An analytical model of an effective atomic number, Z eff , for simultaneous calculation of composition and thickness of ®lms on substrates that allows for backscattering processes is presented. Comparison of dependencies of 9(&z) parameters for ®lm elements on electron beam energy, on atomic numbers of a ®lm and a substrate and on ®lm thickness was done. The errors inherent in EPMA have been determined by comparing experimental data obtained on YBa 2 Cu 3 O 7Àx bulk crystals with model calculations. Possibility of EPMA as an effective technique for investigation of spatially inhomogeneous objects was demonstrated by studying the correlation between composition and local superconducting properties (values of critical temperature and critical current) of these ®lms.The discovery of high temperature superconductivity (HTSC) has resulted in the development of the technology of YBa 2 Cu 3 O 7Àx epitaxial ®lms and in different fundamental and applied studies of their structural and electrophysical properties. The prototypes of practically all known planar devices of the microelectronics have been developed on the base of these ®lms. However, it has been found that even the best YBa 2 Cu 3 O 7Àx ®lms contain signi®cant amounts of different defects and are spatially nonuniform in terms of both their electrophysical properties and composition [1±3]. As a result HTSC microelectronics devices degrade fast, and the yield of those suitable for operation is low [4].Thus, a pressing necessity arose to create technology for the production of high quality YBa 2 Cu 3 O 7Àx ®lms and to develop local high accuracy techniques for determining the composition of the multicomponent structures of the ®lm-substrate type. The use of the EPMA technique has de®nite merits compared with other techniques for the analysis: high spatial resolution of analysis ($ 3 mm), precise observation of the analysed place, availability of well-developed techniques for quanti®cation, and also low sensitivity to artefacts. However, the weaknesses of EPMA technique should be noted: (i) low sensitivity of the analysis (b 0.1±0.001 wt.7), (ii) low possibility to ®x the small difference between concentrations (analytical sensitivity), more then 0.1±0.37 at the concentration of several tens of wt.7 (iii) poor in-depth resolution. Moreover, the procedure for determination of the composition of the ®lms of thicknesses smaller than the X-ray generation depth (R x ) (HTSC ®lms are related just to this class of object) are not up to now suf®ciently developed. The present work is a review devoted to our investigations of HTSC YBa 2 Cu 3 O 7Àx epitaxial ®lms and contains a thorough experimental veri®cation on the correlations between composition and local superconducting properties.
Procedure for Determining Composition and Thickness of Films (Z eff Model)In the case when the ionization path of an electron is greater than the ®lm thickness, the use of a model