Theory and Simulations of Molecular Beam Epitaxy

Crystal growth by molecular beam epitaxy (MBE) is usually described by adding particles to a substrate and allowing the surface to relax via surface diffusion. During this process an initially flat surface grows and roughens. The prediction of the evolving surface morphology from the microscopic kinetic mechanisms is the aim of the theory of these intrinsically nonequilibrium processes.

The early times of the growth process are characterized by layer-by-layer growth or step flow. In this regime the growth proceeds through the nucleation and coalescence of islands on terraces. Here the dependence of the island size distribution on the incoming flux of particles and the diffusion constant is of theoretical interest.

After the deposition of many monolayers the oscillations in, e.g., the step density that are characteristic for layer-by-layer growth vanish and the system evolves into a spatially and temporally scale-invariant state that is described by the theory of kinetic surface roughening. This regime can be characterized by two exponents, the roughness exponent and the dynamical exponent. However, if the diffusion of adatoms at step edges is inhibited by step edge barriers, the growth becomes unstable and pyramidal structures are formed on the surface. The evolution of these instabilities is similar to the problem of phase ordering as in spinodal decomposition.

We are currently working on the following problems:

• Kinetic surface roughening
• Instabilities and pattern formation in surface growth

If you like to know more about the theory of molecular beam epitaxy, pattern formation and ordering dynamics, also have a look at our list of publications.