Background: Charging of insulators is a complex phenomenon to simulate since the accuracy of the simulations is very sensitive to the interaction of electrons with matter and electric fields. Aim: In this study, we report model improvements for a previously developed Monte-Carlo simulator to more accurately simulate samples that charge. Approach: The improvements include both modeling of low energy electron scattering by first-principle approaches and charging of insulators by the redistribution of the charge carriers in the material with an electron beam-induced conductivity and a dielectric breakdown model. Results: The first-principle scattering models provide a more realistic charge distribution cloud in the material and a better match between noncharging simulations and experimental results. The improvements on the charging models, which mainly focus on the redistribution of the charge carriers, lead to a smoother distribution of the charges and better experimental agreement of charging simulations. Conclusions: Combined with a more accurate tracing of low energy electrons in the electric field, we managed to reproduce the dynamically changing charging contrast due to an induced positive surface potential.

Electron beam lithography (EBL) requires conducting substrates to ensure pattern fidelity. However, there is an increasing interest in performing EBL on less well-conducting surfaces or even insulators, usually resulting in seriously distorted pattern formation. To understand the underlying charging phenomena, the authors use Monte Carlo simulations that include models for substrate charging, electron beam-induced current, and electric breakdown. Simulations of electron beam exposure of glass wafers are presented, exposing regular patterns which become distorted due to charge-induced beam deflection. The resulting displacements within the patterns are mapped and compared to experimental displacement maps obtained from patterns in PMMA resist on glass substrates. Displacements up to several hundreds of nanometers were observed at a primary beam energy of 50 keV. Also, various scan strategies were used to write the patterns, in the simulations as well as the experiments, revealing their strong effect on pattern distortion, in shape and in magnitude. A qualitative, in some cases even quantitative, good agreement was found between the simulations and the experiments, providing enough confidence in Monte Carlo simulations to predict charge-induced pattern displacement and shape distortion and to find smart scan strategies to minimize the effects of charging.