We report an original method of GaN/AlN quantum dots (QDs) formation with low density by ammonia MBE on the (0001)AlN surface using a decomposition process of GaN thin layer. The QDs formation has been investigated in situ by reflection high-energy electron diffraction technique. Low density of quantum dots has been obtained in the range 107–109 cm−2. Single quantum dots photoluminescence lines corresponding to exciton and biexiton transitions were observed in micro-photoluminescence spectra. A lattice gas model was developed for correct description of the GaN QDs statistical ensemble on the surface. Effective interaction between QDs results in the discontinuous phase transitions (first-order phase transitions) from low density of QDs (gas branch) to condensed phase of QDs. The GaN QDs formation has been confirmed by high-resolution transmission electron microscopy and micro-photoluminescence of single quantum dots.