document: When dominated by surface shadowing mechanisms, the aggregation of vapor particles onto a surface is a complex, non-local phenomenon. In the literature, there have been many attempts to analyze the growth mechanism by means of pure geometrical considerations; i.e., by assuming that vapor particles arrive at the film surface along a single angular direction [38,41]. Continuum approaches, which are based on the fact that the geometrical features of the film (i.e., the nanocolumns) are much larger than the typical size of an atom [42,266,267], have been also explored. For instance, Poxson et al. [228] developed an analytic model that takes into account geometrical factors as well as surface diffusion. This model accurately predicted the porosity and deposition rate of thin films using a single input parameter related to the cross-sectional area of the nanocolumns, the volume of material and the thickness of the film. Moreover, in Ref. [39], an analytical semi-empirical model was presented to quantitatively describe the aggregation of columnar structures by means of a single parameter dubbed the fan angle. This material-dependent quantity can be experimentally obtained by performing deposition at normal incidence on an imprinted groove seeded substrate, and then measuring the increase in column diameter with film thickness. This model was tested under various conditions [40], which returned good results and an accurate prediction of the relation between the incident angle of the deposition flux and the tilt angle of the columns for several materials.
extractive_keyphrases: aggregation of vapor particles onto a surface analytic model analyze the growth mechanism atom continuum approaches deposition flux film geometrical considerations geometrical factors geometrical features groove seeded substrate nanocolumns quantitatively describe the aggregation of columnar structures single angular direction surface diffusion surface shadowing mechanisms thin films vapor particles
abstractive_keyphrases: analytical semi-empirical model film surface prediction of the relation between the incident angle of the deposition flux and the tilt angle of the columns