Elastic and inelastic mean free paths for scattering of fast electrons in thin-film oxides

Quantitative transmission electron microscopy (TEM) often requires accurate knowledge of sample thickness for determining defect density, structure factors, sample dimensions, electron beam and X-ray photons signal broadening. The most common thickness measurement is by Electron Energy Loss Spectroscopy which can be applied effectively to crystalline and amorphous materials. The drawback is that sample thickness is measured in units of Inelastic Mean Free Path (MFP) which depends on the material, the electron energy and the collection angle of the spectrometer. Furthermore, the Elastic MFP is an essential parameter for selecting optimal sample thickness to reduce dynamical scatterings, such as for short-range-order characterization of amorphous materials. Finally, the Inelastic to Elastic MFP ratio can predict the dominant mechanism for radiation damage due to the electron beam. We implement a fast and precise method for the extraction of inelastic and elastic MFP values in technologically important oxide thin films. The method relies on the crystalline Si substrate for calibration. The Inelastic MFP of Si was measured as a function of collection semi-angle (β) by combining Energy-Filtered TEM thickness maps followed by perpendicular cross-sectioning of the sample by Focused-Ion-Beam. For example, we measured a total Inelastic MFP (β∼157 mrad) in Si of 145 ± 10 nm for 200 keV electrons. The MFP of the thin oxide films is determined by their ratio at their interface with Si or SiO₂. The validity of this method was verified by direct TEM observation of cross-to-cross sectioning of TEM samples. The high precision of this method was enabled mainly by implementing a wedge preparation technique, which provides large sampling areas with uniform thickness. We measured the Elastic and Inelastic Mean Free Paths for 200 keV and 80 keV electrons as a function of collection angle for: SiO₂ (Thermal, CVD), low-κ SiOCH, Al₂O₃, TiO₂, ZnO, Ta₂O₅ and HfO₂. The measured MFP values were compared to calculations based on models of Wenzel, Malis and Iakoubovskii. These models deviate from measurements by up to 30%, especially for 80 keV electrons. Hence, we propose functional relations for the Elastic MFP and Inelastic MFP in oxides with respect to the mass density and effective atomic number, which reduce deviations by a factor of 2-3. In addition, the effects of sample cooling on the measurements and sample stability are examined.