We have investigated Ge-rich dots on Si (100), grown by molecular beam epitaxy. Various growth parameters, including growth temperature, growth rate, composition of the dots, and thickness of the deposited layer, have been varied over a wide range in order to study their influence on the size and areal density of the dots. The samples have been analysed by atomic force microscopy, determining the areal density, height and diameter of the dots. Detailed statistics on the influence of the growth parameters on the size distribution has revealed the optimum conditions for the growth of very homogeneous dot ensembles. Furthermore, first approaches to obtain a self-organized vertical and lateral ordering of the dots will be presented.