Smoothening in thin-film deposition on rough substrates

Accessibility of the surface fractal dimension during film growth

Fractal properties on self-affine surfaces of films growing under nonequilibrium conditions are important in understanding the corresponding universality class. However, measurement of the surface fractal dimension has been intensively investigated and is still very problematic. In this work, we report the behavior of the effective fractal dimension in the context of film growth involving lattice models believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. Our results, which are presented for growth in a d-dimensional substrate (d=1,2) and use the three-point sinuosity (TPS) method, show universal scaling of the measure M, which is defined in terms of discretization of the Laplacian operator applied to the height of the film surface, M=t^{δ}g[Θ], where t is the time, g[Θ] is a scale function, δ=2β, Θ≡τt^{-1/z}, β, and z are the KPZ growth and dynamical exponents, respectively, and τ is a spatial scale length used to compute M. Importantly, we show that the effective fractal dimensions are consistent with the expected KPZ dimensions for d=1,2, if Θ≲0.3, which include a thin film regime for the extraction of the fractal dimension. This establishes the scale limits in which the TPS method can be used to accurately extract effective fractal dimensions that are consistent with those expected for the corresponding universality class. As a consequence, for the steady state, which is inaccessible to experimentalists studying film growth, the TPS method provided effective fractal dimension consistent with the KPZ ones for almost all possible τ, i.e., 1≲τ<L/2, where L is the lateral size of the substrate on which the deposit is grown. In the growth of thin films, the true fractal dimension can be observed in a narrow range of τ, the upper limit of which is of the same order of magnitude as the correlation length of the surface, indicating the limits of self-affinity of a surface in an experimentally accessible regime. This upper limit was comparatively lower for the Higuchi method or the height-difference correlation function. Scaling corrections for the measure M and the height-difference correlation function are studied analytically and compared for the Edwards-Wilkinson class at d=1, yielding similar accuracy for both methods. Importantly, we extend our discussion to a model representing diffusion-dominated growth of films and find that the TPS method achieves the corresponding fractal dimension only at steady state and in a narrow range of the scale length, compared to that found for the KPZ class.

Crossover from compact to branched films in electrodeposition with surface diffusion

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G≫1), a detachment probability ε<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_{c} of that layer increases with G but is weakly affected by ε. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_{c}∼G^{γ}, with γ=1/[2(1-ν)]≈0.43, where ν≈0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_{c} can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter ε are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A pseudo-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of ~10⁴ monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.