In the present work we study the growth by pulsed laser deposition of YBa$_2$Cu$_3$O$_{7-delta}$ (YBCO) films on the r-cut sapphire substrates. To improve the matching of the lattice parameters between the substrate and the film we use CeO$_{2}$ buffer layer, recrystallized prior to the deposition of YBCO. The optimal thickness and temperature of recrystallization of the buffer layer is first determined using atomic force microscopy (AFM) and X-ray diffraction. Next, we use the AFM to examine the dependence of YBCO film roughness on the film thickness, and we study the homogeneity of magnetic flux penetration into the films by magneto-optical imaging. We find that the superconducting critical temperature and critical current density of these films are very similar to those of YBCO films grown on well-matched substrates. It appears that the microstructure of YBCO films is affected by structural defects in the buffer layer as well as variations in oxygen deficiency, which results in high values of critical current density suitable for application.
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