Iso-height lines of multifractal etched silicon rough surfaces

Morphology of etched silicon wafers during anisotropic etching process is investigated utilizing the geometrical exponents of iso-height contour lines. The images obtained from field emission scanning electron microscopy show pyramidal microstructures which disappear in large time scales and porous silicon structures are formed. The morphology of these microstructures is investigated utilizing the data obtained from atomic force microscopy and contour loop analysis. The results show that the anisotropic etching breaks the up-down symmetry in the height fluctuations of etched silicon surfaces. Area of the contour loops increases by enhancement of pyramids sizes. Fractal dimensions of the loops decrease at the beginning of etching process. Distributions of loops and geometrical exponents of iso-height lines in different etching times are determined. The results indicate that in spite of asymmetry in the height fluctuations, the hyperscaling relation and Zipf's law are verified for the multi-affine silicon surfaces during etching process.