RECONSTRUCTION OF THE DEPTH PROFILE FROM ANGLE-RESOLVED AES XPS

The effects of elastic scattering on the information available from angle-resolved electron spectroscopies on non-crystalline materials is studied. These effects force the consideration of elastic scattering cross-sections which are dependent on atomic concentration and therefore on depth. This is done by discretizing the transport equation within a two-stream/transport approximation. The variation of inelastic mean free paths with composition is also included. It is also pointed out that, in addition to the ill-conditioning problems and the possible numerical non-uniqueness, the inversion of the Laplace transform required for reconstruction of the depth profile introduces a second analytical non-uniqueness. it is suggested that the reconstruction of the depth profile should be performed using a high-energy peak to obtain an approximate depth profile (large inelastic mean free path, high depth penetration) and that the full quantification should be performed on a low-energy peak (small inelastic mean free path, low depth penetration).