876,822 research outputs found
Diffusion, super-diffusion and coalescence from single step
From the exact single step evolution equation of the two-point correlation
function of a particle distribution subjected to a stochastic displacement
field \bu(\bx), we derive different dynamical regimes when \bu(\bx) is
iterated to build a velocity field. First we show that spatially uncorrelated
fields \bu(\bx) lead to both standard and anomalous diffusion equation. When
the field \bu(\bx) is spatially correlated each particle performs a simple
free Brownian motion, but the trajectories of different particles result to be
mutually correlated. The two-point statistical properties of the field
\bu(\bx) induce two-point spatial correlations in the particle distribution
satisfying a simple but non-trivial diffusion-like equation. These
displacement-displacement correlations lead the system to three possible
regimes: coalescence, simple clustering and a combination of the two. The
existence of these different regimes, in the one-dimensional system, is shown
through computer simulations and a simple theoretical argument.Comment: RevTeX (iopstyle) 19 pages, 5 eps-figure
Diffusion on a stepped substrate
We present results for collective diffusion of adatoms on a stepped substrate
with a submonolayer coverage. We study the combined effect of the additional
binding at step edge, the Schwoebel barrier, the enhanced diffusion along step
edges, and the finite coverage on diffusion as a function of step density. In
particular, we examine the crossover from step--dominated diffusion at high
step density to terrace-dominated behavior at low step density in a lattice-gas
model using analytical Green's function techniques and Monte Carlo simulations.
The influence of steps on diffusion is shown to be more pronounced than
previously anticipated.Comment: 4 pages, RevTeX, 3 Postscript figure
Quaternionic Diffusion by a Potential Step
In looking for qualitative differences between quaternionic and complex
formulations of quantum physical theories, we provide a detailed discussion of
the behavior of a wave packet in presence of a quaternionic time-independent
potential step. In this paper, we restrict our attention to diffusion
phenomena. For the group velocity of the wave packet moving in the potential
region and for the reflection and transmission times, the study shows a
striking difference between the complex and quaternionic formulations which
could be matter of further theoretical discussions and could represent the
starting point for a possible experimental investigation.Comment: 10 pages, 1 figur
Drift-Induced Step Instabilities Due to the Gap in the Diffusion Coefficient
On a Si(111) vicinal face near the structural transition temperature, the structure and the structure coexist in a terrace: the structure is in the lower side of the step edge and the
structure in the upper side. The diffusion coefficient of adatoms is different
in the two structures. Taking account of the gap in the diffusion coefficient
at the step, we study the possibility of step wandering induced by drift of
adatoms. A linear stability analysis shows that the step wandering always
occurs with step-down drift if the diffusion coefficient has a gap at the step.
Formation of straight grooves by the step wandering is expected from a
nonlinear analysis. The stability analysis also shows that step bunching occurs
irrespective of the drift direction if the diffusion in the lower side of the
step is faster. The step bunching disturbs the formation of grooves. If
step-step repulsion is strong, however, the step bunching is suppressed and the
straight grooves appear. Monte Carlo simulation confirms these predictions.Comment: 5 pages, 6 figure
A Two-Region Diffusion Model for Current-Induced Instabilities of Step Patterns on Vicinal Si(111) Surfaces
We study current-induced step bunching and wandering instabilities with
subsequent pattern formations on vicinal surfaces. A novel two-region diffusion
model is developed, where we assume that there are different diffusion rates on
terraces and in a small region around a step, generally arising from local
differences in surface reconstruction. We determine the steady state solutions
for a uniform train of straight steps, from which step bunching and in-phase
wandering instabilities are deduced. The physically suggestive parameters of
the two-region model are then mapped to the effective parameters in the usual
sharp step models. Interestingly, a negative kinetic coefficient results when
the diffusion in the step region is faster than on terraces. A consistent
physical picture of current-induced instabilities on Si(111) is suggested based
on the results of linear stability analysis. In this picture the step wandering
instability is driven by step edge diffusion and is not of the Mullins-Sekerka
type. Step bunching and wandering patterns at longer times are determined
numerically by solving a set of coupled equations relating the velocity of a
step to local properties of the step and its neighbors. We use a geometric
representation of the step to derive a nonlinear evolution equation describing
step wandering, which can explain experimental results where the peaks of the
wandering steps align with the direction of the driving field.Comment: 11 pages, 10 figure
Evaporation and Step Edge Diffusion in MBE
Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we
investigate the influence of step edge diffusion (SED) and evaporation on
Molecular Beam Epitaxy (MBE). Based on these investigations we propose two
strategies to optimize MBE-growth. The strategies are applicable in different
growth regimes: during layer-by-layer growth one can reduce the desorption rate
using a pulsed flux. In three-dimensional (3D) growth the SED can help to grow
large, smooth structures. For this purpose the flux has to be reduced with time
according to a power law.Comment: 5 pages, 2 figures, latex2e (packages: elsevier,psfig,latexsym
Step Bunching with Alternation of Structural Parameters
By taking account of the alternation of structural parameters, we study
bunching of impermeable steps induced by drift of adatoms on a vicinal face of
Si(001). With the alternation of diffusion coefficient, the step bunching
occurs irrespective of the direction of the drift if the step distance is
large. Like the bunching of permeable steps, the type of large terraces is
determined by the drift direction. With step-down drift, step bunches grows
faster than those with step-up drift. The ratio of the growth rates is larger
than the ratio of the diffusion coefficients. Evaporation of adatoms, which
does not cause the step bunching, decreases the difference. If only the
alternation of kinetic coefficient is taken into account, the step bunching
occurs with step-down drift. In an early stage, the initial fluctuation of the
step distance determines the type of large terraces, but in a late stage, the
type of large terraces is opposite to the case of alternating diffusion
coefficient.Comment: 8pages, 16 figure
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