In the present article SiO₂/Si layers of thickness 200 nm were implanted with 150 keV Ge ions with different fluences varying from 2.5 × 10¹⁶ to 7.5 × 10¹⁶ ions/cm². 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 × 10¹⁶ ions/cm².

在本文中，在200 nm的SiO ₂ / Si层中注入了150 keV Ge离子，其通量范围从2.5×10 ¹⁶到7.5×10 ¹⁶ 离子/ cm ²不等。。通过氩气氛中的高温退火方法去除了由注入引起的无序。透射电子显微镜（TEM）测量确认退火样品中存在5-10 nm尺寸的嵌入Ge纳米晶体。通过原子力显微镜（AFM）捕获植入物和退火样品的形貌研究，并提取诸如平均粗糙度和界面宽度之类的参数。基于分配函数方法的二维多重分形去趋势波动分析（2D-MFDFA）用于研究离子注入和退火样品的表面。分区函数用于计算带有段大小的广义Hurst指数。对于广义的赫斯特指数，观察到随力矩的非线性变化，从而导致了多重分形的性质。¹⁶ 离子/ cm ²。