Mermin Differential Inverse Inelastic Mean Free Path of Electrons in Polymethylmethacrylate

Abstract

INTRODUCTION Electrons continually interact with the matter around us. We use electron beams for our purposes, either on the side of production of materials or on that of their characterization. Let us think to the many applications such as the processing of materials with plasma and to the local melting of materials for joining large components. We use electron beams also in the electron lithography, an important technique utilized for the production of the microelectronics devices. Let us consider the importance of the beams of electrons in the characterization of the materials, performed using techniques such as the electron microscopy and all the electron spectroscopies. Electrons interact with the surfaces of the space-crafts. The plasma– wall interaction in the fusion reactors also involves electron–matter interaction. Electrons play a role also in the cancer proton therapy, where cascades of secondary electrons are produced. These electrons of very low energy are toxic for the human body cells, since they produce damage to the biomolecules due to ionizations/excitations and the resulting break of chemical bonds. Also the secondary electrons which have ultra-low energies – and which, for a long time, were thought to be relatively harmless – are dangerous for the biomolecules due to the so-called “dissociative electron attachment.” And, of course, we wish to minimize the effects of the irradiation on the healthy tissues near to the diseased cells. In all the mentioned cases, the modeling of the interaction of the electrons with the matter is very important, as it can be used to provide a solid theoretical interpretation of the experimental evidences. The interpretation of the experimental results is often based on the Monte Carlo method (MC). The doping contrast in secondary-electron emission of pnjunctions was investigated by the use of the MC method (Dapor et al., 2008; Rodenburg et al., 2010). The modeling of electron interaction with polymers, and in particular with the polymethylmethacrylate, has been demonstrated to be very important in nano-metrology. Line-scan of resist materials with given geometrical cross-sections deposited on silicon or silicon dioxide, and the corresponding linewidth measurements, obtained with the secondary electrons in the CriticalDimension Scanning Electron Microscope (CD SEM), require an interpretation that can be performed using MC calculations (Dapor et al., 2010). The MC method, in turn, requires an accurate description of the differential inverse inelastic mean free path (DIIMFP), in order to calculate the inelastic mean free path (IMFP) and the distribution function for inelastic collisions of electrons causing energy losses less than or equal to given values.