Morgan, Benjamin J

Scanlon, David O

Squires, Alexander G

English

UCL Discovery

py-sc-fermi: self-consistent Fermi energies and defectconcentrations from electronic structure calculationsAlexander G. Squires 1,4, David O. Scanlon 1,3,4, and Benjamin J.Morgan 2,41 Department of Chemistry, University College London, London, United Kingdom 2 Department ofChemistry, University of Bath, Bath, United Kingdom 3 Thomas Young Centre, University CollegeLondon, London, United Kingdom 4 The Faraday Institution, Didcot, United KingdomDOI: 10.21105/joss.04962Software• Review• Repository• ArchiveEditor: Rachel KurchinReviewers:• @hongzhouye• @ajgoyalSubmitted: 10 November 2022Published: 03 February 2023LicenseAuthors of papers retain copyrightand release the work under aCreative Commons Attribution 4.0International License (CC BY 4.0).Summarypy-sc-fermi is a Python package for calculating point-defect concentrations in crystallinematerials, under the constraint of net–charge-neutrality and the assumption of thermodynamic(quasi-)equilibrium. The required inputs are the formation energies of all point defects ofinterest and the electronic density of states. These can be obtained from electronic structurecalculations, e.g., density functional theory.Point defects are atomic-scale imperfections in crystalline materials. They can strongly affecta range of material properties, including electronic structure (Pastor et al., 2022), chargetransport (Maier, 2015), and energy-conversion processes (Kim et al., 2020). Point defectconcentrations are generally sensitive to synthesis conditions and to the inclusion of extrinsicdopants. By understanding the thermodynamics of point-defect formation, it is possible topredict the response of specific material properties to changes in synthesis or doping protocols(Park et al., 2018; Qu et al., 2022; Squires et al., 2019). The quantitative modelling ofpoint-defect populations in functional materials has become common practice in the materialsmodelling community, often undertaken with the aim of informing the design of novel, highlyperformant materials (Ganose et al., 2018; Jackson et al., 2022; Toriyama et al., 2021) or torationalise and optimise the properties of known materials (Kim et al., 2018; Shimoda et al.,2022; Squires et al., 2022).While the formation energies of charge-neutral point defects can be calculated simply, e.g.,from electronic structure calculations, the formation energies of charged defects depend on theelectronic chemical potential (the Fermi energy), which, in turn, depends on the net populationof all charged defects in the system. The equilibrium concentrations of charged point defectsare therefore mutually dependent, and must be solved for as a unified self-consistent system.In practice, self-consistent defect concentrations are calculated by imposing the constraint ofnet–charge-neutrality (Buckeridge, 2019),0 = ∑𝑋,𝑞𝑞 [𝑋, 𝑞] − 𝑛0 + 𝑝0. (1)Here, the first term is a sum over charge contributions from each defect 𝑋 in each of itsaccessible charge states 𝑞, and 𝑛0 and 𝑝0 are the concentrations of free electrons and electronholes respectively.py-sc-fermi provides a Python implementation of an iterative numerical approach for calculat-ing the self-consistent solution for an arbitrary set of point-defects. The resulting self-consistentFermi energy can be used as a general descriptor for the electronic-transport properties of amaterial (Jackson et al., 2022)&emdash;the calculated electronic charge-carrier concentrationscan be used to calculate electronic conductivities (Squires et al., 2022)&emdash;and theSquires et al. (2023). py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations. Journal of OpenSource Software, 8(82), 4962. https://doi.org/10.21105/joss.04962.1point-defect concentrations, and how these vary with synthesis conditions or doping protocol,can be used to model how the formation of competing defects affects material properties ofinterest (Ganose et al., 2018; Kavanagh et al., 2021) as well as quantifying the doping responseof a material (Squires et al., 2019, 2021).Statement of needpy-sc-fermi is a Python package for determining the self-consistent Fermi energy of a materialfrom pre-calculated point-defect data. This code allows the quantification of point defectand electronic carrier concentrations. Other software exists that is written to perform similarcalculations (Arrigoni & Madsen, 2021; Buckeridge, 2019; Neilson & Murphy, 2022; Ogawaet al., 2022). To the best of our knowledge py-sc-fermi is unique in providing all of thefollowing features:• It is built on a flexible Python API which allows for rapid prototyping and convergencetesting of the solved-for Fermi energy.