243 research outputs found
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
Study of Strain and Temperature Dependence of Metal Epitaxy
Metallic films are important in catalysis, magneto-optic storage media, and
interconnects in microelectronics, and it is crucial to predict and control
their morphologies. The evolution of a growing crystal is determined by the
behavior of each individual atom, but technologically relevant structures have
to be described on a time scale of the order of (at least) tenths of a second
and on a length scale of nanometers. An adequate theory of growth should
describe the atomistic level on very short time scales (femtoseconds), the
formation of small islands (microseconds), as well as the evolution of
mesoscopic and macroscopic structures (tenths of seconds).
The development of efficient algorithms combined with the availability of
cheaper and faster computers has turned density functional theory (DFT) into a
reliable and feasible tool to study the microscopic aspects of growth phenomena
(and many other complex processes in materials science, condensed matter
physics, and chemistry). In this paper some DFT results for diffusion
properties on metallic surfaces are presented. Particularly, we will discuss
the current understanding of the influences of strain on the diffusion (energy
barrier and prefactor) of a single adatom on a substrate.
A DFT total energy calculation by its nature is primarily a static
calculation. An accurate way to describe the spatial and temporal development
of a growing crystal is given by kinetic Monte Carlo (KMC). We will describe
the method and its combination with microscopic parameters obtained from ab
initio calculations. It is shown that realistic ab initio kinetic Monte Carlo
simulations are able to predict an evolving mesoscopic structure on the basis
of microscopic details.Comment: 25 pages, 6 figures, In: ``Morphological Organisation during
Epitaxial Growth and Removal'', Eds. Z. Zhang, M. Lagally. World Scientific,
Singapore 1998. other related publications can be found at
http://www.rz-berlin.mpg.de/th/paper.htm
Level Set Approach to Reversible Epitaxial Growth
We generalize the level set approach to model epitaxial growth to include
thermal detachment of atoms from island edges. This means that islands do not
always grow and island dissociation can occur. We make no assumptions about a
critical nucleus. Excellent quantitative agreement is obtained with kinetic
Monte Carlo simulations for island densities and island size distributions in
the submonolayer regime.Comment: 7 pages, 9 figure
Epitaxial Growth Kinetics with Interacting Coherent Islands
The Stranski-Krastanov growth kinetics of undislocated (coherent)
3-dimensional islands is studied with a self-consistent mean field rate theory
that takes account of elastic interactions between the islands. The latter are
presumed to facilitate the detachment of atoms from the islands with a
consequent decrease in their average size. Semi-quantitative agreement with
experiment is found for the time evolution of the total island density and the
mean island size. When combined with scaling ideas, these results provide a
natural way to understand the often-observed initial increase and subsequent
decrease in the width of the coherent island size distribution.Comment: 4 pages, 4 figure
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
Implication of the overlap representation for modelling generalized parton distributions
Based on a field theoretically inspired model of light-cone wave functions,
we derive valence-like generalized parton distributions and their double
distributions from the wave function overlap in the parton number conserved
s-channel. The parton number changing contributions in the t-channel are
restored from duality. In our construction constraints of positivity and
polynomiality are simultaneously satisfied and it also implies a model
dependent relation between generalized parton distributions and transverse
momentum dependent parton distribution functions. The model predicts that the
t-behavior of resulting hadronic amplitudes depends on the Bjorken variable
x_Bj. We also propose an improved ansatz for double distributions that embeds
this property.Comment: 15 pages, 8 eps figure
Magic Islands and Barriers to Attachment: A Si/Si(111)7x7 Growth Model
Surface reconstructions can drastically modify growth kinetics during initial
stages of epitaxial growth as well as during the process of surface
equilibration after termination of growth. We investigate the effect of
activation barriers hindering attachment of material to existing islands on the
density and size distribution of islands in a model of homoepitaxial growth on
Si(111)7x7 reconstructed surface. An unusual distribution of island sizes
peaked around "magic" sizes and a steep dependence of the island density on the
growth rate are observed. "Magic" islands (of a different shape as compared to
those obtained during growth) are observed also during surface equilibration.Comment: 4 pages including 5 figures, REVTeX, submitted to Physical Review
Spatio-temporal distribution of nucleation events during crystal growth
We consider irreversible second-layer nucleation that occurs when two adatoms
on a terrace meet. We solve the problem analytically in one dimension for zero
and infinite step-edge barriers, and numerically for any value of the barriers
in one and two dimensions. For large barriers, the spatial distribution of
nucleation events strongly differs from , where is the
stationary adatom density in the presence of a constant flux. The probability
that nucleation occurs at time after the deposition of the second
adatom, decays for short time as a power law [] in and
logarithmically [] in ; for long time it decays
exponentially. Theories of the nucleation rate based on the assumption
that it is proportional to are shown to overestimate by a
factor proportional to the number of times an adatom diffusing on the terrace
visits an already visited lattice site.Comment: 4 pages, 3 figures; accepted for publication on PR
A Hybrid Monte Carlo Method for Surface Growth Simulations
We introduce an algorithm for treating growth on surfaces which combines
important features of continuum methods (such as the level-set method) and
Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in
continuum theory, but attach them to islands one atom at a time. The technique
is borrowed from the Dielectric Breakdown Model. Our method allows us to give a
realistic account of fluctuations in island shape, which is lacking in
deterministic continuum treatments and which is an important physical effect.
Our method should be most important for problems close to equilibrium where KMC
becomes impractically slow.Comment: 4 pages, 5 figure
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