbital groups s,p,d, and f are converted to numbers 1,2,3, and 4. Based on the organized perovskite materials data, visualization of the 15,000 perovskite materials data is performed in various aspects as shown in Figure 2. Figure 2 reveals the

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hidden trends and periodicities in materials data. The band gap and element D in ABC2 D with corresponding total atomic orbital are visualized in Figure 2 (a) where the total atomic orbitals is defined as the sum of corresponding atomic orbitals in numerical form in ABC2 D. Figure 2 (a) shows that perovskite materials having band gap are concentrated when the atomic number D in ABC2 D is 7-16. Furthermore, a large band gap is observed when the total atomic orbital falls within the range of 9-11. Similarly, electronegativity of A and B in ABC2 D with corresponding formation energy of ABC2 D are visualized in Figure 2 (b). It can be observed that exothermic formation energy, displayed in the blue color, is concentrated at 1.0-1.5 of the electronegativity of A and 1.5-2.0 of the electronegativity of B. Thus, Figure 2 (a) and (b) suggest that manipulating the certain physical factors in material data can surface the unexpected trends in data. In addition, both of Figure 2 (a) and (b) demonstrates clustering of data, leading to the implementation of classification techniques in the machine learning process where those certain physical factors are treated in multi dimensional space which could result the prediction of band gap. Machine learning is implemented in order to predict the band gap of perovskite materials. More specifically, the random forest classification technique is chosen as Figure 2 demonstrates clustering of the data. The objective variable for the random forest classification is set to the indirect band gap where the band gaps in the data are classified into three group: 0, 0 eV-1.7 eV; 1, 1.7eV-3.0eV; and 2, over 3.0eV. Note that 1.7 eV is chosen for the cut off point as the number of small band gap materials is relatively large in data; therefore, a slightly high band gap is selected for better prediction. Descriptors for determining the band gap are explored based on Figure 2. In particular, the following 18 descriptors are found to predict the band gap of perovskite materials(ABC2 (C1,C2)D): A:atomic number of A, An :number of A atoms, Ao:atomic orbital of A, B:atomic number of B, Bn :number of B atoms, Bo:atomic orbital of B, C1:atomic number of C1, C1n :number of C1 atoms, C1o:atomic orbital of C1, C2:atomic number of C2, C2n :number of C2 atoms, C2o:atomic orbital of C2, D:atomic number of D, Dn :number of D atoms, Do:atomic orbital of D, TO: sum of atomic orbital

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(1,2,3,4) of (A, B, C1, C2, D), TEL: sum of electronegativity of (A, B, C1, C2, D), Ef : formation energy of ABC2 (C1,C2)D. Note that atomic orbital and electronegativity of each element is multiplied by the number of atoms presented in ABC2 (C1,C2)D. Random forest classification with the listed 18 descriptors for predicting the band gap is evaluated using cross validation, resulting in the mean score of 0.98 with a standard deviation of 0.002. Hence, descriptors and type of machine learning for predicting the band gap of perovskite materials are determined. Prediction of undiscovered perovskite materials having band gaps within a range of 1.73.0 eV is performed using the trained machine. This approach is carried out by giving all possible combinations of the descriptors variables to the trained machine, allowing the machine to return corresponding band gaps. Expanding the data in this manner allows for the acquisition of an even larger perovskite materials data where the descriptors variables are defined as materials information, allowing for a search for perovskite materials having a band gap within the range of 1.7-3.0 eV. Thus, all possible combinations of descriptors variables must be generated. In particular, the following set of descriptor variables within the found 18 descriptors are considered: A:3-4,11-17,19-57, An :1-2, Ao:corresponding atomic orbital as A, B:3-4,11-17,19-57, Bn :1-2, Bo:corresponding atomic orbital as B, C1:5-9,16-17,2230, C1n 1, C1o:corresponding atomic orbital as C, C2:0, C2n :0, C2o:0, D:5-9,16-17, Dn :2, Do:corresponding atomic orbital as D, TO: corresponding sum of atomic orbital (1,2,3,4) of (A, B, C, D), TEL:corresponding sum of electronegativity of (A, B, C, D), Ef : -1. Here, every possible combination of those descriptors variables, 414,736 combinations, are generated. The generated 414,736 combinations within 18 descriptors variables are then given to the trained machine which then returns 414,736 corresponding band gaps(0, 0 eV-1.7 eV; 1, 1.7 eV-3.0 eV; and 2, over 3.0eV). By doing so, the original 15,000 perovskite materials data is expanded to 414,736 perovskite materials data, demonstrating that rapid expansion of material data is achieved with the implementation of machine learning. Please see the Supporting Information for all predicted perovskite materials data with band gap 1.7-3.0

