Nature of the bandgap in In2O3 revealed by first-principles calculations & X-ray spectroscopy Aron Walsh*, Juarez L. F. Da Silva and Su-Huai Wei National Renewable Energy Laboratory, USA. C. Körber and A. Klein Darmstadt University of Technology, Germany. L. F. J. Piper, A. DeMasi and K. E. Smith Boston University, USA. G. Panaccionea and P. Torellib aLaboratorio TASC and bCNR-INFM, Italy. D.J. Payne, A. Bourlange and R. G. Egdell Oxford Chemistry Research Laboratory, UK.

Why In2O3 ? ★ Widely used n-type transparent conducting oxide (ITO). ★ Quoted band gap of 3.7 eV. ★ Up to 1022 cm-3 charge carriers. ★ Component in solar cells, displays, gas sensors. ★ BCC bixbyite structure ( space group: Ia/3, a = 10.12 Å )

Indirect gap hypothesis 3.7eV ! N ★ Onset of strong direct absorption at ~ 3.7 eV.1 ★ Weak absorption 1 eV lower due to indirect transitions.1 ★ Consistent with XPS measurements.2,3 [1] R.L. Weiher & R.P. Ley, J. Appl. Phys. 37, 299 (1966). [2] P.A. Cox et al., J. Sol. Stat. Chem. 68, 340 (1987). [3] V. Christou et al., J. Appl. Phys. 88, 5180 (2000) ★ CBM at zone centre (magnetoresistance).1 CBM VBM

Band bending hypothesis ★ Weak absorption due to surface upward band bending.4 [4] A. Klein, Appl. Phys. Lett. 77, 2009 (2000). [5] P. Erhart et al., Phys. Rev. B 75, 153205 (2007). 3.7eV ! N 3.7eV Weak absorption below Eopt not a property of the bulk material? Bulk Depletion Layer

★ Band structure calculations: Dispersionless valence band.5 Band bending hypothesis ★ Weak absorption due to surface upward band bending.4 [4] A. Klein, Appl. Phys. Lett. 77, 2009 (2000). [5] P. Erhart et al., Phys. Rev. B 75, 153205 (2007). 3.7eV ! N 3.7eV Weak absorption below Eopt not a property of the bulk material? Bulk Depletion Layer

Our method of resolution Experimental Approach: ★ Use less surface sensitive techniques on high quality epitaxial thin films6 and single crystals. ★ XPS (Daresbury), Hard-XPS (ESRF), XES (Brookhaven). Theoretical Approach: ★ Plane-wave Density Functional Theory (PAW-PBE-VASP). ★ Wavefunction symmetry analysis. ★ Band to band optical transitions calculated (<Ψ2|p|Ψ1>). [6] A. Bourlange et al., Session J6 (11:50am). (hν = 1487 eV, 25 Å) (hν = 6000 eV, 60 Å) (O Kα, 1000 Å)

Spectroscopy Binding energy (eV) -1 0 1 2 3 4 5 6 Al K! XPS OK XES Al K α hν = 1486.6 eV HXPS hν = 6000 eV nominally undoped 2% Sn-doped 10% Sn-doped 10% Sn-doped (a) (b) (c) x 20 x 10 XPS HXPS XES ★ Valence - conduction band separation of 2.9 eV in ‘undoped’ samples. ★ All three independent measurents show the same valence band onset. ★ n-type doping increases the separation due to further occupation of the conduction band.

Simulation -1.0 0.0 1.0 2.0 3.0 4.0 Energy (eV) ! !"#N H " ! ! $ ! % ! & (Ag) (Tg) (Tu) DFT Bandstructure ★ Direct band gap. ★ Flat valence band (ionic O 2p character). ★ Dispersive conduction band: (In / O s hybrid state). ★ VBM (g), CBM (g).

Simulation -1.0 0.0 1.0 2.0 3.0 4.0 Energy (eV) ! !"#N H " ! ! $ ! % ! & (Ag) (Tg) (Tu) DFT Bandstructure ★ Direct band gap. ★ Flat valence band (ionic O 2p character). ★ Dispersive conduction band: (In / O s hybrid state). ★ VBM (g), CBM (g). Direct fundamental transitions are symmetry forbidden!

Simulation DFT Absorption Spectrum ★ Optical transitions calculated over a dense k-mesh sampling the full Brillouin zone. ★ Negligible absorption until 0.8 eV above the fundamental gap! ★ Correlates differences in electronic and optical measurements. Eopt ≠ Efundamental 6 8 Energy (eV) Eg 2 4 Absorption coefficient

Summary & Conclusions 1. The fundamental and optical gaps of In2O3 are inequivalent due to symmetry forbidden optical transitions. 2. We set an upper limit on the fundamental gap of 2.9 eV. (Eg = 2.9eV + ΔBM - ΔRN = 2.7 eV) 3. Revised band structure is crucial for measurement/ calculation of electronic properties: band offsets, defect levels, doping effects. 4. Forbidden direct band gaps are common in oxide systems possessing inversion symmetry: Cu2O, SnO2, TiO2. These systems are not indirect! (Indirect α1/2, Forbidden direct)

Fundamental band gap estimation ★ DFT: Eopt = Efundamental + 0.8eV ★ XPS: ‘undoped’ samples exhibit valence-conduction band separation of 2.9 eV. This represents an upper limit. Need to take into account conduction band occupation. Fundamental Eg = 2.9eV + ΔBM - ΔRN. Current estimation: Eg = 2.7eV Eg ! BM + ! - RN Eg ! BM + Eg VBM CBM