Resistance Fluctuations Due to Hydrogen Diffusion in Niobium Thin Films

Fluctuations of the number of protons (${\mathrm{H}}^{+}$) that scatter conduction electrons dominate lowfrequency resistance fluctuations in Nb films. The excess-noise spectra $S_V(f, T)$ obey a scaling law: $\frac{f{S}_V(f, T)}{〈\delta V^2\mathrm{}\left(T\right)\mathrm{}〉}=g\left(\frac{f}{D\left(T\right)\mathrm{}}\right)$; for our geometry at $260<T<\mathrm{}370\mathrm{}$ K, $S_V(f, T)\propto \frac{c_0\mathrm{}\left(T\right)\mathrm{}}{f^{\alpha }}$, $\alpha =0\mathrm{}$ for $f\ll \frac{D}{\left(\pi L^2\right)}$ and $\alpha =\frac{3}{2}$ for $f\gg \frac{D}{\left(\pi L^2\right)}$, $c_0$ is the ${\mathrm{H}}^{+}$ concentration, $L$ is the film length, and the ${\mathrm{H}}^{+}$ diffusion coefficient is $D\left(T\right)=D_0{e}^{-\frac{E}{\mathrm{kT}}}$ with $D\left(300\mathrm{} \mathrm{K}\right)\simeq {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^2$/s and $E\simeq 0.23$ eV. Studies of $\frac{1}{f}$ noise evoke comparable mechanisms.