Tackling Disorder in $\gamma$-Ga$_2$O$_3$

Ga$_2$O$_3$ and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga$_2$O$_3$ offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. $\gamma$-Ga$_2$O$_3$ presents a particular challenge across synthesis, characterisation, and theory due to its inherent disorder and resulting complex structure -- electronic structure relationship. Here, density functional theory is used in combination with a machine learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the $\gamma$-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of $\gamma$-Ga$_2$O$_3$. The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by PLE spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step towards exploring how their electronic structure can be understood in terms of local coordination and overall structure.