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The formation of three-dimensional structures during the epitaxial growth offilms is associated to the reflection of diffusing particles in descendingterraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier.We generalize this concept in a solid-on-solid growth model, in which a barrierdependent on the particle coordination (number of lateral bonds) existswhenever the particle performs an interlayer diffusion. The rules do notdistinguish explicitly if the particle is executing a descending or anascending interlayer diffusion. We show that the usual model, with a stepbarrier in descending steps, produces spurious, columnar, and highly unstablemorphologies if the growth temperature is varied in a usual range of moundformation experiments. Our model generates well-behaved mounded morphologiesfor the same ES barriers that produce anomalous morphologies in the standardmodel. Moreover, mounds are also obtained when the step barrier has an equalvalue for all particles independently if they are free or bonded. Kineticroughening is observed at long times, when the surface roughness w and thecharacteristic length $\xi$ scale as $w ~ t^\beta$ and $\xi ~ t^\zeta$ where$\beta \approx 0.31$ and $\zeta \approx 0.22$, independently of the growthtemperature.

Kinetic modelling of epitaxial film growth with up- and downward step barriers