Analysis of the proximity function in electron-beam lithography on high-T-c superconducting thin-films

In this paper we approximate by the combination of double Gaussian and exponential functions the radial distributions of the absorbed electron energy density in a 125 nm PMMA resist layer on YBa2Cu3O7 thin-film/substrate targets obtained by means of Monte Carlo simulation for a zero-width delta-function and the following variables (i) the substrate material (SrTiO3 and MgO), (ii) the electron beam energy E(0) (25, 50 and 75 keV) and (iii) the YBa2Cu3O7 film thickness d (0, 100, 200 and 300 nm). The values of the parameters of the analytical function are calculated using an original Monte Carlo technique. These values are presented in the form of 3D diagrams which show their dependences on beam energy and on high-temperature superconducting film thickness and can also be used for approximate determination of the parameters at different initial conditions.