481 research outputs found
Introduction to Step Dynamics and Step Instabilities
This paper provides an elementary introduction to the basic concepts used in
describing epitaxial crystal growth in terms of the thermodynamics and kinetics
of atomic steps. Selected applications to morphological instabilities of
stepped surfaces are reviewed, and some open problems are outlined.Comment: To appear in the Proceedings of the Oberwolfach workshop on
Multiscale Modeling in Epitaxial Growt
Instabilities in crystal growth by atomic or molecular beams
The planar front of a growing a crystal is often destroyed by instabilities.
In the case of growth from a condensed phase, the most frequent ones are
diffusion instabilities, which will be but briefly discussed in simple terms in
chapter II. The present review is mainly devoted to instabilities which arise
in ballistic growth, especially Molecular Beam Epitaxy (MBE). The reasons of
the instabilities can be geometric (shadowing effect), but they are mostly
kinetic or thermodynamic. The kinetic instabilities which will be studied in
detail in chapters IV and V result from the fact that adatoms diffusing on a
surface do not easily cross steps (Ehrlich-Schwoebel or ES effect). When the
growth front is a high symmetry surface, the ES effect produces mounds which
often coarsen in time according to power laws. When the growth front is a
stepped surface, the ES effect initially produces a meandering of the steps,
which eventually may also give rise to mounds. Kinetic instabilities can
usually be avoided by raising the temperature, but this favours thermodynamic
instabilities. Concerning these ones, the attention will be focussed on the
instabilities resulting from slightly different lattice constants of the
substrate and the adsorbate. They can take the following forms. i) Formation of
misfit dislocations (chapter VIII). ii) Formation of isolated epitaxial
clusters which, at least in their earliest form, are `coherent' with the
substrate, i.e. dislocation-free (chapter X). iii) Wavy deformation of the
surface, which is presumably the incipient stage of (ii) (chapter IX). The
theories and the experiments are critically reviewed and their comparison is
qualitatively satisfactory although some important questions have not yet
received a complete answer.Comment: 90 pages in revtex, 45 figures mainly in gif format. Review paper to
be published in Physics Reports. Postscript versions for all the figures can
be found at http://www.theo-phys.uni-essen.de/tp/u/politi
Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling
We present explicit analytic, twice-differentiable expressions for the
temperature-dependent anisotropic step line tension and step stiffness for the
two principal surfaces of face-centered-cubic crystals, the square {001} and
the hexagonal {111}. These expressions improve on simple expressions that are
valid only for low temperatures and away from singular orientations. They are
well suited for implementation into numerical methods such as finite-element
simulation of step evolution.Comment: 10 pages; reformatted with revtex (with typos corrected) from version
accepted by SIAM--Multiscale Modeling and Simulation on Nov. 21, 2006;
greatly expanded introduction, several minor fixes (mostly stylistic
Growth instability due to lattice-induced topological currents in limited mobility epitaxial growth models
The energetically driven Ehrlich-Schwoebel (ES) barrier had been generally
accepted as the primary cause of the growth instability in the form of
quasi-regular mound-like structures observed on the surface of thin film grown
via molecular beam epitaxy (MBE) technique. Recently the second mechanism of
mound formation was proposed in terms of a topologically induced flux of
particles originating from the line tension of the step edges which form the
contour lines around a mound. Through large-scale simulations of MBE growth on
a variety of crystalline lattice planes using limited mobility, solid-on-solid
models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions,
we propose yet another type of topological uphill particle current which is
unique to some lattice, and has hitherto been overlooked in the literature.
Without ES barrier, our simulations produce spectacular mounds very similar, in
some cases, to what have been observed in many recent MBE experiments. On a
lattice where these currents cease to exist, the surface appears to be
scale-invariant, statistically rough as predicted by the conventional continuum
growth equation.Comment: 10 pages, 12 figure
Kinetic modelling of epitaxial film growth with up- and downward step barriers
The formation of three-dimensional structures during the epitaxial growth of
films is associated to the reflection of diffusing particles in descending
terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier.
We generalize this concept in a solid-on-solid growth model, in which a barrier
dependent on the particle coordination (number of lateral bonds) exists
whenever the particle performs an interlayer diffusion. The rules do not
distinguish explicitly if the particle is executing a descending or an
ascending interlayer diffusion. We show that the usual model, with a step
barrier in descending steps, produces spurious, columnar, and highly unstable
morphologies if the growth temperature is varied in a usual range of mound
formation experiments. Our model generates well-behaved mounded morphologies
for the same ES barriers that produce anomalous morphologies in the standard
model. Moreover, mounds are also obtained when the step barrier has an equal
value for all particles independently if they are free or bonded. Kinetic
roughening is observed at long times, when the surface roughness w and the
characteristic length scale as and where
and , independently of the growth
temperature.Comment: 15 pages, 7 figure
Density Functional Theory of Epitaxial Growth of Metals
This chapter starts with a summary of the atomistic processes that occur
during epitaxy. We then introduce density functional theory (DFT) and describe
its implementation into state-of-the-art computations of complex processes in
condensed matter physics and materials science. In particular we discuss how
DFT can be used to calculate parameters of microscopic processes such as
adsorption and surface diffusion, and how they can be used to study the
macroscopic time and length scales of realistic growth conditions. This meso-
and macroscopic regime is described by the ab initio kinetic Monte Carlo
approach. We discuss several specific theoretical studies that highlight the
importance of the different diffusion mechanisms at step edges, the role of
surfactants, and the influence of surface stress. The presented results are for
specific materials (namely silver and aluminum), but they are explained in
simple physical pictures suggesting that they also hold for other systems.Comment: 55 pages, 20 figures, to be published "Growth of Ultrathin Epitaxial
Layers", The Chemical Physics of Soild Surfaces, Vol. 8, Eds D. A. King and
D. P. Woodruff (Elsevier Science, Amsterdam, 1997
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