This review describes recent progress in the understanding of the emergence of scale
invariance in far-from-equilibrium growth. The first section is devoted to 'solvable'needle …

In recent years, new types of semiconductor heterostructures consisting of only one material
in different crystal structures, such as wurtzite/zinc-blende heterostructures (heteropolytypic …

Abstract The Molecular Beam Epitaxial model is derived from the variation of a free energy,
that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear …

The use of fractal concepts in understanding various growth phenomena, such as molecular
beam epitaxy (MBE) or fluid flow in porous media, is increasingly important these days. This …

Numerical methods for solving the continuum model of the dynamics of the molecular beam
epitaxy (MBE) require very large time simulation, and therefore large time steps become …

For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …

A review is given of nucleation and growth models as applied to the earliest stages of thin
film growth. Rate equations, kinetic Monte Carlo, and level set simulations are described in …

The book describes RHEED (reflection high-energy electron diffraction) used as a tool for
crystal growth. New methods using RHEED to characterize surfaces and interfaces during …

We consider the growth of films by molecular beam epitaxy in the presence of step-edge
(Schwoebel) barriers using numerical simulation and experiments. We show that the growth …

Many inhomogeneous systems involve domains of well-de? ned phases se-rated by a
distinct interface. If they are driven out of equilibrium one phase will grow at the cost of the …