• It is not part of a larger “point-defects workflow” package, making it as flexible aspossible for the end user.• It is agnostic towards the choice of simulation code used to generate the input data.• It possess both command-line functionality for those with little Python experience and anobject-oriented API that allows the user to easily construct objects representing individualdefects or complete systems of defects.• It allows for constraints on the concentrations of any combination of defects and specificcharge states of that defect, including the simulation of the influence of effective dopants.• It is fully documented with good unit-test coverage.The code has been used in a number of studies, including some focussed on rationalising theproperties of known materials (Squires et al., 2022, 2021) and others focussed on predicting theproperties of novel materials (Jackson et al., 2022). The code can also assist with visualisingdefect energetics (Haouari et al., 2021).One notable feature of py-sc-fermi is the ability to fix the concentrations of specific defectsor individual defect charge states. Defect and electronic carrier concentrations are functionsof temperature. The initial defect concentrations in a material are often determined by high-temperature synthesis conditions. Subsequent rapid cooling can result in some or all of thesedefect populations being “frozen in” (kinetically trapped) at their initial high-temperaturevalues, while other defect populations remain free to vary, and establish new pseudo-equilibriumdefect concentrations (Maier, 2003). py-sc-fermi allows this scenario to be modelled througha two-step calculation, where in the second step some defect concentrations are fixed to theirhigh temperature “synthesis” values. The new pseudo-equilibrium defect concentrations canbe quickly computed as a function of quenching temperature, allowing defect concentrationsto be calculated under a range of synthesis and quench scenarios (Squires et al., 2022).There is some minor convenience functionality for users of the Vienna Ab initio SoftwarePackage (VASP).AcknowledgementsThe authors are grateful for feature requests and user testing from Seán Kavanagh, Joe Willis,Jiayi Cen, Sabrine Hachmioune, and Lavan Ganeshkumar. This work was supported by theFaraday Institution grant number FIRG017. D.O.S. acknowledges support from the EuropeanResearch Council, ERC (Grant 758345). B.J.M. acknowledges support from the Royal Society(UF13032 and URF\R\191006).Squires et al. (2023). py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations. Journal of OpenSource Software, 8(82), 4962. https://doi.org/10.21105/joss.04962.2ReferencesArrigoni, M., & Madsen, G. K. H. (2021). Spinney: Post-processing of first-principlescalculations of point defects in semiconductors with python. Comput. Phys. Commun.,264, 107946. https://doi.org/10.1016/j.cpc.2021.107946Buckeridge, J. (2019). Equilibrium point defect and charge carrier concentrations in a materialdetermined through calculation of the self-consistent fermi energy. Comput. Phys. Commun.https://doi.org/10.1016/j.cpc.2019.06.017Ganose, A. M., Matsumoto, S., Buckeridge, J., & Scanlon, D. O. (2018). Defect engineeringof Earth-Abundant solar absorbers BiSI and BiSeI. Chem. Mater., 30(11), 3827–3835.https://doi.org/10.1021/acs.chemmater.8b01135.s001Haouari, C., Squires, A. G., Berthelot, R., Stievano, L., Sougrati, M. T., Morgan, B. J.,Lebedev, O. I., Iadecola, A., Borkiewicz, O. J., & Dambournet, D. (2021). Impact ofsolution chemistry on growth and structural features of Mo-Substituted spinel iron oxides.Inorg. Chem., 60(10), 7217–7227. https://doi.org/10.1021/acs.inorgchem.1c00278Jackson, A. J., Parrett, B. J., Willis, J., Ganose, A. M., Leung, W. W. W., Liu, Y., Williamson,B. A. D., Kim, T. K., Hoesch, M., Veiga, L. S. I., Kalra, R., Neu, J., Schmuttenmaer,C. A., Lee, T.