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

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 $8\text{to}300\mathrm{nm}$ were deposited on a Si substrate by dc magnetron sputtering. The values of the penetration depth $\lambda \left(0\right)$ 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 $20\mathrm{nm}$, the absolute values of $\lambda \left(0\right)$ were determined by a microwave transmission method. We found that the reduction of the film thickness below $50\mathrm{nm}$ leads to a significant increase of the magnetic field penetration depth from about $80\mathrm{nm}$ for $300\mathrm{nm}$ thick film up to $230\mathrm{nm}$ for a $8\mathrm{nm}$ 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.

Figure 1

The thickness dependence of the critical temperature (circles) and the residual resistivity in the normal state (triangles) of the Nb films. The solid line is the fit of $T_C\left(d\right)$ by Eq. (11) and the dashed line is the approximation of ${\rho }_0\left(d\right)$ by Eq. (12).

Figure 2

The result of the SIMS study of the Nb film. The solid, dashed, and dotted lines are ion responses of silicon (substrate), carbon, and oxygen, respectively. The areas A and B correspond to 200 and $400\mathrm{nm}$ thick Nb layers, respectively. Area C corresponds to the Si substrate. Peak 1 of the oxygen and carbon responses is the position of the surface layer of the $400\mathrm{nm}$ Nb film. Peak 2 is the position of the film-substrate interface layer.

Figure 3

The temperature dependence of changes in the effective penetration depth $\delta {\lambda }_{\mathit{eff}}$ of the Nb films with the different thicknesses indicated next to each curve. The solid lines are fitted by Eq. (1).

Figure 4

The thickness dependence of the ratio between the coherence length ${\xi }_0$ and the electron mean-free path l of the Nb films determined from experimental data using Eq. (8) and Eq. (9), respectively. The solid line represents the simulation obtained by the substitution of $T_C\left(d\right)$ using Eq. (11) and of ${\rho }_0\left(d\right)$ using Eq. (12) into Eq. (10).

Figure 5

The temperature dependence of the transmission coefficient Tr for three Nb films of different thicknesses $d$ indicated next to each curve.

Figure 6

The thickness dependence of penetration depth at zero temperature $\lambda \left(0\right)$. The circles represent results of resonance technique measurements, and the triangles are results of transmission measurements. The solid line represents the simulation of $\lambda \left(0\right)$ by Eq. (13) using $T_C\left(d\right)$ (11) and ${\rho }_0\left(d\right)$ (12).