Improvements of the Gaussian expression for Phi(rho z) curves

GUSTAVO CASTELLANO; SILVINA SEGUI; JORGE TRINCAVELLI

Barcelona, España

Workshop; 3rd EMAS Regional Workshop; 1998

European Microbeam Analysis Society

The depth distribution of ionizations produced by a collimated electron beam imping-ing on a semi-innite sample is of great interest in electron probe microanalysis, since itallows to relate elementary concentrations with x-ray detected intensities. This distribu-tion is referred to as Phi(rho z), where rho z is the mass depth. Based on the assumption of arandom walk for the electrons travelling within the sample, Packwood and Brown [1] de-veloped a Gaussian model for Phi(rho z) which has shown a good agreement with the behaviourof experimental data:\phi(\rho z)~=~\exp[-\alpha^2 (\rho z)^2] (\gamma - (\gamma - \phi_o) \exp[-\beta \rho z])The four parameters , alpha, beta, gamma and phi_o have been deduced by dierent authors either by theoretical or empirical methods [1, 2, 3, 4]. In a previous paper [5] the parameter gamma was related to the probability of nding the electron at the sample surface after a large number of steps in the random walk approach. The derived model has a good performance in thedescription of Phi(rho z) curves, according to Monte Carlo and experimental data, except forlow atomic numbers Z and high overvoltages Uo. The aim of the present work is toovercome this inconvenience extending the results (obtained for K and L shells) to M shells, as well as to give a complete description for the Phi(rho z) function.Regarding the gamma parameter, a factor depending on Z, Uo and the atomic shell is pro-posed to correct the wrong behaviour mentioned above. In addition, a parameterizationof beta has been formulated, also in terms of Z, Uo and the atomic shell. These developmentswere made by fitting to a large Monte Carlo Phi(rho z) database.The obtained expressions, together with the alpha model given by Packwood and Brown [1]and a model for Phi_o presented in a previous paper [4], were used to evaluate Gaussian Phi(rho z) curves in dierent cases. Comparisons with experimental and Monte Carlo data show agood performance of the complete expression to describe Phi(rho z) function.