We have fabricated linear chains and two-dimensional arrays of Ge islands by self-assembling and self-ordering processes on vicinal Si substrates.Step bunches and stripe-like strain fields caused by underlying Si/SiGe multilayers with periodic wire-like accumulations at step edges induce an alignment of Ge islands. Repulsion of neighboring islands is caused by overlapping short-ranged strain fields surrounding partially strain relaxed dots and defines a minimum island separation. A periodic array of wires forming within the multilayer serves as a self-organized template for twodimensionally ordered Ge islands with a lateral period of 120 nm which is comparable to the island size.In the last decade, the epitaxial self-assembly of semiconductor quantum dots by the Stranski-Krastanov growth mode has developed to one of the most powerful techniques for fabricating quantum structures of high quality. The main material systems used are GaAs/InAs and Si/Ge with a lattice mismatch of about 7% and 4%, respectively. The smaller size and effective electron mass for In(Ga)As dots enhances quantum size effects compared to Ge dots. These features and the efficient optical interband transitions favor In(Ga)As quantum dots for optical fundamental studies and future optoelectronic applications [1,2]. A multitude of studies of the fundamental dot formation processes like nucleation, coalescence, ripening, faceting, shape transitions and ordering of dots, however, were performed on Ge islands on (001)Si substrate [3][4][5]. This may be due to the good knowledge of material parameters and the large accessible range of dot size which can be controlled by substrate temperature, Ge content and coverage. Ge islands with a diameter of about 200 nm down to 10 nm and a height of 10 nm to 1 nm were fabricated just by varying the substrate temperature from about 700 to 500 C. They can be embedded in active Si structures without defects and reveal quantum dot related properties, for example in photocurrent spectroscopy of intra valence band transitions in the mid-infrared spectral range and in admittance spectroscopy [6][7][8]. From these studies, hole localization energies around 350 meV, zero-dimensional (0D) hole quantization energies of about 40 meV and Coulomb blockade energies up to 15 meV were deduced for a dot size of about 20 nm. In this paper, we present a study on self-ordering of Ge islands in one-or two-dimensional arrays. The self-organized process of step-bunching in Si/SiGe multilayers on vicinal Si substrates and Ge island nucleation modified by local strain are combined.