Shot noise of single-electron tunneling in one-dimensional arrays

We have used numerical modeling and a semianalytical calculation method to find the low-frequency value $S_I\mathrm{}\left(0\right)\mathrm{}$ of the spectral density fluctuations of current through one-dimensional arrays of small tunnel junctions, using the “orthodox” theory of single-electron tunneling. In all three array types studied, at low temperature ${(k}_{B}T\ll eV)$ increasing current induces a crossover from the Schottky value $S_I\mathrm{}\left(0\right)=2e〈Ī〉$ to the “reduced Schottky value” $S_I\mathrm{}\left(0\right)=2e〈Ī〉/N$ (where $N$ is the array length) at some crossover current $I_c.$ In uniform arrays over a ground plane, $I_c$ is proportional to $\exp (-\lambda N/3)$, where ${\lambda }^{-1}$ is the single-electron soliton length. In arrays without a ground plane, $I_c$ decreases slowly with both $N$ and $\lambda$. Finally, we have calculated the statistics of $I_c$ for ensembles of arrays with random background charges. The standard deviation of $I_c$ from the ensemble average $〈I_c〉$ is quite large, typically between 0.5 and 0.7 of $〈I_c〉$, while the dependence of $〈I_c〉$ on $N$ or $\lambda$ is so weak that it is hidden within the random fluctuations of the crossover current.