Scaling theory for the growth of amorphous films

Post-Growth Dynamics and Growth Modeling of Organic Semiconductor Thin Films

The ability to control the properties of organic thin films is crucial for obtaining highly performant thin-film devices. However, thin films may experience post-growth processes, even when the most sophisticated and controlled growth techniques such as organic molecular beam epitaxy (OMBE) are used. Such processes can modify the film structure and morphology and, thus, the film properties ultimately affecting device performances. For this reason, probing the occurrence of post-growth evolution is essential. Equally importantly, the processes responsible for this evolution should be addressed in view of finding a strategy to control and, possibly, leverage them for driving film properties. Here, nickel-tetraphenylporphyrin (NiTPP) thin films grown by OMBE on highly oriented pyrolytic graphite (HOPG) are selected as an exemplary system exhibiting a remarkable post-growth morphology evolution consistent with Ostwald-like ripening. To quantitatively describe the growth, the height-height correlation function (HHCF) analysis of the atomic force microscopy (AFM) images is carried out, clarifying the role of the post-growth evolution as an integral part of the whole growth process. The set of scaling exponents obtained confirms that the growth is mainly driven by diffusion combined with the presence of step-edge barriers, in agreement with the observed ripening phenomenon. Finally, the results together with the overall approach adopted demonstrate the reliability of the HHCF analysis in systems displaying post-growth evolution.

Nanostructured surfaces investigated by quantitative morphological studies

The morphology of different surfaces has been investigated by atomic force microscopy and quantitatively analyzed in this paper. Two different tools have been employed to this scope: the analysis of the height-height correlation function and the determination of the mean grain size, which have been combined to obtain a complete characterization of the surfaces. Different materials have been analyzed: SiO(x)N(y), InGaN/GaN quantum wells and Si nanowires, grown with different techniques. Notwithstanding the presence of grain-like structures on all the samples analyzed, they present very diverse surface design, underlying that this procedure can be of general use. Our results show that the quantitative analysis of nanostructured surfaces allows us to obtain interesting information, such as grain clustering, from the comparison of the lateral correlation length and the grain size.

Linear surface roughness growth and flow smoothening in a three-dimensional biofilm model

The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based biofilm model to include affine flow and employ it to analyze the growth of surface roughness of single-species, three-dimensional biofilms. We find linear growth laws for surface geometry in both horizontal and vertical directions and measure the thickness of the active surface layer, which is shown to anticorrelate with roughness. Flow is shown to monotonically reduce surface roughness without affecting the thickness of the active layer. We argue that the rapid roughening is due to nonlocal surface interactions mediated by the nutrient field, which are curtailed when advection competes with diffusion. We further argue the need for simplified models to elucidate the underlying mechanisms coupling flow to growth.

Memory effects in a nonequilibrium growth model

We study memory effects in a kinetic roughening model. For d=1, a different dynamic scaling is uncovered in the memory dominated phases; the Kardar-Parisi-Zhang scaling is restored in the absence of noise. dc=2 represents the critical dimension where memory is shown to smoothen the roughening front (alpha<or=0). Studies on a discrete atomistic model in the same universality class reconfirm the analytical results in the large time limit, while a different scaling behavior shows up for t<tau, with tau being the memory characteristic of the atomistic model. Results can be generalized for other nonconservative systems.

Breakdown of dynamic scaling in surface growth under shadowing

Using Monte Carlo simulations and experimental results, we show that for common thin film deposition techniques, such as sputter deposition and chemical vapor deposition, a mound structure can be formed with a characteristic length scale, or "wavelength" lambda, that describes the separation of the mounds. We show that the temporal evolution of lambda is distinctly different from that of the mound size, or lateral correlation length xi. The formation of a mound structure is due to nonlocal growth effects, such as shadowing, that lead to the breakdown of the self-affinity of the morphology described by the well-established dynamic scaling theory. We show that the wavelength grows as a function of time in a power law form, lambda approximately t(p), where p approximately equals 0.5 for a wide range of growth conditions, while the mound size grows as xi approximately t(1-z), where 1/z varies depending on growth conditions.

The relationship between interface structure, conformality and perpendicular anisotropy in CoPd multilayers

The relationship between the interface structure and perpendicular anisotropy in sputtered Co/Pd multilayers has been investigated using grazing incidence x-ray scattering and vibrating sample magnetometry. Using fits to a self-affine fractal model of the interfaces, the variation in in-plane correlation length, fractal parameter and conformality has been determined as a function of the number of repeats in the Co/Pd bilayers. As the number of interfaces rises, the roughness becomes predominantly non-conformal and the in-plane length scale associated with the roughness increases as a power law with multilayer thickness. It is suggested that the loss of conformality, characterized by a relatively short out-of-plane correlation length, may be the cause of the reduction in anisotropy energy per interface observed for high numbers of bilayer repeats. There is a weak association between fractal parameter and interface anisotropy; a reduction in the fractal dimension of the interface appears to result in a higher surface anisotropy.

