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.

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In this work, we report on a model that describes the microscopic electrical transport as a transmission problem using the invariant embedding technique. Analytical expressions for the transport coefficients under non-steady-state conditions are derived allowing us to calculate carrier concentration and time-dependent conductivity. Employing measurable magnitudes, our theoretical results allow us to determine defect concentrations, carrier generation rates, cross sections of recombination, and capture by traps. This model can be employed to study the conduction processes of semiconductors and test their band and defect structure. In particular, time-dependent photoconductivity measurements of a ZnO microwire have been well fitted using our model indicating a relevant role of intrinsic point defects in this material.