Influence of nano-sized horizontal inhomogeneities on surface profiling by means of XPS

Quantitative analysis of thin films surface is performed by means of X-ray electron spectroscopy (XPS) according to a calculation model assuming surface layers of the target to be homogeneous and parallel. However, almost every surface of an ultra-thin film is rough. A study of such surface using the plane-parallel layer model will lead to incorrect results. This work proposes to use the model of inhomogeneous stochastic nano-structured surface layer for ultra-thin film profiling. Surface stochastic nano-structured inhomogeneities are described by the normal Gauss distribution function. To determine these inhomogeneities, three parameters are specified: dispersion (spread of thicknesses by the layer), mean and maximal thickness of the surface layer. For the first time, the type of X-ray photoelectron spectrum of an inhomogeneous stochastic nano-structured surface is found that is determined by functions of photoelectron production and transmission through that surface layer. The designed model is based on the following assumptions: photoelectrons are produced in substance and travel straight-forward (Straight Line Approximation) along the surface, photoelectron flux density decreases in the layer according to the Bouguer–Lambert law, photoelectrons of different energies lose energy differently, photoelectron energy losses in bulk and on surface differ. Modeling of X-ray photoelectron spectra of an oxidized metal film is performed using different models: homogeneous plane-parallel layers, an island nano-structured surface layer and an inhomogeneous stochastic nano-structured surface layer. Ranges of applicability of plane-parallel layer models and simple periodical nano-structured island surface layer for inhomogeneous stochastic nano-structured surface profiling are determined. The model of homogeneous plane-parallel layers shows satisfactory profiling results by some values of parameters of an inhomogeneous stochastic surface layer. It is shown that the model of a simple periodically nano-structured island layer leads to inadequate results by profiling of an inhomogeneous stochastic surface. The investigation shows that for more accurate profiling of an inhomogeneous ultra-thin film, it is necessary to consider inhomogeneity of a real surface, otherwise the calculated results would not match the true profile.