ANGLE-RESOLVED XPS AND AES - DEPTH-RESOLUTION LIMITS AND A GENERAL COMPARISON OF PROPERTIES OF DEPTH-PROFILE RECONSTRUCTION METHODS

Many algorithms for calculating concentration depth profiles (CDPs) fr om ARXPS or ARAES measurements have been published over the last decad e, ranging from simple least-squares fitting to the Tikhonov Regulariz ation and Maximum Entropy methods. We review all of the published comp uterised methods, and show how they are related, with common limitatio ns imposed by the low information content of ARXPS measurements. By ap plication of a sampling model, we show that depth resolution Delta z i s limited to about 0.81z; this is a poorer fractional depth resolution than can be routinely achieved by sputter depth-profiling (SDP) in th e depth range of approximate to 10-500 nm, but better than SDP in the near surface (0 to about 5 nm) region accessible to ARXPS. We derive q uantitative estimates of uncertainties, depth resolution and informati on content. These lead to definite conclusions for the best method of analysis for particular experimental situations. The depth resolution in ARXPS is limited by signal-to-noise ratio, not the number of emissi on angles for which data is acquired. We deduce the optimum placement of layers to use when least-squares fitting to a ''layer-by-layer'' mo del and the optimum emission angles to use: 0 degrees, 40 degrees, 55 degrees, 63 degrees, 70 degrees for a weakly elastic scattering specim en such as a polymer, or 0 degrees, 33 degrees, 45 degrees, 54 degrees , 60 degrees for a specimen containing elements of larger atomic numbe r, such as an iron alloy, where elastic scattering is stronger. Provid ed these optimal conditions are met, all the information present in th e data is used to give the CDP. By applying published results on Lapla ce transform inversion, it is shown that depth resolution can be impro ved by up to a factor of about 2 by confining the interval over which the CDP is reconstructed.