Defects and diffusion in metal oxides: Challenges for first-principles modelling

Transcription

1 Defects and diffusion in metal oxides: Challenges for first-principles modelling Karsten Albe, FG Materialmodellierung, TU Darmstadt Johan Pohl, Peter Agoston, Paul Erhart, Manuel Diehm FUNDING: ICTP Workshop DFG-SFB , BMBF Gracis, Helmholtz Virtual Institute MiCo, Schott Solar

2 How To Get Hydrogen? Renewable Energy Heat Biomass Mechanical Energy Thermolysis Electricity Electrolysis Conversion Photolysis No CO 2 emission 20% theo. efficiency Hydrogen

3 Photocatalysis: Desired Materials Properties 1.23 ev < band gap 3eV Engineered pathways of electron-hole pairs No defects acting as recombination sites Charge transfer used for water splitting instead of corrosion Efficient H 2 production and low overvoltages h Identify transparent passivating surface layer Couple Fermi level of metal catalyst to the quasi-fermi levels of the semiconductor under illumination Design a working device Design and implement assembling procedures n-region p-region

4 Materials by Design Design Concept Device Integration Tailored Band Gaps Tailored Surfaces and Interfaces Tailored Nanostructures

5 Materials by Design Design Concept Tailored Band Gaps

6 Electronic Structure Theory

7 Defects in Semiconductors

8 Ab-initio Thermodynamics of Point Defects Determination of the ground-state properties of pure phases Ground-states of defects in super cells Calculation of the formation energies at the VBM Correction of size effects Determination of the defect formation enthalpies as a function of the fermi energy and the chemical potentials in equilibrium Self-consistent determination of the fermi level

9 When DFT fails In defect calculations: band gaps Heavily underestimated Both LDA/GGA functionals Affects: Defect levels Defect formation energies Correction: scissor operation! Shift the conduction band Align E g (DFT) and E g (EXP) Donor type defects follow CB Correct formation energies Alternative: hybrid or semi-empirical functionals

10 Pt/CuGaSe2 and Pt/CdS/CuGaSe2 as Photoelectrode 0.1 M Na 2 SO 4 aq. (ph 9), 300 W Xe lamp, 5 mv s- 1

11 Band gap in ev Chalcopyrite Band Gaps from HSE06 Electronic band gaps (ev) with optimized exchange screening parameter = 0.13: 3,00 2,50 2,00 1,50 1,00 GGA HSE06 Experiment Chalcopyrite 0,50 0,00 CuInSe 2 CuGaSe 2 CuInS 2 CuGaS 2 CuIn 5 Se 8 J. Pohl, K. Albe, J. Appl. Phys. 108, (2010)

12 Defects in CuInSe 2 Phase stability Point defect formation enthalpies J. Pohl, K. Albe, Phys. Rev. B 87, (2013)

13 Defects in CuInSe 2 Phase stability Point defect formation enthalpies J. Pohl, K. Albe, Phys. Rev. B 87, (2013)

14 Defects in CuInSe 2 Phase stability Point defect formation enthalpies J. Pohl, K. Albe, Phys. Rev. B 87, (2013)

15 Defects in CuGaSe 2 Phase stability Point defect formation enthalpies J. Pohl, K. Albe, Phys. Rev. B 87, (2013)

16 Antisite Defects in CuInSe 2 and CuGaSe 2 Conduction band edge 1.68 ev 1.04 ev Ga Cu 1.33 ev (+1/0) 1.26 ev (+2/+1) 0.67 ev 0.74 ev (-1/-2) Cu In,Ga 0.11 ev 0.21 ev (0/-1) 0.0 CuInSe 2 Valence band edge CuGaSe 2

17 Conclusions on CIGS For a typical Cu(In,Ga)Se 2 absorber with [Ga]/[Ga]+[In]=0.25, Cu In and Cu Ga hole traps are the most detrimental defects! Copper-rich conditions maximize the concentration of this defect. For [Ga]/[Ga]+[In] > 0.5, Ga Cu becomes a deep minority carrier trap and can limit device efficiency. Optimal conditions to minimize Cu In and Cu Ga are located on the copper-poor side, with not too high Se/metal-ratio!

18 SnO 2 : Intrinsic Conductivity and p(o 2 ) 1 2 K O V 2e O O 2 ( T) O 1 P [ V ][ e ] 1/2 2 O O 2 O Is standard defect chemistry correct? Whats about other intrinsic defects?

19 TCO: What do we expect? deep - Donor Intrinsic n-typetco shallow - Donor In principle oxygen vacancies or cation interstitals can be donors

20 O-Vacancy Constant formation energies for the neutral charge state Strongly reduced formation energies for positive charge states Indium oxide and tin oxide are truly intrinsically n-type semiconductors The behavior is more complex for ZnO Agoston, Albe/ Phys. Rev. Lett. 103 (2009) , Phys. Rev. Lett. 106 (2011)

21 Band Gaps and Defect States Phys. Rev. Lett. 103 (2009) , Phys. Rev. Lett. 106 (2011)

22 Acceptor Defects Increased formation energies of acceptor defects in all TCOs Doping limits agree with experiment for In 2 O 3 but not for SnO 2

