Recent experiments [N\'eel et al., PRL, vol. 91, p. 226103,
2003] have established that one- and two-dimensional instabilities,
bunching and meandering respectively, occur simultaneously during
step-flow growth on copper vicinal surfaces, in contrast to the
predictions of existing models that trace back to the 1951 article by
Burton, Cabrera, and Frank. Indeed, in the BCF framework, meandering
is contingent upon the existence of an Ehrlich--Schwoebel barrier, one
that favors adatom attachment to ascending steps, whereas bunching
requires an inverse ES effect (whereby the barrier to adatom
incorporation to a descending step is lower than that which
characterizes ordinary diffusion). Bunching and meandering appear
therefore to be a priori mutually exclusive. In this talk, a
thermodynamically consistent theory is presented that resolves this
apparent paradox, in the sense that it yields bunching under the
assumption of an ES barrier. A main ingredient of the theory is the
step chemical potential for which a generalized Gibbs--Thomson
relation is derived via a direct energy-rate calculation, resulting in
boundary conditions along step edges that couple adjacent terraces.
Specialization to the case of a periodic train of initially
equidistant rectilinear steps reveals a competition between the
stabilizing ES effect and a destabilizing energetic correction that,
for sufficiently high adatom equilibrium coverage, leads to step
collisions. The underlying physics can be understood in terms of the
tendency of the crystalline surface to minimize its total grand
canonical potential. An extension of the model to account for the
growth of binary compounds will also be discussed. [Joint work with P.
Cermelli.]