1 02/05/2023 Impact of Defects on Solar Cell Performance in Selenium Seán Kavanagh Profs: David O. Scanlon & Aron Walsh [email protected] (University College London & Imperial College London) Y.-T. Huang, S. R. Kavanagh, D.O. Scanlon, A. Walsh, R.L.Z. Hoye, Nanotechnology 32, 132004 (2021) 

2 02/05/2023 Impact of Defects on Solar Cell Performance in Selenium Seán Kavanagh Profs: David O. Scanlon & Aron Walsh [email protected] (University College London & Imperial College London) Y.-T. Huang, S. R. Kavanagh, D.O. Scanlon, A. Walsh, R.L.Z. Hoye, Nanotechnology 32, 132004 (2021) 

Why Selenium? • First material used for photovoltaic (PV) solar cells, in 1883 (η < 1%). • Researchers then moved on to c-Si, CdTe, CZTS/CIGS, perovskites... • Recent surge in interest after decades of neglect, following Todorov et al. record efficiency η = 6.5% in 2017. • Low-temperature solution-growth & processing, “simple” chemistry, chain-like structure could yield benign grain boundaries. • Wide-bandgap (~1.9 eV) suitable for single-junction or tandem PV. 3 

Se PV Efficiency: Limiting Factor? 4 2Nielsen et al. J Mater Chem A 2022 Record Efficiency:1 η = 6.5% with Voc = 969 mV Theoretical max η ~ 24% (detailed balance limit) Record Voc 2 = 991 mV Eg (Se, direct) = 1.95 eV ➡ Voc deficit > 600 mV, suggesting non-radiative recombination at defects to be the key contributing factor. 1Todorov et al. Nat. Commun. 2017 

Selenium: Bulk Properties 5 Strong inter-chain vdW dispersion interactions ~10% volume decrease when including vdW effects Theory (Hybrid DFT + vdW) Experiment Direction a,b c a,b c Lattice Parameter (Å) 4.34 4.96 4.37 4.95 Volume (Å3) 81.1 81.9 εionic 0.63 0.94 0.461 0.621 ε∞ (optical) 6.71 10.28 6.971 11.621 Esurface (J/m2) 0.18 0.1752 1Danielewicz & Coleman Appl. Opt, 1974 210.1016/0022-3093(71)90004-4 

Selenium: Bulk Properties 6 Se p Direct band gap Eg, dir = 1.83 eV (Expt: 1.95 eV)1 Indirect gap Eg, indir = 1.71 eV (Expt: 1.85 eV)2 ➡ Partial contribution to Voc deficit from indirect gap 1Nielsen et al. J Mater Chem A 2022 2Moreth Phys Rev Lett 1979 CBM: VBM: Theory = HSE06+vdW+SOC 

Defect Calculation Workflow 7 Host primitive cell Goyal et al, Comp Mater Sci 2017 

Defect Calculation Workflow 8 Host primitive cell Goyal et al, Comp Mater Sci 2017 

Defect Calculation Workflow 9 

Defect Calculation Workflow 10 

Defect Calculation Workflow 11 

Defect Calculation Workflow 12 

Defect Calculation Workflow 13 

Defect Calculation Workflow 14 

Defect Calculation Workflow 15 ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ … 

Computational Defect Thermodynamics VBM CBM D+1 D0 D-1 Fermi Level E F (eV) Formation Energy ΔH X,q (eV) ε(+1/0) ε(0/-1) E F VBM CBM ε(+1/0) ε(0/-1) Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022 

Intrinsic Defect Formation Energy Diagram 17 Sei 0 = Dominant, lowest energy native defect • Electrically benign • Neutral across most of the bandgap, with a negative-U (0/-2) level just below the CBM. 0 -1 -2 0 -2 +1 Calculated with doped (GitHub.com/SMTG-UCL/doped) & ShakeNBreak (shakenbreak.readthedocs.io), using VASP 

Why is Sei 0 so low energy? Split-interstitial motif: Sei 0 joins Se chain which twists to accommodate. ➡ Low-energy & no dangling bonds -> stays neutral. 18 

Intrinsic Defect Formation Energy Diagram 19 0 -1 -2 0 -2 +1 Calculated with doped (GitHub.com/SMTG-UCL/doped) & ShakeNBreak (shakenbreak.readthedocs.io), using VASP VSe (0/-1) VSe (+1/0) VSe (-1/-2) VSe -> Moderate formation energy, expect low but non-negligible concentrations. • Multiple in-gap defect levels, which could be active for carrier recombination. 

