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ELECTRONIC and DEFECT PROPERTIES of ENERGY MATERIALS

ELECTRONIC and DEFECT PROPERTIES of ENERGY MATERIALS. Richard Catlow, Chemistry Department, University College London;. THEMES. Electronic Structure and Disorder in Inorganic Energy Materials - Electronic structure of TiO 2 polymorphs

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ELECTRONIC and DEFECT PROPERTIES of ENERGY MATERIALS

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  1. ELECTRONIC and DEFECT PROPERTIES of ENERGY MATERIALS Richard Catlow, Chemistry Department, University College London;

  2. THEMES • Electronic Structure and Disorder in Inorganic Energy Materials - Electronic structure of TiO2 polymorphs - Doping limits in wide band gap semiconductors; the search for “p-type” materials - High temperature CeO2 - Photo-active MOFs • Application of embedded cluster (QM/MM) and periodic, electronic structure methods

  3. Modelling at the Atomic and Molecular Level • Structures (crystal and amorphous) • Surfaces and Interfaces • Defects and Atomic Transport • Sorption and Diffusion • Synthesis, Nucleation and growth • Nanochemistry • Reactivity and Catalysis Link with larger length and time-scales increasingly important All relevant to Energy materials

  4. METHODS for MODELLING MATTER at the ATOMIC LEVEL • Interatomic Potentials: - minimisation (running downhill in energy) - molecular dynamics (Newtonian dynamics for molecules) - Monte-Carlo (Rolling dice to generate ensembles) • Electronic Structure: solve Schrodinger equation - Hartree-Fock (The Wavefunction) - Density Functional Theory (DFT) (The Electron Density) Materials Modelling needs them all!

  5. TECHNIQUES • Periodic Density Functional Electronic Structure Calculations (VASP and CP2K) • QM/MM Embedded Cluster Calculations (CHEMSHELL)

  6. BAND ALIGNMENT IN RUTILE/ANATASE David Scanlon, Ivan Parkin, Richard Catlow et al., Nature Materials, 12,798,2013

  7. 2) Rutile/Anatase Band Alignment • TiO2 – most widely used oxide for photocatalysis. • >10000 TiO2 papers on WoK in 2012 alone. counterparts • TiO2 has two main polymorphs: • Anatase - 3.2 eV band gap, good photocatalyst. • Rutile – 3.0 eV band gap, poor photocatalyst. • Mixed phase anatase/rutile samples show improved performance. - What is the origin? • 1996 - impedence measurements place the CBM of Anatase 0.2 eV above that of Rutile. Currently the accepted model, but correct? Li et al., Chem. Phys. 339, 173 (2007) Kavan et al., J. Am. Chem. Soc. 118, 6716 (1996)

  8. Three Alignment Models (a) 1996 measurement – normal model. (b) 2007 UPS workfunction (W) study: Anatase 5.1 eV, Rutile 4.9 eV • Challenges normal model? (c) EPR experiments indicate that electrons flow into anatase, but use “deep trap levels” to explain, still based on 1996 model

  9. Bonding in TiO2(Periodic calculationsusing DFT) • Valence band edge dominated by O 2p states, Conduction band edge dominated by Ti 3d states. • Width of the upper valence band similar for both phases • .Thus band edge positions determined by onsite electrostatic potential and optical dielectric response.

  10. Madelung Potential Alignments • Calculated Madelung potentials using polarizable shell model, fitted to reproduce the high frequency dielectric constants of anatase and rutile TiO2. Indicates the VBM of rutile is 0.47 eV above that of anatase – opposite to the normal model. • Places the CBM of anatase 0.17 below rutile • Can also calculated the energy of charge carriers propagating at the band edges using Mott-Littleton approach. • Agrees with the Madelung alignment – VBM of rutile 0.39 eV above anatase, and CBM of anatase 0.24 eV below rutile

  11. QM/MM ChemShell Approach B97-1,2/TZV2P QM region Interface QM active site Trapped electron MM active region MM frozen region Pointcharges Embedding

  12. QM/MM ChemShell approach B97-1,2/TZV2P No spurious interactions between periodically repeated charged defects as in plane wave supercell methods Unambiguous energy reference  ionization energies QM region Interface QM active site Trapped electron MM active region MM frozen region Pointcharges Embedding

  13. QM/MM Alignment • QM/MM calculations of ionization potentials for rutile and anatase for a range of cluster sizes (~50 to ~80 atoms). • IP of Rutile = 7.83 eV; IP of Anatase = 8.30 eV – offset of 0.47 eV. • Calculated IP of ZnO is 7.71 eV, which is 0.12 eV higher in energy than rutile – experimental offset is 0.14 eV – excellent agreement. All calculations suggest the “accepted model” is incorrect.

