Fractal character of the distribution of surface potential irregularities in epitaxial n-GaAs (100)

The fractal geometric properties of the relief of the surface potential of a heavily doped n (+)-GaAs (100) wafer are studied by Kelvin's method of atomic force microscopy. The average fractal dimensionalities determined by the triangulation method (D (f) ), the method of horizontal cross sections (D (c) ), and the method of similarity (D (s) ) are rather close to each other, which is indicative of a unified nature of the fractal relief of the surface potential. In general, the fractal dimensionalities determined in the study suggest that the relative arrangement of local irregularities of the potential profile of the heavily doped n (+)-GaAs (100) wafer subjected to chemical and dynamic polishing is similar to the pattern corresponding to the fractal curve known as Serpinsky's napkin. It is found that the fractal irregularities of the potential vary much more gradually than it happens in the twodimensional case: the variations are proportional to linear dimensions to the power 2/D (c) (1 < D (c) < 2) rather than to the square of linear dimensions of the regions under study.