Band alignment and defect chemistry of functional oxides: A concise discussion
A presentation delivered at a special workshop on transparent conducting oxides at Trinity College Dublin in September 2009. Later summarised in http://pubs.acs.org/doi/abs/10.1021/ar400115x
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).
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
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).
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).
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.
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.
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