Shot Noise of Single-Electron Tunneling in 1D Arrays

TL;DR

This paper investigates the shot noise and current fluctuations in one-dimensional arrays of tunnel junctions using numerical and semi-analytical methods, revealing a crossover in noise behavior and the influence of array parameters on the crossover current.

Contribution

It introduces a detailed analysis of shot noise in 1D tunnel junction arrays, including the effects of array length, soliton length, and background charge randomness on the crossover current.

Findings

Crossover from Schottky to reduced Schottky noise at a specific current I_c.

I_c is proportional to exp(-λN) in arrays with a ground plane.

Large fluctuations in I_c due to background charge randomness.

Abstract

We have used numerical modeling and a semi-analytical calculation method to find the low frequency value S_{I}(0) of the spectral density of fluctuations of current through 1D arrays of small tunnel junctions, using the ``orthodox theory'' of single-electron tunneling. In all three array types studied, at low temperature (kT << eV), increasing current induces a crossover from the Schottky value S_{I}(0)=2e<I> to the ``reduced Schottky value'' S_{I}(0)=2e<I>/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), where 1/\lambda 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.