A Numerical Study of Transport and Shot Noise at 2D Hopping

Abstract

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field $E$ and temperature $T$, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit $1/f$ noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor $F$. For sufficiently large samples, $F$ scales with conductor length $L$ as $(L_c/L{)}^{\alpha }$, where $\alpha =0.76\pm 0.08<1$, and parameter $L_c$ is interpreted as the average percolation cluster length. At relatively low $E$, the electric field dependence of parameter $L_c$ is compatible with the law $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.

17 pages, 8 figures; Fixed minor typos and updated references

References in corpus (8)

• Shot Noise in Mesoscopic Conductors
• $1/f$ noise in variable range hopping conduction
• Shot noise suppression at 1D hopping
• Shot Noise Suppression at 2D Hopping
• Shot Noise of Single-Electron Tunneling in 1D Arrays
• Shot noise at hopping via two sites
• A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport
• Shot Noise in Mesoscopic Transport Through Localised States

Cited by in corpus (7)

• Electronic shot noise in fractal conductors
• Noise insights into electronic transport
• A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport
• Finite-size effect in shot noise in hopping conduction
• Non linear transport properties of an insulating YBCO nano-bridge
• Variable range hopping in a non-equilibrium steady state
• Sub-electron Charge Relaxation via 2D Hopping Conductors