Self-assembled quantum dots can be the building blocks of a variety of mesoscopic devices. However, in order to use these structures in large-scale integrated devices, accurate control over their spatial positioning is required. We show here that, by a suitable engineering of the deposition process, it is possible to obtain self-organization resulting in well ordered clusters composed of regularly disposed nano-sized islands. Elastically relaxed Ge islands act as a stressor for a Si layer subsequently deposited (Ge has a 4 % larger lattice cell). This effect results in a modulation of the lattice parameter and strain field in the Si over-layer. In particular the Si lattice in the columnar region on top of the buried islands is tensile strained and will act as preferential nucleation site for the subsequent Ge island growth. We have generated a square array of tensile-strained regions oriented along the [010]-[100] directions on the Si(001) surface exploiting the self-ordering occurring in the growth at 750 degrees C of Ge island multi-layers used as a template. The strain field intensity and shape was modified by changing the thickness of the template Si over-layer: the thicker the overlayer the wider and less intense the strain field in the Si tensile regions. On this template we have grown a Ge island layer at the lower temperature of 600 degrees C. At this growth temperature the islands are much smaller than the lateral extension of the strain field on the Si surface of the template and the nucleation and evolution of several islands inside a single tensile-strained regions is promoted. Upon decreasing the template Si over-layer thickness from 200 to 35 nm the Ge island spatial distribution changes from random to a well-ordered square lattice of multi-island clusters. At intermediate Si over-layer thickness (65 nm), the Ge islands are confined in cluster regions only at the first stage of their evolution (pyramids), while for thinner over-layer (35 nm) islands are assembled in clusters up to the last stage their growth dynamics (relaxed domes). The strong dome-to-dome interaction within a cluster, due to their small mutual separation, has impact also on the dome size by reducing their mean base width of about 35%. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim