We present a new kinetic model for molecular beam epitaxial growth on
a singular surface which combines the modified rate equations approach
with a concept of a feeding zone. The model involves irreversible nuc
leation, growth and coalescence of 2D islands in each layer and consis
ts of an infinite set of coupled differential equations for adatom and
2D island densities and coverage in successive growing layers. It is
shown that in the complete condensation regime and in the absence of s
tep edge barriers, the homoepitaxial growth mode is fully determined b
y a single dimensionless parameter which is proportional to the ratio
of the surface diffusion coefficient and the deposition flux. With dec
reasing this parameter, the growth mechanism crosses over from smooth
2D layer-by-layer growth to rough multilayer growth and eventually to
very rough Poisson random deposition growth with time-divergent rms ro
ughness. The extension of the model to the case of the heteroepitaxy b
y introducing different diffusion coefficients in the first and the ne
xt layers is presented as well. (C) 1997 Elsevier Science S.A.