Superlattices of Si3N4 and Si-rich silicon nitride thin layers with varying thickness were prepared by plasma enhanced chemical vapor deposition. After high temperature annealing, Si nanocrystals were formed in the former Si-rich nitride layers. The control of the Si quantum dots size via the SiNx layer thickness was confirmed by transmission electron microscopy. The size of the nanocrystals was well in agreement with the former thickness of the respective Si-rich silicon nitride layers. In addition X-ray diffraction evidenced that the Si quantum dots are crystalline whereas the Si3N4 matrix remains amorphous even after annealing at 1200 degrees C. Despite the proven Si nanocrystals formation with controlled sizes, the photoluminescence was 2 orders of magnitude weaker than for Si nanocrystals in SiO2 matrix. Also, a systematic peak shift was not found. The SiNx/Si3N4 superlattices showed photoluminescence peak positions in the range of 540-660nm (2.3-1.9 eV), thus quite similar to the bulk Si3N4 film having peak position at 577nm (2.15 eV). These rather weak shifts and scattering around the position observed for stoichiometric Si3N4 are not in agreement with quantum confinement theory. Therefore theoretical calculations coupled with the experimental results of different barrier thicknesses were performed. As a result the commonly observed photoluminescence red shift, which was previously often attributed to quantum-confinement effect for silicon nanocrystals, was well described by the interference effect of Si3N4 surrounding matrix luminescence