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

Abstract

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 method (MEM) that allows obtaining in-depth concentration profiles of layered surfaces from nondestructive ARXPS measurements. Numerical experiments were performed on a large series of computer generated, ideal, and error-containing ARXPS data from model depthprofiles with up to four layers and up to eight components. The new algorithm enabled us to reconstruct these depth profiles with a maximum uncertainty of ±20% for layer thickness and of ±30% for composition of the individual layers. Moreover, the new protocol involves an iterative procedure for calculating the IMFP values of the different components, taking into account the actual depth concentration profile of the sample surface under investigation. The new protocol proved to be more powerful than any of the existing algorithms since it has been successfully applied for reconstructing depth profiles with up to eight components.