Semi-empirical derivation of the physical approximants to a-CN:H film deposition

An extremely simplified picture of the film deposition process is demonstrated by a semi-empirical application of the Π theorem of dimensional analysis. The growth of hydrogenated carbon-nitrides (a-CN:H) by reactive sputtering is considered as an example and elementarily modelled. By theoretically deriving a scaling law for the microscopic variables involved, a single dimensionless combination of the deposition parameters is generated, providing the rules according to which the growth conditions can be changed without significantly modifying the film nanostructure and stoichiometry. The physical laws governing the process are approximated through analytical functions of this combination, able to effectively account for the compositional and structural changes described by the evolution of the Raman spectra of the films. These functions, theoretically deduced from very simple models, are empirically demonstrated by fitting the experimental data. The efficacy of the proposed method, applicable to all materials and deposition techniques, is here shown for a given variation range of the growth conditions.