Epitaxial growth in one dimension.

The final structure and properties of layers grown by epitaxy techniques are determined in the very early stage of the process. This review describes one-dimensional models for epitaxial growth, emphasizing the basic theoretical concepts employed to analyze nucleation and aggregation phenomena in the submonolayer regime. The main findings regarding the evolution of quantities that define the properties of the system, such as monomer and island densities, and the associated island size, gap length, and capture zone distributions are discussed, as well as the analytical tools used to evaluate them. This review provides a concise overview of the most widely used algorithms for simulating growth processes, discusses relevant experimental results, and establishes connections with existing theoretical studies.