145 research outputs found
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
Current-Induced Step Bending Instability on Vicinal Surfaces
We model an apparent instability seen in recent experiments on current
induced step bunching on Si(111) surfaces using a generalized 2D BCF model,
where adatoms have a diffusion bias parallel to the step edges and there is an
attachment barrier at the step edge. We find a new linear instability with
novel step patterns. Monte Carlo simulations on a solid-on-solid model are used
to study the instability beyond the linear regime.Comment: 4 pages, 4 figure
The effect of monomer evaporation on a simple model of submonolayer growth
We present a model for thin film growth by particle deposition that takes
into account the possible evaporation of the particles deposited on the
surface. Our model focuses on the formation of two-dimensional structures. We
find that the presence of evaporation can dramatically affect the growth
kinetics of the film, and can give rise to regimes characterized by different
``growth'' exponents and island size distributions. Our results are obtained by
extensive computer simulations as well as through a simple scaling approach and
the analysis of rate equations describing the system. We carefully discuss the
relationship of our model with previous studies by Venables and Stoyanov of the
same physical situation, and we show that our analysis is more general.Comment: 41 pages including figures, Revtex, to be published in Physical
Review
A quantitative theory of current-induced step bunching on Si(111)
We use a one-dimensional step model to study quantitatively the growth of
step bunches on Si(111) surfaces induced by a direct heating current.
Parameters in the model are fixed from experimental measurements near 900 deg C
under the assumption that there is local mass transport through surface
diffusion and that step motion is limited by the attachment rate of adatoms to
step edges. The direct heating current is treated as an external driving force
acting on each adatom. Numerical calculations show both qualitative and
quantitative agreement with experiment. A force in the step down direction will
destabilize the uniform step train towards step bunching. The average size of
the step bunches grows with electromigration time as t^beta, with beta = 0.5,
in agreement with experiment and with an analytical treatment of the steady
states. The model is extended to include the effect of direct hopping of
adatoms between different terraces. Monte-Carlo simulations of a solid-on-solid
model, using physically motivated assumptions about the dynamics of surface
diffusion and attachment at step edges, are carried out to study two
dimensional features that are left out of the present step model and to test
its validity. These simulations give much better agreement with experiment than
previous work. We find a new step bending instability when the driving force is
along the step edge direction. This instability causes the formation of step
bunches and antisteps that is similar to that observed in experiment.Comment: 11 pages, 7 figure
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
Unconventional MBE Strategies from Computer Simulations for Optimized Growth Conditions
We investigate the influence of step edge diffusion (SED) and desorption on
Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the
solid-on-solid (SOS) model. 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 exploit the presence of
desorption in order to achieve smooth surfaces. By additional short high flux
pulses of particles one can increase the growth rate and assist layer-by-layer
growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can
be used to control size and shape of the three-dimensional structures. By
controlled reduction of the flux with time we achieve a fast coarsening
together with smooth step edges.Comment: 19 pages, 7 figures, submitted to Phys. Rev.
Non-conserved dynamics of steps on vicinal surfaces during electromigration-induced step bunching
We report new results on the non-conserved dynamics of parallel steps on
vicinal surfaces in the case of sublimation with electromigration and step-step
interactions. The derived equations are valid in the quasistatic approximation
and in the limit , where is the inverse
electromigration length, the diffusion length, the kinetic
lengths and the terrace widths. The coupling between crystal sublimation
and step-step interactions induces non-linear, non-conservative terms in the
equations of motion. Depending on the initial conditions, this leads to
interrupted coarsening, anticoarsening of step bunches or periodic switching
between step trains of different numbers of bunches.Comment: 11 pages, 4 figures; revised and extended versio
Morphology of epitaxial core-shell nanowires
We analyze the morphological stability against azimuthal, axial, and general
helical perturbations for epitaxial core-shell nanowires in the growth regimes
limited by either surface diffusion or evaporation-condensation surface
kinetics. For both regimes, we find that geometric parameters (i.e., core
radius and shell thickness) play a central role in determining whether the
nanowire remains cylindrical or its shell breaks up into epitaxial islands
similar to those observed during Stranski-Krastanow growth in thin epilayers.
The combination of small cores and rapid growth of the shell emerge as key
ingredients for stable shell growth. Our results provide an explanation for the
different core-shell morphologies reported in the Si-Ge system experimentally,
and also identify a growth-induced intrinsic mechanism for the formation of
helical nanowires.Comment: In press, Nano Letters (7 pages, 4 figures
Adatom diffusion on vicinal surfaces with permeable steps
We study the behavior of single atoms on an infinite vicinal surface assuming
certain degree of step permeability. Assuming complete lack of re-evaporation
an ruling out nucleation the atoms will inevitably join kink sites at the steps
but can do many attempts before that. Increasing the probability of step
permeability or the kink spacing lead to increase of the number of steps
crossed before incorporation of the atoms into kink sites. The asymmetry of the
attachment-detachment kinetics (Ehrlich-Schwoebel effect) suppresses the step
permeability and completely eliminates it in the extreme case of infinite
Ehrlich-Schwoebel barrier. The average number of permeability events per atom
scales with the average kink spacing. A negligibly small drift of the adatoms
in a direction perpendicular to the steps leads to a significant asymmetry of
the distribution of the permeability events the atoms thus visiting more
distant steps in the direction of the drift.Comment: 12 pages, 6 figure
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