Aron Walsh, Richard Catlow, Alexey Sokol and Scott Woodley Materials Chemistry, Department of Chemistry, University College London Global and Local Minimum Structures for Clusters of Indium Sesquioxide

Transparent Conducting Oxides Combine optical transparency with electronic conductivity > 3 eV EF n-type: In2 O3 , SnO2 , ZnO In2 O3 :Sn, SnO2 :F, ZnO:Al p-type: CuAlO2 , SrCu2 O2 CuAlO2 :Mg, SrCu2 O2 :Ca Applications: Flat-panel displays, organic and inorganic solar cells, organic light-emitting diodes, transparent displays, chemical sensors, smart windows.

Reduce Indium Dependence • Lower Cost • Increase Stability • Optoelectronic Control • Parent Binary Oxides: ZnO, In2 O3 , Al2 O3 , Ga2 O3 , SnO2 • Electronic Band Gaps: Al >> Ga > Sn > Zn > In • Resistivity: Al >> Ga > Sn > Zn > In In2 O3 (ZnO) In2 O3 (ZnO)3 In2 O3 (ZnO)5 A. Walsh et al. Phys. Rev. B 79, 073105 (2009).

Nanostructures • An alternative approach to reduce indium usage.

Goal and Methods • Derive robust interatomic In2 O3 potential. Explore high pressure behaviour. • Determine lowest energy structures formed from stoichiometric building blocks: (In2 O3 )n n = 1 – 7 Global optimization: Evolutionary algorithm (GULP). • Validate and characterize using a first-principles method. Density functional theory calculations (VASP). • Assess structural trends, stability and optoelectronic properties.

Goal and Methods

Indium Sesquioxide • Crystal Structure: Cubic bixbyite lattice (80 atom cell). • Band Gap: Fundamental 2.9 eV1; optical > 3.5 eV. • Conductivity: Oxygen deficient; intrinsically n-type. 1A. Walsh et al. Phys. Rev. Lett. 100, 167402 (2008).

Interatomic Potential: In2 O3 6 exp i j ij ij ij ij q q r C U A r r ρ ⎛ ⎞ = + − − ⎜ ⎟ ⎝ ⎠ Property Experiment Literature Potential1 Sokol Potential2 LDA-DFT a (Å) 10.117 10.120 10.121 10.094 B (GPa) 194.24 222.79 193.77 174 ε0 8.9-9.5 6.87 9.05 ε∞ 4.0 3.53 3.90 3.82 • Buckingham potential with shell polarization on oxygen. 1O. Warschkow et al., J. Am. Ceram. Soc. 86, 1700 (2003). 2A. Walsh et al, Chemistry of Materials 21, 4962 (2009).

Interatomic Potential: In2 O3 • Reproduces high pressure phase stabilities.

Clusters: n = 1 0.00 eV (C2v ) 0.11 eV (D∞ ) 0.49 eV (C2v ) 1.69 eV (D3h )

Clusters: n = 2 0.00 eV (C2h ) 1.04 eV (Td ) 1.22 eV (D2h ) 1.20 eV (C2v )

Clusters: n = 3 0.60 eV (C2v ) 0.00 eV (C2s ) 1.53 eV (D3h )

Clusters: n = 4 1.16 eV (C2v ) 0.00 eV (D3d ) 3.84 eV (Oh )

Clusters: n = 5 0.30 eV (C2 ) 0.00 eV (C1 ) 4.60 eV (D5h )

Clusters: n = 6 6.06 eV (D6h ) 0.00 eV (C1 ) 0.42 eV (D3d )

Clusters: n = 7 0.35 eV (D3 ) 0.10 eV (C1 ) 0.00 eV (C1 )

Nanoclusters: n = 1 - 7 1. C2v 2. C2h 3. C2s 4. D3d 5. C1 6. C1 7. C1

Cluster Stability 0 2 4 6 8 1 2 3 4 5 6 7 Energy (eV per n) (In2 O3 )n 1 E n ∝

Frontier Orbitals (n = 1, 2) n = 1 n = 2 HOMO LUMO HOMO LUMO

Frontier Orbitals (n = 4) HOMO LUMO

Frontier Orbitals (n = 6) HOMO LUMO

Frontier Orbital Separation -7 -6 -5 -4 1 2 3 4 5 6 7 GGA HOMO-LUMO Levels (eV ) (In2 O3 )n HOMO LUMO

Conclusion • Presented a new In2 O3 interatomic potential that describes bulk and cluster properties. • n < 4 clusters have distinct symmetric global minima. • n > 4 clusters tend towards bulk-like, low symmetry particles. • Open framework clusters have high energetic cost. • HOMO and LUMO character is consistent with bulk. Future work: • Extend to higher n. • Explore excited state properties. Acknowledgements: Materials Chemistry Consortium (Access to Hector); EU FP7 (Marie Curie Fellowship).

Bonus Slides

Interatomic Potential: In2 O3 • Anion Frenkel Formation

TCO Applications Source: Nikkei Electronics Asia

Nanocluster Paper