The 2D-3D crossover and anisotropy of upper critical fields in Nb and NbN superconducting thin films

The upper critical field (Bc2) of superconducting thin films of Nb (film thickness d = 40 nm) and NbN (d=  10, 50 and 100 nm) have been measured and analyzed as a function of temperature (T= 1.8-15 K) in both parallel and perpendicular magnetic field (B=  0-7 T) directions with respect to the film plane. Dimensional crossover from 2D to 3D is observed for all the thin films except for the 10 nm thick NbN film which exhibits only 2D behavior in the measured T and B range. Further, the upper critical fields were found to be anisotropic in case of both Nb and NbN films. However, the anisotropy shows different behavior in all the four samples. In case of Nb, below the 2D-3D crossover temperature, the Bc2∥(T) is higher than Bc2⊥(T) and both curves branch away further from each other. On the other hand, in case of NbN (50 and 100 nm), there is a reversal of anisotropy, i.e., in the 2D region Bc2∥(T) > Bc2⊥(T) and in the 3D region at some temperature Bc2⊥(T) > Bc2∥(T). In the NbN films with increasing thickness, the 2D region shrinks and 3D region expands, and the 2D-3D crossover and anisotropy reversal characteristic temperatures shift toward Tc. These observations are quantitatively explained using the Ginzburg-Landau theoretical approach after Schneider and Locquet (Physica C, 179 (1991) 125).