  The alloying of the group-III transparent semiconducting sesquioxides
In$_2$O$_3$ and Ga$_2$O$_3$ can lead to a modulation of the properties of the
parent compounds, e.g., the shallow- and deep-donor character of the oxygen
vacancy or the presence and absence of a surface electron accumulation layer,
respectively. In this work, we investigate the effect of alloying on the
electron transport properties of unintentionally-doped single-crystalline and
textured bixbyite (In$_{1-x}$Ga$_x$)$_2$O$_3$ thin films annealed in oxygen and
vacuum with Ga contents up to $x$=0.18. Hall effect measurements demonstrate a
surprising increase in electron density due to native defects with added Ga.
This increase may be related to the incorporation of Ga-interstitials or oxygen
vacancies induced by Ga-related unit-cell distortions. A combined investigation
based on hard and soft x-ray photoelectron spectroscopy measurements
demonstrates the existence of the surface electron accumulation layer for all
alloy films and, hence, no depletion up to $x$=0.18. Finally, we additionally
demonstrate a single-crystalline (In$_{0.92}$Ga$_{0.08}$)$_2$O$_3$:Sn film, as
a possible transparent conductive oxide with a wider band gap than that of
(Sn-doped) In$_2$O$_3$.
