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SCIENCE CHINA Materials, Volume 63 , Issue 6 : 1024-1035(2020) https://doi.org/10.1007/s40843-019-1255-4

Bayesian optimization based on a unified figure of merit for accelerated materials screening: A case study of halide perovskites

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  • ReceivedDec 24, 2019
  • AcceptedJan 15, 2020
  • PublishedMar 16, 2020

Abstract

The figure of merit is of crucial importance in materials design to search for candidates with optimal functionality. In the field of photovoltaics, the bandgap (Eg) is a well-recognized figure of merit for screening solar cell absorbers subject to the Shockley-Queisser limit. In this paper, the bandgap as the figure of merit is challenged since an ideal solar cell absorber requires multiple criteria such as stability, optical absorption, and carrier lifetime. Multiple criteria make the quantitative description of material candidates difficult and computationally time-consuming. Taking halide perovskites as an example, we combine thermodynamic stability (ΔHd) and Eg into a unified figure of merit and use Bayesian optimization (BO) to accelerate materials screening. We have found that, in comparison to an exhaustive search via multiple parameters, BO based on the unified figure of merit can screen optimal candidates (Eg,PBE between 0.6–1.2 eV, ΔHd>−29 meV per atom) more efficiently. Therefore, the proposed method opens a viable route for the search of optimal solar cell absorbers from a large amount of material candidates with less computational cost.


Funded by

Yin WJ acknowledges funding support from the National Key Research and Development Program of China(2016YFB0700700)

the National Natural Science Foundation of China(11974257,11674237,51602211)

the Natural Science Foundation of Jiangsu Province of China(BK20160299)

and the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)


Acknowledgment

Yin WJ acknowledges funding support from the National Key Research and Development Program of China (2016YFB0700700), the National Natural Science Foundation of China (11974257, 11674237 and 51602211), the Natural Science Foundation of Jiangsu Province of China (BK20160299), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The theoretical work was carried out at the National Supercomputer Center in Tianjin and the calculations were performed on TianHe-1(A).


Interest statement

The authors declare that they have no conflict of interest.


Contributions statement

Yin WJ supervised the project. Chen X, Wang C, and Li Z performed the calculations. Hou Z provided guidance for algorithm. Chen X and Yin WJ wrote the paper. All authors attended on discussion.


Author information

Xiwen Chen is a master student at the College of Energy, Soochow Institute for Energy and Materials InnovationS (SIEMIS), Soochow University. Her interest focuses on the search and design of perovskite photovoltaic materials.


Wan-Jian Yin is a professor in SIEMIS, Soochow University, China. He received his BS degree (2004) and PhD degree (2009) from Fudan University, China. He worked in the National Renewable Energy Laboratory (NREL) and University of Toledo, USA from 2009 to 2015. His research interests include computational study of solar energy materials, defect physics in semiconductors and machine-learning on materials design.


Supplement

Supplementary information

Supporting data are available in the online version.


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  • Figure 1

    The hierarchical structure of materials design for solar cell absorber. The color-highlighted part are considered in this work.

  • Figure 2

    Schematic approach for (a) exhaustive search, and (b) Bayesian optimization.

  • Figure 3

    Material systems considered in this work, including 18 single perovskites and 420 double perovskites.

  • Figure 4

    The comparison of (a) conventional methods and (b) linear programming to calculate the decomposition energies of materials.

  • Figure 5

    Schematics of the searching for solar cell absorbers combing density of function (DFT) and BO.

  • Figure 6

    Pearson correlation map for features. The color varies with the absolute value of the associated Pearson correlation coefficient. The lighter the tone used, the less significant is the corresponding correlation.

  • Figure 7

    Screening for stable perovskites through (a) random search (RS), and (b) BO with No. 5 feature set in Table 2. Materials before 0 are used as training dataset for BO.

  • Figure 8

    Success rate (within 400 times of BO calculations) for identifying the most stable perovskites within 80 steps. The features used in the search are shown along the horizontal axis: the numbers denote the features listed in Table 2.

