Photoferroic Materials for Defect-Tolerant Solar Cells
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The document summarizes research on photoferroic materials for solar cell applications. It discusses computational studies of the electronic and optical properties of three candidate photoferroic minerals: enargite, stephanite, and bournonite. The studies show they have suitable bandgaps and absorption properties. Rashba splitting was also found in bournonite. The document then discusses how defects could be tolerated in these materials through shallow defect levels related to their electronic structure. Finally, methods for further computational investigation of defects and spontaneous polarization are presented.
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Photoferroic Materials for Defect-Tolerant Solar Cells
- 1. Centre for Sustainable Chemical Technologies Accelerating the development of photoferroic solar cells Suzanne K. Wallace Supervisor: Prof Aron Walsh 3rd October 2017
- 2. Centre for Sustainable Chemical TechnologiesPhotoferroic materials for solar cells Bulk photovoltaic effect (BPE) photocurrents measured in single crystals (p-n or p-i-n junctions not needed) Anomalous photovoltaic effect (APE) measured photovoltages >> band gap trieste.nffa.eu/areas/theory/ferroelectric-properties/ photoferroic = photoactive ferroelectric K. T. Butler, J. M. Frost and A. Walsh, Energy Environ. Sci., 2015, 8, 838–848.
- 3. Centre for Sustainable Chemical Technologies 1. Ferroelectric domains Enhanced carrier separation [1] 2. Large dielectric constant Defect-tolerant carrier transport [2] 3. APE in MAPI Measured photovoltage of ~12 V [3] CH3NH3PbI3 (MAPI) methylammonium lead iodide Design principles inspired by MAPI [1] J. M. Frost et al, Nano Letters, 2014, 14, 2584–2590 [2] R. E. Brandt et al. MRS Commun., 2015, 5, 265–275 [3] Yuan et al. Science Advances, 2017, vol. 3, no. 3, e1602164 DOI:10.1038/nature12509
- 4. Centre for Sustainable Chemical Technologies ~200 naturally occurring minerals
- 5. Centre for Sustainable Chemical TechnologiesChemically stable ~200 naturally occurring minerals
- 6. Centre for Sustainable Chemical Technologies ~200 naturally occurring minerals Chemically stable Dark streak colour Eg in visible range
- 7. Centre for Sustainable Chemical Technologies ~200 naturally occurring minerals Chemically stable Dark streak colour Eg in visible range Polar crystal structure Potential ferroelectric Candidate photoferroic minerals
- 8. Centre for Sustainable Chemical TechnologiesCandidate photoferroics: Sulfosalt minerals Cu Ag Pb Sb S As Enargite Cu3AsS4 Stephanite Ag5SbS4 Bournonite CuPbSbS3
- 9. Centre for Sustainable Chemical TechnologiesCandidate photoferroics: Sulfosalt minerals Cu Ag Pb Sb S As Enargite Cu3AsS4 Stephanite Ag5SbS4 Bournonite CuPbSbS3
- 10. Centre for Sustainable Chemical TechnologiesPV design principles
- 11. Centre for Sustainable Chemical Technologies 1. Magnitude of the band gap Sunlight-matched (~ 1.0-1.7 eV) 2. Strength of optical absorption • Direct band gap • Abrupt of absorption edge • c.f. SLME metric [4] 3. Light charge-carrier effective-mass Better carrier mobility and long diffusion length [4] Yu, L.; Zunger, A. Phys. Rev. Lett. 2012, 108 (6), 68701 DOI: 10.1126/science.aad4424 Standard PV design principles
