29 research outputs found
The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions
We study irreversible dimer nucleation on top of terraces during epitaxial
growth in one and two dimensions, for all values of the step-edge barrier. The
problem is solved exactly by transforming it into a first passage problem for a
random walker in a higher-dimensional space. The spatial distribution of
nucleation events is shown to differ markedly from the mean-field estimate
except in the limit of very weak step-edge barriers. The nucleation rate is
computed exactly, including numerical prefactors.Comment: 22 pages, 10 figures. To appear in Phys. Rev.
Relaxation kinetics in two-dimensional structures
We have studied the approach to equilibrium of islands and pores in two
dimensions. The two-regime scenario observed when islands evolve according to a
set of particular rules, namely relaxation by steps at low temperature and
smooth at high temperature, is generalized to a wide class of kinetic models
and the two kinds of structures. Scaling laws for equilibration times are
analytically derived and confirmed by kinetic Monte Carlo simulations.Comment: 6 pages, 7 figures, 1 tabl
Determination of step--edge barriers to interlayer transport from surface morphology during the initial stages of homoepitaxial growth
We use analytic formulae obtained from a simple model of crystal growth by
molecular--beam epitaxy to determine step--edge barriers to interlayer
transport. The method is based on information about the surface morphology at
the onset of nucleation on top of first--layer islands in the submonolayer
coverage regime of homoepitaxial growth. The formulae are tested using kinetic
Monte Carlo simulations of a solid--on--solid model and applied to estimate
step--edge barriers from scanning--tunneling microscopy data on initial stages
of Fe(001), Pt(111), and Ag(111) homoepitaxy.Comment: 4 pages, a Postscript file, uuencoded and compressed. Physical Review
B, Rapid Communications, in press
Coarsening of Surface Structures in Unstable Epitaxial Growth
We study unstable epitaxy on singular surfaces using continuum equations with
a prescribed slope-dependent surface current. We derive scaling relations for
the late stage of growth, where power law coarsening of the mound morphology is
observed. For the lateral size of mounds we obtain with . An analytic treatment within a self-consistent mean-field
approximation predicts multiscaling of the height-height correlation function,
while the direct numerical solution of the continuum equation shows
conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR
The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach
The formation of stable dimers on top of terraces during epitaxial growth is
investigated in detail. In this paper we focus on mean-field theory, the
standard approach to study nucleation. Such theory is shown to be unsuitable
for the present problem, because it is equivalent to considering adatoms as
independent diffusing particles. This leads to an overestimate of the correct
nucleation rate by a factor N, which has a direct physical meaning: in average,
a visited lattice site is visited N times by a diffusing adatom. The dependence
of N on the size of the terrace and on the strength of step-edge barriers is
derived from well known results for random walks. The spatial distribution of
nucleation events is shown to be different from the mean-field prediction, for
the same physical reason. In the following paper we develop an exact treatment
of the problem.Comment: 19 pages, 3 figures. To appear in Phys. Rev.
Analytical solution of generalized Burton--Cabrera--Frank equations for growth and post--growth equilibration on vicinal surfaces
We investigate growth on vicinal surfaces by molecular beam epitaxy making
use of a generalized Burton--Cabrera--Frank model. Our primary aim is to
propose and implement a novel analytical program based on a perturbative
solution of the non--linear equations describing the coupled adatom and dimer
kinetics. These equations are considered as originating from a fully
microscopic description that allows the step boundary conditions to be directly
formulated in terms of the sticking coefficients at each step. As an example,
we study the importance of diffusion barriers for adatoms hopping down
descending steps (Schwoebel effect) during growth and post-growth equilibration
of the surface.Comment: 16 pages, REVTeX 3.0, IC-DDV-94-00
Mounding Instability and Incoherent Surface Kinetics
Mounding instability in a conserved growth from vapor is analysed within the
framework of adatom kinetics on the growing surface. The analysis shows that
depending on the local structure on the surface, kinetics of adatoms may vary,
leading to disjoint regions in the sense of a continuum description. This is
manifested particularly under the conditions of instability. Mounds grow on
these disjoint regions and their lateral growth is governed by the flux of
adatoms hopping across the steps in the downward direction. Asymptotically
ln(t) dependence is expected in 1+1- dimensions. Simulation results confirm the
prediction. Growth in 2+1- dimensions is also discussed.Comment: 4 pages, 4 figure
Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces
We study a recently proposed nonlinear evolution equation describing the
collective step meander on a vicinal surface subject to the Bales-Zangwill
growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221
(1998)]. A careful numerical analysis shows that the dynamically selected step
profile consists of sloped segments, given by an inverse error function and
steepening as sqrt(t), which are matched to pieces of a stationary
(time-independent) solution describing the maxima and minima. The effect of
smoothening by step edge diffusion is included heuristically, and a
one-parameter family of evolution equations is introduced which contains
relaxation by step edge diffusion and by attachment-detachment as special
cases. The question of the persistence of an initially imposed meander
wavelength is investigated in relation to recent experiments.Comment: 4 pages, 5 included figures. Typo in Eq.(5) corrected, section
headlines added and Ref.[12] update
Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions
The hopping motion of lattice gases through potentials without
mirror-reflection symmetry is investigated under various bias conditions. The
model of 2 particles on a ring with 4 sites is solved explicitly; the resulting
current in a sawtooth potential is discussed. The current of lattice gases in
extended systems consisting of periodic repetitions of segments with sawtooth
potentials is studied for different concentrations and values of the bias.
Rectification effects are observed, similar to the single-particle case. A
mean-field approximation for the current in the case of strong bias acting
against the highest barriers in the system is made and compared with numerical
simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.
Influence of adatom interactions on second layer nucleation
We develop a theory for the inclusion of adatom interactions in second layer
nucleation occurring in epitaxial growth. The interactions considered are due
to ring barriers between pairs of adatoms and binding energies of unstable
clusters. The theory is based on a master equation, which describes the time
development of microscopic states that are specified by cluster configurations
on top of an island. The transition rates are derived by scaling arguments and
tested against kinetic Monte-Carlo simulations. As an application we reanalyze
experiments to determine the step edge barrier for Ag/Pt(111).Comment: 4 pages, 4 figure