The proximity effect in electron beam lithography (EBL) is the phenomenon that the exposure dose distribution, and hence the developed pattern, is wider than the scanned pattern due to the interactions of the primary beam electrons with the resist and substrate.
The forward scattering process is due to electron-electron interactions which deflect the primary electrons by a typically small angle, thus statistically broadening the beam in the resist (and further in the substrate).
The Rutherford backscattering probability increases quickly with substrate nuclear charge.
The above effects can be approximated by a simple two-gaussian model where a perfect point-like electron beam is broadened to a superposition of a Gaussian with a width
The two-gaussian model parameters, including the development process, can be determined experimentally by exposing shapes for which the Gaussian integral is easily solved, i.e. donuts, with increasing dose and observing at which dose the center resist clears or does not clear.
A thin resist with a low electron density will reduce forward scattering.
When electron beam lithography is performed on substrates with 'heavy' films, such as gold coatings, the backscatter effect will (depending on thickness) significantly increase.