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Angle-dependent XPS thickness determinations of thin overlayers are often based on a simple model assuming a perfectly flat substrate. In this paper we analyze the errors involved in applying this method to uniform overlayers on rough substrates. The analysis is based on an algorithm for simulation of fractional Brownian motion to model substrate roughness and on a Monte Carlo method for electron trajectory simulation. Calculations for a SiO,/Si and Au/Si system show that the errors strongly depend on off-axis angle, ranging from -SO% to i.50% and more. At _ 35", however, the error is remarkably small, and even negligible compared to errors caused by neglecting elastic scattering. Atomic Force Microscopy and XPS measurements on a roughened silicon wafer confirm these findings.

Investigating the effect of a cleaner (used to remove lubrication oil residues) on the surface composition of rolled aluminium foils, we applied angledependent XPS to determine the thickness of the passivation layer on these foils. We found the simple uniform overlayer model, which bas frequently been applied to translate XPS intensity ratios into a value for the overlayer thickness, to be inapplicable on these aluminium foils. However, data obtained from an Si(100) singlecrystal surface were in rather good agreement with the model. SEM images from the aluminium foils show that their surface is rough on the (sub)micron scale. We believe this roughness to be the reason for the inapplicability of the uniform overlayer model. Simulations of XPS intensity ratios for model rough surfaces support this point of view. Both experiment and simulations make it clear that one should not base XPS thickness determinations on one measurement only, because in that case the applicability of the uniform overlayer model cannot be checked.

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Thickness determination of uniform overlayers on rough substrates: A comparison of calculations for Al2O3/Al to x-ray photoelectron spectroscopy and atomic force microscopy experiments on technical aluminium foils.