Vacancy Defects (VSe ) +1: Terminated + Bridging Chain 0* (ΔE = 27 meV): ‘Self-healed’ Chain 0 and -1: Two Terminated Chains -2: Elongated Bonds; ‘Self- healed’ + Bridging 

Intrinsic Defect Formation Energy Diagram 21 0 -1 -2 0 -2 +1 Calculated with py-sc-fermi = EF Anneal Temperature = 300K Fermi level (EF ) determined by charge neutrality condition: p + ND + = n + NA – 

22 0 -1 -2 0 -2 +1 = EF Intrinsic Defect Formation Energy Diagram Anneal Temperature = 463 K (190℃) Calculated with py-sc-fermi Fermi level (EF ) determined by charge neutrality condition: p + ND + = n + NA – 

23 0 -1 -2 0 -2 +1 = EF Intrinsic Defect Formation Energy Diagram Anneal Temperature = 1000K Calculated with py-sc-fermi Fermi level (EF ) determined by charge neutrality condition: p + ND + = n + NA – 

24 • Se without impurities -> insulating/weakly p-type • Large p-type doping window • High sensitivity to p-type impurities • n-type doping not possible • But experiment1 sees ~1016 holes/cm-3… 1Nielsen et al. J Mater Chem A 2022 0 -1 -2 0 -2 +1 Calculated with doped (GitHub.com/SMTG-UCL/doped) & ShakeNBreak (shakenbreak.readthedocs.io), using VASP = EF Sei VSe Anneal Temperature = 463 K (190℃) 

What Else is In There? Potential impurities: • Halogens are common impurities in chalcogenide materials, often present in supplier precursors ➡ F, Cl, Br • Typically grown on Tellurium substrates ➡ Te • Typically annealed in air to aid crystallization ➡ O • Hydrogen is a very common impurity in materials ➡ H • Sulfur present in precursors, can bond easily with Se ➡ S 25 • Experiment1 sees ~1016 holes/cm-3… • Not from intrinsic defects 

26 Substitutions: XSe Interstitials: Xi F Cl Br H O S Te Calculated with doped (GitHub.com/SMTG-UCL/doped) & ShakeNBreak (shakenbreak.readthedocs.io) Using dopant-rich chemical potential limits Halogens Chalcogens Hydrogen 

VSe +1: Terminated + Bridging Chain Stable Positive Halogen Interstitials? Fi +1: Two Bridging Chains + Se-F Bond Fi -1: Intercalated F-1 ion 

Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. Selenium no different: Large energy lowering of ΔE: 0.1 – 1.1 eV (avg. ~0.6 eV) for: • VSe 0 • FSe -1, BrSe -1, ClSe -1 • Fi 0, Fi +1 • Bri 0, Bri +1 • Cli 0, Cli +1 • Si 0, Si -1, Hi -1, Oi -1, Tei -1… 28 e.g. Si 0 Importance of Defect Structure Searching! More details in Thursday morning’s talk: EL04.05.02: Symmetry-Breaking and Reconstruction at Point Defects in Perovskites April 13, 9-9.15 AM shakenbreak.readthedocs.io 1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023 2. Mannodi-Kanakkithodi Nature Physics 2023 3. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022 4. Mosquera-Lois & Kavanagh*, Matter 2021 5. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 6. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022 

0.0 0.8 1.6 Fermi Level (eV) 0.0 0.5 1.0 1.5 Formation Energy (eV) Sei VSe Fi 29 • Fluorine interstitials could increase hole concentrations slightly, but still <1013 cm-3 • Experiment sees ~1016 holes/cm-3… Calculated with doped (GitHub.com/SMTG-UCL/doped) & ShakeNBreak (shakenbreak.readthedocs.io), using VASP = EF Anneal Temperature = 463 K (190℃) 0.0 0.5 1.0 1.5 Sei VSe Fi 

Conclusions & Future Steps • Self-interstitials are neutral and benign for recombination, but Se vacancies could capture charge carriers. • ➡ Explicitly calculate non-radiative recombination rates of Vse • ➡ Devise passivation strategies; out-of-equilibrium Se over-pressures? Fermi level control during growth/annealing? • Hydrogen/halogens/chalcogens do not seem to be the cause of p- type doping in Selenium. Se chains show strong valence alternation & re-bonding to self-compensate. • ➡ Pnictogens (N, P, As) perhaps? Chalcogen substitutions are low energy, pnictogens could also substitute and be under-valent (-> negatively-charged) 30 

Acknowledgements 31 @Kavanagh_Sean_ [email protected] Rasmus Nielsen @ DTU Physics -> Growing & characterizing Selenium thin-films for PV Talk Friday morning: EN04.14.02: The Renaissance of Selenium Thin-Film Solar Cells; April 14, 8.45-9 AM Profs David Scanlon & Aron Walsh Alp Samli Intrinsic: 

Other Results: Band Alignment Lower VBM compared to Sb2 Se3 as expected (anti-bonding Sb s – Se p interaction in Sb2 Se3 gives raised VBM) 32 

Other results: • Interestingly, PBEsol seems to perform terribly for this material, with or without D3 vdW dispersion correction. Gives lattice parameter errors ~8%, HSE06-on-PBEsol structure gives a bandgap underestimated by 50% compared to HSE06-on-HSE06 or experiment, and the ionic dielectric is off by an order of magnitude (again compared to HSE06 or experiment which match) due to the severely underestimated interchain distances (which makes a big difference to inter-chain interactions) • PBE does better, but still not great (checked against Materials Project PBE results). Errors of around 3-4% in the lattice parameters both with and without D3 (overestimates a,b without D3, underestimates with D3). • Dispersion-corrected hybrid DFT (HSE06+D3) is very accurate for the bulk properties of Se on the other hand; gives lattice parameters matching experiment to 1%, closely matches the experimental bandgap (ΔEg <0.1 eV), matches the experimental dielectric screening (both ionic and electronic contributions) very well… 33