Numerical study of discrete models in the class of the nonlinear molecular beam epitaxy equation

Abstract

We study numerically some discrete growth models belonging to the class of the nonlinear molecular beam epitaxy equation, or Villain-Lai-Das Sarma (VLDS) equation. The conserved restricted solid-on-solid model (CRSOS) with maximum heights differences H_m=1 and H_m=2 was analyzed in substrate dimensions d=1 and d=2. The Das Sarma and Tamborenea (DT) model and a competitive model involving random deposition and CRSOS deposition were studied in d=1. For the CRSOS model with H_m=1 we obtain the more accurate estimates of scaling exponents in d=1: roughness exponent alpha = 0.94 +- 0.02 and dynamical exponent z = 2.88 +- 0.04. These estimates are significantly below the values of one-loop renormalization for the VLDS theory, which confirms Janssen's proposal of the existence of higher order corrections. The roughness exponent in d=2 is very near the one-loop result alpha=2/3, in agreement with previous works. The moments W_n of orders n=2,3,4 of the heights distribution were calculated for all models and the skewness S = W_3/{W_2}^{3/2} and the kurtosis Q = W_4/{W_2}^{2}-3 were estimated. At the steady states, the CRSOS models and the competitive model have nearly the same values of S and Q in d=1, which suggests that these amplitude ratios are universal in the VLDS class. The estimates for the DT model are different, possibly due to their typically long crossover to asymptotic values. Results for the CRSOS models in d=2 also suggest that those quantities are universal.

10 pages, 11 figures, to appear in Phys. Rev. E

References in corpus (4)

• Universality in two-dimensional Kardar-Parisi-Zhang growth
• Scaling of local interface width of statistical growth models
• Derivation of continuum stochastic equations for discrete growth models
• Universality class of the restricted solid-on-solid model with hopping

Cited by in corpus (23)

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• Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
• Roughness fluctuations, roughness exponents and the universality class of ballistic deposition
• Finite-size effects in roughness distribution scaling
• Thin film growth models with long surface diffusion lengths
• Maximal and minimal height distributions of fluctuating interfaces
• Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension
• Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening
• Crossover from compact to branched films in electrodeposition with surface diffusion
• Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces
• Scaling of local roughness distributions
• Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth
• Modeling of nonequilibrium surface growth by a limited mobility model with distributed diffusion length
• Effects of The Ehrlich-Schwoebel Potential Barrier on the Wolf-Villain Model Simulations for Thin Film Growth
• Thin film deposition with time varying temperature
• A Renormalization Scheme and Skewness of Height Fluctuations in $(1+1)$-dimensional VLDS Dynamics
• Kurtosis of height fluctuations in $(1+1)$ dimensional KPZ Dynamics
• Effects of a kinetic barrier on limited-mobility interface growth models
• Transition from compact to porous films in deposition with temperature activated diffusion
• Height distributions in interface growth: The role of the averaging process
• Dimensional crossover in surface growth on rectangular substrates