Island nucleation in the presence of step-edge barriers: Theory and applications

Abstract

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier ∆ES 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 ∆ES ≥ 0.33 eV for the additional energy barrier at CO-decorated steps.

Formation and morphological evolution of self-similar 3D nanostructures on weakly interacting substrates

“…However, vapor condensation and film growth proceed far from thermodynamic equilibrium and thus morphological evolution is primarily determined by the relative rates of competing atomistic structure-forming processes (i.e., by kinetics) [1][2][3]. Currently, the most detailed atomistic * kostas.sarakinos@liu.se description of far-from-equilibrium 3D island formation is based on homoepitaxial systems in which 3D islands (mounds) form by deposition onto existing small islands, followed by atomic-step descent limited by the Ehlrich-Schwöbel barrier [15][16][17][18][19]. However, for weakly interacting film/substrate systems-including Ag/SiO 2 [20][21][22][23][24], Pd/TiO 2 [25], Cu/ZnO [26,27], and Dy/graphene [4,28]-3D islands develop before the initially formed one-atom-high islands are large enough to efficiently capture vapor-phase deposition flux.…”

Spiral Growth and Step Edge Barriers

“…Even the answer to the simple question as to which of the two grows faster under a given set of conditions is not obvious. The growth of wedding cakes is governed by the rate of two-dimensional nucleation of islands on the top terrace, which is enhanced by the confinement of atoms due to the SEB [21]. In contrast, atoms landing near the top of the spiral mound can avoid the SEB by moving around the core, which should reduce the local adatom concentration and hence the growth rate.…”

“…4(d) and 4(e). This corresponds to the perimeter of the base terrace, the terrace below the top terrace of a wedding cake, which is known to show less scatter than the top terrace size itself [21]. Using formulas of second layer nucleation theory [14], the base terrace perimeter translates into estimates for E S for the two kinds of mounds, which are displayed in Fig.…”

“…Via the theory of second layer nucleation [14,21], the critical coverage c can be linked to the additional SEB E S , which is defined as the difference between the activation energy for a descending hop into the step position compared to a hop within the layer [25]. A large value of E S enhances the confinement of adatoms on the top terrace, which increases the probability for nucleation, decreases c , and increases the height of the mound.…”

“…For wedding cakes the key process is two-dimensional nucleation [14,21]. For the spiral mounds on Pt(111), the appropriate physical picture is that of a polygonized spiral growing by the motion of straight segments that follow the crystallographic directions of the surface [7].…”