Shot Noise Suppression at 2D Hopping

We have used Monte Carlo simulation to calculate the shot noise intensity $S_I(\omega )$ at 2D hopping using two models: a slanted lattice of localized sites with equal energies and a set of localized sites with random positions and energies. For wide samples we have found a similar dependence of the Fano factor $F\equiv S_I(0)\mathrm{/}2eI$ on the sample length $L$: $F\propto L^{-\alpha }$ where $\alpha =0.85\pm 0.02$ and $\alpha =0.85\pm 0.07$ in uniform and random models, respectively. Moreover, at least for the uniform model, all the data for $F$ as the function of sample length $L$ and width $W$ may be presented via a single function of the ratio $W\mathrm{/}{L}^{\beta }$, with $\beta = 2\alpha-1 \approx 0.7$. This relation has been interpreted using a simple scaling theory.