  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.
