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

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 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

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

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!

TECHNIQUES

• Periodic Density Functional Electronic Structure Calculations (VASP and CP2K)

• QM/MM Embedded Cluster Calculations (CHEMSHELL)

BAND ALIGNMENT IN RUTILE/ANATASE

David Scanlon, Ivan Parkin, Richard Catlow et al., Nature Materials, 12,798,2013

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?

7

Li et al., Chem. Phys. 339, 173 (2007)

Kavan et al., J. Am. Chem. Soc. 118, 6716 (1996)

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

8

Bonding in TiO2

(Periodic calculations

using 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.

9

Madelung Potential Alignments

• Calculated Madelung potentials using polarizable shell model, fitted to reproduce the high frequency dielectric constants of anatase and rutile TiO 2.

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

10

Madelung potential for O

Madelung potential for Ti

Anatase 26.232 V -45.025 V

Rutile 25.767 V -45.199 V

QM active site Interface

MM frozen region

Point charge

sEmbedding

QM region

MM active region

Trapped electron

B97-1,2/TZV2PQM/MM ChemShell ApproachQM/MM ChemShell Approach

QM active site Interface

MM frozen region

Point charge

sEmbedding

QM region

MM active region

Trapped electron

B97-1,2/TZV2PNo spurious interactions between periodically repeated charged defects as in plane wave supercell methods

Unambiguous energy reference ionization energies

QM/MM ChemShell approachQM/MM ChemShell approach

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.

13

XPS Alignment

• Independent XPS measurements on rutile/anatase heterojunctions 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.

14

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.

15

LIMITS to DOPING in WIDE BAND GAP SEMICONDUCTORS

• Richard Catlow, Alexei Sokol, Scott Woodley and Aron Walsh

(1)Wide-gap SemiconductorsTransparent conducting oxides: combine optical transparency with electronic conductivity

> 3 eV

EF

n-type:In2O3, SnO2, ZnO

In2O3:Sn, SnO2:F, ZnO:Al

p-type:CuAlO2, SrCu2O2

CuAlO2:Mg, SrCu2O2:Ca

Applications:Flat-panel displays, organicand inorganic solar cells, organic light-emitting diodes, transparent displays, chemical sensors, smart windows.

(1) Wide-gap Semiconductors Transparent conducting oxides: combine optical transparency with electronic conductivity

> 3 eV

EF

n-type:In2O3, SnO2, ZnO

In2O3:Sn, SnO2:F, ZnO:Al

p-type:CuAlO2, SrCu2O2

CuAlO2:Mg, SrCu2O2:Ca

Applications:Flat-panel displays, organicand inorganic solar cells, organic light-emitting diodes, transparent displays, chemical sensors, smart windows.

GaN solar cell schematic Photo micrograph of SiC MOSFET operational amplifier chip

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.

19

Doping bottlenecks• N-type defects favoured.• P-type defects form localized holes

(polarons).• Holes even “self trap”.

20 Varley et al., Phys. Rev. B, 85, 081109(R) (2012)

Lany and Zunger, Phys. Rev. B, 80, 085202 (2009)

Catlow et al., Chem. Commun., 47, 3386 (2011)

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.

21

Scanlon and Watson, J. Mater. Chem., 22, 25326 (2012)

Role of Dopants and DefectsRole of Dopants and Defects

Insulator(e.g. CaF2, NaCl)

≈ 7 eV

CB

VB

Frenkel and Schottky pairs

Ionic disorder



Semiconductor(e.g. Si, Ge)

≈ 1 eV≈ 7 eV

CB

CB

VB

VB


Electron and hole conduction

Ionic disorder Electronic disorder




Wide-gap semiconductor(e.g. ZnO, GaN)

≈ 3 eV ≈ 1 eV≈ 7 eV

CBCB

CB

VBVB

VB



Ionic disorder Electronic disorder?


