Fractal assessment of thin films deposited by random and ballistic deposition models

Abstract

The fractal scaling properties of the thin films deposited using the random and ballistic deposition models have been studied in this work along with the conventional statistical analysis. Inadequacy of the conventional statistical parameters regardingthe assessment of the growth of surface height profilesis comprehended. The generated height profiles show the expected scaling properties, which designates that the surface profiles do have the statistical self-affine structure. The fractal parameters reveal that the height profiles generated by a random deposition model are slightly anti-persistent and in case of ballistic deposition model, it is Brownian. The roughness exponent calculated from the fractal dimension is verified with the continuum growth equations. Its value for the ballistic deposition model is well-matched with the Kardar-Parisi-Zhang (KPZ) equation and thus, verifies the fractal approach of calculating this exponent. So, determination of the fractal dimension and calculation of roughness exponent from it can tell us the model of surface growth followed during deposition. Also, the present study indicatesthe possibility of investigating underlying growth mechanisms of various real experimental thin film surfaces by comparingthe exponents calculated by fractal assessmentswith the theoretically modeled surfaces.