  $\mathrm{\beta}$-Gallium oxide ($\mathrm{\beta\mbox{-}Ga_{2}O_{3}}$) is an
emerging widebandgap semiconductor for potential application in power and RF
electronics applications. Initial theoretical calculation on a 2-dimensional
electron gas (2DEG) in
$\mathrm{\beta\mbox{-}(Al_{x}Ga_{1-x})_{2}O_{3}/Ga_{2}O_{3}}$ heterostructures
show the promise for high speed transistors. However, the experimental results
do not get close to the predicted mobility values. In this work, We perform
more comprehensive calculations to study the low field 2DEG transport
properties in the $\mathrm{\beta\mbox{-}(Al_{x}Ga_{1-x})_{2}O_{3}/Ga_{2}O_{3}}$
heterostructure. A self-consistent Poisson-Schrodinger simulation of
heterostructure is used to obtain the subband energies and wavefunctions. The
electronic structure, assuming confinement in a particular direction, and the
phonon dispersion is calculated based on first principle methods under DFT and
DFPT framework. Phonon confinement is not considered for the sake of
simplicity. The different scattering mechanisms that are included in the
calculation are phonon (polar and non-polar), remote impurity, alloy and
interface-roughness. We include the full dynamic screening polar optical phonon
screening. We report the temperature dependent low-field electron mobility.
