Band alignment and defect chemistry of functional oxides: A concise discussion Aron Walsh Department of Chemistry, University College London

Defect Phenomenology

Reduction of Metal Oxides / O 2 1 = E[V ] O 2 2 reduction CB E e •• + + Presume that oxygen vacancies are the source of n-type behaviour (electron carriers): Defect Energy Molecular O2 Conduction Band Energy In2 O3 : J. H. W. De Wit, J. Sol. State Chem. 8, 142 (1973)

The Case of Tin Dioxide C. M. Freeman and C. R. A. Catlow, J. Sol. State Chem. 85, 65 (1990). Conduction Band: Defect Formation energy Schottky Trio 5.19 eV Anion Frenkel Pair 5.54 eV Cation Frenkel Pair 9.63 eV

Valence Band Conduction Band 0 µe (eV) 3 Band edges and Reduction / O 2 1 = E[V ] O 2 2 reduction CB E e •• + + O 2 1 ( ) = E[V ] O 2 2 reduction e e E µ µ •• + + Ereduction = 6.0 eV O Vx = 5.0 eV O O (V / V ) x ε •• “Spaghetti defects” In2 O3 : Lany and Zunger, Phys. Rev. Lett. 98, 045501 (2007).

Metal Oxide “Doping Asymmetry” Cu / Ag d Zn / Cd / Sn / In s Ti / V d Sn / Pb / Bi s Conduction Band Valence Band [O p]

Metal Oxide “Doping Asymmetry” Characteristics: Reducible species; low electron affinity; low conduction band. In2 O3 > SnO2 > ZnO > TiO2 Characteristics: Oxidizable species; low ionization potential; high valence band. Cu2 O > PbO > SnO > NiO p-type (electron deficient) n-type (electron rich) 1D. O. Scanlon, B. J. Morgan, G. W. Watson and A. Walsh, Phys. Rev. Lett. 103, 096405 (2009). 1

Quantitative Band Offsets How to quantitatively calculate the ‘natural’ band edge positions of two materials? Hi ε(+/-)

Offset Classification Type I: Electrons and holes confined in one layer (A). Type IIA: ‘Spatially Indirect’. Electron and hole separation. Type IIB: Effective ‘zero gap’. Electron transfer from B to A. Reference: Yu and Cardona, Fundamentals of Semiconductors. e.g. (GaAs|GaAlAs) (AlAs|GaAs) (InAs|GaSb) Type I Type IIA Type IIB A B A B A B

Experimental Offsets

Theory: Choice of Reference Level Different studies adopt different reference levels, even within the same code (here VASP). This applies to both band offsets and charged defect cell alignment. Q. Is this choice important? • Deep (atomic-like) core level, e.g. O 1s. Walsh & Wei, Phys. Rev. B 76, 195208 (2007). • Local electrostatic potential (integrated in fixed radius). Lany & Zunger, Phys. Rev. B 78, 235104 (2008). • Averaged electrostatic potential. Janotti & Van de Walle, Phys. Rev. B 75, 121201 (2007).

Theory: Choice of Reference Level An example: (AlAs|GaAs); isovalent, isostructural, lattice matched. AlAs: Reference – VBM (eV) GaAs: Reference – VBM (eV) Bulk Difference Superlattice (Δ Reference) Total Difference 11714.407 11715.316 0.909 -0.426 0.48 53.543 54.339 0.796 -0.304 0.49 4.183 4.604 0.421 0.106 0.53 Isolated

Quantitative Band Offsets

Choice of Heterojunction Interface Ensure no dipole across heterostructure.

Oxides ≠ III-Vs BiVO4 Bi2 Sn2 O7 CuAlO2 CoAl2 O4 PbO In2 O3

Charge Neutrality Level a.k.a. Effective midgap energy or Branch-point energy Γ-centered k-mesh DFT eigenvalues

Charge Neutrality Level Acoustic deformation potentials and heterostructure band offsets in semiconductors. M. Cardona and N. E. Christensen, Phys. Rev. B 35, 6182 (1987). Band offsets of wide band-gap oxides and implications for future electronic devices. J. Roberston, J. Vac. Sci. Technol. B 18, 1785 (2000). Branch-point energies and band discontinuities of III-nitrides and III-/II-oxides from quasiparticle band-structure calculations. A. Schleife, F. Fuchs, J. Furthmuller and F. Bechstedt, Appl. Phys. Lett. 94, 152104 (2009).

Charge Neutrality Level Schleife et al., APL ‘09 R In2 O3 PbO2 BiVO4 TiO2 C Walsh, Unpublished’09 MgO ZnO CdO In2 O3

An ‘Inspired’ Approach Objectives: • To define an absolute valence band position with reference to the vacuum level. • Obtain offsets without performing a heterojunction calculation. • Can use core level or electrostatic potential as the bulk reference.

Vacuum Level AlAs GaAs GaN (110) 4.99 4.84 5.57 (110)+H* 5.03 4.55 5.41 Bare: Pseudo-H: Wei’09: (AlAs|GaAs) 0.16 0.48 0.56 (GaN|GaAs) 0.73 0.86 2.55 Open questions: Surface polarisation? Surface relaxation? Surface passivation? • Vacuum Level – Bulk valence band separation.

Summary • Doping asymmetry in metal oxides can be understood by simple chemical principles. • Absolute band offsets are a challenging problem for bulk solid-state systems, especially with the structural diversity of metal oxides. • Charge neutrality level is a useful concept for a given material, but no universal alignment for different types of system. • Vacuum alignment for “bulk” band edges deserves more detailed exploration. Acknowledgements: Useful discussions with Graeme Watson, Su-Huai Wei and Richard Catlow. EU for Marie-Curie Fellowship.