  • Figure 9

    The comparisons of number of steps for RS and BO to select a fraction of perovskites that (a) have ∆Hd greater than −29 meV per atom; (b) have Eg between 0.6–1.2 eV; (c) meet both criteria in (a) and (b). In (c), the performances of two unified figures of merit (line: ΔHd−100×|Eg−0.9|, exp: e(ΔHd29)2(Eg0.9)2) are shown.

  • Figure 10

    The perovskites for solar cell absorbers screened by (a) exhaustive search, (b) BO based on the linearly combined figure of merit and (c) BO based on the exponentially combined figure of merit. D, I and I/D represent direct bandgap, indirect bandgap, and quasi-direct bandgap respectively. Materials before 0 are used as training dataset for BO.

  • Table 1   Table 1 The 14 features used in BO

    No.

    Feature symbol

    Feature introduction

    1

    Z

    Atomic number

    2

    G

    The group of atom in periodic table of elements

    3

    P

    The period of atom in periodic table of elements

    4

    IR

    Ionic radius

    5

    s

    The number of electrons in the s orbit

    6

    p

    The number of electrons in the p orbit

    7

    d

    The number of electrons in the d orbit

    8

    Es

    s orbital energy

    9

    Ep

    p orbital energy

    10

    Ed

    d orbital energy

    11

    h

    Highest occupied atomic level

    12

    l

    Lowest unoccupied atomic level

    13

    SSE

    The atomic solid state energy [69]

    14

    χ

    Pauling’s electronegativity

  • Table 2   Table 2 The 5 feature sets used in the BO

    Nos.

    Feature sets

    1

    IR

    2

    IR, SSE

    3

    P, IR, SSE

    4

    P, IR, Es

    5

    P, IR, Ep, Ed

  • Table 3   Table 3 For 100 times random selection of 20 initial perovskites, the average steps were needed by using exhaustive search or BO to find the most stable perovskite.

    Feature sets

    The average step

    RS

    211

    No. 1

    71

    No. 2

    91

    No. 3

    66

    No. 4

    63

    No. 5

    53

  • Table 4   Table 4 The promising perovskite compounds hunted by BO based on thermodynamic stability and PBE-bandgap. The results of the synthesis or unsynthesis on the experiment are also shown.

    Nos.

    Compound

    ΔHd (meV per atom)

    Eg (eV)

    D or I

    Exp

    Refs.

    1

    Cs2AgInCl6

    7.8806

    1.017

    D

    y

    [40]

    2

    Cs2AgSbBr6

    −2.0142

    0.855

    I

    y

    [44]

    3

    Cs2TlTlCl6

    4.1792

    0.787

    I

    y

    [37]

    4

    CsSnCl3

    −5.3077

    0.919

    D

    y

    [72]

    5

    Rb2AgSbBr6

    −6.9130

    0.856

    I

     

    6

    Rb2AgInCl6

    −2.9178

    0.985

    I/D

     

    7

    Cs2InBiBr6

    −4.8178

    0.828

    D

    n

    [42]

    8

    K2AgSbBr6

    −6.9195

    0.830

    I

     

    9

    Cs2NaTlBr6

    −2.0768

    0.702

    D

     

    10

    Cs2TlSbI6

    −17.2836

    0.958

    D

     

    11

    Rb2NaTlBr6

    −3.5934

    0.699

    D

     

    12

    Cs2CuBiCl6

    −25.2816

    0.913

    I

     

    13

    CsSnBr3

    −0.7284

    0.629

    D

    y

    [72]

    14

    K2AgInCl6

    −22.7029

    0.953

    D

     

    15

    Cs2AgBiI6

    −28.4603

    0.900

    I

    y

    [62]

    16

    Rb2TlSbI6

    −28.2046

    0.926

    D

     

    17

    Rb2InInBr6

    −9.0265

    0.666

    I

     

    18

    Rb2InBiBr6

    −27.3527

    0.753

    D

     

    19

    Rb2TlTlCl6

    −27.2889

    0.710

    I

     

    20

    Rb2AgBiBr6

    −17.5889

    1.199

    I

     

    21

    Cs2InBiCl6

    −23.8300

    1.167

    D

    n

    [42]

    22

    Rb2CuSbCl6

    −27.8889

    0.646

    I

     

    23

    Rb2TlSbBr6

    −28.6685

    1.193

    D

     

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