Inelastic mean free path

Index of how far electrons travel through a solid before losing energy

The inelastic mean free path (IMFP) is an index of how far an electron on average travels through a solid before losing energy. [[Image:E IMFP universal en. svg|thumb|Universal curve for the electron inelastic mean free path in elements based on equation (5) in. The intensity of the primary electrons, , 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 (mathematical constant) 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). This method measures the intensity of elastically backscattered electrons with a certain energy from a sample material in a certain direction. Applying a similar technique to materials whose IMFP is known, the measurements are compared with the results from the Monte Carlo simulations under the same conditions. Thus, one obtains the IMFP of a certain material in a certain energy spectrum. EPES measurements show a root mean square (RMS) difference between 12% and 17% from the theoretical expected values. For energies below 100 eV, IMFP can be evaluated in high energy secondary electron yield (SEY) experiments. Therefore, the SEY for an arbitrary incident energy between 0.1 keV 10 keV is analyzed. According to these experiments, a Monte Carlo model can be used to simulate the SEYs and determine the IMFP below 100 eV.