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.

Universal curve for the electron inelastic mean free path in elements based on equation (5) in.[1]

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.[2] The intensity of the primary electrons, $\textstyle I_0$, is damped as a function of the distance, $\textstyle d$, into the solid. The intensity decay can be expressed as follows:

$I(d) = I_0 \ e^{-d \ / \lambda(E)}$

where $\textstyle I(d)$ is the intensity after the primary electron beam has traveled through the solid. The parameter $\textstyle \lambda(E)$, termed the inelastic mean free path (IMFP), is defined as the distance an electron beam can travel before its intensity decays to $\textstyle 1/e$ of its initial value. The inelastic mean free path of electrons can roughly be described by a universal curve, which is the same for all materials.[1][3]