Self-assembled GeSi dots on Si (001) substrates have attracted broad attentions not only because of their potential applications in novel devices compatible with the sophisticated Si-integration technology [1], but also to understand the fundamental physics during heteroepitaxial growth as a prototype model. The GeSi dots via Stranski-Krastanov (SK) growth mode during heteroepitaxy result from the balance between the relaxation of misfit strain and the cost of the surface energy [2]. They are dislocation free and small. On the other hand, these self-assembled dots are always spatially random, and their size uniformity is rather poor. Such disadvantages degrade the properties of these dots, which hamper their applications in devices. Enormous effort has been devoted to improve the size homogeneity and to control the site of self-assembled GeSi dots. Remarkable progresses have been made particularly on prepatterned Si (001) , and nanosphere lithography [7]. Those nanostructures considerably affect both the surface energy and the misfit strain energy. As a result, the nucleation and the evolution of dots on patterned Si (001) substrates are much different from those on flat Si (001) substrates.It is well documented that GeSi dots preferentially grow within trenches or pits [3][4][5][6][7][8][9]. Such preferentially growth is energetically favorable [8,9]. As a result, ordered or site-controlled dots can be realized on patterned substrates, as shown in Figure 1b. Such ordered dots always exhibit remarkably improved size uniformity in comparison with that on flat substrates [3]. In addition, the nucleation and the evolution of dots on patterned substrates are intimately related to the geometrical morphology of the nanostructures [8][9][10][11][12][13][14], as well as the growth conditions [15,16]. Enhanced strain relaxation and intermixing in GeSi dots on pre patterned Si (001) substrates were also found [17].The preliminary results about the physical properties of GeSi dots on pre patterned Si (001) substrates demonstrate that these controlled dots exhibit some unique features. It is feasible to explore the properties of single nano island [18] and the transportation properties of holes between dots [19]. The controlled dots of a large period on patterned substrates may have a distributed feedback effect, which improve the optical properties of dots [20]. The strong coupling of ordered GeSi dots with a small period on patterned substrates can make them act as a quantum dot crystal [21]. Given the precise control ability of GeSi dots on prepatterned Si (001) substrates, they can act as excellent candidates to thoroughly explore the unique properties of single dot and coupled dot molecule, as well as the collective properties of ordered dots.