Physical approximants to electron scattering

In this paper, Monte Carlo modelling of electron scattering in a general composite substrate in the elastic regime is considered. In spite of the great number of physical variables involved in the process, a simplified formulation of the problem in terms of a limited number of dimensionless parameters is demonstrated by a modified application of Buckingham's theorem of Dimensional Analysis. A single generalised Buckingham argument is introduced and demonstrated to ultimately intervene in determining both forward and backscattering. This approach is exemplified in the case of electron beam lithography, by evaluating the backscattering coefficient eta and the forward scattering width w. By interpolation of the numerical data, simple Buckingham approximants to the physical laws governing the process are finally derived, and they are applicable to all elemental and composite materials with e-beam voltages from 5 to 150 kV and substrate thickness from 1 to 5000 nm. The unique position of diamond as a substrate material in electron beam lithography is emphasised.