For the calculation of X-ray intensities emitted by elements present in multi-layer systems it is vital to have an accurate knowledge of the x-ray ionization vs. mass-depth (ϕ(ρz)) curves as a function of accelerating voltage and atomic number of films and substrate. Once this knowledge is available the way is open to the analysis of thin films in which both the thicknesses as well as the compositions can usually be determined simultaneously.Our bulk matrix correction “PROZA” with its proven excellent performance for a wide variety of applications (e.g., ultra-light element analysis, extremes in accelerating voltage) has been used as the basis for the development of the software package discussed here. The PROZA program is based on our own modifications of the surface-centred Gaussian ϕ(ρz) model, originally introduced by Packwood and Brown. For its extension towards thin film applications it is required to know how the 4 Gaussian parameters α, β, γ and ϕ(o) for each element in each of the films are affected by the film thickness and the presence of other layers and the substrate.
Error covariance matrix correction based approach to functional coefficient regression models with generated covariates