222 research outputs found
Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation
The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth
poissonian process in space, has been implemented by taking into account
spatial correlation among nuclei. This is achieved through a detailed study of
a system of distinguishable and correlated dots (nuclei). The probability that
no dots be in a region of the space has been evaluated in terms of correlation
functions. The theory has been applied to describe nucleation and growth in two
dimensions under constant nucleation rate, where correlation among nuclei
depends upon the size of the nucleus. We propose a simple formula for
describing the phase transition kinetics in the presence of correlation among
nuclei. The theory is applied to the constant nucleation rate process when
correlation depends upon the nucleus-birth time. It is shown that the random
sequential adsorption and Tobin process can be analyzed in the framework of the
simultaneous nucleation case, admitting a common rationale that is apart from
an appropriate re-scaling they represent the same process from the mathematical
point of view.Comment: 28 pages, no figure
Eliminating overgrowth effects in Poisson spatial process through the correlation among actual nuclei
It has been shown that the KJMA (Kolmogorov-Johnson-Mehl-Avrami) solution of
phase transition kinetics can be set as a problem of correlated nucleation
[Phys.Rev.B65, 172301 (2002)]. In this paper the equivalence between the
standard solution and the approach that makes use of the actual nucleation
rate, i.e. that takes into account spatial correlation among nuclei and/or
grains, is shown by a direct calculation in case of linear growth and constant
nucleation rate. As a consequence, the intrinsic limit of KJMA theory due to
the phenomenon of phantom overgrowth is, at last, overcome. This means that
thanks to this new approach it is possible, for instance, to describe phase
transition governed by diffusion.Comment: 9 pages, 3 figure
Ripple-to-dome transition: the growth evolution of Ge on vicinal Si(1 1 10) surface
We present a detailed scanning tunnelling microscopy study which describes
the morphological transition from ripple to dome islands during the growth of
Ge on the vicinal Si(1 1 10) surface . Our experimental results show that the
shape evolution of Ge islands on this surface is markedly different from that
on the flat Si(001) substrate and is accomplished by agglomeration and
coalescence of several ripples. By combining first principle calculations with
continuum elasticity theory, we provide an accurate explanation of our
experimental observations
Hug-like island growth of Ge on strained vicinal Si(111) surfaces
We examine the structure and the evolution of Ge islands epitaxially grown on
vicinal Si(111) surfaces by scanning tunneling microscopy. Contrary to what is
observed on the singular surface, three-dimensional Ge nanoislands form
directly through the elastic relaxation of step-edge protrusions during the
unstable step-flow growth. As the substrate misorientation is increased, the
islands undergo a shape transformation which is driven by surface energy
minimization and controlled by the miscut angle. Using finite element
simulations, we show that the dynamics of islanding observed in the experiment
results from the anisotropy of the strain relaxation.Comment: 4 figure
How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: the case of InAs/GaAs(001)
The two- to three-dimensional growth transition in the InAs/GaAs(001)
heterostructure has been investigated by atomic force microscopy. The kinetics
of the density of three dimensional quantum dots evidences two transition
thresholds at 1.45 and 1.59 ML of InAs coverage, corresponding to two separate
families, small and large. Based on the scaling analysis, such families are
characterized by different mechanisms of aggregation, involving the change of
the critical nucleus size. Remarkably, the small ones give rise to a wealth of
"monomers" through the erosion of the step edges, favoring the explosive
nucleation of the large ones.Comment: 10 pages, 3 figures. Submitted to Phys. Rev. Let
Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws
The theory of Kolmogorov-Johnson-Mehl-Avrami (KJMA) for phase transition
kinetics is subjected to severe limitations concerning the functional form of
the growth law. This paper is devoted to side step this drawback through the
use of correlation function approach. Moreover, we put forward an
easy-to-handle formula, written in terms of the experimentally accessible
actual extended volume fraction, which is found to match several types of
growths. Computer simulations have been done for corroborating the theoretical
approach.Comment: 18 pages ;11 figure
Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks
The paper centres on the evaluation of the function n(theta)=N(theta)/N0,
that is the normalized number of islands as a function of coverage 0<theta<1,
given N0 initial nucleation centres (dots) having any degree of spatial
correlation. A mean field approach has been employed: the islands have the same
size at any coverage. In particular, as far as the random distribution of dots
is concerned, the problem has been solved by considering the contribution of
binary collisions between islands only. With regard to correlated dots, we
generalize a method previously applied to the random case only. In passing, we
have made use of the exclusion probability reported in [S. Torquato, B. Lu, J.
Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of
surface coverage in the case of correlated dots, improving our previous
calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure
Islanding, growth mode and ordering in Si heteroepitaxy on Ge(001) substrates structured by thermal annealing
Si/Ge heteroepitaxial dots under tensile strain are grown on nanostructured
Ge substrates produced by high-temperature flash heating exploiting the
spontaneous faceting of the Ge(001) surface close to the onset of surface
melting. A very diverse growth mode is obtained depending on the specific
atomic structure and step density of nearby surface domains with different
vicinal crystallographic orientations. On highly-miscut areas of the Ge(001)
substrate, the critical thickness for islanding is lowered to about 5 ML, in
contrast to the 11 ML reported for the flat Ge(001) surface, while on
unreconstructed (1x1) domains the growth is Volmer-Weber driven. An explanation
is proposed considering the diverse relative contributions of step and surface
energies on misoriented substrates. In addition, we show that the bottom-up
pattern of the substrate naturally formed by thermal annealing determines a
spatial correlation for the dot sites
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