Numerical approximation of the physical laws governing scattering in electron beam lithography

The typical problem is addressed of the numerical approximation of the physical laws ruling the behaviour of systems, whose modelling requires handling a great number of variables. A semi-empirical method is proposed as a physical approach to the solution of this problem, usually faced by means of purely mathematical techniques. Demonstration considers the example of electron scattering in solids, modelled by Monte Carlo methods and applied to electron beam lithography. Nevertheless, the generality of the presented method suggests the possibility of its extensive application to all technologies, involving physical processes able to be mathematically modelled. The physical laws governing the electron scattering are approximated through analytical functions of a single dimensionless argument, effective in describing the transmission and the backscattering through a general layer in the nearly elastic regime, independently of its chemical composition.