  14. XPS Alignment • Independent XPS measurements on rutile/anataseheterojunctions find a shift in the core level alignment of 0.44 eV. • Taking Core level to VBM separations into account, this indicates a VBM offset of 0.39 +/- 0.02 eV, with the VBM of rutile above that of anatase. • Effective band gap at interface is ~2.8 eV.

  15. Conclusions 3: TiO2 Alignment • Analysis of bonding in anatase and rutile TiO2 reveals that alignment of VBM and CBM should be determined by madelung potentials. • Madelung potentials indicate that the VBM of rutile should be 0.47 eV above that of anatase – opposite to the “accepted” model. • Mott-Littleton approach supports this, with an offsett of 0.39 eV. • QM/MM alignment place the VBM of Rutile 0.47 eV above Anatase. • This approach allows access to the vacuum level – not surface dependent like periodic approaches. • XPS alignment of rutile/anatase interfaces place the VBM of rutile 0.39 +/- 0.02 eV above anatase. • Experiments carried out independently of calculations.

  16. LIMITS to DOPING in WIDE BAND GAP SEMICONDUCTORS • Richard Catlow, Alexei Sokol, Scott Woodley and Aron Walsh

  17. (1)Wide-gap Semiconductors Transparent conducting oxides: combine optical transparency with electronic conductivity n-type: In2O3, SnO2, ZnO In2O3:Sn, SnO2:F, ZnO:Al p-type: CuAlO2, SrCu2O2 CuAlO2:Mg, SrCu2O2:Ca Applications: Flat-panel displays, organic and inorganic solar cells, organic light-emitting diodes, transparent displays, chemical sensors, smart windows. EF > 3 eV

  18. (1) Wide-gap Semiconductors Transparent conducting oxides: combine optical transparency with electronic conductivity n-type: In2O3, SnO2, ZnO In2O3:Sn, SnO2:F, ZnO:Al p-type: CuAlO2, SrCu2O2 CuAlO2:Mg, SrCu2O2:Ca Applications: Flat-panel displays, organic and inorganic solar cells, organic light-emitting diodes, transparent displays, chemical sensors, smart windows. EF > 3 eV Photo micrograph of SiC MOSFET operational amplifier chip GaN solar cell schematic

  19. TCOs - conductivity • Conductivity controlled by defects • Intrinsic/extrinsic. • n-type semiconductors (donors) • Anion vacancies and cation interstitials, donor dopants • p-type semiconductors (acceptors) • Cation vacancies, anion interstitials, acceptor dopants.

  20. Doping bottlenecks • N-type defects favoured. • P-type defects form localized holes (polarons). • Holes even “self trap”. Lany and Zunger, Phys. Rev. B, 80, 085202 (2009) Varley et al., Phys. Rev. B, 85, 081109(R) (2012) Catlow et al., Chem. Commun., 47, 3386 (2011)

  21. A good p-type oxide is hard to find! • O 2p dominated VBs lie very deep relative to the vacuum level . • Larger ionization potentials indicate hole formation is less favourable. Scanlon and Watson, J. Mater. Chem., 22, 25326 (2012)

  22. Role of Dopants and Defects Insulator (e.g. CaF2, NaCl) CB ≈ 7 eV VB Frenkel and Schottky pairs Ionic disorder

  23. Role of Dopants and Defects Insulator (e.g. CaF2, NaCl) Semiconductor (e.g. Si, Ge) CB CB ≈ 7 eV ≈ 1 eV VB VB Frenkel and Schottky pairs Electron and hole conduction Ionic disorder Electronic disorder

  24. Role of Dopants and Defects Insulator (e.g. CaF2, NaCl) Wide-gap semiconductor (e.g. ZnO, GaN) Semiconductor (e.g. Si, Ge) CB CB CB ≈ 7 eV ≈ 1 eV ≈ 3 eV VB VB VB Frenkel and Schottky pairs Electron and hole conduction ? Ionic disorder Electronic disorder

  25. Role of Dopants and Defects Insulator (e.g. CaF2, NaCl) Wide-gap semiconductor (e.g. ZnO, GaN) Semiconductor (e.g. Si, Ge) CB CB CB ≈ 7 eV ≈ 1 eV ≈ 3 eV VB VB VB Frenkel and Schottky pairs Electron and hole conduction ? Ionic disorder Electronic disorder Calculate defect reaction energies constrained by electroneutrality:

