Determination of Energy Loss Functions for GaN, GaP, and GaSb by Angle-resolved Electron Energy Loss Spectroscopy with Factor Analysis: Applications to Electron Transport Parameter Calculations

We measured a series of energy loss spectra (ELS) for GaN, GaP, and GaSb using a 4500 eV primary electron beam over an energy loss range of 1 to 50 eV with angle-resolved reflection electron energy loss spectroscopy. From these ELS data and atomic scattering factors in the range of 50 eV to 30 keV, the energy loss function (ELF) within the range of 1 eV to 30 keV was determined by applying factor analysis and the Kramers-Kronig sum rule. Key results include the identification of various energy loss structures, such as plasmon peaks and band gaps, the derivation of the real and imaginary components of the dielectric function, refractive index, and extinction coefficient. These results were compared with existing experimental and theoretical data, showing consistent trends and providing new insights. The motivation for this study stems from the lack of detailed optical constants for III-V semiconductors in this energy range, which are critical for the analysis of electronic structure and chemical states by X-ray photoelectron and Auger electron spectroscopy. We also calculated and reported two electron transport parameters: inelastic mean free paths (IMFPs) and collision stopping powers (SPs) for GaN, GaP, and GaSb in the energy range of 50 eV to 30 keV. These values were derived from the resulting ELFs using the full Penn algorithm with band gap correction. The IMFP values calculated from the obtained ELF were well-fitted to the energy range of 50 eV to 30 keV using the modified Bethe equation, with a root mean square (RMS) deviation of less than 1%. Moreover, the RMS deviation between the IMFP values calculated in this study and those predicted by the general Jablonski-Tanuma-Powell equation [A. Jablonski et al., Surf. Interface Anal. 55, 609 (2023)] was less than 4% for the three compounds analyzed within the same energy range. Using the mean excitation energy (MEE) values derived from the obtained ELF, the SP was calculated based on the relativistic Bethe SP equation. A comparison showed that the difference between the two values was approximately 5% in the energy range of 2 to 30 keV. Based on these findings, we have proposed a new fitting function derived by extending the relativistic Bethe SP equation to describe the energy dependence of SP over a wide range from 50 eV to 30 keV. By applying this fitting function, the SP values for the three compounds examined in this study could be reproduced with an RMS deviation of less than 3% across the energy range of 50 eV to 30 keV using four parameters.