F. D. A. Aarao Reis

Effects of grains’ features in surface roughness scaling

We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length rc, from a rapid increase with exponent α1 to a slower increase with exponent α2. The result α1≈1 is explained by the large height differences in the borders of the grains when compared to intragrain roughness, and must not be interpreted as a consequence of a diffusion dominated intragrain dynamics. This exponent shows a weak dependence on the shape and size distribution of the grains, and typically ranges from 0.85 for rounded grain surfaces to one for the sharpest ones. The scaling corrections of exactly solvable models suggest the possibility of slightly smaller values due to other smoothing effects of the surface images. The crossover length rc provides a reasonable estimate of the average grain size in all model systems, including the cases of wide grain size distributions. In Kardar-Parisi-Zhang ...

Roughness exponents and grain shapes.

In surfaces with grainy features, the local roughness w shows a crossover at a characteristic length r(c), with roughness exponent changing from α(1)≈1 to a smaller α(2). The grain shape, the choice of w or height-height correlation function (HHCF) C, and the procedure to calculate root-mean-square averages are shown to have remarkable effects on α(1). With grains of pyramidal shape, α(1) can be as low as 0.71, which is much lower than the previous prediction 0.85 for rounded grains. The same crossover is observed in the HHCF, but with initial exponent χ(1)≈0.5 for flat grains, while for some conical grains it may increase to χ(1)≈0.7. The universality class of the growth process determines the exponents α(2)=χ(2) after the crossover, but has no effect on the initial exponents α(1) and χ(1), supporting the geometric interpretation of their values. For all grain shapes and different definitions of surface roughness or HHCF, we still observe that the crossover length r(c) is an accurate estimate of the grain size. The exponents obtained in several recent experimental works on different materials are explained by those models, with some surface images qualitatively similar to our model films.

Scaling in the crossover from random to correlated growth.

In systems where deposition rates are high compared to diffusion, desorption, and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t0. This crossover is analyzed in lattice models via scaling arguments, with support from simulation results presented here and in other works. We argue that the amplitudes of the saturation roughness and of the saturation time t(x) scale as t0(1/2) and t0, respectively. For models with lateral aggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, we show that t0 approximately p(-1), where p is the probability of the correlated aggregation mechanism to take place. However, t0 approximately p(-2) is obtained in solid-on-solid models with single-particle deposition attempts. This group includes models in various universality classes, with numerical examples being provided in the Edwards-Wilkinson (EW), KPZ, and Villain-Lai-Das Sarma (nonlinear molecular-beam epitaxy) classes. Most applications are for two-component models in which random deposition, with probability 1-p, competes with a correlated aggregation process with probability p. However, our approach can be extended to other systems with the same crossover, such as the generalized restricted solid-on-solid model with maximum height difference S, for large S. Moreover, the scaling approach applies to all dimensions. In the particular case of one-dimensional KPZ processes with this crossover, we show that t0 approximately nu(-1) and nu approximately lambda(2/3), where nu and lambda are the coefficients of the linear and nonlinear terms of the associated KPZ equations. The applicability of previous results to models in the EW and KPZ classes is discussed.

Universality in two-dimensional Kardar-Parisi-Zhang growth

We analyze simulation results of a model proposed for etching of a crystalline solid and results of other discrete models in the (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W(n) of orders n=2,3,4 of the height distribution are estimated. Results for the etching model, the ballistic deposition model, and the temperature-dependent body-centered restricted solid-on-solid model suggest the universality of the absolute value of the skewness S identical with W(3)/W(3/2)(2) and of the value of the kurtosis Q identical with W(4)/W(2)(2)-3. The sign of the skewness is the same as of the parameter lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are absolute value of S=0.26+/-0.01 and Q=0.134+/-0.015. For this model, the roughness exponent alpha=0.383+/-0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605< or =z< or =1.64 and beta=0.229+/-0.005, respectively, which are consistent with the relations alpha+z=2 and z=alpha/beta.

Universal fluctuations in the growth of semiconductor thin films

Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the auto-correlation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse with those of the KPZ class, giving the first experimental observation of KPZ distributions in

Roughness fluctuations, roughness exponents and the universality class of ballistic deposition

2+1

Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

dimensions. Deviations from KPZ values in the long-time estimates of dynamic and roughness exponents are explained by spurious effects of multi-peaked coalescing mounds and by effects of grain shapes. Thus, this scheme for investigating universality classes of growing films advances over the simple comparison of scaling exponents.

Finite-size scaling for random walks on fractals

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 for two models in the 2+1-dimensional Kardar–Parisi–Zhang (KPZ) class and for a model in the 1+1-dimensional Villain–Lai–Das Sarma (VLDS) class. The values obtained from σ provide consistent asymptotic estimates, eventually with smaller finite-size corrections. For the VLDS (nonlinear molecular beam epitaxy) class, we obtain α=0.93±0.01, improving previous estimates. We also apply this method to two versions of the ballistic deposition model in two-dimensional substrates, in order to clarify the controversy in terms of its universality class raised by numerical results and a recent derivation of its continuous equation. Effective exponents calculated from σ suggest that both versions are in the KPZ class. Additional support for this conclusion is obtained by a comparison of the full-roughness distributions of these models and the distribution of other discrete KPZ models.

Scaling in reversible submonolayer deposition

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferromagnetic and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling.

\ensuremath{\gamma}/\ensuremath{\nu},