Analytical evaluation of the energy deposition function in electron-beam lithography in the case of a composite substrate

In this article the energy deposition function in the case of e-beam lithography is calculated analytically. The distribution of electrons as a function of depth and energy is calculated first using a method based on the Boltzmann transport equation which is easily applicable in the case of multilayer substrates. Next the lateral distribution of the electrons is calculated and each contribution (primary, secondary, and backscattered electrons) is considered separately. Energy dissipation results are used as input to a cell removal model for the resist development simulation.