Unified view of step-edge kinetics and fluctuations

Abstract

We study theoretically the equilibrium fluctuations of steps on vicinal surfaces. From an analytical continuum description of the step edge, we find a single Langevin equation governing the motion of an isolated step around its equilibrium position that includes attachment/detachment of atoms, diffusion over the terrace, diffusion along the edge, and evaporation. We then extend this approach to treat an array of steps, i.e., a vicinal surface. We also present, in an appendix, an alternative formalism in which detachment to terrace and to step-edge diffusion can take place independently. In established as well as some new limits, and for numerous special cases, we study the wave-vector dependence-both exponent and prefactor-of the relaxation time of fluctuations. From this we recover scaling relations for early-time dependence of the mean-square fluctuations. We discuss how to extract the ͓mesoscopic͔ transport coefficients associated with different atomistic mechanisms of surface mass transport and how to distinguish between mechanisms having the same power-law dependence on wavelength in the capillary-wave analysis. To examine the crossovers between limiting regimes, we compute and explore an effective exponent for this power law and show that the crossover occurs over a narrow region of phase space. Furthermore, we find that single-sided approximations are valid only in the limit of extreme Schwoebel barriers. ͓S0163-1829͑98͒09008-0͔

Universal width distributions in non-Markovian Gaussian processes

“…For this reason it is possible to determine in detail its geometric properties (for a recent review see [8]). For α = 2, instead, the process u(t) is non-Markovian: In the case α = 4 (the driven curvature model [1,9]), the evolution of the derivativeu(t) is Markovian, but not the one of u(t) itself. For not-integer α/2, the non-Markovian properties reflect the non-local character of the action.…”

Thin film epitaxy with or without slope selection

“…Figure 1.1. This asymmetry in attachment and detachment of adatoms to and from terrace boundaries has many important consequences: it induces an uphill current which in general destabilizes nominal surfaces (high symmetry surfaces) [7,30,31], but stabilizes vicinal surfaces (surfaces that are in the vicinity of high symmetry surfaces) with large slope, preventing step bunching [35]; it also leads to the Bales-Zangwill morphological instability of atomic steps [2,29]; Finally, it contributes to the kinetic roughening of film surfaces [17,27,35].…”

Finite element method for epitaxial growth with attachment–detachment kinetics

“…In order to stick to the boundary from an upper terrace, an adatom must overcome a higher energy barrier-the Ehrlich-Schwoebel barrier [13,36,37]. This asymmetry in attachment and detachment of adatoms to and from terrace boundaries has many important consequences: It induces an uphill current which in general destabilizes nominal surfaces (high symmetry surfaces) [13,36,37], but stabilizes vicinal surfaces (surfaces that are in the vicinity of high symmetry surfaces) with large slope, preventing step bunching [41]; It also leads to the Bales-Zangwill morphological instability of atomic steps [1,31]; Finally, it contributes to the kinetic roughening of film surfaces [20,29,41].…”