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Open spaces in amorphous Al2O3 films fabricated by atomic layer deposition and in AlONx deposited by a reactive sputtering technique were probed by using monoenergetic positron beams. In these films, open spaces with three different sizes were found to coexist. The mean size and the concentration of open spaces were decreased by annealing at 800 °C in N2 atmosphere, which was associated with rearrangements of the amorphous network in the films and their crystallization. Nitrogen incorporation into Al2O3 suppressed the shrinkage of network structures due to the annealing, which was attributed to the formation of a stable network through the introduction of Al-N bonding. For Al2O3 deposited on GaN, the temperature treatment above 800 °C led to the introduction of vacancytype defects in the GaN substrate. This fact suggests that the change in the network structure of Al2O3 enhances chemical instability at the Al2O3/GaN interface and the out-diffusion of atoms from the substrate. [ABSTRACT FROM AUTHOR]