The use of self-organization of nanostructures during growth of materials having a high lattice mismatch e.g. Ge on Si offers new possibilities for device applications. The Ge layers were grown on Si(001) substrates by low pressure chemical vapour deposition. Island size statistics derived from the atomic force micrographs show a trimodal size distribution at high average Gr layer thicknesses, whereas at low Ge layer thicknesses only a narrow monomodal island size distribution exists. Transmission electron micrographs reveal the type of relaxation of the Ge islands and the shape of islands after being capped by a Si overlayer. A correspondence beta cen the broadening of the spectral emission and the island morphology can be concluded from photoluminescence measurements. Multiple stacked island layers exhibit a significant increase of integral intensity in comparison with a single layer of islands, grown under equal conditions. A clear vertical correlation between island positions in different lavers and a continuous enlargement of island size in upper layers is found on transmission electron micrographs of stacked island layers.