Reaction limited aggregation in surfactant-mediated epitaxy

Abstract

A theoretical model for reaction limited aggregation (RLA) is introduced to study the effect of a monolayer of surfactant on the formation of two-dimensional islands in heteroepitaxial and homoepitaxial growth. In this model the basic atomic processes are considered as follows. A stable island consists of the adatoms that have exchanged positions with the surfactant atoms beneath them. Movable active adatoms may (a) diffuse on the surfactant terrace, (b) exchange positions with the surfactant atoms beneath them and become island seeds (seed exchange), or (c) stick to stable islands and become stuck but still active adatoms. The rate-limiting step for the formation of a stable island is the seed exchange. Furthermore, a stuck but still active adatom must overcome a sizable potential-energy barrier to exchange positions with the surfactant atom beneath it and become a member of the stable island (aided exchange). The seed exchange process can occur with an adatom or collectively with an addimer. In the case of dimer exchange, the diffusing adatoms on the surfactant terrace can meet and (after exchanging) form stable dimers, which can then become island seeds. Systematic kinetic Monte Carlo simulations and rate-equation analysis of the model are carried out. The key finding of these simulations is that a counterintuitive fractal-to-compact island shape transition can be induced either by increasing deposition flux or by decreasing growth temperature. This major qualitative conclusion is valid for both the monomer and the dimer seed exchanges and for two different substrate lattices (square and triangular, respectively), although there are some quantitative differences in the flux and temperature dependence of the island density. The shape transition observed is contrary to the prediction of the classic diffusion-limited aggregation (DLA) theory, but in excellent qualitative agreement with recent experiments. In rationalizing the main finding, it is crucial to realize that the adatoms stuck to a stable island edge are still active and are surrounded by the surfactant atoms. Therefore, these stuck atoms cannot capture incoming adatoms before they join the island through aided exchange. As a result, an incoming adatom must on average hit the island many times before it finally finds a free edge site to stick to. This search is effectively equivalent to edge diffusion in DLA theory. The stuck adatoms thus act as shields which prevent other mobile adatoms from sticking to the stable islands. This shielding effect, determined by the aided exchange barrier and the density of the mobile adatoms, plays an essential role in inducing the above shape transition in surfactant-mediated epitaxial growth.