Facet formation in the negative quenched Kardar-Parisi-Zhang equation

Abstract

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<s(c), the transition is discontinuous and the critical value of the driving force F,(m) is independent of m, while the transition is continuous and F(c)(ln) increases with In when m>s(c). We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation. [S1063-651X(99)12602-3].