  A comprehensive bulk and surface investigation of high-quality
In$_2$O$_3$(001) single crystals is reported. The transparent-yellow,
cube-shaped single crystals were grown using the flux method. Inductively
coupled plasma mass spectrometry (ICP-MS) reveals small residues of Pb, Mg, and
Pt in the crystals. Four-point-probe measurements show a resistivity of 2.0
$\pm$ 0.5 $\times$ 10$^5$ {\Omega} cm, which translates into a carrier
concentration of $\approx$10$^{12}$ cm$^{-3}$. The results from x-ray
diffraction (XRD) measurements revise the lattice constant to 10.1150(5) {\AA}
from the previously accepted value of 10.117 {\AA}. Scanning tunneling
microscopy (STM) images of a reduced (sputtered/annealed) and oxidized
(exposure to atomic oxygen at 300 {\deg}C) surface show a step height of 5
{\AA}, which indicates a preference for one type of surface termination. The
surfaces stay flat without any evidence for macroscopic faceting under any of
these preparation conditions. A combination of low-energy ion scattering (LEIS)
and atomically resolved STM indicates an indium-terminated surface with small
islands of 2.5 {\AA} height under reducing conditions, with a surface structure
corresponding to a strongly distorted indium lattice. Scanning tunneling
spectroscopy (STS) reveals a pronounced surface state at the Fermi level
($E_F$). Photoelectron spectroscopy (PES) shows additional, deep-lying band gap
states, which can be removed by exposure of the surface to atomic oxygen.
Oxidation also results in a shoulder at the O 1s core level at a higher binding
energy, possibly indicative of a surface peroxide species. A downward band
bending of 0.4 eV is observed for the reduced surface, while the band bending
of the oxidized surface is of the order of 0.1 eV or less.
