Modern material science and engineering rely on models based on fundamental laws to link material structure and properties to the many parameters that control the adopted production process. Unfortunately, the full comprehension of the main features characterizing the synthesis of these materials is complicated by the fact that chemical and physical events occur at length scales differing for even some orders of magnitudes. An example well suited to illustrate these aspects is represented by the solid films deposition by means of chemical vapor deposition processes. There, the characteristic length ranges from the nanometers up the centimeters, going by through the microns. The former is the scale at which the chemical phenomena can be described through quantum chemical methods, the latter is that where the overall reactor behavior can be depicted. The meso-scales are instead of interest to describe aspect interesting the collective surface behavior, like the description of the trench filling, the obtained film morphology or the various types of defects formation. Here, different mathematical models suitable to study the mentioned multi-scale phenomena and the hierarchy that can be adopted to their link will be reviewed with particular reference to silicon film deposition processes of interest for the microelectronic industry.
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