Theoretical analysis of the atomic force microscopy characterization of columnar thin films

In this paper, the theoretical analysis of the influence of finite linear dimensions of an atomic force microscope tip on profiles of the upper boundaries of columnar thin films and their statistical quantities is performed. This analysis is based on a numerical evaluation of the main statistical quantities, i.e. the standard deviations of the heights and slopes, one-dimensional distributions of the probability density of heights and slopes and power spectral density function, corresponding to a simulated columnar structure of the thin films. It is shown that the strongest misrepresentation of the measured profiles of the upper boundaries of the columnar films originates in the cases when the linear dimensions of the columns are smaller or comparable with the linear dimensions of the tip. Further, it is shown that using a surface reconstruction procedure one can correct (improve) the boundary profiles and their statistical quantities partially. The results of this analysis enable us to perform rough estimation of the errors achieved within atomic force microscopy studies of the real columnar thin films. Moreover, these results allow to estimate the corrections of the statistical quantities mentioned above to be obtained using the surface reconstruction.