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, ${\displaystyle I_{0}}$, is damped as a function of the distance, d, into the solid. The intensity decay can be expressed as follows:

${\displaystyle I(d)=I_{0}\ e^{-d\ /\lambda (E)}}$

where ${\displaystyle \textstyle I(d)}$ is the intensity after the primary electron beam has traveled through the solid to a distance ${\displaystyle \textstyle d}$. The parameter ${\displaystyle \textstyle \lambda (E)}$, termed the inelastic mean free path (IMFP), is defined as the distance an electron beam can travel before its intensity decays to ${\displaystyle \textstyle 1/e}$ 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.[1][3]