The quenched Kardar-Parisi-Zhang equation with negative nonlinear term shows a first order pinning-depinning (PD) transition as the driving force F is varied. We study the substrate-tilt dependence of the dynamic transition properties in $1+1$ dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope $s_c$ as long as the substrate tilt m is less than $s_c.$ When $m<\mathrm{}{s}_c,$ the transition is discontinuous and the critical value of the driving force $F_c\mathrm{}\left(m\right)\mathrm{}$ is independent of m, while the transition is continuous and $F_c\mathrm{}\left(m\right)\mathrm{}$ increases with m when $m>\mathrm{}{s}_c.$ We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation.

• Received 8 June 1998

DOI:https://doi.org/10.1103/PhysRevE.59.1570