Influence of the atomic force microscope tip on the multifractal analysis of rough surfaces

In this paper, the influence of atomic force microscope tip on the multifractal analysis of rough surfaces is discussed. This analysis is based on two methods, i.e. on the correlation function method and the wavelet transform modulus maxima method. The principles of both methods are briefly described. Both methods are applied to simulated rough surfaces (simulation is performed by the spectral synthesis method). It is shown that the finite dimensions of the microscope tip misrepresent the values of the quantities expressing the multifractal analysis of rough surfaces within both the methods. Thus, it was concretely shown that the influence of the finite dimensions of the microscope tip changed mono-fractal properties of simulated rough surface to multifractal ones. Further, it is shown that a surface reconstruction method developed for removing the negative influence of the microscope tip does not improve the results obtained in a substantial way. The theoretical procedures concerning both the methods, i.e. the correlation function method and the wavelet transform modulus maxima method, are illustrated for the multifractal analysis of randomly rough gallium arsenide surfaces prepared by means of the thermal oxidation of smooth gallium arsenide surfaces and subsequent dissolution of the oxide films. (C) 2004 Elsevier B.V. All rights reserved.