XPS topofactors: determining overlayer thickness on particles and fibres

We introduce the concept of an XPS 'Topofactor', which can be used in conjunction with the XPS 'Thickogram', to provide overlayer thicknesses on topographic samples of known geometry. The concept is essentially simple; analysis is performed with the sample normal directed towards the XPS analyser, the equivalent planar thickness is calculated from the Thickogram and the Topofactor applied to the result to provide the actual thickness. The Topofactor is thus defined as the ratio of the true overlayer thickness to the apparent overlayer thickness obtained by assuming the sample is ideally planar. Within this paper we describe how Topofactors can be calculated and consider cylinders (fibres) and spheres (particles) in some detail. For spheres, a Topofactor of 0.67 is a useful average value and for cylinders, a Topofactor of 0.79 is useful, (i.e. similar to 2/3 and 4/5, respectively) both values would typically provide overlayer thicknesses within 10% of the actual value. An analytical description of cylindrical and spherical Topofactors to within 1% error is provided which accounts for variations in thickness and relative electron attenuation lengths. The Topofactors are useful for macroscopic and microscopic samples, but not for nanoscopic samples such as nanofibres and nanoparticles. In this case, we provide an analytical model that can predict the relative XPS signals from the core and the shell of nanomaterials to an error that is typically better than 10%. (C) Crown copyright 2009. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.