- 12. Centre for Sustainable Chemical Technologies 4. Rashba splitting: may reduce radiative recombination rate and contribute to long carrier lifetimes in MAPI [5, 6] [5] P. Azarhoosh et al, APL Materials, 2016, 4, 091501 [6] Wang et al, Energy Environ. Sci., 2017, 10, 509-515 [7] R. E. Brandt et al, MRS Communications, 2015, 5(2), 1–11 5. Possible indicators of defect tolerance • Active ns2 lone pairs: character of band extrema implies shallow defects are likely [7] • Large dielectric constant: enhanced charge screening [7] More novel PV design principles
- 13. Centre for Sustainable Chemical TechnologiesDefect tolerance 1. Shallow defects • Reduction in SRH e--h+ recombination • Possible link to character of band extrema [7-9] Host material with antibonding upper VB and bonding lower CB Dangling bond defects repelled into continuum bands instead of band gap 2. Reduced scattering • Carrier transport less hindered by presence of charged defects • Long diffusion lengths in defective materials • Linked to large dielectric constant [7] DOI: 10.1021/jz5001787 [7] R. E. Brandt et al, MRS Communications, 2015, 5(2), 1–11 [8] S. B. Zhang et al, Phys.Rev. B, 1998, 57, 9642–9656 [9] A. Zakutayev et al, Phys. Chem. Lett., 2014, 5, 1117–1125
- 14. Centre for Sustainable Chemical TechnologiesComputational methods • HSE06+SOC • Default ‘tight’ settings for basis set Geometry optimisation • Lattice parameters fixed to high-quality XRD data from the ICSD • Internal coordinates relaxed to within a tolerance of 1x10-3 eV/ Å • 4x4x4 gamma-centred k-point grid Band structure calculations • 8x8x8 k-point grid Optical dielectric function, 𝜺 𝝎 • Random phase approximation • Bournonite: 8x8x8 k-point grid • Enargite and stephanite: 10x10x10 k-point grid Absorption co-efficient, 𝜶(𝝎) All-electron electronic structure code Numeric atom-centred orbital basis sets
- 15. Centre for Sustainable Chemical TechnologiesOptoelectronic properties for PV Enargite Cu3AsS4 Stephanite Ag5SbS4 Bournonite CuPbSbS3 1.24 eV 1.37 eV 1.42 eV 1.59 eV Enargite Stephanite Bournonite me cond 0.21 0.33 0.45 mh cond 0.49 0.86 0.94
- 16. Centre for Sustainable Chemical TechnologiesRashba splitting for PV Bournonite (CuPbSbS3) - with SOC - without SOC No SOC direct gap SOC Rashba split
- 17. Centre for Sustainable Chemical TechnologiesAbsorption coefficient
- 18. Centre for Sustainable Chemical TechnologiesDefect tolerance from electronic structure Bonding character of VBM Bournonite CuPbSbS3 Enargite Cu3AsS4 Stephanite Ag5SbS4 Cu d-orbital S p-orbital Ag d-orbital S p-orbital Cu d-orbital S p-orbital
- 19. Centre for Sustainable Chemical TechnologiesSpontaneous lattice polarisation Katrine Svane [10] R. Wahl, D. Vogtenhuber and G. Kresse, Phys. Rev. B, 2008, 78, 104116 [11] H. H. Wieder, Phys. Rev., 1955, 99, 1161–1165 [12] I. Grinberg and A. M. Rappe, Phys. Rev. B, 2004, 70, 220101 [10] [11] [12] Computational details • 500 eV cut-off energy • 2x2x2 k-point grid • HSE06 functional
- 20. Centre for Sustainable Chemical Technologies DOI: 10.1039/c7se00277g 1. Optoelectronic properties for PV • Sunlight-matched optical band gap • m* < 1me • Strong absorption • Rashba splitting in bournonite 2. Strong lattice polarisation of enargite and stephanite Conclusion (part one of two!)
- 21. Centre for Sustainable Chemical Technologies 1. Predict suitable device architectures VOC losses linked to misalignment of bands with contact materials Poor epitaxy from lattice mismatch 2. Investigate defect physics of the materials Likely impact of defects on PV performance Predicting and tuning impact? Will they grow up to be solar cells?
