Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions

A simple model of epitaxial growth proposed by Wolf and Villain is investigated using extensive computer simulations. We find an unexpectedly complex crossover behavior of the original model in both 1+1 and 2+1 dimensions. A crossover from the effective growth exponent $\beta_{\rm eff}\!\approx\!0.37$ to $\beta_{\rm eff}\!\approx\!0.33$ is observed in 1+1 dimensions, whereas additional crossovers, which we believe are to the scaling behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1 dimensions. Anomalous scaling due to power--law growth of the average step height is found in 1+1 D, and also at short time and length scales in 2+1~D. The roughness exponents $\zeta_{\rm eff}^{\rm c}$ obtained from the height--height correlation functions in 1+1~D ($\approx\!3/4$) and 2+1~D ($\approx\!2/3$) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.Comment: 11 pages, REVTeX 3.0, IC-DDV-93-00

Kinetic modelling of epitaxial film growth with up- and downward step barriers

The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We generalize this concept in a solid-on-solid growth model, in which a barrier dependent on the particle coordination (number of lateral bonds) exists whenever the particle performs an interlayer diffusion. The rules do not distinguish explicitly if the particle is executing a descending or an ascending interlayer diffusion. We show that the usual model, with a step barrier in descending steps, produces spurious, columnar, and highly unstable morphologies if the growth temperature is varied in a usual range of mound formation experiments. Our model generates well-behaved mounded morphologies for the same ES barriers that produce anomalous morphologies in the standard model. Moreover, mounds are also obtained when the step barrier has an equal value for all particles independently if they are free or bonded. Kinetic roughening is observed at long times, when the surface roughness w and the characteristic length $\xi$ scale as $w ~ t^\beta$ and $\xi ~ t^\zeta$ where $\beta \approx 0.31$ and $\zeta \approx 0.22$, independently of the growth temperature.Comment: 15 pages, 7 figure

Damping of Growth Oscillations in Molecular Beam Epitaxy: A Renormalization Group Approach

The conserved Sine-Gordon Equation with nonconserved shot noise is used to model homoepitaxial crystal growth. With increasing coverage the renormalized pinning potential changes from strong to weak. This is interpreted as a transition from layer-by-layer to rough growth. The associated length and time scales are identified, and found to agree with recent scaling arguments. A heuristically postulated nonlinear term $\nabla^2 (\nabla h)^2$ is created under renormalization.Comment: 17 Pages Late

Kardar-Parisi-Zhang Universality, Anomalous Scaling and Crossover Effects in the Growth of Cdte Thin Films

We report on the growth dynamic of CdTe thin films for deposition temperatures ($T$) in the range of 150\,^{\circ}\mathrm{C} to 300\,^{\circ}\mathrm{C}. A relation between mound evolution and large-wavelength fluctuations at CdTe surface has been established. One finds that short-length scales are dictated by an interplay between the effects of the formation of defects at boundaries of neighbouring grains and a relaxation process which stems from the diffusion and deposition of particles (CdTe molecules) torward these regions. A Kinetic Monte Carlo model corroborates these reasonings. As $T$ is increased, the competition gives rise to different scenarios in the roughening scaling such as: uncorrelated growth, a crossover from random to correlated growth and transient anomalous scaling. In particular, for T = 250\,^{\circ}\mathrm{C}, one shows that surface fluctuations are described by the celebrated Kardar-Parisi-Zhang (KPZ) equation, in the meantime that, the universality of height, local roughness and maximal height distributions for the KPZ class is, finally, experimentally demonstrated. The dynamic of fluctuations at the CdTe surface for other temperatures still is described by the KPZ equation, but with different values for the superficial tension ($\nu$) and excess of velocity ($\lambda$). Namely, for T = 150\,^{\circ}\mathrm{C} one finds a Poissonian growth that indicates $\nu = \lambda = 0$. For T = 200\,^{\circ}\mathrm{C}, however, a Random-to-KPZ crossover is found, with $\lambda > 0$ in the second regime. Finally, for films grown at T = 300\,^{\circ}\mathrm{C}, one demonstrates that a KPZ growth with $\lambda < 0$ takes place. We discuss the different mechanisms leading to KPZ scaling which depend on $T$, and conjecture the behavior of the phenomenological parameter $\lambda$ as function of the deposition temperature.Comment: 117 pages, 46 figures, Dissertation Thesi

Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension

We report local roughness exponents, $\alpha_{\text{loc}}$, for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval $\alpha_{\text{loc}}\in[0.96,0.98]$ consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form $\alpha_{\text{loc}}=1-\epsilon$ of the one-loop renormalization group analysis of the VLDS equation