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eV. Within the 414,736 perovskite materials data, materials with band gap 1.7-3.0 eV are sought for and extracted where 9,328 perovskite materials are discovered to have band gap 1.7-3.0 eV. Thus, machine learning rapidly predicts 9,328 perovskite materials for solar light capturing based on the trend and periodicities in the original 15,000 perovskite materials data.

Figure 3: Formation energy and band gap of predicted Li(Na)BC2 D perovskite materials using first principle calculations. The ideal solar light capturing is marked as red square which as the formation energy under 0.5 eV and band gap range 1.5-3.0 eV.

The selected predicted perovskite materials having band gap 1.7-3.0 eV are investigated using the first principle calculations where thermal stability and the band gap are calculated. In particular, Li and Na based perovskite materials(Li(Na)BC2 D) are selected where previously-undiscovered 14 LiBC2 D and 16 NaBC2 D perovskite materials are predicted. The band gap and formation energy of those 14 LiBC2 D and 16 NaBC2 D perovskites are then calculated using the first principle calculations and results are shown in Figure 3. Please see the Supporting Information of the lattice constant, formation energy, and band gap of each Li(Na)BC2 D shown in Figure 3. Figure 3 shows that 10 Li(Na)BC2 D based perovskite materials fall into the ideal range for solar light capturing applications which require formation energies under 0.5 eV as well as band gap falling within a band gap range of 1.5-3.0 eV. It must be noted that these discovered Li and Na based perovskite materials shown in

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Figure 3 are not present in the original 15,000 perovskite materials data. 17 It is worth to especially mention that predicted perovskite materials containing Cl atoms are not presented within the original 15,000 data. This indicates that Cl atoms could play an important role for having band gap 1.5-3.0 eV. Thus, the first principle calculations confirm that the some of predicted Li and Na based perovskite materials have a band gap range of 1.5-3.0 eV with stable formation energy. As a result, Figure 3 provides that random forest classification along with the found 18 descriptors is able to estimate band gap in multi dimensional space. In addition to the prediction of the band gap, one can also consider the prediction of the lattice constant to be performable using machine learning. 23 Hence, the design of perovskite materials can be achievable using machine learning. Data science is implemented to predict undiscovered perovskite materials for capturing solar light using 15,000 perovskite materials data created by first principle calculations. The visualization of data of 15,000 perovskite materials from various physical aspects reveals clustering features of data, leading towards the implementation of machine learning classification. In particular, random forest classification is implemented where 18 descriptors are revealed to determine the band gap of perovskite materials. With the trained random forest classification, 9,328 perovskite materials with ideal band gaps for solar light capturing are predicted. The first principle calculations are performed for evaluating the 30 selected Li and Na based perovskite materials. As a result, 10 thermodynamically stable undiscovered perovskite materials with ideal band gaps for solar light capturing are revealed. Hence, the approach taken in this work is innovative and can be applied to the materials science field in general, which would allow for the acceleration of materials discovery. This work is funded by JSPS KAKENHI, Grant-in-Aid for Young Scientists (B), Grant Number JP17K14803 and Materials research by Information Integration Initiative (MI2 I) project of the Support Program for Starting Up Innovation Hub from Japan Science and Technology Agency (JST). Computational work is supported in part by Hokkaido university academic cloud,information initiative center, Hokkaido University, Sapporo, Japan.

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