Multifractal analysis of SiO 2 surface embedded with Ge nanocrystal

In the present article SiO 2 /Si layers of thickness 200 nm were implanted with 150 keV Ge ions with different fluences varying from 2.5 × 10 16 to 7.5 × 10 16 ions/cm 2 . The implantation-induced disorder was removed via high temperature annealing method in Ar ambience. Transmission electron microscopy (TEM) measurement confirmed the presence of embedded Ge nanocrystals of 5–10 nm size in annealed samples. Topographical studies of implanted as well as annealed samples were captured by the atomic force microscopy (AFM) and parameters such as average roughness and interface width were extracted. Two dimensional multifractal detrended fluctuation analysis (2D-MFDFA) based on the partition function approach was used to study the surfaces of ion implanted and annealed samples. The partition function is used to calculate generalized Hurst exponent with the segment size. A nonlinear variation with moment is observed for generalized Hurst exponents, leading to the multifractal nature. The multifractality of surface is pronounced after annealing for the surface implanted with fluence of 7.5 × 10 16 ions/cm 2 .