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Self-organized GaN islands of nanometric scale were fabricated by controlling the Stranski–Krastanov growth mode of GaN deposited by molecular beam epitaxy on AlN. Evidence for ripening of dots under vacuum has been observed, resulting in changes in dot size distribution. We also show that in superlattice samples, consisting of multiple layers of GaN islands separated by AlN, the GaN islands are vertically correlated provided that the AlN layer thickness remains small enough. The luminescence peak of GaN dots is blueshifted with respect to bulk emission and its intensity does not vary with temperature, both effects demonstrating the strongly zero-dimensional character of these nanostructures.