Modeling of band alignment at the $\beta $-Ga$_{2}$O$_{3}$/$\beta $-(Ga$_{\mathrm{1-x}}$M$_{\mathrm{x}})_{2}$O$_{3}$ interface (M$=$Al, In)

Beta gallium oxide ($\beta $-Ga$_{2}$O$_{3})$ is receiving a significant attention as a possible native substrate for electronic devices. The band alignment and electron accumulation at the interface between $\beta $-Ga$_{2}$O$_{3}$ and its alloys remains an open question. We describe our modeling of $\beta $-Ga$_{2}$O$_{3}$/$\beta $-(Ga$_{\mathrm{1-x}}$M$_{\mathrm{x}})_{2}$O$_{3}$ (M$=$Al, In) interfaces based on the density functional theory. These are using the LDA$+$U method with large simulation cells with Hubbard U parameters extracted from accurate GW models. We find a range of compositions with relevant band shifts and a range of alloy epilayer thickness as a function of lattice mismatch.