Inelastic mean free path

The inelastic mean free path (IMFP) is an index of how far an electron on average travels through a solid before losing energy. If a monochromatic, primary beam of electrons is incident on a solid surface, the majority of incident electrons lose their energy because they interact strongly with matter, leading to plasmon excitation, electron-hole pair formation, and vibrational excitation. The intensity of the primary electrons, I_0, is damped as a function of the distance, d, into the solid. The intensity decay can be expressed as follows: where I(d) is the intensity after the primary electron beam has traveled through the solid to a distance d. The parameter λ(E), termed the inelastic mean free path (IMFP), is defined as the distance an electron beam can travel before its intensity decays to 1/e of its initial value. (Note that this is equation is closely related to the Beer–Lambert law.) The inelastic mean free path of electrons can roughly be described by a universal curve that is the same for all materials. The knowledge of the IMFP is indispensable for several electron spectroscopy and microscopy measurements. Following, the IMFP is employed to calculate the effective attenuation length (EAL), the mean escape depth (MED) and the information depth (ID). Besides, one can utilize the IMFP to make matrix corrections for the relative sensitivity factor in quantitative surface analysis. Moreover, the IMFP is an important parameter in Monte Carlo simulations of photoelectron transport in matter. Calculations of the IMFP are mostly based on the algorithm (full Penn algorithm, FPA) developed by Penn, experimental optical constants or calculated optical data (for compounds). The FPA considers an inelastic scattering event and the dependence of the energy-loss function (EFL) on momentum transfer which describes the probability for inelastic scattering as a function of momentum transfer. To measure the IMFP, one well known method is elastic-peak electron spectroscopy (EPES).