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.

Pattern Formation in Molecular Beam Epitaxy

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.


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Address: Martin Siegert
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