A single quality factor for electron backscattering from thin films

In this paper, Buckingham's theorem on physically similar systems is applied for the first time to the derivation of interpolation curves of numerical data. A simplified dependence of the curves on a limited number of effective dimensionless parameters is found by a novel approach. In particular, the method is applied to Monte Carlo modelling and the calculation is considered of the backscattering coefficient η from a general substrate in the elastic regime. A single dimensionless backscattering parameter is introduced and a simple scaling law is determined, indicating how the configuration of the many variables involved can eventually change without affecting the result. The validity of the law is demonstrated in the 5 to 100 keV energy range, with substrate thicknesses ranging from 10 to 21000A °and for all the substrates of the periodic table.