The effect of vertical ordering in superlattices of self-assembled Ge/Si(0 0 1) quantum dots was investigated by a combination of structural and optical characterizations via in situ reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), atomic force microscopy (AFM) and photoluminescence (PL) spectroscopy. We show that the vertical ordering observed in quantum-dot superlattices is characterized not only by the alignment of islands along the growth direction but also by a reduction of the critical thickness. The better the vertical ordering is, the more pronounced the reduction of the critical thickness will be. Such an evolution of the critical thickness could be explained by elastic strain fields induced by buried islands and propagate through the spacer layers. An important result issued from this work is the realization of superlattices in which dots can have equal size in all layers. On the other hand, experiments performed on the transformation of the island shape versus the spacer layer thickness suggest that preferential nucleation induced by surface roughness may be the main mechanism responsible for the vertical ordering observed in quantum-dot superlattices. (C) 2003 Elsevier Science B.V. All rights reserved.