Fast coarsening in unstable epitaxy with desorption

An examination of scaling behavior in unstable epitaxial mound growth via kinetic Monte Carlo simulations

We investigate the scaling behavior for roughening and coarsening of mounds during unstable epitaxial growth. By using kinetic Monte Carlo (KMC) simulations of two lattice-gas models of crystal surfaces, we find scaling exponents that characterize roughening and coarsening at long times. Our simulation data show that these exponents have a complicated dependence on key model parameters that describe a step edge barrier and downward transport mechanisms. This behavior has not been fully described in previous works. In particular, we find that these scaling exponents vary continuously with parameters controlling the surface current. The kinetic processes of the KMC models that we employ include surface diffusion, edge diffusion, step-edge barriers, and also account for transient kinetics during deposition via downward funneling and transient mobility. Our extensive simulations make evident the salient interplay between step-edge barrier strength and transient kinetic processes.

Emergent parabolic scaling of nano-faceting crystal growth

Nano-faceted crystals answer the call for self-assembled, physico-chemically tailored materials, with those arising from a kinetically mediated response to free-energy disequilibria (thermokinetics) holding the greatest promise. The dynamics of slightly undercooled crystal–melt interfaces possessing strongly anisotropic and curvature-dependent surface energy and evolving under attachment–detachment limited kinetics offer a model system for the study ofthermokineticeffects. The fundamental non-equilibrium feature of this dynamics is explicated through our discovery of one-dimensional convex and concave translating fronts (solitons) whose constant asymptotic angles provably deviate from the thermodynamically expectedWulffangles in direct proportion to the degree of undercooling. Thesethermokineticsolitons induce a novel emergent facet dynamics, which is exactly characterized via an original geometric matched-asymptotic analysis. We thereby discover an emergent parabolic symmetry of its coarsening facet ensembles, which naturally implies the universal scaling lawL∼t1/2for the growth in timetof the characteristic lengthL.

Continuum imit of a tep Flow odel of Epitaxial Growth

We examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. ur goal is to derive a consistent contin uummodel for the ev olutionof the lm surface. Away from peaks and valleys, the surface height solves a Hamilton- acobi equation (H E). he peaks are free boundaries for this H E. heir evolution must be speci ed by boundary conditions re ecting the microscopic physics of nucleation. e investigate this boundary condition by numerical simulation of the step ow dynamics using a simple n ucleationlaw. ur results rev ealthe presence of sp ecial structures in the pro le near a peak; we discuss the relationship between these structures and the contin uumequation. e further address the importance of ev aporationfor matching the local behavior near the peak to the solution of the contin uum equation.

Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation

We consider the coarsening dynamics of multiscale solutions to a dissipative singularly perturbed partial differential equation which models the evolution of a thermodynamically unstable crystalline surface. The late-time leading-order behavior of solutions is identified, through the asymptotic expansion of a maximal-dissipation principle, with a completely faceted surface governed by an intrinsic dynamical system. The properties of the resulting piecewise-affine dynamic surface predict the scaling law L(Mu) approximately t(1/3), for the growth in time of a characteristic morphological length scale L(Mu). A novel computational geometry tool which directly simulates a million-facet piecewise-affine dynamic surface is also introduced. Our computed data are consistent with the dynamic scaling hypothesis, and we report a variety of associated morphometric scaling functions.

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 the local growth equation. It can be generalized to any growth problem where surface morphology is governed by adatom diffusion. The method can be easily extended to higher dimensions. The kinetic processes contributing to various terms in the growth equation are identified from the analysis of in-plane and downward hops. In particular, processes corresponding to the term that breaks h-->-h symmetry and the curvature dependent term are discussed. Effects of these terms on the stable to unstable transition in (1+1) dimension are analyzed. In (2+1) dimensions, it is shown that an additional asymmetric term is generated due to the in-plane curvature associated with mound-like structures. This term is independent of any diffusion barrier differences between in-plane and out-of-plane migration. It is shown that terms generated in the presence of downward hops are the relevant terms in a growth equation. A growth equation in closed form is obtained for various growth models introduced to capture most of the processes in experimental molecular beam epitaxial growth. The effect of dissociation is also considered and is seen to have a stabilizing effect on growth. It is shown that for uphill current the growth equation approach fails to describe the growth since a given single equation does not apply over the entire substrate.

Faceting of a growing crystal surface by surface diffusion

Consider faceting of a crystal surface caused by strongly anisotropic surface tension, driven by surface diffusion and accompanied by deposition (etching) due to fluxes normal to the surface. Nonlinear evolution equations describing the faceting of 1+1 and 2+1 crystal surfaces are studied analytically, by means of matched asymptotic expansions for small growth rates, and numerically otherwise. Stationary shapes and dynamics of faceted pyramidal structures are found as functions of the growth rate. In the 1+1 case it is shown that a solitary hill as well as periodic hill-and-valley solutions are unique, while solutions in the form of a solitary valley form a one-parameter family. It is found that with the increase of the growth rate, the faceting dynamics exhibits transitions from the power-law coarsening to the formation of pyramidal structures with a fixed average size and finally to spatiotemporally chaotic surfaces resembling the kinetic roughening.

Ripple formation through an interface instability from moving growth and erosion sources

The propagation of material interfaces is investigated under the action of a localized moving source which deposits or removes material. Among others the latter process applies to beam cutting techniques. We develop a Kuramoto-Sivashinsky-type model and find a new type of ripple forming mechanism. This theory offers a new explanation for the occurrence of striation patterns which often degrade the quality of cutting edges.