Inelastic mean free path

The inelastic mean free path (IMFP) is an index of how far an <a href="/facts/Electron/L0KBo5cW">electron</a> on average travels through a <a href="/facts/Solid/hj5UsXno">solid</a> before losing energy.

If a <a href="/facts/Monochromatic/CMCsjH2N">monochromatic</a>, primary <a href="/facts/Cathode_ray/9jRXSquS">beam of electrons</a> is incident on a solid surface, the majority of incident electrons lose their energy because they interact strongly with <a href="/facts/Matter/osyc04UN">matter</a>, leading to <a href="/facts/Plasmon/kuCMxx5f">plasmon</a> excitation, <a href="/facts/Electron_hole/YymdTv9d">electron-hole</a> pair formation, and vibrational excitation. The <a href="/facts/Intensity_(physics)/KFWkJkJI">intensity</a> of the primary electrons, I0, is <a href="/facts/Damped/UW3RsjEd">damped</a> as a function of the distance, d, into the solid. The intensity decay can be expressed as follows:

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

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/<a href="/facts/E_(mathematical_constant)/coEtSBk8">e</a> of its initial value. (Note that this is equation is closely related to the <a href="/facts/Beer%25E2%2580%2593Lambert_law/nl64rI1C">Beer–Lambert law</a>.)
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 <a href="/facts/Electron_spectroscopy/4SFmzqjX">electron spectroscopy</a> and <a href="/facts/Electron_microscope/XtaBktwF">microscopy</a> measurements.

Inelastic mean free path open-in-new

Inelastic mean free path