Upper critical field and fluctuation conductivity in Nb-doped strontium titanate thin films

We show that the transition temperature $T_c$ of Nb-doped strontium titanate thin films grown in vacuum by pulsed laser deposition is similar to bulk and that these films follow a similar dependence of $T_c$ on the carrier density as bulk. We have measured the temperature dependence of the upper critical field $H_{c2\mathrm{}}$ in thin films. We fit the data to the empirical temperature dependence $H_{c2\mathrm{}}\propto \left(1\mathrm{}-t^2{)/(1+t}^2\right),$ where ${t=T/T}_c,$ and determined the electronic diffusion constant from the slope of ${\mathrm{dH}}_{c2\mathrm{}}/dT$ near $T_c.$ We further fit the temperature dependence of the fluctuation conductivity above $T_c$ successfully to the theories of Aslamazov-Larkin and Maki-Thompson.