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$\mathrm{\beta}$-Gallium oxide ($\mathrm{\beta\mbox{-}Ga_{2}O_{3}}$) is anemerging widebandgap semiconductor for potential application in power and RFelectronics applications. Initial theoretical calculation on a 2-dimensionalelectron gas (2DEG) in$\mathrm{\beta\mbox{-}(Al_{x}Ga_{1-x})_{2}O_{3}/Ga_{2}O_{3}}$ heterostructuresshow the promise for high speed transistors. However, the experimental resultsdo not get close to the predicted mobility values. In this work, We performmore comprehensive calculations to study the low field 2DEG transportproperties in the $\mathrm{\beta\mbox{-}(Al_{x}Ga_{1-x})_{2}O_{3}/Ga_{2}O_{3}}$heterostructure. A self-consistent Poisson-Schrodinger simulation ofheterostructure is used to obtain the subband energies and wavefunctions. Theelectronic structure, assuming confinement in a particular direction, and thephonon dispersion is calculated based on first principle methods under DFT andDFPT framework. Phonon confinement is not considered for the sake ofsimplicity. The different scattering mechanisms that are included in thecalculation are phonon (polar and non-polar), remote impurity, alloy andinterface-roughness. We include the full dynamic screening polar optical phononscreening. We report the temperature dependent low-field electron mobility.

Low field transport calculations in 2-dimensional electron gas in $\mathrm{\beta\mbox{-}(Al_{x}Ga_{1-x})_{2}O_{3}/Ga_{2}O_{3}}$ heterostructures