Fractal and Dendritic Growth of Surface Aggregates

Differential Entropy: An Appropriate Analysis to Interpret the Shape Complexity of Self-Similar Organic Islands

Differential entropy, along with fractal dimension, is herein employed to describe and interpret the shape complexity of self-similar organic islands. The islands are imaged with in situ Atomic Force Microscopy, following, step-by-step, the evolution of their shape while deposition proceeds. The fractal dimension shows a linear correlation with the film thickness, whereas the differential entropy presents an exponential plateau. Plotting differential entropy versus fractal dimension, a linear correlation can be found. This analysis enables one to discern the 6T growth on different surfaces, i.e., native SiO_x or 6T layer, and suggests a more comprehensive interpretation of the shape evolution. Changes in fractal dimension reflect rougher variations of the island contour, whereas changes in differential entropy correlates with finer contour details. The computation of differential entropy therefore helps to obtain more physical information on the island shape dependence on the substrate, beyond the standard description obtained with the fractal dimension.

Two-Dimensional to Three-Dimensional Growth of Transition Metal Diselenides by Chemical Vapor Deposition: Interplay between Fractal, Dendritic, and Compact Morphologies

We investigate the role of growth temperature and metal/chalcogen flux in atmospheric pressure chemical vapor deposition growth of MoSe₂ and WSe₂ on Si/SiO₂ substrates. Using scanning electron microscopy and atomic force microscopy, we observe that the growth temperature and transition metal flux strongly influence the domain morphology, and the compact triangular or hexagonal domains ramify into branched structures as the growth temperature (metal flux) is decreased (increased). The competition between adatom attachment to the domain edges and diffusion of adatoms along the domain boundary determines the evolution of the observed growth morphology. Depending on the growth temperature and flux, two different branched structures-fractals and dendrites-grow. The fractals (with a dimension of ∼1.67) obey a diffusion-limited aggregation mechanism, whereas the dendrites with a higher fractal dimension of ∼1.80 exhibit preferential growth along the symmetry-governed directions. The effect of chalcogen environment is studied, where a Se-rich condition helps restrict Mo-rich nucleus formation, promoting lateral growth. For a Se-deficient environment, several multilayer islands cluster on two-dimensional domains, suggesting a transition from lateral to vertical growth because of insufficient Se passivation. X-ray photoelectron spectroscopy analysis shows a near perfect stoichiometry (Mo/Se = 1:1.98) of MoSe₂ grown in a Se-rich environment, whereas in the Se-deficient condition, a ratio of Mo/Se = 1:1.68 is observed. This also supports the formation of metal-rich nuclei (Mo_1+xSe_2-x) under Se-deficient conditions, leading to three-dimensional clustering. Tuning the growth temperature and metal/chalcogen flux, we propose an optimized CVD growth window for synthesizing large-area Mo(W) selenide.

Two-dimensional growth of dendritic islands of NTCDA on Cu(001) studied in real time

The success of future organic electronic devices distinctively depends on the electronic and geometric properties of thin organic films. Although obviously these properties are strongly influenced by the growth mechanisms, real time growth studies are relatively rare since not many experimental techniques exist that allow in situ studies in ultra high vacuum. In this context, we investigated the prototypical system 1,4,5,8-naphtalene-tetracarboxylic-dianhydride (NTCDA) on Cu(001). We used low-energy electron microscopy (LEEM) for the real-time growth study, and a variety of other techniques for investigating the geometric and electronic structure. While for similar model systems well known and well characterized growth modi occur (e.g., compact, well ordered islands or disordered, gas-like layers), for NTCDA/Cu(001) we observe the growth of dendrite-like, fractal structures. The dendritic structures arise from a strongly preferred one-dimensional growth mode forming a long-range ordered network of thin molecular chains spanning over the entire surface already at small coverages. Later in the growth process, the voids in the network structure are incrementally filled. These results are very unexpected for such a simple adsorbate system consisting of well investigated components, the properties of which were believed to be already well understood. We explain this unexpected behavior by a dendritic growth model that is supported by energetic arguments based on pair-potential calculations. These calculations give reason for the experimentally observed growth of one-dimensional structures, and therefore represent the key to a semi-quantitative understanding of this dendritic growth mode.