75 research outputs found
Island nucleation in the presence of step edge barriers: Theory and applications
We develop a theory of nucleation on top of two-dimensional islands bordered
by steps with an additional energy barrier for descending atoms.
The theory is based on the concept of the residence time of an adatom on the
island,and yields an expression for the nucleation rate which becomes exact in
the limit of strong step edge barriers. This expression differs qualitatively
and quantitatively from that obtained using the conventional rate equation
approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We
argue that rate equation theory fails because nucleation is dominated by the
rare instances when two atoms are present on the island simultaneously. The
theory is applied to two distinct problems: The onset of second layer
nucleation in submonolayer growth, and the distribution of the sizes of top
terraces of multilayer mounds under conditions of strong step edge barriers.
Application to homoepitaxial growth on Pt(111) yields the estimate eV for the additional energy barrier at CO-decorated steps.Comment: 13 pages, 3 figure
Single-Particle Diffusion-Coefficient on Surfaces with Ehrlich-Schwoebel-Barriers
The diffusion coefficient of single particles in the presence of
Ehrlich-Schwoebel barriers (ESB)is considered. An exact expression is given for
the diffusion coefficient on linear chains with random arrangements of ESB. The
results are extended to surfaces having ESB with uniform extension in one or
both directions. All results are verified by Monte Carlo simulations.Comment: 11 pages, LaTeX2e, 6 eps-figure
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
The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions
We study irreversible dimer nucleation on top of terraces during epitaxial
growth in one and two dimensions, for all values of the step-edge barrier. The
problem is solved exactly by transforming it into a first passage problem for a
random walker in a higher-dimensional space. The spatial distribution of
nucleation events is shown to differ markedly from the mean-field estimate
except in the limit of very weak step-edge barriers. The nucleation rate is
computed exactly, including numerical prefactors.Comment: 22 pages, 10 figures. To appear in Phys. Rev.
Irreversible nucleation in molecular beam epitaxy: From theory to experiments
Recently, the nucleation rate on top of a terrace during the irreversible
growth of a crystal surface by MBE has been determined exactly. In this paper
we go beyond the standard model usually employed to study the nucleation
process, and we analyze the qualitative and quantitative consequences of two
important additional physical ingredients: the nonuniformity of the
Ehrlich-Schwoebel barrier at the step-edge, because of the existence of kinks,
and the steering effects, due to the interaction between the atoms of the flux
and the substrate. We apply our results to typical experiments of second layer
nucleation.Comment: 11 pages. Table I corrected and one appendix added. To be published
in Phys. Rev. B (scheduled issue: 15 February 2003
Diffusion of Pt dimers on Pt(111)
We report the results of a density-functional study of the diffusion of Pt
dimers on the (111) surface of Pt. The calculated activation energy of 0.37 eV
is in {\em exact} agreement with the recent experiment of Kyuno {\em et al.}
\protect{[}Surf. Sci. {\bf 397}, 191 (1998)\protect{]}. Our calculations
establish that the dimers are mobile at temperatures of interest for adatom
diffusion, and thus contribute to mass transport. They also indicate that the
diffusion path for dimers consists of a sequence of one-atom and (concerted)
two-atom jumps.Comment: Pour pages postscript formatted, including one figure; submitted to
Physical Review B; other papers of interest can be found at url
http://www.centrcn.umontreal.ca/~lewi
The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach
The formation of stable dimers on top of terraces during epitaxial growth is
investigated in detail. In this paper we focus on mean-field theory, the
standard approach to study nucleation. Such theory is shown to be unsuitable
for the present problem, because it is equivalent to considering adatoms as
independent diffusing particles. This leads to an overestimate of the correct
nucleation rate by a factor N, which has a direct physical meaning: in average,
a visited lattice site is visited N times by a diffusing adatom. The dependence
of N on the size of the terrace and on the strength of step-edge barriers is
derived from well known results for random walks. The spatial distribution of
nucleation events is shown to be different from the mean-field prediction, for
the same physical reason. In the following paper we develop an exact treatment
of the problem.Comment: 19 pages, 3 figures. To appear in Phys. Rev.
Crater formation by fast ions: comparison of experiment with Molecular Dynamics simulations
An incident fast ion in the electronic stopping regime produces a track of
excitations which can lead to particle ejection and cratering. Molecular
Dynamics simulations of the evolution of the deposited energy were used to
study the resulting crater morphology as a function of the excitation density
in a cylindrical track for large angle of incidence with respect to the surface
normal. Surprisingly, the overall behavior is shown to be similar to that seen
in the experimental data for crater formation in polymers. However, the
simulations give greater insight into the cratering process. The threshold for
crater formation occurs when the excitation density approaches the cohesive
energy density, and a crater rim is formed at about six times that energy
density. The crater length scales roughly as the square root of the electronic
stopping power, and the crater width and depth seem to saturate for the largest
energy densities considered here. The number of ejected particles, the
sputtering yield, is shown to be much smaller than simple estimates based on
crater size unless the full crater morphology is considered. Therefore, crater
size can not easily be used to estimate the sputtering yield.Comment: LaTeX, 7 pages, 5 EPS figures. For related figures/movies, see:
http://dirac.ms.virginia.edu/~emb3t/craters/craters.html New version uploaded
5/16/01, with minor text changes + new figure
Signature of multilayer growth of 2D layered Bi2Se3 through heteroatom-assisted step-edge barrier reduction
During growth of two-dimensional (2D) materials, abrupt growth of multilayers is practically unavoidable even in the case of well-controlled growth. In epitaxial growth of a quintuple-layered Bi2Se3 film, we observe that the multilayer growth pattern deduced from in situ x-ray diffraction implies nontrivial interlayer diffusion process. Here we find that an intriguing diffusion process occurs at step edges where a slowly downward-diffusing Se adatom having a high step-edge barrier interacts with a Bi adatom pre-existing at step edges. The Se???Bi interaction lowers the high step-edge barrier of Se adatoms. This drastic reduction of the overall step-edge barrier and hence increased interlayer diffusion modifies the overall growth significantly. Thus, a step-edge barrier reduction mechanism assisted by hetero adatom???adatom interaction could be fairly general in multilayer growth of 2D heteroatomic materials
Self-diffusion along step bottoms on Pt(111)
First-principles total energies of periodic vicinals are used to estimate barriers for Pt-adatom diffusion along straight and kinked steps on Pt(111), and around a corner where straight steps intersect. In all cases studied, hopping diffusion has a lower barrier than concerted substitution. In conflict with simulations of dendritic Pt island formation on Pt(111), hopping from a corner site to a step whose riser is a (111)-micro facet is predicted to be more facile than to one whose riser is a (100)
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