A one-dimensional Stefan problem describing growth limited by surface proce
sses is set and the time evolution of a spiral growing hillock calculated.
The model is self-consistent in the sense that the critical surface supersa
turation for the production of a new step, the slope and the growth rate of
the hillock, strictly depend on a set of phenomenological parameters descr
ibing diffusion and matter exchange at the steps. The quasi-steady states c
alculated for several sets of values of the parameters, art illustrated and
compared with classical models. Some criteria are proposed to correlate th
e features of the growth hillocks and the steps rates, to the kinetics. (C)
2001 Elsevier Science B.V. All rights reserved.