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-r(0) 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 much less than eV) increasing current induces a crossover from the Schottky value S-l(0)=2e <(I) over bar > to the "reduced Schottky value" S-l(0)=2e <(I) over bar >/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, for ensembles of arrays with random background charges. The standard deviation of I, 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.