Simulation And Modelling Of Thin Film Phi(rho-z) Curves For Electron Probe Microanalysis

Abstract

Quantitative analysis of homogeneous bulk unknowns using an electron probe microanalyzer requires the accurate knowledge of the depth distributions of x-ray production ({dollar}\phi{dollar}({dollar}\rho{dollar}z) curves). Straight line behaviour is observed in the plot of ln{dollar}\phi{dollar}({dollar}\rho{dollar}z) versus ({dollar}\rho{dollar}z){dollar}\sp2{dollar} for most experimentally measured data. Monte Carlo calculations can be used to simulate {dollar}\phi{dollar}({dollar}\rho{dollar}z) curves. However, ln {dollar}\phi{dollar}({dollar}\rho{dollar}z) versus ({dollar}\rho{dollar}z){dollar}\sp2{dollar} plots of these {dollar}\phi{dollar}({dollar}\rho{dollar}z) curves, in general, are nonlinear and concave downward. By introducing the concept of electron straggling into a multiple scattering Monte Carlo model, agreement with the behaviour of experimental curves is achieved.;Electron probe microanalysis can also be used for the characterization of thin films on substrates. The multiple scattering Monte Carlo program was used to simulate more than 300 thin film {dollar}\phi{dollar}({dollar}\rho{dollar}z) curves with different film/substrate combinations. The simulations were made at normal electron incidence in the energy range from 10-30 keV. Using these data and based on the concept of the ratio of {dollar}\phi{dollar}({dollar}\rho{dollar}z) values from the thin film to the corresponding bulk {dollar}\phi{dollar}({dollar}\rho{dollar}z) value at the same thickness, general equations were developed which allow prediction of thin film {dollar}\phi{dollar}({dollar}\rho{dollar}z) curves for any film/substrate combination at any electron energy. The equations can used with any bulk {dollar}\phi{dollar}({dollar}\rho{dollar}z) model. Comparisons were made with literature values of measured k-ratios in order to confirm the validity of the present model

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