Analysis of island morphology in a model for Pb-mediated growth of Ge on Si(111)

Abstract

Analysis of island morphology in a realistic model of surfactant-mediated epitaxial growth is presented and compared with experimental results obtained for Pb-mediated growth of Ge on Si͑111͒. In kinetic Monte Carlo simulations it is found that the clustering of Ge atoms above the surfactant obeys an anomalous scaling, and that the cluster size distribution is self-similar in time, up to the latest stages of coarsening, where Ostwald ripening predominates. The clustering process is limited in time due to the irreversible exchange of Ge atoms with surfactant. Further growth of islands below surfactant leads to their ramification. Islands which do not significantly grow below surfactant are compact, and are characterized by a size distribution whose shape is similar to that obtained within the cluster diffusion model of crystal growth.

Fragmentation pathways of nanofractal structures on surfaces

“…The scaling of the island size distribution, island density, monomer density, and other morphology characteristics of the system are often studied as a function of the surface coverage, and as a function of the ratio of the diffusion rate to the deposition rate. [38][39][40][41] The scaling of the aforementioned quantities allows us to determine important physical parameters describing the kinetic growth processes on a surface, such as, e.g., the activation energy and the diffusion constant. 39,41 An important characteristic of the island size distribution scaling is the scaling function.…”

“…43 The scaling of the island size distribution emerging during the postdeposition growth processes on a surface was also suggested. 44 The scaling of island morphology characteristics has been performed for various model systems, [38][39][40][41] and allows us to characterize complex kinetic processes occurring on a surface.…”

“…The island size distribution function is a fundamental quantity in the kinetic description of island growth. It has been widely used to characterize the experimentally measured [35][36][37] as well as computed [38][39][40][41][42] surface morphologies. The scaling of the island size distribution, island density, monomer density and other morphology characteristics of the system are often studied as a function of the surface coverage, and as a function of the ratio of the diffusion rate to the deposition rate [38][39][40][41].…”

“…It has been widely used to characterize the experimentally measured [35][36][37] as well as computed [38][39][40][41][42] surface morphologies. The scaling of the island size distribution, island density, monomer density and other morphology characteristics of the system are often studied as a function of the surface coverage, and as a function of the ratio of the diffusion rate to the deposition rate [38][39][40][41]. The scaling of the afore mentioned quantities allows to determine important physical parameters describing the kinetic growth processes on a surface, as, e.g., the activation energy and the diffusion constant [39,41].…”

Simulation of Surfactant Effects on Growth of Semiconductor Hetero-Epitaxial Sb-Ge/Si(111)

“…[1] Using scanning tunneling microscopy, a compact-to-fractal island shape transition is observed as the deposition flux is lowered or the temperature is raised which is completely opposite to diffusion-limited aggregation and is exchangereaction rate limited. [2] Based on their experimental results, Janusz Beben et al described the early stage of growth of Ge on Si(111) mediated by Pb surfactant using a kinetic Monte Carlo method [3] and a mean-field approximation. [4] In their model, atoms above the surfactant can exchange positions with surfactant and stick irreversibly to the substrate, moreover, a cluster sizedependent barrier for exchange is assumed.…”