/ /[ ] [ ] [ ] [ ]e A h D



Wide-gap semiconductor(e.g. ZnO, GaN)

≈ 3 eV ≈ 1 eV≈ 7 eV

CBCB

CB

VBVB

VB



Ionic disorder Electronic disorder?Calculate defect reaction energies constrained by electroneutrality:

Electronic Versus Ionic DisorderElectronic Versus Ionic Disorder

Study 3 representative materials:

ZnO (II-VI)

GaN (III-V)

SiC (IV-IV)



ZnO (II-VI)

GaN (III-V)

SiC (IV-IV)

ZnO, GaN wurtzite

SiC Many polymorphs, use wurtzite

Use DFT with hybrid functional



ZnO (II-VI)

GaN (III-V)

SiC (IV-IV)

ZnO, GaN wurtzite


Hybrid QM/MM approach (ChemShell)




ZnO (II-VI)

GaN (III-V)

SiC (IV-IV)

ZnO, GaN wurtzite



Need interatomic potential model with polarizable shells


Electronic Versus Ionic Disorder


ZnO (II-VI)

GaN (III-V)

SiC (IV-IV)

ZnO, GaN wurtzite



Supercell approach (CP2K)

Need interatomic potential model with polarizable shells


Supercell CP2K approachSupercell 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

Defects and Electroneutrality

Charge Neutrality Condition:

Charge Carrier Generation:

Non-stoichiometry

Extrinsic Doping

Charge Carrier Compensation:

/ /[ ] [ ] [ ] [ ]e A h D

/A A h /D D e

Electron Carriers

Electron Carriers

Electrons stable in all 3 materials

Hole Carriers

Hole Carriers

Holes unstable in ZnO and GaN

Valence band

Conduction band

ZnO GaN SiC

3.44 eV

3.50 eV3.33 eV

Calculated Band OffsetsCalculated Band Offsets

7.7 eV

Vacuum

1.5 eV0.8 eV

0.7 eV0.7 eV

• 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)

Conclusions 1. Doping LimitsConclusions 1. Doping Limits

Catlow, Sokol, Walsh et al., Chem. Commun. 47, 3386 (2011)Walsh et al., J. Phys.: Condens. Matter 23, 334217 (2011)

Walsh, Buckeridge, Catlow, Sokol et al., Chem Mater,,25, 2924, (2013)

The Defect Chemistry of LaCuOSe

David O. Scanlon,a John Buckeridge,a C. Richard A. Catlow,a and Graeme W. Watson.b

Strategies for producing p-type TCOs

• Chemical Modulation of the Valence Band – Hosono.

• Inverse Design approach - establishing defect/doping rules.

40

Use chemical intuition to influence valence band design

Hideo Hosono, MRS Bull., 25, 28-36 (2000)

Perkins et al. Phys. Rev. B., 84, 205207 (2011)

Chemical Modulation of the VB• 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. O 2p6d10s0

(Cu+, Ag+)

CBM

VBM

41

Kawazoe et al., Nature., 389, 939 (1997)

Scanlon et al, J. Chem. Phys., 132, 024707 (2010)

Drawbacks to Cu-oxide based Drawbacks to Cu-oxide based TCOsTCOs• 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.

Extending the concept furtherExtending 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.

43Hosono in “Handbook of Transparent Conductors”

Layered oxychalcogenides- Layered oxychalcogenides- promising?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 10-1 S 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

44

Scanlon and Watson, Chem Mater, 21, 5435 (2009)

Hiramatsu et al., Thin Solid Films, 411, 125 (2002)

Hiramatsu et al., Appl. Phys. Lett., 91, 012104 (2007)

Hiramatsu et al., Appl. Phys. Lett., 87, 211107 (2005)

Calculation MethodologyCalculation 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

Geometry and Electronic Geometry and Electronic StructureStructure• 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.

46

Chemical Potential LimitsChemical 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. 47J. Buckeridge, D. O. Scanlon,C.R.A Catlow et al., Comp.

Phys. Commun. 185 , 330 (2014)

CPLAP!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 48

Defect MethodologyDefect 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

Intrinsic DefectsIntrinsic Defects

• Cu-poor: p-type; Se-poor: resistive → growth conditions vital.

Cu – poorintersection with

LaCuSe2, La4Se3O4.

Se – poorintersection with La2O3,

LaSeO4 and LaCu5.

50

Acceptor DopingAcceptor Doping• MgLa high in energy, but not compensated by MgCu.

• CaLa doping easier, SrLa most favoured.– Why is Mg a better dopant in experiment?

51

ConclusionsConclusions

• Growth environment vital– Cu poor growth conditions necessary for

uncompensated p-type behaviour

• VCu is the dominant defect, but is not a shallow acceptor

• SrLa is the lowest energy acceptor.

