Kinetic Surface Roughening
Surface growth as in molecular beam epitaxy or vapor deposition is
typically characterized by dynamics far away from equilibrium, i.e.,
the deposition rate is sufficiently large so that the surface does not relax
through surface diffusion to a state of thermal equilibrium between
successive deposition events. Since equilibrium surface diffusion is an
extremely slow process this condition is almost always fulfilled.
Consequently the dynamics are not restricted by a flucutation-dissipation
theorem. Typically the late stages of these growth process are characterized
by generic scale-invariance of the correlation functions that is reflected in
power law behavior in space and time. Since the corresponding exponents do
not depend on the microscopic details of the system under investigation it
is possible to divide growth processes according to the values of these
characteristic exponents into kinetic universality classes. The association
with one particular class depends only on a few properties of the
growth dynamics like conservation laws, the importance of defects in
the growing film, etc. The determination of these relevant
features is one of the important problems that have to be addressed by
the theory of kinetic surface roughening. Conversely, as soon as these
relations are known the determination of scaling exponents allows
conclusions about the physical processes that dominate the growth dynamics.
For conditions that are typical for molecular beam epitaxy many models
predicted a surface roughness that is much larger than the equilibrium
roughness. This conclusion is reached if one describes the growth process
by the same equation that is valid for equilibrium surface diffusion and
adds particle deposition as an external source. In a series of papers
we have shown that this conclusion is incorrect: Generically, the dependence
of the diffusion current on the surface morphology is different in the
non-equilibrium case. We find that the growth process either leads to only
logarithmically rough surfaces or becomes unstable and leads to the
formation of pyramidal structures on the surfaces. The latter case can
no longer be described within the theory of kinetic surface roughning.
If the diffusion of adatoms at step edges is inhibited by so-called
Ehrlich-Schwoebel barriers that suppress the diffusion to lower lying
terraces the equation of motion of the surface becomes linearly unstable.
The evolution of this instability is similar to the problem of domain
growth in a magnetic system: the slope of the emerging pyramids corresponds
to the order parameter of the magnet. The selected slopes are determined
by the zeros of the surface diffusion current. As time proceeds the
system coarsens: smaller pyramids disappear and the size of the larger
pyramids increases as a power law. Numerical integrations of the equation
of motion and Monte-Carlo simulations indicated an exponenent of 1/4.
For more information see our publication list.
Address: Martin Siegert
Department of Physics Phone: (604) 291-3051
Simon Fraser University Fax: (604) 291-3592
Burnaby, British Columbia Email: siegert@sfu.ca
Canada V5A 1S6