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 timescales 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.
Li et al., Chem. Phys. 339, 173 (2007)
-
What is the origin?
• 1996 - impedence measurements place the CBM
of Anatase 0.2 eV above that of Rutile.
Kavan et al., J. Am. Chem. Soc. 118, 6716 (1996)
Currently the accepted model, but correct?
7
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
Madelung potential for O
Madelung potential for Ti
Anatase
26.232 V
-45.025 V
Rutile
25.767 V
-45.199 V
• 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 10
QM/MM ChemShell Approach
B97-1,2/TZV2P
QM region
QM active site
Interface
MM active
region
Point
charges
MM frozen
region
Trapped
electron
Embedding
QM/MM ChemShell approach
QM region
No spurious
interactions between
B97-1,2/TZV2P
periodically repeated charged
defects as in plane wave
supercell methods
Unambiguous energy reference
 ionization energies
QM active site
Interface
MM active
region
Point
charges
MM frozen
region
Trapped
electron
Embedding
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.
14
– Effective band gap at interface is ~2.8 eV.
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 Semiconductors
Transparent conducting oxides: combine optical transparency with
electronic conductivity
EF
> 3 eV
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.
(1) Wide-gap Semiconductors
Transparent conducting oxides: combine optical transparency with
electronic conductivity
EF
> 3 eV
n-type:
In2O3, SnO2, ZnO
In2O3:Sn, SnO2:F, ZnO:Al
p-type:
CuAlO2, SrCu2O2
CuAlO2:Mg, SrCu2O2:Ca
GaN solar cell schematic
Applications:
Flat-panel displays, organic
and inorganic solar cells,
organic light-emitting
diodes, transparent
displays, chemical sensors,
smart windows.
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”.
Lany and Zunger, Phys. Rev. B, 80, 085202 (2009)
Varley et al., Phys. Rev. B, 85, 081109(R) (2012)
20
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 (20
Role of Dopants and Defects
Insulator
(e.g. CaF2, NaCl)
CB
≈ 7 eV
VB
Frenkel and Schottky
pairs
Ionic disorder
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
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
Ionic disorder
?
Electron and hole
conduction
Electronic disorder
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
Ionic disorder
?
Calculate defect reaction energies
constrained by electroneutrality:
Electron and hole
conduction
Electronic disorder
[e/ ]  [ A/ ]  [h ]  [ D ]
Electronic Versus Ionic Disorder
Study 3 representative materials:
 ZnO (II-VI)
 GaN (III-V)
 SiC (IV-IV)
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
Electronic Versus Ionic Disorder
Study 3 representative materials:
 ZnO (II-VI)
 GaN (III-V)
}
Hybrid QM/MM approach (ChemShell)
 SiC (IV-IV)
ZnO, GaN  wurtzite
SiC  Many polymorphs,
use wurtzite
Use DFT with hybrid
functional
Electronic Versus Ionic Disorder
Study 3 representative materials:
 ZnO (II-VI)
 GaN (III-V)
}
Hybrid QM/MM approach (ChemShell)
Need interatomic potential model with
polarizable shells
 SiC (IV-IV)
ZnO, GaN  wurtzite
SiC  Many polymorphs,
use wurtzite
Use DFT with hybrid
functional
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
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
Defects and Electroneutrality
Charge Neutrality Condition:
[e/ ]  [ A/ ]  [h ]  [ D ]
Charge Carrier Generation:
Non-stoichiometry
Extrinsic Doping
A  A/  h
D  D  e/
Charge Carrier Compensation:
Electron Carriers
Electron Carriers
Electrons stable in all 3 materials
Hole Carriers
Hole Carriers
Holes unstable in ZnO and GaN
Calculated Band Offsets
Vacuum
Conduction band
0.7 eV
0.7 eV
3.33 eV
7.7 eV
3.50 eV
3.44 eV
0.8 eV
1.5 eV
Valence band
ZnO
GaN
SiC
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. 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
Use chemical intuition to influence valence band design
• Chemical Modulation of the Valence Band –
Hideo Hosono, MRS Bull., 25, 28-36
Hosono.
(2000)
• Inverse Design approach - establishing
defect/doping rules. Perkins et al. Phys. Rev. B., 84, 205207 (2011)40
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.
CBM
VBM
d10s0
(Cu+, Ag+)
O 2p6
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.
41
Scanlon et al, J. Chem. Phys., 132, 024707 (2010)
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.
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”
43
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 10-1 S cm-1.
Hiramatsu et al., Thin Solid Films, 411, 125 (2002)
– [Cu2S2][Sr3Sc2O5], 3.1 eV band gap,
conductivity of 2.8 S cm-1.
Scanlon and Watson, Chem Mater, 21, 5435 (2009)
• 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.
Hiramatsu et al., Appl. Phys. Lett., 91, 012104 (2007)
• Successfully used as the p-type anode
in OLEDS and excitonic blue LEDS.5
Hiramatsu et al., Appl. Phys. Lett., 87, 211107 (2005)
44
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
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.
46
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)
47
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 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 Freysoldt et al., Phys. Rev. Lett., 102 (2009) 016402
• Thermodynamic Transition (ionization) levels:
Intrinsic Defects
Cu – poor
intersection with
LaCuSe2, La4Se3O4.
Se – poor
intersection with La2O3,
LaSeO4 and LaCu5.
• Cu-poor: p-type; Se-poor: resistive → growth conditions vital.
50
Acceptor 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
Conclusions
• 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.
Catlow
PHYSICAL REVIEW B 87, 214304 (2013)
Applications and properties of ceria
high-κ dielectrics
catalysis
glass-polishing
CeO2
ceramics
Fluorite:
nano-medicine
solid-state electrochemistry
Low VO formation energy:
High ionic conductivity – O vacancies
High thermal stability
SOFC application of ceria
• Good SOFC electrolyte: high
ionic, low electronic conductivity
• Solution  dope with trivalent
cations (Sm, Gd, Y…)
* Dopant – defect interactions
control conductivity (Butler et al;
Solid State Ionics,8,109,(1983)
Ceria as electrolyte – medium
temperature operation
Behaviour at high temperature
Due to reduction at high T?
Evidence of O [111] displacement at high T
Surprising result –
different Gd contents
but conductivities
converge at high T!
Calculation details
To investigate interesting experimental results =>
Calculate phonon dispersion as a function of isotropic strain
a - a0
e=
a0
• 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 coupling
B1u
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
A novel TiO2 octameric framework with benzyl linkers.
Synthesised: Dan-Hardi et al. J. Am. Chem. Soc. (2009)
Complex Unit Cell: 240 atoms
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
3.14
~ 4 eV
Eg (eV)
Hybrid Network: Reduction
Density of States
Defect Properties:
• Defect reactions involving reduction of
Ti(IV)  Ti(III) are low in energy.
New
state
• Loss of oxygen from the lattice can occur
from sub-band gap excitations:
1
2Ti Ti +O O
V +2Ti + O 2
2
(E = 2.72 eV)
••
O
/
Ti
• Loss of oxygen creates a new photoactive
state deep in the band gap.
Hybrid Network: Photochromic
Light driven chemical reduction.
Striking colour change
under UV irradiation.
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)