Mathematical model for evaluation of surface analysis data by total reflection XRF

The general problem of an electromagnetic wave moving through a stratified medium appears naturally in all the techniques associated with surface anal ysis by total reflection, It is a consequence of the theoretical models tha t describe that describe the physical processes involved in these technique s. This problem has been extensively studied erring to its importance in op tics, The mentioned techniques are known as grazing incidence x-ray fluores cence (GIXRF) and grazing exit x-ray fluorescence (GEXRF). In this work, th e electric field in a stratified medium was calculated using basic mathemat ical tools, The model uses a matrix approach to take advantage of well-know n mathematical results (such as Hessenberg's matrix properties). In this wa y, the model optimizes and facilitates the data analysis in GIXRF measureme nts and GEXRF experiments, The simplicity of the formalism admits approxima tions of the electric field, which allow a better understanding of the expe rimental data in both techniques. The model was used to analyze experimenta l data on silicon wafers with surface layers of different elements, showing excellent results. Copyright (C) 1999 John Wiley & Sons, Ltd.