  26. Electronic Versus Ionic Disorder • Study 3 representative materials: • ZnO (II-VI) • GaN (III-V) • SiC (IV-IV)

  27. Electronic Versus Ionic Disorder • Study 3 representative materials: • ZnO (II-VI) • GaN (III-V) • SiC (IV-IV) ZnO, GaN  wurtzite SiC  Many polymorphs, use wurtzite Use DFT with hybrid functional

  28. Electronic Versus Ionic Disorder • Study 3 representative materials: • ZnO (II-VI) • GaN (III-V) • SiC (IV-IV) Hybrid QM/MM approach (ChemShell) ZnO, GaN  wurtzite SiC  Many polymorphs, use wurtzite Use DFT with hybrid functional

  29. Electronic Versus Ionic Disorder • Study 3 representative materials: • ZnO (II-VI) • GaN (III-V) • SiC (IV-IV) Hybrid QM/MM approach (ChemShell) Need interatomic potential model with polarizable shells ZnO, GaN  wurtzite SiC  Many polymorphs, use wurtzite Use DFT with hybrid functional

  30. Electronic Versus Ionic Disorder • Study 3 representative materials: • ZnO (II-VI) • GaN (III-V) • SiC (IV-IV) Hybrid QM/MM approach (ChemShell) Need interatomic potential model with polarizable shells Supercell approach (CP2K) ZnO, GaN  wurtzite SiC  Many polymorphs, use wurtzite Use DFT with hybrid functional

  31. Supercell CP2K approach • CP2K Quickstep DFT module • Gaussians and plane-waves method • Gaussian basis sets: DZVP for geometry optimisation and TZV2P single point • 150 Hartree energy cutoff for plane waves • GTH pseudopotentials • Forces < 0.025 eV/Å • PBE0-TC-LRC HSE like functional, ERI truncated at 0.2 nm • optimized TZV density fitting basis used for HF exchange (ADMM) • ADMM = Guidon, Hutter, VandeVondele, J. Chem. Theory Comput. 2010, 6, 2348 • PBE0-TC-LRC = Guidon, Hutter, VandeVondele, J. Chem. Theory Comput. 2009, 5, 3010

  32. Charge Neutrality Condition: Defects and Electroneutrality Charge Carrier Generation: Non-stoichiometry Extrinsic Doping Charge Carrier Compensation:

  33. Electron Carriers

  34. Electron Carriers Electrons stable in all 3 materials

  35. Hole Carriers

  36. Hole Carriers Holes unstable in ZnO and GaN

  37. Calculated Band Offsets Vacuum Conduction band 0.7 eV 0.7 eV 3.33 eV 7.7 eV 3.50 eV 3.44 eV 1.5 eV 0.8 eV Valence band SiC GaN ZnO

  38. Conclusions 1. Doping Limits • Used hybrid DFT to calculate intrinsic defect formation energies in wide-gap semiconductors ZnO, GaN, SiC • Analysed defect reactions to determine balance of ionic vs. electronic disorder • Electrons are stable in all 3 materials • Holes unstable in ZnO and GaN (but stable in SiC) Catlow, Sokol, Walsh et al., Chem. Commun. 47, 3386 (2011) Walsh et al., J. Phys.: Condens. Matter23, 334217 (2011) Walsh, Buckeridge, Catlow, Sokol et al., Chem Mater,,25, 2924, (2013)

  39. The Defect Chemistry of LaCuOSe David O. Scanlon,a John Buckeridge,a C. Richard A. Catlow,a and Graeme W. Watson.b

  40. Strategies for producing p-type TCOs Usechemical intuition to influence valence band design • Chemical Modulation of the Valence Band – Hosono. • Inverse Design approach - establishing defect/doping rules. Hideo Hosono, MRS Bull., 25, 28-36 (2000) Perkins et al. Phys. Rev. B., 84, 205207 (2011)

  41. Chemical Modulation of the VB Kawazoe et al., Nature., 389, 939 (1997) • 1997- Kawazoe et al. report simultaneous transparency and p-type conductivity in CuAlO2 thin films. But why p-type? • Answer: retains the p-type character of Cu2O. These design principles were used to discover that a range of CuMO2 (M = B, Al, Sc, Cr, Y, Ga, In) delafossites and SrCu2O2 were p-type TCOs. CBM VBM O 2p6 d10s0 (Cu+, Ag+) Scanlon et al, J. Chem. Phys., 132, 024707 (2010)

  42. Drawbacks to Cu-oxide based TCOs • Indirect band gaps. • Poor conductivity. • Polaronic hopping mechanisms. • Deep hole traps. • Highest conductivity1: CuCrO2:Mg - 220 S cm-1 • NEVER going to produce a degenerate p-type TCO to rival the n-type counterparts.

