We investigate theoretically the Zeeman effect on the hole states in quantum dots. In frame of tight-binding approach, we propose a method of calculating the g factor for localized states. The principal values of the g factor for the ground hole state in the self-assembled Ge/Si quantum dot are calculated. We find the strong g-factor anisotropy-the components g xx , g yy are one order smaller than the g zz component, g zz ϭ12.28, g xx ϭ0.69, g yy ϭ1.59. The efficiency of the developed method is demonstrated by calculating of the size dependence of g factor and by establishment of the connection with two-dimensional case. The g-factor anisotropy increases with the size of the quantum dot. The analysis of the wave function structure shows that the g factor and its size dependence are mainly controlled by the contribution of the state with J z ϭϮ 3 2 , where J z is the angular momentum projection on the growth direction of the quantum dot.where , are the azimuth and polar angles of the vector h in the coordinate system (x,y,z) and the matrix R can be expressed via standard rotation matrix: R

The growth of Ge nanoclusters on a prepatterned Si (100) surface formed by imprint lithography in combination with subsequent irradiation with Ge + ions is studied. The prepatterned surface presents a sys tem of parallel 10 nm wide grooves repeating with a period of 180 nm. Irradiation of the substrate was con ducted at two temperatures, room temperature (cold irradiation) and 400°C (hot irradiation). It is shown that, during epitaxy (550-700°C), the residual radiation defects located in the bulk under the grooves sup press the nucleation of Ge nanoclusters in the grooves. In the case of prepatterned substrates, from which imperfect regions are completely removed, nanoclusters grow in the grooves.

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