Surface pattern formation and scaling described by conserved lattice gases

Scaling of surface roughness in film deposition with height-dependent step edge barriers

We perform kinetic Monte Carlo simulations of film growth in simple cubic lattices with solid-on-solid conditions, Ehrlich-Schwoebel (ES) barriers at step edges, and a kinetic barrier related to the hidden off-plane diffusion at multilayer steps. Broad ranges of the diffusion-to-deposition ratio R, detachment probability per lateral neighbor, ε, and monolayer step crossing probability P=exp[-E_{ES}/(k_{B}T)] are studied. Without the ES barrier, four possible scaling regimes are shown as the coverage θ increases: nearly layer-by-layer growth with damped roughness oscillations; kinetic roughening in the Villain-Lai-Das Sarma (VLDS) universality class when the roughness is W∼1 (in lattice units); unstable roughening with mound nucleation and growth, where slopes of logW×logθ plots reach values larger than 0.5; and asymptotic statistical growth with W=θ^{1/2} solely due to the kinetic barrier at multilayer steps. If the ES barrier is present, the layer-by-layer growth crosses over directly to the unstable regime, with no transient VLDS scaling. However, in simulations up to θ=10^{4} (typical of films with a few micrometers), low temperatures (small R, ε, or P) may suppress the two or three initial regimes, while high temperatures and P∼1 produce smooth surfaces at all thicknesses. These crossovers help to explain proposals of nonuniversal exponents in previous works. We define a smooth film thickness θ_{c} where W=1 and show that VLDS scaling at that point indicates negligible ES barriers, while rapidly increasing roughness indicates a small ES barrier (E_{ES}∼k_{B}T). θ_{c} scales as ∼exp(const×P^{2/3}) if the other parameters are kept fixed, which represents a high sensitivity on the ES barrier. The analysis of recent experimental data in the light of our results distinguishes cases where E_{ES}/(k_{B}T) is negligible, ∼1, or ≪1.

Scaling and width distributions of parity-conserving interfaces

We present an alternative finite-size approach to a set of parity-conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and Dhar in related systems [Phys. Rev. Lett. 73, 2135 (1994)], we circumvent the subdiffusive dynamics and examine close-to-equilibrium aspects of these interfaces by assembling states of much smaller, numerically accessible scales. As a result, roughening exponents, height correlations, and width distributions exhibiting universal scaling functions are evaluated for interfaces virtually grown out of dimers and trimers on large-scale substrates. Dynamic exponents are also studied by finite-size scaling of the spectrum gaps of evolution operators.

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large-scale simulations via binary lattice gases and bit-coded algorithms. We confirm scaling behavior belonging to the two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: β = 0.2415(15) on 2(17) × 2(17) systems, ruling out β = 1/4 suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite-size scaling and a growth exponent α = 0.393(4) is found. Correction-to-scaling-exponent are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behavior of the steady-state scaling function of the interface width.