with the minimum (maximum) energy loss ω ω m i n ( ω ω m a x ), the dielectric function ϵ ϵ , the energy loss function (ELF) I m ( − − 1 ϵ ϵ ( k , ω ω ) ) and the smallest and largest momentum transfer k ± ± = 2 E ± ± 2 ( E − − ω ω ) . In general, solving this integral is quite challenging and only applies for energies above 100 eV. Thus, (semi)empirical formulas were introduced to determine the IMFP.