Nondestructive Surface Depth Profiles from Angle-Resolved X-ray Photoelectron Spectroscopy Data Using the Maximum Entropy Method. I. A New Protocol

The knowledge of the depth concentration profile of thin-layered surfaces a few nanometers thick is very important for research and applications in microelectronics, corrosion, wear, and tribology. In-depth profiling methods reported in the literature are either destructive (ion sputtering), based on severe approximations (concentration gradients are not taken into account, and electron inelastic mean free paths (IMFPs) are calculated for electrons traveling throughout pure elemental materials) or limited to relatively simple profiles (less than three components and constant IMFPs). A reconstructed depth profile should be consistent with the angle-resolved X-ray photoelectron spectroscopy (ARXPS) data acquired, but transformation of XPS signal intensities vs emission angle into chemical species concentrations vs depth is an ill-posed mathematical problem which requires inversion of a Laplace transform. The main goal of this work was thus to develop a new, iterative protocol based on the maximum entropy me...