Nonequilibrium phase transition in surface growth

– Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the introduction of an infinite series of higher-order nonlinear terms, these models exhibit, as function of a control parameter, a non-equilibrium phase transition between a kinetically rough phase with self-affine scaling and a phase that exhibits mound formation, slope selection and power-law coarsening. The nonequilibrium kinetics of the growth of films by the deposition of atoms on a substrate is of considerable experimental and theoretical interest [1, 2]. While the process of kinetic roughening [1] leading to a self-affine interface profile has been extensively studied, there has been much recent interest [2,3,4] in a different mode of surface growth, involving the formation and coarsening of “mounds” (pyramid-like structures). The system is said to exhibit slope selection if the typical slope of the sides of the mounds remains constant during the coarsening process. Traditionally, the formation of mounds has been attributed to the presence of an Ehrlich-Schwoebel (ES) step-edge barrier [5, 6] that hinders the downward motion of atoms across the edge of a step. The destabilizing effect of the resulting “uphill” surface current is usually modeled in continuum growth equations [7, 8] as a linear instability arising from a Laplacian of the height variable with a negative coefficient. In this Letter, we show that mound formation and power-law coarsening with slope selection occurs in a class of well-known, conserved surface growth models as a result of a nonlinear instability which leads to a dynamical phase transition between kinetically rough and mounded morphologies. We consider the conserved, fourth-order, nonlinear growth equation proposed by Lai and Das Sarma [9] and by Villain [10]: ∂h(r, t)/∂t = −ν∇h + λ∇|∇h| + η(r, t), (1) (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]