Shot Noise Suppression and Enhancement at 2D Hopping and in Single-Electron Arrays

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We have carried out numerical simulations of shot noise at two‐dimensional (2D) hopping and in 2D arrays of single‐electron islands with and without random background charges. Such key transport characteristics as the average (dc) current 〈I〉, the single‐particle density of states and the current fluctuation spectrum, have been calculated within a broad range of the applied electric field E and temperature T. Substantial Coulomb interaction effects are shown to not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, at sufficiently low frequencies (f → 0) the spectral density SI (f) of current fluctuations exhibits a 1/f‐like increase which approximately follows the Hooge scaling. As f increases, there is a crossover to a broad range of frequencies in which SI (f) is nearly constant, hence allowing characterization of the current noise by the Fano factor F ≡ SI (f) /2e 〈I〉. For sufficiently large samples and low temperature, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the sample length L as F = (Lc/L)α. The exponent α is significantly affected by the inclusion of Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter Lc, interpreted as the average percolation cluster length along the electric field direction, scales as Lc ∝ E−(0.98±0.08) when Coulomb interaction effects are negligible and Lc ∝ E−(1.26±0.15) when such effects are substantial, in good agreement with results of directed percolation theory.In arrays of single‐electron islands with completely random background charges, the current noise is strongly colored at low currents, and its spectral density levels off at very low frequencies. The Fano factor may be much larger than unity, due to the remnants of single‐electron/hole avalanches. However, even very small thermal fluctuations reduced the Fano factor below unity for almost any bias.