Superlattices containing 3 nm thick silicon rich silicon nitride sublayers and 3 nm and 10 nm thick SiO2 barriers were prepared by plasma enhanced chemical vapor deposition. Despite the as-prepared samples represented a well-kept multilayer structure with smooth interfaces, the high temperature annealing resulted in the total destruction of multilayer structure in the samples containing 3 nm SiO2 barriers. Energy-filtered transmission electron microscopy images of these samples indicated a silicon nanoclusters formation with sizes of 2.5–12.5 nm, which were randomly distributed within the structure. Although in the sample with 10 nm SiO2 barriers some fragments of the multilayer structure could be still observed after thermal annealing, nevertheless, the formation of large nanocrystals with diameters up to 10 nm was confirmed by dark field transmission electron microscopy. Thus, in contrast to the previously published results, the expected size control of silicon nanocrystals was lost. According to the FTIR results, the thermal annealing of SiNx/SiO2 superlattices led to the formation of silicon nanocrystals in mostly oxynitride matrix. Annealed samples demonstrated a photoluminescence peak at 885 nm related to the luminescence of silicon nanocrystals, as confirmed by time-resolved photoluminescence measurements. The loss of nanocrystals size control is discussed in terms of the migration of oxygen atoms from the SiO2 barriers into the silicon rich silicon nitride sublayers. A thermodynamic mechanism responsible for this process is proposed. According to this mechanism, the driving force for the oxygen migration is the gain in the configuration entropy related to the relative arrangements of oxygen and nitrogen atoms.