Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Calculations of Stopping Powers of 100 eV to 30 keV Electrons in 31 Elemental Solids



S Tanuma, Cedric J. Powell, David R. Penn


We present calculated electron stopping powers (SPs) for 31 elemental solids (Li, Be, glassy C, graphite, diamond, Na, Mg, K, Sc, Ti, V, Fe, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, and Bi). These SPs were determined with an algorithm previously used for the calculation of electron inelastic mean free paths and from energy-loss functions (ELFs) derived from experimental optical data. The SP calculations were made for electron energies between 100 eV and 30 keV, and supplement our earlier SP calculations for 10 additional solids (Al, Si, Cr, Ni, Cu, Ge, Pd, Ag, Pt, and Au). Plots of SP versus atomic number for the group of 41 solids show clear trends. Multiple peaks and shoulders are seen that result from the contributions of valence-electron and various inner-shell excitations. Satisfactory agreement was found between the calculated SPs and values from the relativistic Bethe SP equation with recommended values of the mean excitation energy (MEE) for energies above 10 keV. We determined effective MEEs versus maximum excitation energy from the ELFs for each solid. Plots of effective MEE versus atomic number showed the relative contributions of valence-electron and different core-electron excitations to the MEE. For a maximum excitation energy of 30 keV, our effective MEEs agreed well for Be, graphite, Na, Al, and Si with recommended MEEs; a difference for Li was attributed to sample oxidation in the SP measurements for the recommended MEE. Substantially different effective MEEs were found for the three carbon allotropes (graphite,diamond, and glassy C).
Journal of Applied Physics


electron stopping power, elemental solids, mean excitation energy


Tanuma, S. , Powell, C. and Penn, D. (2008), Calculations of Stopping Powers of 100 eV to 30 keV Electrons in 31 Elemental Solids, Journal of Applied Physics, [online], (Accessed July 15, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created March 18, 2008, Updated October 12, 2021