– MgLa is much higher in energy, but is the only dopant that works in experiment?• Testing more compensation mechanisms.

D. O. Scanlon, CRA Catlow et al., J. Mater. Chem. C. 2 , 3429 (2014)

High Temperature Structure and

Properties of Cerium Dioxide

John Buckeridge, David O. Scanlon, Aron Walsh, Alexey A. Sokol and C. Richard A.

CatlowPHYSICAL REVIEW B 87, 214304 (2013)

Applications and properties of ceria

CeO2

nano-medicineceramics

solid-state electrochemistry

high-κ dielectrics

glass-polishingcatalysis

Low VO formation energy:

High ionic conductivity – O vacancies High thermal stability

Fluorite:

SOFC application of ceria

• Good SOFC electrolyte: high ionic, low electronic conductivity

Ceria as electrolyte – medium temperature operation

• Solution dope with trivalent cations (Sm, Gd, Y…)

* Dopant – defect interactions control conductivity (Butler et al; Solid State Ionics,8,109,(1983)

Behaviour at high temperature

Surprising result – different Gd contents

but conductivities converge at high T!

Due to reduction at high T?

Evidence of O [111] displacement at high T

Calculation details

To investigate interesting experimental results =>Calculate phonon dispersion as a function of isotropic strain

• Use plane wave DFT (VASP)• GGA+U U = 5 eV• Cut-off 800 eV, 8x8x8 k-points, PAW core – valence

interaction• 4x4x4 supercells for dispersion calculation (frozen phonon

approach)• PHONOPY for post-processing• Validate calculations using hybrid DFT (HSE06)• Use cubic unit cell and 2x2x2 supercells for hybrid DFT

calcs – to get high symmetry points of interest

Results – unstrained ceria

Results – applying strain

Mode crossing at T

= 1600 K corresponds to Hohnke

result

Results – mode couplingB1u Eu

Coupling => O motion along [111] towards interstitial site

Conclusions• Determined phonon dispersion as a function of strain to

study dynamical stability of ceria (using plane-wave DFT)

• Found considerable softening of B1u mode at X-point

• At strain = 0.016 (T = 1600 K), B1u and Eu modes cross

• Propose that they couple, leading to increased probability of interstitial site occupation by O

• Provides mechanism of ionic conduction along [001], explaining experimental results of Hohnke

• Indicates change to thermally disordered phase with cubic symmetry – anion sublattice ‘melting’

Mechanism of Photochromism in Titania/Organic Hybrid Materials

Aron Walsh and Richard Catlow

Titania Metal-Organic Framework

Synthesised: Dan-Hardi et al. J. Am. Chem. Soc. (2009)

Complex Unit Cell: 240 atoms

A novel TiO2 octameric framework with benzyl linkers.

Hybrid Network: Photochromic

Striking colour change under UV irradiation.

Investigate using an electronic structure approach (DFT)

TiO2 Hybrid Network: Electronic

Bulk Properties:

• Insulating Band Gap > 3 eV.

• Spatial separation between

VBM and CBM.

GGA+U Experiment

a (Å) 19.21 18.65

b (Å) 19.21 18.65

c (Å) 18.19 18.14

Ti – O (Å) 2×2.09 2×1.98

2×2.08 2×1.94

2×1.89 2×1.89

Eg (eV) 3.14 ~ 4 eV

Hybrid Network: Reduction

•• /Ti O O Ti 2

12Ti +O V +2Ti + O

2( E = 2.72 eV)

Defect Properties:

• Defect reactions involving reduction of

Ti(IV) Ti(III) are low in energy.

• Loss of oxygen from the lattice can occur

from sub-band gap excitations:

• Loss of oxygen creates a new photoactive

state deep in the band gap.

Den

sity

of S

tate

s

New state

Hybrid Network: Photochromic

Striking colour change under UV irradiation.

Light driven chemical reduction.

A. Walsh and C. R. A. Catlow, ChemPhysChem, (2010).

Thanks to :

John Buckeridge , David Scanlon, Alexei Sokol, Scott Woodley, Aron Walsh

and to EPSRC and EU for funding

READ ALL ABOUT IT!

Walsh, Sokol and Catlow, Computational Approaches to Energy Materials, (Wiley, 2013)

Documents

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