Nature of the Band Gap of ${\mathrm{In}}_2{\mathrm{O}}_3$ Revealed by First-Principles Calculations and X-Ray Spectroscopy

Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for ${\mathrm{In}}_2{\mathrm{O}}_3$ is found significantly closer to the bottom of the conduction band than expected on the basis of the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of ${\mathrm{In}}_2{\mathrm{O}}_3$ exhibit a small dispersion and the conduction band minimum is positioned at $\Gamma$. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band maximum. The results set an upper limit on the fundamental band gap of 2.9 eV.

Figure 1

(a) Al $K\alpha$ XPS ($h\nu =1486.6\mathrm{eV}$) of nominally undoped and 2% and 10% Sn-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films. (b) HXPS ($h\nu =6000\mathrm{eV}$) of the same films. (c) Al $K\alpha$ XPS and O $K$ shell XES of 10% Sn-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ aligned using the Fermi edge (0 eV) visible in both spectra.

Figure 2

Band structure of ${\mathrm{In}}_2{\mathrm{O}}_3$ (along the $H\mathrm{\text{−}}\Gamma \mathrm{\text{−}}N$ lines). The highest energy valence bands resulting in strong optical absorption to the conduction band are light gray. A rigid shift of the conduction band is applied to offset the density-functional theory band gap underestimation [22].

Figure 3

Calculated absorption spectrum of bulk ${\mathrm{In}}_2{\mathrm{O}}_3$. Note that the onset of optical absorption is 0.81 eV higher in energy than the fundamental band gap [22].