38 research outputs found
Long-wave Marangoni convection in a thin film heated from below
We consider long-wave Marangoni convection in a liquid layer atop a substrate of low thermal conductivity,
heated from below.We demonstrate that the critical perturbations are materialized at the wave number K ∼
√Bi, where Bi is the Biot number which characterizes the weak heat flux from the free surface. In addition to the
conventional monotonic mode, a novel oscillatory mode is found. Applying the K ∼ √Bi scaling, we derivea new set of amplitude equations. Pattern selection on square and hexagonal lattices shows that supercritical branching is possible. A large variety of stable patterns is found for both modes of instability. Finite-amplitude
one-dimensional solutions of the set, corresponding to either steady or traveling rolls, are studied numerically;
a complicated sequence of bifurcations is found in the former case. The emergence of an oscillatory mode in the case of heating from below and stable patterns with finite-amplitude surface deformation are shown in this system for the first time
Motion of Contact Line of a Crystal Over the Edge of Solid Mask in Epitaxial Lateral Overgrowth
Mathematical model that allows for direct tracking of the homoepitaxial
crystal growth out of the window etched in the solid, pre-deposited layer on
the substrate is described. The growth is governed by the normal (to the
crystal-vapor interface) flux from the vapor phase and by the interface
diffusion. The model accounts for possibly inhomogeneous energy of the mask
surface and for strong anisotropies of crystal-vapor interfacial energy and
kinetic mobility. Results demonstrate that the motion of the crystal-mask
contact line slows down abruptly as radius of curvature of the mask edge
approaches zero. Numerical procedure is suggested to overcome difficulties
associated with ill-posedness of the evolution problem for the interface with
strong energy anisotropy.
Keywords: Thin films, epitaxy, MOCVD, surface diffusion, interface dynamics,
contact lines, rough surfaces, wetting, regularization of ill-posed evolution
problems.Comment: 21 pages, 11 figures; to appear in Computational Materials Scienc
Thermocapillary effects in driven dewetting and self-assembly of pulsed laser-irradiated metallic films
In this paper the lubrication-type dynamical model is developed of a molten,
pulsed laser-irradiated metallic film. The heat transfer problem that
incorporates the absorbed heat from a single beam or interfering beams is
solved analytically. Using this temperature field, we derive the 3D long-wave
evolution PDE for the film height. To get insights into dynamics of dewetting,
we study the 2D version of the evolution equation by means of a linear
stability analysis and by numerical simulations. The stabilizing and
destabilizing effects of various system parameters, such as the peak laser beam
intensity, the film optical thickness, the Biot and Marangoni numbers, etc. are
elucidated. It is observed that the film stability is promoted for such
parameters variations that increase the heat production in the film. In the
numerical simulations the impacts of different irradiation modes are
investigated. In particular, we obtain that in the interference heating mode
the spatially periodic irradiation results in a spatially periodic film rupture
with the same, or nearly equal period. The 2D model qualitatively reproduces
the results of the experimental observations of a film stability and spatial
ordering of a re-solidified nanostructures
Numerical Simulation of Grain Boundary Grooving By Level Set Method
A numerical investigation of grain-boundary grooving by means of a Level Set
method is carried out. An idealized polygranular interconnect which consists of
grains separated by parallel grain boundaries aligned normal to the average
orientation of the surface is considered. The surface diffusion is the only
physical mechanism assumed. The surface diffusion is driven by surface
curvature gradients, and a fixed surface slope and zero atomic flux are assumed
at the groove root. The corresponding mathematical system is an initial
boundary value problem for a two-dimensional Hamilton-Jacobi type equation. The
results obtained are in good agreement with both Mullins' analytical "small
slope" solution of the linearized problem (W.W. Mullins, 1957) (for the case of
an isolated grain boundary) and with solution for the periodic array of grain
boundaries (S.A. Hackney, 1988).Comment: Submitted to the Journal of Computational Physics (19 pages, 8
Postscript figures, 3 tables, 29 references
Atomic step motion during the dewetting of ultra-thin films
We report on three key processes involving atomic step motion during the
dewetting of thin solid films: (i) the growth of an isolated island nucleated
far from a hole, (ii) the spreading of a monolayer rim, and (iii) the zipping
of a monolayer island along a straight dewetting front. Kinetic Monte Carlo
results are in good agreement with simple analytical models assuming
diffusion-limited dynamics.Comment: 7 pages, 5 figure
Dewetting of an ultrathin solid film on a lattice-matched or amorphous substrate
An evolution partial differential equation for the surface of a non-wetting
single-crystal film in an attractive substrate potential is derived and used to
study the dynamics of a pinhole for the varying initial depth of a pinhole and
the strengths of the potential and the surface energy anisotropy. The results
of the simulations demonstrate how the corresponding parameters may lead to
complete or partial dewetting of the film. Anisotropy of the surface energy,
through faceting of the pinhole walls, is found to most drastically affect the
time to film rupture. In particular, the similations support the conjecture
that the strong anisotropy is capable of the complete suppression of dewetting
even when the attractive substrate potential is strong.Comment: Submitted to PR
Thickness-dependent spontaneous dewetting morphology of ultrathin Ag films
We show here that the morphological pathway of spontaneous dewetting of
ultrathin Ag films on SiO2 under nanosecond laser melting is found to be film
thickness dependent. For films with thickness h between 2 <= h <= 9.5 nm, the
morphology during the intermediate stages of dewetting consisted of
bicontinuous structures. For films 11.5 <= h <= 20 nm, the intermediate stages
consisted of regularly-sized holes. Measurement of the characteristic length
scales for different stages of dewetting as a function of film thickness showed
a systematic increase, which is consistent with the spinodal dewetting
instability over the entire thickness range investigated. This change in
morphology with thickness is consistent with observations made previously for
polymer films [A. Sharma et al, Phys. Rev. Lett., v81, pp3463 (1998); R.
Seemann et al, J. Phys. Cond. Matt., v13, pp4925, (2001)]. Based on the
behavior of free energy curvature that incorporates intermolecular forces, we
have estimated the morphological transition thickness for the intermolecular
forces for Ag on SiO2 . The theory predictions agree well with observations for
Ag. These results show that it is possible to form a variety of complex Ag
nanomorphologies in a consistent manner, which could be useful in optical
applications of Ag surfaces, such as in surface enhanced Raman sensing.Comment: 20 pages, 5 figure
A Model for Isotropic Crystal Growth from Vapor on a Patterned Substrate
We developed a consistent mathematical model for isotropic crystal growth on
a substrate covered by the mask material with a periodic series of parallel
long trenches where the substrate is exposed to the vapor phase. Surface
diffusion and the flux of particles from vapor are assumed to be the main
mechanisms of growth. A geometrical approach to the motion of crystal surface
in two dimensions is adopted and nonlinear evolution equations are solved by a
finite-difference method. The model allows the direct computation of the
crystal surface shape, as well as the study of the effects due to mask regions
of effectively nonzero thickness. As in experiments, lateral overgrowth of
crystal onto the mask and enhanced growth in the region near the contact of the
crystal and the mask is found, as well as the comparable crystal shapes. The
growth rates in vertical and lateral directions are investigated.Comment: 21 pages; submitted to the Journal of Crystal Growt