Model Of Interface Growth Research Articles

Molecular beam epitaxial growth: simulation and continuum theory

We present results of atomistic simulations of an ideal MBE growth process in 1 + 1 dimensions and make a connection with continuum models of interface growth. We argue that the KPZ equation is not the relevant continuum equation for MBE growth at intermediate temperatures, where overhangs and bulk defects can be neglected. Instead, a fourth-order linear equation gives the same growth exponents obtained in the numerical simulations but leads to unphysical properties of the long-time surface morphology. We propose a new non-linear growth equation different from the KPZ equation, as the relevant dynamical equation for ideal MBE growth.

Two-spin-majority cellular automaton as a model of 2D cluster and interface growth

A new probabilistic cellular automaton model is introduced to simulate cluster and interface growth in two dimensions. The dynamics of this model is an extension to higher dimensions of the compact directed percolation studied by Essam. Numerical results indicate that the two-dimensional cluster coarsening and growth can be described only approximately by the conventional cluster size scaling due to a crossover in the growth mode. The spreading of the initially flat interface follows a purely diffusional,t 1/2, law.

Numerical study of a model for interface growth.

We present the first numerical study of the nonlinear stochastic differential equation characterizing interface growth, originally proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)]. Our studies are carried out in two dimensions which would correspond to three-dimensional studies of microscopic models such as the Eden or ballistic-deposition models. We find that the interface width satisfies the proposed scaling relations. The exponents associated with this scaling relation are calculated for different strengths of the effective coupling in the model and seem to be different from previous calculations on microscopic models.

Quantitative model of reactive metal-semiconductor interface growth using high-resolution photoemission results.

High-resolution core-level photoemission studies of the reactive metal-semiconductor interfaces V/Ge(111), Ce/Si(111), and Ce/Ge(111) show that intermixing leads to unique chemical environments or species having well-defined chemical shifts. Decomposition of the coverage-dependent core-level emission shows the growth and attenuation of each of these species. We present a model which quantitatively describes the evolution of the interface. We show that two-phase growth can be described by the lever rule, such that bulk thermodynamic partitioning applies to interfaces having thicknesses of tens of angstroms or less. From the modeling, we extract values for the onset coverage of each phase, the composition of each phase, and the coverage at which each ceases to form. These interface phase diagrams indicate that the first phase is not consumed when subsequent phases form. Application and refinement of these analysis techniques should lead to predictive abilities for junction formation and interface stability.

Simple models of interface growth

We propose a simple class of models for interface growth. These models are characterized by the idea that the growth velocity be locally determined by the interface geometry. Study of these systems should clarify the mechanisms involved in pattern formation.