  This paper concerns new continuum phenomenological model for epitaxial thin
film growth with three different forms of the Ehrlich-Schwoebel current. Two of
these forms were first proposed by Politi and Villain [1996] and then studied
by Evans, Thiel and Bartelt [2006]. The other one is completely new. Following
the techniques used in Li and Liu [2003], we present rigorous analysis of the
well-posedness, regularity and time stability for the new model. We also
studied both the global and the local behavior of the surface roughness in the
growth process. The new model differs from other known models in that it
features a linear convex part and a nonlinear concave part, and thus by using a
convex-concave time splitting scheme, one can naturally build unconditionally
stable semi-implicit numerical discretizations with linear implicit parts,
which is much easier to implement than conventional models requiring nonlinear
implicit parts. Despite this fundamental difference in the model, numerical
experiments show that the nonlinear morphological instability of the new model
agrees well with results of other models published in Li and Liu [2003], which
indicates that the new model correctly captures the essential morphological
states in the thin film growth process.
