SURFACE AND INTERFACE ANALYSIS, VOL. 20. 719_726 ft993\ Dielectric Loss Functionof Si and SiO2 from Quantitative Analysis of REELS Spectra F. Yubero,l S. Tougaard,2 E. Elizaldel and J. M. Sanzl I Departamento de Fisica Aplicada C-XII, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain 2 Fysisk Institut, Odense University, DK 5230 Odense M, Denmark A recently proposed model for quantitative analysis of reflection electron energy-loss spectra (REELS) has been applied to evaluate the dielectric loss function of Si and SiO, in the 4-1fi) eV energy range, and to determine inelastic scattering properties for these materials for low-energy electrons (500-10m0 eV). Appropriste trial energy-loss functions (i.e. Im{l/e}) are used and the best loss function is found from the criterion that a satisfactory quantitative agreemeot is obtained between tbe simulated and experimental inelastic scattering cross-sections at several primary electron energies.The fact that the energyJoss functions determined in this work agree remarkably well with optical data gives some confidence in the applied procedure. In addition, the effective inelastic mean free paths of the electrons as a function of tbe primary energy and the path travelled inside tbe medium hsve also been determined in terms of the respectiveenergyJoss functions. INTRODUCTION The main purpose of this paper is to apply a recently proposed modelr for quantitative analysis of reflection electron energy-loss spectra to evaluate the dielectric function of solids and to determine the inelastic scat- tering properties of low-energy electrons (500 eV < Eo < 10000 eV) in Si and SiOr. Reflection electron energyJossspectroscopy (REELS) has attracted a great deal of interest as a method to evaluate inelastic scattering cross-sections for low- energy electrons.2-ro In general, it is accepted that the dielectric formulation provides a useful approach to the problem. In practice, however, the lack of realistic models that include surface and momentum transfer effects has handicapped its quantification. In the pasta-8 several attempts were performed based on the idea that REELS spectra could be considered as a linear com- bination of the surface and bulk energy-lossfunctions, whose relative importance could be modulated by changing the primary electron energy and the experi- mental geometry. The validity of this assumption has been questioned and it has been shownrl that a mean- ingful description of a REELS experiment cannot be obtained with such a simple linear combination. A model that takes into account the physical pro- cesses occurring in a REELS experiment was recently proposed.r It includes surface effects, the interference between the field set up by the incoming electron on the outgoing electron and the momentum transfer during the inelastic scattering processes. Within this model, the inelastic scattering cross-sectioncan be expressed as a function of the energy of the primary electrons if the dielectric function e(o) is known. In fact, the model has been applied successfully to the determination of inelas- tic cross-sections of a large variety of metals in a wide ot42-2421 l93l0807l9 08 $09.00 O 1993 by John Wiley & Sons, Lrd. range of primary electron energies,r making use of optical data for e(ro). In this paper, experimental REELS spectra of Si and SiO2 are analysed quantitatively according to the above-mentionedmodelr and inelastic scattering cross- sectionsfor severalprimary electron energies are deter- mined. Furthermore, the model has been used to evaluate the dielectric loss function (i.e.Im{lie(rr;)}) bV a trial-and-error procedure that finishes when a satisfac- tory quantitative agreement is reached between the experimental and calculated cross-sectionsat several primary electron energies. This procedure was suggested in Ref. 1, but its applicability is demonstrated in this paper for both Si and SiOr. The corresponding effective inelastic mean free paths for different paths travelled by the electron were also calculated for several primary electron energies. The limits of the applicability of the model are also discussed. THEORETICAL DETERMINATION OF THE INELASTIC SCATTERING CROS$SECTION According to Ref. 1, the effective inelastic scattering cross-section K"rr(Eo , hot,x) for an electron travelling in a REELS geometry can be calculated within a dielectric response formalism, K.rr(Eo , ha, x) is defined as the average probability that an electron shall lose energy ha per unit energy loss and per unit path length after being backscatteredat depth xl2. The model considers an electron with energy Eo and velocity u coming lrom the vacuum normal to the surface of a semi-infinite medium, characterized by a dielectric function e(k,a). The electron is supposedto have an elastic backscatter- ing event at the depth xl2: c, going back to the vacuum through the same path. Then, the effective inelasticcross-section is given byr Receiued 17 Nouember 1992 Accepted 9 February 1993