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, DyxOy 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 DyxOy films grown on Si substrates has been studied using grazing synchrotron radiation diffraction (XRD) and atomic field microscopy. The DyxOy films were obtained by Dy evaporation in the Ar/O2 (6%) environment followed by annealing in oxygen or argon. The crystalline structure of the DyxOy 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 DyxOy films with thickness 20.0-30.0 nm deposited at relatively low rates and annealed in oxygen. The thicker DyxOy films deposited at higher rates and annealed in argon have the best polycrystalline structure. The DyxOy roughness is correlated with their crystalline structure. The thinner DyxOy films with the structure closed to amorphous are the smoother. The DyxOy films roughness increases with increasing the drain sizes. There is conformity of the DyxOy surface roughness to the underlying Si surface morphology. The smoother DyxOy surface has the smoother DyxOy-Si interface. The minimum value of the average interface roughness is found to be 0.8 nm in the DyxOy films closed to amorphous. The average interface roughness is measured to be 1.2 nm and 2.0 nm in polycrystalline DyxOy films annealed in O2 and N2, respectively. Based on the obtained results it is concluded that studied DyxOy films are suitable for the further investigation as a gate dielectric in the MOS devices.