128 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.
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.
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
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
Fast coarsening in unstable epitaxy with desorption
Homoepitaxial growth is unstable towards the formation of pyramidal mounds
when interlayer transport is reduced due to activation barriers to hopping at
step edges. Simulations of a lattice model and a continuum equation show that a
small amount of desorption dramatically speeds up the coarsening of the mound
array, leading to coarsening exponents between 1/3 and 1/2. The underlying
mechanism is the faster growth of larger mounds due to their lower evaporation
rate.Comment: 4 pages, 4 PostScript figure
Irreversible nucleation in molecular beam epitaxy: From theory to experiments
Recently, the nucleation rate on top of a terrace during the irreversible
growth of a crystal surface by MBE has been determined exactly. In this paper
we go beyond the standard model usually employed to study the nucleation
process, and we analyze the qualitative and quantitative consequences of two
important additional physical ingredients: the nonuniformity of the
Ehrlich-Schwoebel barrier at the step-edge, because of the existence of kinks,
and the steering effects, due to the interaction between the atoms of the flux
and the substrate. We apply our results to typical experiments of second layer
nucleation.Comment: 11 pages. Table I corrected and one appendix added. To be published
in Phys. Rev. B (scheduled issue: 15 February 2003
Surface Kinetics and Generation of Different Terms in a Conservative Growth Equation
A method based on the kinetics of adatoms on a growing surface under
epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a
closed form of local growth equation. It can be generalized to any growth
problem as long as diffusion of adatoms govern the surface morphology. The
method can be easily extended to higher dimensions. The kinetic processes
contributing to various terms in the growth equation (GE) are identified from
the analysis of in-plane and downward hops. In particular, processes
corresponding to the (h -> -h) symmetry breaking term and curvature dependent
term are discussed. Consequence of these terms on the stable and unstable
transition in (1+1) dimensions is analyzed. In (2+1) dimensions it is shown
that an additional (h -> -h) symmetry breaking term is generated due to the
in-plane curvature associated with the mound like structures. This term is
independent of any diffusion barrier differences between in-plane and out
of-plane migration. It is argued that terms generated in the presence of
downward hops are the relevant terms in a GE. Growth equation in the closed
form is obtained for various growth models introduced to capture most of the
processes in experimental Molecular Beam Epitaxial growth. Effect of
dissociation is also considered and is seen to have stabilizing effect on the
growth. It is shown that for uphill current the GE approach fails to describe
the growth since a given GE is not valid over the entire substrate.Comment: 14 pages, 7 figure
Island nucleation in the presence of step edge barriers: Theory and applications
We develop a theory of nucleation on top of two-dimensional islands bordered
by steps with an additional energy barrier for descending atoms.
The theory is based on the concept of the residence time of an adatom on the
island,and yields an expression for the nucleation rate which becomes exact in
the limit of strong step edge barriers. This expression differs qualitatively
and quantitatively from that obtained using the conventional rate equation
approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We
argue that rate equation theory fails because nucleation is dominated by the
rare instances when two atoms are present on the island simultaneously. The
theory is applied to two distinct problems: The onset of second layer
nucleation in submonolayer growth, and the distribution of the sizes of top
terraces of multilayer mounds under conditions of strong step edge barriers.
Application to homoepitaxial growth on Pt(111) yields the estimate eV for the additional energy barrier at CO-decorated steps.Comment: 13 pages, 3 figure
Survival-Time Distribution for Inelastic Collapse
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a
randomly forced particle which collides inelastically with a boundary can
undergo inelastic collapse and come to rest in a finite time. Here we discuss
the survival probability for the inelastic collapse transition. It is found
that the collapse-time distribution behaves asymptotically as a power-law in
time, and that the exponent governing this decay is non-universal. An
approximate calculation of the collapse-time exponent confirms this behaviour
and shows how inelastic collapse can be viewed as a generalised persistence
phenomenon.Comment: 4 pages, RevTe
Quantum Dimensional Zeeman Effect in the Magneto-optical Absorption Spectrum for Quantum Dot - Impurity Center Systems
Magneto-optical properties of the quantum dot - impurity center (QD-IC)
systems synthesized in a transparent dielectric matrix are considered. For the
QD one-electron state description the parabolic model of the confinement
potential is used. Within the framework of zero-range potential model and the
effective mass approach, the light impurity absorption coefficient for the case
of transversal polarization with respect to the applied magnetic field
direction, with consideration of the QD size dispersion, has been analytically
calculated. It is shown that for the case of transversal polarization the light
impurity absorption spectrum is characterized by the quantum dimensional Zeeman
effect.Comment: 18 pages, 1 figure, PDF fil
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