Statistical characterization of thermally evaporated rough CaF2 films

Thermal deposition of CaF2 onto a glass substrate creates a nanoscale rough surface. A series of samples with differing nominal CaF2 film thicknesses have been fabricated, and the topography has been investigated using atomic force microscopy. Measured values for the statistical characterization of the samples are presented including the exponents describing the scaling behavior of the surfaces. We find that the roughness exponent alpha=0.88+/-0.03 , the growth exponent beta=0.75+/-0.03 , and the dynamical exponent z=alpha/beta=1.17+/-0.06 . We also measure the multifractal spectra and nearest neighbor height difference probability distribution. The results are consistent with noise dominated by a power-law distribution with exponent mu+1 approximately equal to 4.6. Profilometer measurements were used to determine the porosity phi of the deposited films, which we find to be constant for all film thicknesses with phi approximately 0.46 .

Evidence for power-law dominated noise in vacuum deposited CaF2

We have studied the surface roughness of CaF2 vacuum deposited on glass using atomic force microscopy for film coverages spanning an order of magnitude. We find the roughness exponent alpha=0.88+/-0.03, the growth exponent beta=0.75+/-0.03, and the dynamic exponent z=alpha/beta=1.17+/-0.06. Multifractality is also present, along with power-law behavior in the nearest neighbor height difference probability distribution. The results indicate noise dominated by a power-law distribution with exponent micro+1 approximately 4.6.

Dynamical scaling behavior in two-dimensional ballistic deposition with shadowing

The dynamical scaling behavior in two-dimensional ballistic deposition with shadowing is studied as a function of the angular distribution of incoming particles and of the underlying lattice structure. Using a dynamical scaling form for the surface box number, results for the scaling of the surface fractal dimension are also presented. Our results indicate that, in addition to the usual self-affine universality class corresponding to vertical deposition, there exist at least two additional universality classes characterized by distinct values of the coarsening and roughening exponents p and beta describing the evolution of the lateral feature size and surface roughness with film thickness, as well as the surface fractal dimension D(f). For the case of a uniform angular distribution corresponding to an anisotropic flux, we find p=beta=1 and D(f) approximately 1.7. However, for ballistic deposition with an isotropic flux (corresponding to a "cosine" angular distribution), we find p approximately 2/3 and D(f) approximately 1.5 while the effective roughening exponent beta approximately 0.52-0.64 was found to be slightly lattice dependent. In both cases, anomalous scaling of the height-height correlation function is also observed. In contrast, vertical deposition leads to a self-affine surface with p=2/3, beta=1/3, and D(f)=1. The asymptotic scaling behavior appears to depend on the behavior of the angular distribution at large angles but does not depend on other details. An analysis that clarifies the relationship between the launch angle distribution used in the simulations and the flux distribution is also presented.

Passive random walkers and riverlike networks on growing surfaces

Passive random walker dynamics is introduced on a growing surface. The walker is designed to drift upward or downward and then follow specific topological features, such as hill tops or valley bottoms, of the fluctuating surface. The passive random walker can thus be used to directly explore scaling properties of otherwise somewhat hidden topological features. For example, the walker allows us to directly measure the dynamical exponent of the underlying growth dynamics. We use the Kardar-Parisi-Zhang (KPZ) -type surface growth as an example. The world lines of a set of merging passive walkers show nontrivial coalescence behaviors and display the riverlike network structures of surface ridges in space-time. In other dynamics, such as Edwards-Wilkinson growth, this does not happen. The passive random walkers in KPZ-type surface growth are closely related to the shock waves in the noiseless Burgers equation. We also briefly discuss their relations to the passive scalar dynamics in turbulence.

Growth and Erosion of Thin Solid Films

Thin films that are grown by the process of sputtering are, by and large, quite unlike the smooth, featureless structures that one might expect. In general, these films have a complicated surface morphology and an extended network of grooves and voids in their interiors. Such features can have a profound effect on the physical properties of a thin film. The surface irregularities and the bulk defects are the result of a growth instability due to competitive shadowing, an effect that also plays a role in geological processes such as erosion. For amorphous thin films, the shadow instability can be described by a remarkably simple model, which can be shown to reproduce many important observed characteristics of thin film morphology.