23 SnO 2 vs. In 2 O 3 Doped SnO 2 has no oxygen interstitials! Therefore high conductivities can be expected P. Agoston, C. Körber, A. Klein, M. J. Puska, R. M. Nieminen and K. Albe, J. Appl. Phys C. Körber P. Ágoston, A. Klein Sensors and Actuators B (2009)

24 Diffusion: Migration Barriers D f m f O (, 2 m S S H E f p ) H ( E f) 2 0 f exp exp k kt D 0 G TST 0 G 0 G m

25 Point defects in ZnO: Kinetics Appl. Phys. Lett. 88, (2006)

26 Materials by Design Design Concept Tailored Band Gaps Tailored Surfaces and Interfaces

27 ITO-(001) Oxygen : Indium : Oxygen (1. layer) : Indium (1. layer) : Experiment Experiment E. Morales, U. Diebold, Appl. Phys. Lett., 139, (2009)

28 In 2 O 3 -(001) Oxygen : Indium : Oxygen (1. layer) : Indium (1. layer) : Simulation Simulation Simulation Experiment Experiment 2 3 5

29 In 2 O 3 -(001) Oxygen : Indium : Oxygen (1. layer) : Indium (1. layer) : Simulation Simulation Simulation Experiment No compelling agreement with experiment Experiment 2 3 5

30 Doping Effect Peroxide splitting highly favorable

31 ITO-(001) Oxygen : Indium : Oxygen (1. layer) : Indium (1. layer) : Simulation Experiment P. Agoston, K. Albe, Phys. Rev. B 84, (2011)

32 ITO-(001) Oxygen : Indium : Oxygen (1. layer) : Indium (1. layer) : Improved agreement with experiment when the effect of doping is considered

33 Thermodynamics of Nanomaterials

34 Materials by Design Design Concept Tailored Band Gaps Tailored Surfaces and Interfaces Tailored Nanostructures

35 Volume Strain by Surface Stresses MgO (compressive): GaN (tensile)

36 Surface Energy vs. Surface Stress Surface Energy Surface Stress f ij Work required to produce extra surface Work required to enlarge/minimize existing surface dw da dw d A f Ad ij ij f f ij 1 A d A d d d ij

37 Calculated Surface Stresses (DFT)

38 Lattice Expansion

39 Stress Distribution: MD vs. FEM

40 Ab-initio Phase Diagrams Calculate the total energies of a set of structures (e.g. from DFT) Fit a model Hamiltonian to the set of structures (least squares fit / genetic algorithm) Predict new ground states or just include more structures Calculate the phase diagram (using Monte Carlo)

41 BOS-Model How to calculate the energy of a binary alloy system with two species A and B? Refined Bond Order Simulation Mixing model (BOS: Zhu, depristo 1995) where is the site energy of an atom of species A with coordination Z is the number of odd neighbors in the n-th shell is the difference in the site energy when changing a n-th neighbor to odd species is an asymmetry parameter (asymmetry considered for nearest neighbors only) (for species B replace and ) (Pohl, Albe, Acta Materialia 57, 4140 (2009))

42 Bulk Phase Diagram Pt-Rh Theoretical Pt-Rh Bulk phase diagram Gibb s Free Energy surface Warren-Cowley Short Range Order Parameters (Pohl, Albe, ACTA MAT 57, 4140 (2009))

43 Nanophase diagram Effects for shrinking particle size: ordering temperature sinks concentration stability range of some ordered phases broadens stable phases shift towards higher concentrations of segregating species (Pt) two-phase regions shrink Beilstein J. Nanotechnol. 2012, 3, 1 11.

44 2 % Pt, Diameter 7.8 nm

45 6 % Pt

46 10 % Pt

47 18% Pt

48 28 % Pt

49 28% Pt

50 42% Pt

51 44% Pt

52 46% Pt

53 46% Pt

54 60% Pt

55 60% Pt

56 86% Pt

57 86% Pt

58 Size-dependent Diffusion? Vacancy Mechanism D D 0 exp E k mig B T C V

59 Vacancies in Lattice Model: KMC Müller/Albe Acta Mat. (2007)

60 Vacancies in Lattice Model: KMC f E v 1.28 ev Model: Cu

61 Vacancy Formation Energy: Lattice model

62 Vacancies in Lattice Model f f 2 Ev( R) Ev( R ) R Surface energy Surface stress 2 /R f E v

63 Vacancies in Nanoparticles E ( R) E ( R ) f v f v 2 f V R Surface energy Surface stress f 2 /R f E v 2f / R V f E v : atomic volume V = : - Vrel:= formation volume

64 Surface Energy vs. Surface Stress Surface Energy Surface Stress f ij Work required to produce extra surface Work required to enlarge/minimize existing surface dw da dw d A f Ad ij ij f f ij 1 A d A d d d ij

65 Materials by Design Design Concept Device Integration Tailored Band Gaps Tailored Surfaces and Interfaces Tailored Nanostructures

66 Take home messages The properties of point defects and surfaces in oxides are most sensitive to the Fermi-energy We need Fermi-level engineering Defects not only go along with excess energies but also stresses Strain effects due to point, line and planar defects can be significant Thermodynamics and kinetics on the nanoscale can be very different We need a better understanding of nanoeffects