Elastic scattering model for electron-beam lithography simulation

The conventional Rutherford elastic scattering model is not suitable to describe the elastic interaction between electron and higher atomic number (Z>4) materials. A new model based on non-relativistic wave equation of Schrodinger was presented, in which the atomic potential was Thomas-Fermi-Dirac (TFD) potential. The elastic scattering cross-sections of elements H, Li, C, O, Si were calculated by the new model and the results were compared to those of Rutherford elastic scattering model and precise elastic scattering model-Mott cross-section model. It was found that under the condition of higher incident electron energy (E>5 keV) and higher atomic number (Z>4), the results of the new model approaches that of Mott cross-section, more than that of Rutherford elastic scattering model, so it can make a decision that the new model is more precise and it is suitable to describe the elastic interaction between higher energy electrons and higher atomic number (Z>4) materials. Furthermore, the new model was corrected by the relativistic theory. The results show that when the incident electron energy is up to 100 keV, the relativistic effect is remarkable.