Fractal analysis of hillocks: A case of RF sputtered aluminum thin films

Abstract

A monofractal and multifractal approach on quantification of hillocks on Al thin films deposited on glass substrates at a varying substrate temperature (Ts) has been reported in this work. The relationship between the fractal characteristics and mechanical properties of the hillocks are established. The lowest density and dimensions of hillocks were obtained at 95 °C while the highest at 65 °C. A power law relationship (with fractal dimension (D) as the power) is established between the perimeter and areas of the individual hillocks with a considerably large coefficient of regression (R2 ≈ 0.9) for all the temperatures. The fractal examinations of the segmented hillock structures revealed that these structures exhibit multifractal characteristics. The line profiles from optical profiling images of the hillock-dominant regions revealed non-uniform sinusoids which further confirm the fractal nature of these structures. The deformation mechanism of the hillocks under normal nanoindentation loading was described by evaluating the indentation impression against the nanoindentation curves.