Theoretical modelling of X-ray production in thin films characterization with electron probe: Invariant embedding results

Employing the invariant embedding principle, theoretical expressions for the detected characteristic X-ray intensities generated in electron probe microanalysis of thin films are obtained. Characteristic X-ray emission from the elements present in a solid is calculated from the probabilities of the backscattered and transmitted electron trajectories within the film and the substrate. The theoretical expressions mentioned provide for the possibility of developing procedures for microanalysis directly from the experimental results without making approaches for the estimation of the phi(ρz) function. The procedure used permits to calculate the recorded X-rays as a function of incident beam voltage and also as a function of the sample thickness. The method presented here gives the possibility of obtaining calibration curves for thin films and multi-layers. The results obtained are found to agree with experimental ones