  In this article, the electronic band structure $\beta-(Al_xGa_{1-x})_2O_3$
alloy system is calculated with $\beta-Ga_2O_3$ as the bulk crystal. The
technique of band unfolding is implemented to obtain the effective
bandstructure \textit{(EBS)} for aluminium fractions varying between 12.5\% and
62.5\% with respect to the gallium atoms. A 160 atom supercell is used to model
the disordered system that is generated using the technique of special
quasirandom structures which mimics the site correlation of a truly random
alloy and reduces the configurational space that arises due to the vast
enumeration of alloy occupation sites. The impact of the disorder is then
evaluated on the electron effective mass and bandgap which is calculated under
the generalized gradient approximation \textit{(GGA)}. The EBS of disordered
systems gives an insight into the effect of the loss of translational symmetry
on the band topology which manifests as band broadening and can be used to
evaluate disorder induced scattering rates and electron lifetimes. This
technique of band unfolding can be further extended to alloy phonon dispersion
and subsequently phonon lifetimes can also be evaluated from the band
broadening.
