The importance of design in nanoarchitectonics: multifractality in MACE silicon nanowires

Background: Mechanisms of self-assembly/self-organization are fundamental for the emergence of nanoarchitectonic systems composed by elemental units, and it is important to build a theoretical framework for them. Additionally, because the enhanced functionalities of these systems are related to their spatial morphologies, it is necessary to quantify the self-organized design through suited statistical analysis tools. Results: We have investigated the self-assembly bundling process of nanowires fabricated by metal-assisted chemical etching (MACE). First, we have applied theoretical models in order to obtain a quantitative estimation of the driving forces leading to self-assembly. Then, we have studied the surfaces of the nanoarchitectures by means of multifractal analysis. We have found that these systems are not simple monofractals, but that the more complex paradigm of multifractality (different fractal dimensions across different scales) has to be applied to describe their morphology. Conclusion: The multifractal analysis approach has proven its ability to discriminate among different MACE nanoarchitectures. Additionally, it has demonstrated its capacity to measure the degree of homogeneity of these surfaces. Finally, a correlation between the growth conditions and the capacity dimension of the nanowires was obtained.