Title: Utilizing (Al, Ga)2O3/Ga2O3 superlattices to measure cation vacancy diffusion and vacancy-concentration-dependent diffusion of Al, Sn, and Fe in \b{eta} -Ga2O3

Abstract: Diffusion of native defects such as vacancies and their interactions with impurities are fundamental in semiconductor crystal growth, device processing, and long-term aging of equilibration and transient diffusion of vacancies are rarely investigated. We used aluminum-gallium oxide/gallium oxide superlattices (SLs) to detect and analyze transient diffusion of cation vacancies during annealing in O2 at 1000-1100 C. Using a novel finite difference scheme for the diffusion equation with time- and space-varying diffusion constant, we extract diffusion constants for Al, Fe, and cation vacancies under the given conditions, including the vacancy concentration dependence for Al. indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on Sn-doped beta-gallium oxide substrates, gradients observed in the extent of Al diffusion indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on (010) Fe-doped substrates, the Al diffusion is uniform through the SLs, indicating a depth-uniform concentration of vacancies. We find no evidence in either case for the introduction of gallium vacancies from the free surface at rates sufficient to affect Al diffusion down to ppm concentrations, which has important bearing on the validity of typically-made assumptions of vacancy equilibration. Additionally, we show that unintentional impurities in Sn-doped gallium oxide such as Fe, Ni, Mn, Cu, and Li also diffuse towards the surface and accumulate. Many of these likely have fast interstitial diffusion modes capable of destabilizing devices over time, thus highlighting the importance of controlling unintentional impurities in beta-gallium oxide wafers.