An analytical approach to ion energy loss distributions capable of simplifying medium energy ion scattering ͑MEIS͒ spectral analysis is presented. This analytical approach preserves the accuracy of recent numerical models that evaluate energy loss effects overlooked by standard calculations based on the Gaussian approximation. Results are compared to first principle calculations and experimental MEIS spectra from 0.2-to 1.5-nm-thick HfO 2 films on Si, supporting the application of this analytical model for proton scattering in the kinetic energy range from 100 to 200 keV. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2918443͔The depth distribution of chemical elements near the surface of solids is of major relevance in many aspects of science and technology. In principle, it can be quantitatively determined on an absolute scale ͑i.e., without reference to standards͒ by using ion scattering. Subnanometric depth resolution can be achieved in near-surface regions through the combined use of high resolution energy analyzers 1 and incident ions with a kinetic energy corresponding to the maximum stopping power of the sample. 2 This setup corresponds to the technique of medium energy ion scattering ͑MEIS͒, 3 which became a natural solution for material characterization in current microelectronics research. 4 Quantitative interpretation of MEIS spectra demands an accurate description of ion energy loss distributions as a function of depth of the backscattering event in the sample. [5][6][7][8][9][10][11] Owing to its simplicity and to its analytical expression, Gaussian ion energy loss distribution functions are used aiming at the high depth resolution that can, in principle, be provided by MEIS. [12][13][14][15][16][17] The use of Gaussian distributions is supported by the central limit theorem, according to which the energy loss is normally distributed if the number of energy loss events ͑atomic collisions͒ is large. 11,18 This condition, however, is not satisfied in the characterization of near-surface, nanoscale structures, where only a small number of energy loss events comes into play. 4,19 A more accurate, stochastic approach to ion energy loss distributions was recently demonstrated 5 to be necessary in this case, which takes into account also electronic excitations of the target atom as obtained from ab initio calculations. However, the computational budget required for these calculations prevents their widespread application to data analysis.In this letter, we propose a semiempirical, analytical solution of the Bothe-Landau equation 11 that can conveniently replace both the Gaussian approximation and the more complete numerical approach of Ref. 5 in data analysis software. The validity of the present analytical energy loss distribution model is verified by comparison with full ab initio simulations 6 and experimental MEIS spectra determined from HfO 2 films on Si in the thickness range from 0.2 to 1.5 nm.It can be shown that for ions interacting with amorphous or polycrystalline targets, the energy los...