31 research outputs found
Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth
Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett.
{\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate
analytically the asymptotic scaled capture-number distribution (CND) for
one-dimensional irreversible submonolayer growth of point islands. The
predicted asymptotic CND is in reasonably good agreement with kinetic
Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic}
scaled island-size distribution (ISD). We then show that a slight modification
of our analytical form leads to an analytic expression for the asymptotic CND
and a resulting asymptotic ISD which are in excellent agreement with KMC
simulations. We also show that in the asymptotic limit the self-averaging
property of the capture zones holds exactly while the asymptotic scaled gap
distribution is equal to the scaled CND.Comment: 4 pages, 1 figure, submitted to Phys. Rev.
Submonolayer Epitaxy Without A Critical Nucleus
The nucleation and growth of two--dimensional islands is studied with Monte
Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth.
The conventional description of this problem in terms of a well--defined
critical island size fails because no islands are absolutely stable against
single atom detachment by thermal bond breaking. When two--bond scission is
negligible, we find that the ratio of the dimer dissociation rate to the rate
of adatom capture by dimers uniquely indexes both the island size distribution
scaling function and the dependence of the island density on the flux and the
substrate temperature. Effective pair-bond model parameters are found that
yield excellent quantitative agreement with scaling functions measured for
Fe/Fe(001).Comment: 8 pages, Postscript files (the paper and Figs. 1-3), uuencoded,
compressed and tarred. Surface Science Letters, in press
Spatial distribution of photoelectrons participating in formation of x-ray absorption spectra
Interpretation of x-ray absorption near-edge structure (XANES) experiments is
often done via analyzing the role of particular atoms in the formation of
specific peaks in the calculated spectrum. Typically, this is achieved by
calculating the spectrum for a series of trial structures where various atoms
are moved and/or removed. A more quantitative approach is presented here, based
on comparing the probabilities that a XANES photoelectron of a given energy can
be found near particular atoms. Such a photoelectron probability density can be
consistently defined as a sum over squares of wave functions which describe
participating photoelectron diffraction processes, weighted by their normalized
cross sections. A fine structure in the energy dependence of these
probabilities can be extracted and compared to XANES spectrum. As an
illustration of this novel technique, we analyze the photoelectron probability
density at the Ti K pre-edge of TiS2 and at the Ti K-edge of rutile TiO2.Comment: Journal abstract available on-line at
http://link.aps.org/abstract/PRB/v65/e20511
Model for nucleation in GaAs homoepitaxy derived from first principles
The initial steps of MBE growth of GaAs on beta 2-reconstructed GaAs(001) are
investigated by performing total energy and electronic structure calculations
using density functional theory and a repeated slab model of the surface. We
study the interaction and clustering of adsorbed Ga atoms and the adsorption of
As_2 molecules onto Ga atom clusters adsorbed on the surface. The stable nuclei
consist of bound pairs of Ga adatoms, which originate either from dimerization
or from an indirect interaction mediated through the substrate reconstruction.
As_2 adsorption is found to be strongly exothermic on sites with a square array
of four Ga dangling bonds. Comparing two scenarios where the first As_2 gets
incorporated in the incomplete surface layer, or alternatively in a new added
layer, we find the first scenario to be preferable. In summary, the
calculations suggest that nucleation of a new atomic layer is most likely on
top of those surface regions where a partial filling of trenches in the surface
has occurred before.Comment: 8 pages, 14 figures, Submitted to Phys. Rev. B (December 15, 1998).
Other related publications can be found at
http://www.fhi-berlin.mpg.de/th/paper.htm
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
Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions
A simple model of epitaxial growth proposed by Wolf and Villain is
investigated using extensive computer simulations. We find an unexpectedly
complex crossover behavior of the original model in both 1+1 and 2+1
dimensions. A crossover from the effective growth exponent to is observed in 1+1
dimensions, whereas additional crossovers, which we believe are to the scaling
behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1
dimensions. Anomalous scaling due to power--law growth of the average step
height is found in 1+1 D, and also at short time and length scales in 2+1~D.
The roughness exponents obtained from the
height--height correlation functions in 1+1~D () and 2+1~D
() cannot be simultaneously explained by any of the continuum
equations proposed so far to describe epitaxial growth.Comment: 11 pages, REVTeX 3.0, IC-DDV-93-00
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
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
Polarized x-ray absorption spectra of CuGeO3 at the Cu and Ge K edges
Polarized x-ray absorption near edge structure (XANES) spectra at both the Cu
and the Ge K-edges of CuGeO3 are measured and calculated relying on the
real-space multiple-scattering formalism within a one-electron approach. The
polarization components are resolved not only in the unit cell coordinate
system but also in a local frame attached to the nearest neighborhood of the
photoabsorbing Cu atom. In that way, features which resist a particular
theoretical description can be identified. We have found that it is the
out-of-CuO4-plane p_{z'} component which defies the one-electron calculation
based on the muffin-tin potential. For the Ge K-edge XANES, the agreement
between the theory and the experiment appears to be better for those
polarization components which probe more compact local surroundings than for
those which probe regions with lower atomic density. Paper published in Phys.
Rev. B 66, 155119 (2002) and available on-line at
http://link.aps.org/abstract/PRB/v66/e155119.Comment: 15 pages, 6 figures. Published in Physical Review B, abstract
available on-line at http://link.aps.org/abstract/PRB/e15511
From dynamical scaling to local scale-invariance: a tutorial
Dynamical scaling arises naturally in various many-body systems far from
equilibrium. After a short historical overview, the elements of possible
extensions of dynamical scaling to a local scale-invariance will be introduced.
Schr\"odinger-invariance, the most simple example of local scale-invariance,
will be introduced as a dynamical symmetry in the Edwards-Wilkinson
universality class of interface growth. The Lie algebra construction, its
representations and the Bargman superselection rules will be combined with
non-equilibrium Janssen-de Dominicis field-theory to produce explicit
predictions for responses and correlators, which can be compared to the results
of explicit model studies.
At the next level, the study of non-stationary states requires to go over,
from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits
new representations, which acts as dynamical symmetries on more general
equations, and imply that each non-equilibrium scaling operator is
characterised by two distinct, independent scaling dimensions. Tests of
ageing-invariance are described, in the Glauber-Ising and spherical models of a
phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for