Mathematical modeling of temperature dependence of the second critical field of thin films of niobium nitride

Temperature dependence of the second critical field $H_{c2}(T)$ for superconductors due to different values of Maki parameter and of spin-orbit scattering parameter is modeled mathematically within the framework of WHH-theory (Werthamer, Helfand, Hohenberg). Temperature dependencies of superconducting transition for the first harmonic of voltage of thin niobium nitride (NbN) films are investigated in dc magnetic fields up to 8 T. By approximating experimental temperature dependence of the upper critical field of NbN films by theoretical dependence $H_{c2}(T)$ Maki parameter is obtained, that takes into account the spin paramagnetism effect in this material. From transport and optical measurements done in this and other studies the most important parameters of NbN superconductor are evaluated that are consistent with the data of present work.