4 research outputs found
Strong coupling probe for the Kardar-Parisi-Zhang equation
We present an exact solution of the {\it deterministic} Kardar-Parisi-Zhang
(KPZ) equation under the influence of a local driving force . For substrate
dimension we recover the well-known result that for arbitrarily small
, the interface develops a non-zero velocity . Novel behaviour is
found in the strong-coupling regime for , in which must exceed a
critical force in order to drive the interface with constant velocity. We
find for . In particular,
the exponent for , but saturates at
for , indicating that for this simple problem, there exists a finite upper
critical dimension . For the surface distortion caused by the
applied force scales logarithmically with distance within a critical radius
, where . Connections
between these results, and the critical properties of the weak/strong-coupling
transition in the noisy KPZ equation are pursued.Comment: 18 pages, RevTex, to appear in J. Phys. I Franc
Island Distance in One-Dimensional Epitaxial Growth
The typical island distance in submonlayer epitaxial growth depends on
the growth conditions via an exponent . This exponent is known to
depend on the substrate dimensionality, the dimension of the islands, and the
size of the critical nucleus for island formation. In this paper we study
the dependence of on in one--dimensional epitaxial growth. We
derive that for and confirm this result
by computer simulations.Comment: 5 pages, 3 figures, uses revtex, psfig, 'Note added in proof'
appende
Conserved Growth on Vicinal Surfaces
A crystal surface which is miscut with respect to a high symmetry plane
exhibits steps with a characteristic distance. It is argued that the continuum
description of growth on such a surface, when desorption can be neglected, is
given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo,
and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A
one--loop dynamical renormalization group calculation yields the values of the
dynamical exponent and the roughness exponent which are shown to be the same as
in the isotropic case. The results presented here should apply in particular to
growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte
Growth of Patterned Surfaces
During epitaxial crystal growth a pattern that has initially been imprinted
on a surface approximately reproduces itself after the deposition of an integer
number of monolayers. Computer simulations of the one-dimensional case show
that the quality of reproduction decays exponentially with a characteristic
time which is linear in the activation energy of surface diffusion. We argue
that this life time of a pattern is optimized, if the characteristic feature
size of the pattern is larger than , where is the surface
diffusion constant, the deposition rate and the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let