Dependence of magnetic penetration depth on the thickness of superconducting Nb thin films

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In this paper we present the results of a systematic study on the magnetic field penetration depth of superconducting niobium thin films. The films of thicknesses ranging from $8\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ were deposited on a Si substrate by dc magnetron sputtering. The values of the penetration depth $\ensuremath{\lambda}(0)$ were obtained from the measurements of the effective microwave surface impedance by employing a sapphire resonator technique. Additionally, for the films of thickness smaller than $20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the absolute values of $\ensuremath{\lambda}(0)$ were determined by a microwave transmission method. We found that the reduction of the film thickness below $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ leads to a significant increase of the magnetic field penetration depth from about $80\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for $300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick film up to $230\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for a $8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick film. The dependence of the penetration depth on film thickness is described well by taking into account the experimental dependences of the critical temperature and residual resistivity on the thickness of the niobium films. Structural disordering of the films and suppression of superconductivity due to the proximity effect are considered as mechanisms responsible for the increase of the penetration depth in ultrathin films.