  43. Extending the concept further • Design principles not just for materials with O as the anion. • Extend to other chalcogenides – Cu2S, Cu2Se, etc? • Often smaller band gaps but with greater hole mobility due to greater Ch-Cu mixing at the VBM. Hosono in “Handbook of Transparent Conductors”

  44. Layered oxychalcogenides- promising? • Layered oxysulfides keep the large band gaps and improve the mixing at the VBM: • LaCuOS:Sr, 3.1 eV band gap, conductivity of 2.6 x 10-1S cm-1. • [Cu2S2][Sr3Sc2O5], 3.1 eV band gap, conductivity of 2.8 S cm-1. • LaCuOSe:Mg – degenerate p-type semiconductor,hole mobility of 3.5 cm2V-1s-1; conductivity of 910 S cm-1. • Band gap of ~2.8 eV. • Successfully used as the p-type anode in OLEDS and excitonic blue LEDS.5 Hiramatsu et al., Thin Solid Films, 411, 125 (2002) Scanlon and Watson, Chem Mater, 21, 5435 (2009) Hiramatsu et al., Appl. Phys. Lett., 91, 012104 (2007) Hiramatsu et al., Appl. Phys. Lett., 87, 211107 (2005)

  45. Calculation Methodology • Periodic DFT in the VASP code • HSE06 functional approach • 25% HF screened exchange • Bulk • Cutoff 500 eV; MP k-points of 4x4x4; 0.01 eV Å-1 convergence • 72 atom supercell • Cutoff 500 eV; MP 2x2x2; 0.01 eV Å-1 convergence

  46. Geometry and Electronic Structure • HSE06 in VASP. • LaCuOSe crystalizes in a tetragonal layered structure • Space group P4/nmm • Calculated lattice constants: • a = 4.065 Å; c = 8.806 Å. • Within 0.09% of experiment. • Direct band gap of 2.71 eV. • Expt is ~2.8 eV. • Good curvature at the VBM. • Much better than for metal oxides.

  47. Chemical Potential Limits • LaCuOSe chemical potential limits: • Not as simple as a binary oxide! • Boundaries created by the formation of: • La2CuO4, CuLaO2, La2O3, La3Se4, LaCuSe2, LaSe2, LaSe, CuSe, Cu2Se, Cu3Se2, La, Cu, Se, O, La2Cu(SeO3)4, CuSe2, CuSe2O5, La2(SeO3)3, La4Se3O4, LaCuO2, La(CuO2)2, LaCuO3, Se2O5, SeO2. • Perform individual HSE06 minimizations of each. J. Buckeridge, D. O. Scanlon,C.R.A Catlow et al., Comp. Phys. Commun. 185 , 330 (2014)

  48. CPLAP! • Chemical Potential Limits Analysis Program (CPLAP) • Assume formation of the material of interest occurs, rather than competing phases or standard states of the constituent elements. • Derive a series of conditions on the elemental chemical potentials. • Convert these to a system of m linear equations with n unknowns, m > n • Solve all combinations of n linear combinations, and test which solutions are compatible with the original conditions. • -none – system is unstable • -otherwise – compatible results define the boundary points

  49. Defect Methodology • ED,q= Energy of supercell containing defect D in charge state q • EH = Energy of the host supercell • n = number of species i added to or taken away from an external reservoir • Ei = Elemental energy of species i. (e.g. La(s), Cu(s), O2(g), Se(s)) • μ = chemical potential of the species i • EF = Fermi level, ranging from the VBM to the CBM • εVBMH = VBM of the host • Ealign[q] = corrections that accounts for: • (i) valence band alignment between bulk and supercell • (ii) image charge correction • Thermodynamic Transition (ionization) levels: Freysoldt et al., Phys. Rev. Lett., 102 (2009) 016402

  50. Intrinsic Defects • Cu-poor: p-type; Se-poor: resistive → growth conditions vital. Se – poor intersection with La2O3, LaSeO4 and LaCu5. Cu – poor intersection with LaCuSe2, La4Se3O4.

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