Theoretical analysis of mound slope selection during unstable multilayer growth

Slope selection in unstable multilayer growth in 1+1 dimensions: Step flow models with downward funneling

We study analytically and numerically aspects of the dynamics of slope selection for one-dimensional models describing the motion of line defects, steps, in homoepitaxial crystal growth. The kinetic processes include diffusion of adsorbed atoms (adatoms) on terraces, attachment and detachment of atoms at steps with large yet finite, positive Ehrlich-Schwoebel step-edge barriers, material deposition on the surface from above, and the mechanism of downward funneling (DF) via a phenomenological parameter. In this context, we account for the influence of boundary conditions at extremal steps on the dynamics of slope selection. Furthermore, we consider the effect of repulsive, nearest-neighbor force-dipole step-step interactions. For geometries with straight steps, we carry out numerical simulations of step flow, which demonstrate that slope selection eventually occurs. We apply perturbation theory to characterize time-periodic solutions of step flow for slope-selected profiles. By this method, we show how a simplified step flow theory with constant probabilities for the motion of deposited atoms can serve as an effective model of slope selection in the presence of DF. Our analytical findings compare favorably to step simulations.

Island-dynamics model for mound formation: effect of a step-edge barrier

We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachment of atoms at step edges. For this purpose, we invoke a mixed, Robin-type, boundary condition for the flux of adsorbed atoms (adatoms) at each step edge. In addition, we provide an analytic expression for the requisite equilibrium adatom concentration at the island boundary. The only inputs are atomistic kinetic rates. We present a numerical scheme for solving the adatom diffusion equation with such a mixed boundary condition. Our simulation results demonstrate that mounds form when the step-edge barrier is included, and that these mounds steepen as the step-edge barrier increases.

Experimental modelling of single-particle dynamic processes in crystallization by controlled colloidal assembly

A comprehensive review of the experimental modeling of single particle dynamics in crystallization is presented.

Formation of complex wedding-cake morphologies during homoepitaxial film growth of Ag on Ag(111): atomistic, step-dynamics, and continuum modeling

An atomistic lattice-gas model is developed which successfully describes all key features of the complex mounded morphologies which develop during deposition of Ag films on Ag(111) surfaces. We focus on this homoepitaxial thin film growth process below 200 K. The unstable multilayer growth mode derives from the presence of a large Ehrlich-Schwoebel step-edge barrier, for which we characterize both the step-orientation dependence and the magnitude. Step-dynamics modeling is applied to further characterize and elucidate the evolution of the vertical profiles of these wedding-cake-like mounds. Suitable coarse-graining of these step-dynamics equations leads to instructive continuum formulations for mound evolution.

Vertical asymmetry and the ripple-rotation transition in epitaxial growth and erosion on (110) crystal surfaces

Vertical (up-down) asymmetry is ubiquitous feature of the nonequilibrium statistical mechanics of realistic growing interfaces. Yet, the actual role of vertical asymmetry (VA) in epitaxial growth on crystal surfaces is still elusive. Is vertical asymmetry a primary or secondary factor in epitaxial growth and erosion? Can vertical asymmetry alone produce major qualitative effects on long length scale interface morphologies? To address these questions in depth, we theoretically discuss the effects of vertical growth asymmetry on far-from-equilibrium interfacial morphologies occurring in the epitaxial growth and erosion of (110) crystal surfaces. We theoretically elucidate the so-called ripple rotation transition on the Ag(110) crystal surface [F. B. de Mongeot; Phys. Rev. Lett. 84, 2445 (2000), G. Constantini, J. Phys.: Condens. Matter 13, 5875 (2001)], as the transition between the rectangular rippled states (checker-board structures of alternating rectangular pyramids and pits). We show that the experimental surface diffraction data seen in this transition can be understood only by invoking vertical growth asymmetry. In the proximity of the transition point, we find that vertical asymmetry itself produces an interface morphology yielding a four-lobe near in-phase diffraction pattern having four peaks along the principal axes of the (110) surface, in accord with the experiments on Ag(110). Moreover, on the two sides of the ripple rotation transition, we find two exotic interface states induced by vertical asymmetry, which correspond well /to the interface morphologies seen on Ag(110). We document our results by numerical simulations and by analytic arguments. Our theoretical findings, in combination with experiments, provide the first rigorous evidence that VA plays a significant role in epitaxial growth and erosion on crystal surfaces.

Interfacial states and far-from-equilibrium transitions in the epitaxial growth and erosion on (110) crystal surfaces

We discuss the far-from-equilibrium interfacial phenomena occurring in the multilayer homoepitaxial growth and erosion on (110) crystal surfaces. Experimentally, these rectangular symmetry surfaces exhibit a multitude of interesting nonequilibrium interfacial structures, such as the rippled one-dimensional periodic states that are not present in the homoepitaxial growth and erosion on the high symmetry (100) and (111) crystal surfaces. Within a unified phenomenological model, we reveal and elucidate this multitude of states on (110) surfaces as well as the transitions between them. By analytic arguments and numerical simulations, we address experimentally observed transitions between two types of rippled states on (110) surfaces. We discuss several intermediary interface states intervening, via consecutive transitions, between the two rippled states. One of them is the rhomboidal pyramid state, theoretically predicted by Golubovic [Phys. Rev. Lett. 89, 266104 (2002)] and subsequently seen, by de Mongeot and co-workers, in the epitaxial erosion of Cu(110) and Rh(110) surfaces [A. Molle, Phys. Rev. Lett. 93, 256103 (2004), and A. Molle, Phys. Rev. B 73, 155418 (2006)]. In addition, we find a number of interesting intermediary states having structural properties somewhere between those of rippled and pyramidal states. Prominent among them are the rectangular rippled states of long rooflike objects (huts) recently seen on Ag(110) surface. We also predict the existence of a striking interfacial structure that carries nonzero, persistent surface currents. Periodic surface currents vortex lattice formed in this so-called buckled rippled interface state is a far-from-equilibrium relative of the self-organized convective flow patterns in hydrodynamic systems. We discuss the coarsening growth of the multitude of the interfacial states on (110) crystal surfaces.