In the last decade a lot of attention was devoted to study the high-k dielectrics (Si₃N₄, Al₂O₃, HfO₂, ZrO₂, La₂O₃) for producing the microelectronic devices and integrated circuits with the equivalent properties to very thin SiO₂. Among the high-k dielectrics being studied, Dy_xO_y appears promising due to its relatively high dielectric constant (k=12) as compared to SiO₂ (k =3.9). The crystalline structure and surface morphology of the Dy_xO_y films grown on Si substrates has been studied using grazing synchrotron radiation diffraction (XRD) and atomic field microscopy. The Dy_xO_y films were obtained by Dy evaporation in the Ar/O₂ (6%) environment followed by annealing in oxygen or argon. The crystalline structure of the Dy_xO_y films becomes better with increasing their thickness and deposition rate in Ar/O₂ environment. The "worth" fine-grained structure closed to amorphous is observed in the Dy_xO_y films with thickness 20.0-30.0 nm deposited at relatively low rates and annealed in oxygen. The thicker Dy_xO_y films deposited at higher rates and annealed in argon have the best polycrystalline structure. The Dy_xO_y roughness is correlated with their crystalline structure. The thinner Dy_xO_y films with the structure closed to amorphous are the smoother. The Dy_xO_y films roughness increases with increasing the drain sizes. There is conformity of the Dy_xO_y surface roughness to the underlying Si surface morphology. The smoother Dy_xO_y surface has the smoother Dy_xO_y-Si interface. The minimum value of the average interface roughness is found to be 0.8 nm in the Dy_xO_y films closed to amorphous. The average interface roughness is measured to be 1.2 nm and 2.0 nm in polycrystalline Dy_xO_y films annealed in O₂ and N₂, respectively. Based on the obtained results it is concluded that studied Dy_xO_y films are suitable for the further investigation as a gate dielectric in the MOS devices.