The form of liquidus and solidus curves in binary alloys

Abstract

Nucleation and growth of epitaxial films are described within the framework of a unified approach that includes the kinetic theory of thin-film nucleation and the classic TLK model of crystal growth. The evolution process of atoms adsorbed on vicinal surfaces is shown to consist of three stages. An intensive nucleation of a new phase takes place on substrate steps at the first stage. Under certain conditions it leads to formation of cigar-shaped clusters. Generation of islands of suitable shape on terraces at this stage proceeds less intensively. At the second stage the cigar-shaped clusters grow and merge with the islands, and the Ostwald ripening process occurs in the combination. Finally, a change in the film microrelief induced by formation of non-linear “cigar” density waves takes place at the third stage. A rigorous theory of non-linear step density waves for epitaxial film growth is constructed. The evolution of growing surfaces is shown to be described by means of a Korteweg-de Vries-type or Burgers-type equation. In the process, solitons, kinks, shock waves, saw-shaped waves, etc. may be formed, depending on initial conditions and external parameters. Each stage is analytically described, and all the main characteristics of nucleation and growth processes in epitaxial films are calculated. In particular, an optimum time dependence for the matter source intensity is found and the evolution of a growing surface under various initial conditions is studied.