From depth resolution to depth resolution function: refinement of the concept for delta layers, single layers and multilayers

At present, the definition of the depth resolution, Δz, recommended by the International Union of Pure and Applied Chemistry (IUPAC) and by committee E 42 of the American Society of Testing and Materials (ASTM-E42), is given by the distance over which the change between 16% and 84% of the intensity of the profile at a sharp interface is measured. This definition has a precise physical meaning only for a Gaussian shape of the depth resolution function. With the advances in high-resolution depth profiling during the past decade and the increasing demand for profile reconstruction with monolayer accuracy, the often strongly asymmetric depth resolution functions cannot be represented by Δz with sufficient accuracy. Using the mixing-roughness-information depth (MRI) model for the calculation of sputter depth profiles, it is shown that, for the same Δz, different resolution functions can be obtained with different full width at half-maximum (FWHM) values. The consequences for profiles of delta layers, single layers and multilayers are outlined. Although an exact characterization of the depth resolution in general needs three parameters, characterization with one parameter superior to Δz is the inverse maximum slope of an interface profile or the FWHM of the according depth resolution function.