Thickness determination of uniform overlayers on rough substrates by angle-dependent XPS

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 SiO2Si and AuSi system show that the errors strongly depend on off-axis angle, ranging from −50% to +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.