Energy-loss dependence of inelastic interactions between high-energy electrons and semiconductors: a model to determine the spatial distribution of electron-hole pairs generation

A scattering model to evaluate the extent of generated electron-hole pairs (e-h) in semiconductors during electron beam excitation in the 5-40 keV beam energy range is presented. From a modified Kanaya and Okayama model, the range R and energy-loss equation dE/dS dependence on the inelastic and elastic scattering cross-section proportion are analytically deduced, The presented model allows to modulate the proportion of inelastic-elastic scattering cross-section versus the energy of the incident electrons as occurs for each different interaction. Into this formalism is introduced the rate of Kα ionization events at different incident electron energy. This model is then used in Monte Carlo calculations to deduce the e-h generation function g(x, y, z) at different electron beam energy (Eb) levels. As a result, both depth and lateral dependences of e-h generation are found to fit successfully the experimental distributions of Bonard et al. (J. Appl. Phys., 79 (1996) 8693.