  Epitaxial growth on a surface vicinal to a high-symmetry crystallographic
plane occurs through the propagation of atomic steps, a process called
step-flow growth. In some instances, the steps tend to form close groups (or
bunches), a phenomenon termed step bunching, which corresponds to an
instability of the equal-spacing step propagation. Over the last fifty years,
various mechanisms have been proposed to explain step bunching, the most
prominent of which are the inverse Ehrlich-Schwoebel effect (i.e., the
asymmetry which favors the attachment of adatoms from the upper terrace),
elastically mediated interactions between steps (in heteroepitaxy), step
permeability (in electromigration-controlled growth), and the chemical effect
(which couples the diffusion fields on all terraces). Beyond the discussion of
the influence of each of these mechanisms taken independently on the propensity
to bunching, we propose a unified treatment of the effect of these mechanisms
on the onset of the bunching instability, which also accounts for their
interplay. This is done in the setting of the so-called quasistatic
approximation, which by permitting mostly analytical treatment, offers a clear
view of the influence on stability of the combined mechanisms. In particular,
we find that the Ehrlich-Schwoebel effect, elastic step-interactions and the
chemical effect combine in a quasi-additive fashion, whereas step permeability
is neither stabilizing nor destabilizing per se but changes the relative
influence of the three aforementioned mechanisms. In a companion paper, we
demonstrate and discuss the importance of another mechanism, which we call the
dynamics effect, that emerges when relaxing the simplifying but questionable
quasistatic approximation.
