This "TPP-2M" formula for estimating electron inelastic mean free paths (IMFPs) has been proposed by Tanuma, Powell, and Penn (see Tanuma, Powell, and Penn, Surf. and Interface Anal. 17, 927 (1991); Tanuma, Powell, and Penn, Surf. Interface Anal. 21, 165 (1994); S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interface Anal. 21, 165 (1994); and C. J. Powell and A. Jablonski, J. Phys. Chem. Ref. Data 28, 19 (1999) and Surf. and Interface Anal. 29, 108 (2000)). The TPP-2M formula is derived from fits to IMFPs that were calculated for many solids from optical data. The formula can thus be used to estimate IMFPs for any solid material for which certain physical parameters are known or can be reasonably estimated.
The main parameters in this formula are
ρ, the solid density in g/cm3
Nv, the number of valence electrons per atom (or molecule for a compound) (for transition metals, include the d electrons; for rare earth or actinide elements, do not include the 4f electrons
Ep, the plasmon frequency in eV, which can be determined from the atomic weight for an element (or the molecular weight for a compound) AW, rho, and Nv as Ep = 28.8 (Nvρ/AW)^0.5 in eV.
Eg, the energy gap in eV (0 for metals or semimetals)
Note that the IMFP as appropriate to a photoelectron diffraction
calculation is not necessarily equal to the effective attenuation length
(EAL), with the latter also including elastic scattering effects such as
those involved in photoelectron diffraction (see e.g. Jablonski and
Powell, J. Electron Spect. 98-99, 1 (1999) and 100, 137 (1999)).
Lastly, IMFP and EAL data for solid elements and compounds can be obtained from databases available without charge from the National Institute for Standards and Technology via http://www.nist.gov/srd/surface.htm. The IMFP data should be used whenever possible for the IMFP inputs to this program.