Resistance Fluctuations Due to Hydrogen Diffusion in Niobium Thin Films

Abstract

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: $\frac{f{S}_{V}(f, T)}{〈\ensuremath{\delta}{V}^{2}(T)〉}=g(\frac{f}{D(T)})$; for our geometry at $260<T<370$ K, ${S}_{V}(f, T)\ensuremath{\propto}\frac{{c}_{0}(T)}{{f}^{\ensuremath{\alpha}}}$, $\ensuremath{\alpha}=0$ for $f\ensuremath{\ll}\frac{D}{(\ensuremath{\pi}{L}^{2})}$ and $\ensuremath{\alpha}=\frac{3}{2}$ for $f\ensuremath{\gg}\frac{D}{(\ensuremath{\pi}{L}^{2})}$, ${c}_{0}$ is the ${\mathrm{H}}^{+}$ concentration, $L$ is the film length, and the ${\mathrm{H}}^{+}$ diffusion coefficient is $D(T)={D}_{0}{e}^{\ensuremath{-}\frac{E}{\mathrm{kT}}}$ with $D(300 \mathrm{K})\ensuremath{\simeq}{10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{2}$/s and $E\ensuremath{\simeq}0.23$ eV. Studies of $\frac{1}{f}$ noise evoke comparable mechanisms.