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) from ARXPS or ARAES measurements have been published over the last decade, ranging from simple least-squares fitting to the Tikhonov Regularization and Maximum Entropy methods. We review all of the published computerised methods, and show how they are related, with common limitations imposed by the low information content of ARXPS measurements. By application of a sampling model, we show that depth resolution Delta z is limited to about 0.81z; this is a poorer fractional depth resolution than can be routinely achieved by sputter depth-profiling (SDP) in the 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 quantitative estimates of uncertainties, depth resolution and information 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 emission angles for which data is acquired. We deduce the optimum placement of layers to use when least-squares fitting to a ''layer-by-layer'' model and the optimum emission angles to use: 0 degrees, 40 degrees, 55 degrees, 63 degrees, 70 degrees for a weakly elastic scattering specimen such as a polymer, or 0 degrees, 33 degrees, 45 degrees, 54 degrees, 60 degrees for a specimen containing elements of larger atomic number, such as an iron alloy, where elastic scattering is stronger. Provided these optimal conditions are met, all the information present in the data is used to give the CDP. By applying published results on Laplace transform inversion, it is shown that depth resolution can be improved by up to a factor of about 2 by confining the interval over which the CDP is reconstructed.