The growth of Ge dots has been achieved by molecular beam epitaxy on a Si (001) surface covered by an ultra thin (20 A) silicon nitride Si 3 N 4 layer. The Ge dots exhibit an epitaxial relationship with the underlying silicon substrate, despite the presence of the dielectric layer. The atomic force microscopy results show that the Ge dots have a hemispherical shape with 10 nm average size and the density of the dots is as high as 4 × 10 11 cm -2 . Moreover, we show that the silicon, grown in order to embed the Ge dots deposited on silicon nitride Si 3 N 4 layer, exhibits a quasi-two-dimensional growth of single crystal.