-L., Regoutz, A., Lee, T.-C., Veal, T. D., Palgrave, R. G., Perry, R., &Scanlon, D. O. (2022). Computational prediction and experimental realization of Earth-Abundant transparent conducting oxide Ga-Doped ZnSb2O6. ACS Energy Lett., 3807–3816.https://doi.org/10.1021/acsenergylett.2c01961Kavanagh, S. R., Walsh, A., & Scanlon, D. O. (2021). Rapid recombination by cadmium vacan-cies in CdTe. ACS Energy Lett, 6(4), 1392–1398. https://doi.org/10.1021/acsenergylett.1c00380.s001Kim, S., Márquez, J. A., Unold, T., & Walsh, A. (2020). Upper limit to the photovoltaicefficiency of imperfect crystals from first principles. Energy Environ. Sci., 13, 1481–1491.https://doi.org/10.1039/d0ee00291gKim, S., Park, J.-S., & Walsh, A. (2018). Identification of killer defects in kesterite Thin-Filmsolar cells. ACS Energy Lett., 3(2), 496–500. https://doi.org/10.1021/acsenergylett.7b01313.s001Maier, J. (2003). Complex oxides: High temperature defect chemistry vs. Low temperaturedefect chemistry. Phys. Chem. Chem. Phys., 5(11), 2164–2173. https://doi.org/10.1039/b300139nMaier, J. (2015). Review— battery materials: Why defect chemistry? Journal of TheElectrochemical Society, 162(14), A2380–A2386. https://doi.org/10.1149/2.0011514jesNeilson, W. D., & Murphy, S. T. (2022). DefAP: A python code for the analysis of pointdefects in crystalline solids. Comput. Mater. Sci., 210, 111434. https://doi.org/10.1016/j.commatsci.2022.111434Ogawa, T., Taguchi, A., & Kuwabara, A. (2022). An extended computational approach forpoint-defect equilibria in semiconductor materials. Npj Computational Materials, 8(1),1–11. https://doi.org/10.1038/s41524-022-00756-0Park, J. S., Kim, S., Xie, Z., & Walsh, A. (2018). Point defect engineering in thin-film solar cells.Nature Reviews Materials, 3(7), 194–210. https://doi.org/10.1038/s41578-018-0026-7Pastor, E., Sachs, M., Selim, S., Durrant, J. R., Bakulin, A. A., & Walsh, A. (2022).Electronic defects in metal oxide photocatalysts. Nature Reviews Materials, 7 (7), 503–521.https://doi.org/10.1038/s41578-022-00433-0Squires et al. (2023). py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations. Journal of OpenSource Software, 8(82), 4962. https://doi.org/10.21105/joss.04962.3Qu, J., Balvanz, A., Baranets, S., Bobev, S., & Gorai, P. (2022). Computational design ofthermoelectric alloys through optimization of transport and dopability. Mater. Horiz., 9,720–730. https://doi.org/10.1039/D1MH01539GShimoda, M., Maegawa, M., Yoshida, S., Akamatsu, H., Hayashi, K., Gorai, P., & Ohno, S.(2022). Controlling defects to achieve reproducibly high ionic conductivity in Na3SbS4 solidelectrolytes. Chem. Mater., 34(12), 5634–5643. https://doi.org/10.1021/acs.chemmater.2c00944Squires, A. G., Davies, D. W., Kim, S., Scanlon, D. O., Walsh, A., & Morgan, B. J. (2022).Low electronic conductivity of Li7La3Zr2O12 solid electrolytes from first principles. Phys.Rev. Mater., 6(8). https://doi.org/10.1103/PhysRevMaterials.6.085401Squires, A. G., Dean, J. M., & Morgan, B. J. (2021). Aliovalent doping strategies for enhancingionic conductivity in Li3OCl solid electrolytes: A first-principles assessment. ChemRxiv.https://doi.org/10.26434/chemrxiv-2021-hzrlsSquires, A. G., Scanlon, D. O., & Morgan, B. J. (2019). Native defects and their dopingresponse in the lithium solid electrolyte Li7La3Zr2O12. Chem. Mater. https://doi.org/10.1021/acs.chemmater.9b04319Toriyama, M. Y., Qu, J., Snyder, G. J., & Gorai, P. (2021). Defect chemistry and dopingof BiCuSeO. J. Mater. Chem. A Mater. Energy Sustain., 9(36), 20685–20694. https://doi.org/10.1039/D1TA05112ASquires et al. (2023). py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations. Journal of OpenSource Software, 8(82), 4962. https://doi.org/10.21105/joss.04962.4

py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations

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py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations

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