To use the concept of strain-induced spatial arrangement with an increasing number of quantum-dot layers stacked on top of each other, a rather high number of layers are needed to obtain signišcant ordering, as the bottom layers do hardly show any lateral correlation. For an improvement, regular spacing between quantum dots already in the šrst layer would be desirable. Various approaches for the realization of such wellordered Ge nanostructure arrays have been developed, most prominently by the use of lithography. While optical lithography, due to the di£raction limit, cannot provide suÀcient resolution for the fabrication of Ge quantum dots with dimensions of only a few 10 nm, electron-beam lithography in conjunction with reactive ion etching has been shown to enable the selective growth of ordered Ge dot arrays [15,16]. Alternatively, a prepatterning of the Si substrate by scanning probe techniques is a viable concept . Although these artišcial patterning techniques o£er a very precise control of the island nucleation sites, they require a sequential substrate manipulation and, therefore, these techniques are very time consuming and expensive. In this respect, concepts relying on self-organization are much better suited for technological applications, since they enable parallelized fabrication.