Reaction-diffusion study of electron-beam-induced contamination growth

Abstract

A time-dependent reaction-diffusion model was elaborated to better understand the dynamical growth of contamination on surfaces illuminated by an electron beam. The goal of this work was to fully describe the flow of hydrocarbon molecules, denoted as contaminants, and their polymerization in the irradiated area with the number of parameters reduced to a minimum necessary. It was considered that the diffusion process of contaminants is driven by the gradient of their surface density generated by the impact of a circular homogeneous electron beam. The contribution of the residual gas atmosphere in the instrument was described by the tendency to reestablish the initial equilibrium surface density of contaminants before irradiation. The four unknown parameters of the model, the electron interaction cross-section, the diffusion coefficient, the initial surface density of contaminants, and the frequency of the supply of contaminants from the residual gas atmosphere were determined by comparing the modeled contamination growth with experimental results. The experiments were designed such that the influence of the single parameters could be unequivocally separated. To follow the dynamical evolution of the system and to generate time-resolved distinct experimental data, successive contamination measurements were performed at short time intervals up to 20 min. The local height and shape of the grown contamination were quantified by evaluating high-angle annular dark-field (HAADF) scanning-transmission- electron-microcopy (STEM) image intensities and corresponding Monte-Carlo simulations. Our model also applies to nonhomogeneous initial conditions like the reduced local surface density of contaminants after previous beam-showering. The dynamic analyses of this process might provide hints regarding the relative size of the contaminant molecules and also indicate some measures for the reduction of contamination growth.