3 research outputs found
A Numerical Study of Transport and Shot Noise at 2D Hopping
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 and
temperature , 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 noise, so
that the low-frequency noise at low temperatures may be characterized by the
Fano factor . For sufficiently large samples, scales with conductor
length as , where , and
parameter is interpreted as the average percolation cluster length. At
relatively low , the electric field dependence of parameter is
compatible with the law which follows from directed
percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference
A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport
We have extended our supercomputer-enabled Monte Carlo simulations of hopping
transport in completely disordered 2D conductors to the case of substantial
electron-electron Coulomb interaction. Such interaction may not only suppress
the average value of hopping current, but also affect its fluctuations rather
substantially. In particular, the spectral density of current
fluctuations exhibits, at sufficiently low frequencies, a -like increase
which approximately follows the Hooge scaling, even at vanishing temperature.
At higher , there is a crossover to a broad range of frequencies in which
is nearly constant, hence allowing characterization of the current
noise by the effective Fano factor F\equiv S_I(f)/2e \left. For
sufficiently large conductor samples and low temperatures, the Fano factor is
suppressed below the Schottky value (F=1), scaling with the length of the
conductor as . The exponent is significantly
affected by the Coulomb interaction effects, changing from when such effects are negligible to virtually unity when they are
substantial. The scaling parameter , interpreted as the average
percolation cluster length along the electric field direction, scales as when Coulomb interaction effects are negligible
and when such effects are substantial, in
good agreement with estimates based on the theory of directed percolation.Comment: 19 pages, 7 figures. Fixed minor typos and updated reference
Sub-electron Charge Relaxation via 2D Hopping Conductors
We have extended Monte Carlo simulations of hopping transport in completely
disordered 2D conductors to the process of external charge relaxation. In this
situation, a conductor of area shunts an external capacitor
with initial charge . At low temperatures, the charge relaxation process
stops at some "residual" charge value corresponding to the effective threshold
of the Coulomb blockade of hopping. We have calculated the r.m.s value
of the residual charge for a statistical ensemble of capacitor-shunting
conductors with random distribution of localized sites in space and energy and
random , as a function of macroscopic parameters of the system. Rather
unexpectedly, has turned out to depend only on some parameter
combination: for negligible Coulomb interaction
and for substantial interaction. (Here
is the seed density of localized states, while is the
dielectric constant.) For sufficiently large conductors, both functions
follow the power law , but with different
exponents: for negligible and
for significant Coulomb interaction. We have been able to derive this law
analytically for the former (most practical) case, and also explain the scaling
(but not the exact value of the exponent) for the latter case. In conclusion,
we discuss possible applications of the sub-electron charge transfer for
"grounding" random background charge in single-electron devices.Comment: 12 pages, 5 figures. In addition to fixing minor typos and updating
references, the discussion has been changed and expande