Rate equation modelling of epitaxial growth

• Published in: Surface science 1989-06, Vol.216 (3), p.557-578
• Main Authors: Kariotis, R, Lagally, M.G
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Physics; Solid surfaces and solid-solid interfaces; Surface and interface dynamics and vibrations; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Thin film structure and morphology
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/0039-6028(89)90395-6

A rate equation model describing molecular beam epitaxy (MBE) is presented. This formulation of the problem consists of a set of equations that govern the population of islands of varying sizes and heights above the substrate. There is one equation for the time rate of change of the number of islands of each possible size at the jth level above the substrate. Use of this information is made in combination with some simple arguments from statistical mechanics to obtain a qualitatively detailed pair correlation function, and from this the scattered intensity as a function of time. The rate equation approach allows for a compact and fast method of simulation of film growth, complementing the more complete but time consuming Monte Carlo (MC) and molecular dynamics (MD) methods. By varying the different energy parameters in the equations it is possible to model situations in which the interface grows approximately in the layer-by-layer, or in the completely rough, mode. As a particular application we discuss the problem of the interface width growth (IWG) as a function of temperature, deposition rate, and binding energies. This width is essentially the number of incomplete layers (coverage different from either 0 or 1) at any given instant, and is a useful measure of the extent to which the system has made the transition from the bounded to unbounded IWG mode.