- 22. Centre for Sustainable Chemical Technologies Python script: https://github.com/keeeto/ElectronicLatticeMatch 1. Predictions for device architecture Screen by necessary conditions for a good contact Keith Butler: k.t.butler@bath.ac.uk 1. Electronic matching Optimal band offsets Screen by IP and EA Minimise VOC loss across junction 2. Lattice strain Match crystal lattices Minimal for good epitaxy DOI: 10.1039/c5tc04091d
- 23. Centre for Sustainable Chemical TechnologiesDefect-tolerant p-n junctions? DOI: 10.1063/1.4953820 p-type CB VB n-type −Δ𝐸 𝐶𝐵 e- Type II ‘cliff’ CBO p-type CB VB n-type +Δ𝐸 𝐶𝐵 e- Type I ‘spike’ CBO h+ h+
- 24. Centre for Sustainable Chemical TechnologiesDefect-tolerant p-n junctions? p-type CB VB n-type −Δ𝐸 𝐶𝐵 e- Type II ‘cliff’ CBO p-type CB VB n-type +Δ𝐸 𝐶𝐵 e- Type I ‘spike’ CBO h+ h+ • Create a h+ barrier at the interface • Not enough h+ present for e--h+ recombination at interface defect states Optimal CBO spike: 0.1 eV ≤ ∆EC ≤ 0.3 eV Barrier too large: ∆EC ≥ 0.4 eV Cliff CBO: ∆EC < 0 Allows h+ in high concentrations at interface Allows for e--h+ recombination at defect trap states Inhibits e- transport across interface
- 25. Centre for Sustainable Chemical Technologies2. Defect physics DOI: 10.1038/nmat4973 Defect ‘flavours’ • Doping/ conductivity promoting • Charge-scattering • Killer, deep, charged recombination centres Good Bad
- 26. Centre for Sustainable Chemical Technologies2. Defect physics DOI: 10.1038/nmat4973 Defect ‘flavours’ • Doping/ conductivity promoting • Charge-scattering • Killer, deep, charged recombination centres Good Bad
- 27. Centre for Sustainable Chemical Technologies Predict concentration of deep vs. shallow defects DOI: 10.1002/adma.201203146 n = N exp −∆𝑮 𝒌 𝑩 𝑻 Equilibrium defect concentration Defect transition levels no. of lattice sites defect formation energy Predicting impact Frenkel (1925); Jost (1933); Mott & Littleton (1938)
- 28. Centre for Sustainable Chemical TechnologiesTuning impact F. A. Kröger “Chemistry of Imperfect Crystals” (1964) Defect free energy of formation, ∆𝑮 𝝁𝒊, 𝑬 𝑭 Fermi level (function of n, p, T) Atomic chemical potentials (growth and annealing conditions)
- 29. Centre for Sustainable Chemical Technologies 𝝁i during synthesis Using accessible 𝜇 range Increase energy for deep defects DOI: 10.1002/adma.201203146 Tuning impact F. A. Kröger “Chemistry of Imperfect Crystals” (1964) ∆𝑮 𝝁𝒊, 𝑬 𝑭 Defect free energy of formation, Fermi level (function of n, p, T) Atomic chemical potentials (growth and annealing conditions)
- 30. Centre for Sustainable Chemical Technologies DOI: 10.1038/nmat4973 Tuning impact Benign defect complexes Encourage formation of defect pairs to ‘clean up’ the band gap? D+ = donor A- = acceptor Defect-defect interactions Form charge-neutral complex Remove deep levels e.g. InCu 2+ + 2VCu - (InCu + 2VCu)0 in CuInSe2 S. B. Zhang, et al, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57
- 31. Centre for Sustainable Chemical TechnologiesConclusion (part two of two!) Acknowledgements Duke University: Volker Blum, David Mitzi, Will Huhn, Tong Zhu University of Bath: Katrine Svane, Keith Butler, Jonathan Skelton Imperial College London: Aron Walsh NREL: Stephan Lany, Jie Pan, Prashun Gorai, Anuj Goyal Thanks for listening!
- 32. Centre for Sustainable Chemical Technologies Energy barriers to polarisation switching
- 33. Centre for Sustainable Chemical Technologies Electronic band structures with FHI-aims FHI-aims: all-electron electronic structure code based on numeric atom-centred orbital basis sets Geometry optimization • Initial structures taken from high-quality XRD data from the icsd • Default ‘tight’ settings • HSE06+SOC • 4x4x4 gamma-centred k-point grid • Lattice parameters fixed to unit cell from high quality XRD data • Internal coordinates relaxed to within a tolerance of 1x10-3 eV/ Å Band structure calculations • HSE06+SOC • 8x8x8 k-point grid
- 34. Centre for Sustainable Chemical Technologies Absorption co-efficients with FHI-aims Optical dielectric function, 𝜺(𝝎) • Random phase approximation (RPA) • HSE06+SOC • 10x10x10 k-point grid for enargite and stephanite • 8x8x8 k-point grid for bournonite Absorption co-efficient, 𝜶(𝝎)
- 35. Centre for Sustainable Chemical Technologies Spontaneous lattice polarisation with VASP VASP: plane-wave electronic structure code using PAW pseudopotentials • Using Berry-phase formalism • Polarisation only allowed along z-axis for all 3 materials (based on symmetry) • Only differences in polarisation are meaningful • Optimise +PS structure • Invert to obtain structure with opposite polarisation, -PS • Calculate polarisation difference between two structures, 2PS • To verify that change in polarisation is continuous, calculate P of a number of configurations connecting the +PS and -PS structures VASP calculation settings: • 500 eV cut-off energy for plan-wave basis set • 2x2x2 k-point grid • HSE06 functional K. L. Svane and A. Walsh, The Journal of Physical Chemistry C, 2016.