DYNAMICS AND FLUCTUATIONS DURING MBE ON VICINAL SURFACES - II - NONLINEAR-ANALYSIS

This paper is the natural next step beyond the linear regime presented in the preceding paper. By concentrating on the situation close to th e step morphological instability threshold, we derive nonlinear evolut ion equations for interacting steps on a vicinal train. This treatment is coherent in that it retains only relevant nonlinearities close eno ugh to the threshold. Our analysis provides the expression of the coef ficients in terms of thermodynamic and transport coefficients. Numeric al analysis of these equations reveals spatially and temporally disord ered patterns. We give a criterion specifying the region where step ro ughness is due to both stochastic effects (associated with various sou rces of noise) and deterministic ones (stemming from deterministic spa tiotemporal chaos). Outside this region, the roughness is dominated by either stochastic or deterministic effects. Starting from the discret e version (this is taken to mean that each step is described as an ent ity) of step dynamics (that is to say, each step is separately describ ed by an evolution equation), we derive a coarse-grained evolution equ ation for the surface. This results in an anisotropic Kuramoto-Sivashi nsky equation including propagative effects. Numerical analysis reveal s situations where the original surface undergoes a secondary instabil ity leading ultimately to a rough pattern. The surface looks as if two -dimensional nucleation were allowed. Implication and outlooks are dis cussed.