Invariant embedding approach to microanalysis: Procedure to thin film characterization

Abstract

By the use of invariance principles a procedure to characterize thin films using an electron microprobe is reported. Experimental quantities such as the detected intensities and electron fluxes in the boundaries of a solid system are described by the invariant embedding method. In addition, differential equations are given for the probabilities of the different “destinations” of the electrons inside a solid as functions of the sample thickness. The procedure reported here makes it possible to perform microanalysis without the need of making approaches to estimate the ionization distribution function. The decaying in the energy of the electrons is described by a state ladder model. A few but usual cases for which this method gives fairly good agreement with experimental results are reported. The method seems to be promising to obtain procedures in microanalysis.

Convergence method for calculating solutions to the 3D invariant embedding integro-differential equations describing electron transport processes

“…In this work, the states ladder model described in ref 14 will be used considering five energy states. The energy range of active electrons (i.e.…”

“…Using a simple 1D model, expressions for the detected X-rays characteristic intensities had shown a good performance in the interpretation of experimental data. 13,14 .…”

The method of convergence to calculate particles fluxes in X rays spectrometry techniques. Application in nuclear compounds

“…The states ladder model and MC were are described in previous reports [25]. Basically, after impinging with energy E0, electrons can suffer two kinds of interactions: elastic or inelastic.…”

“…In the last two decades a few authors demonstrated the efficiency of the Invariant Embedding (IE) method to describe the scattering of electrons inside a solid sample [20][21][22][23][24][25][26][27].…”

Application of the electron probe microanalysis in nitride‐based heterostructures investigation

“…One of popular techniques used in modern material science is electron probe microanalysis (EPMA) which is frequently used in scanning electron microscopes. However, this technique is overwhelmingly used for analysis of bulk samples or thick films (∼500 nm) 1–3.…”