There is a growing interest for patterning on curved or tilted surfaces using electron beam lithography. Computational proximity correction techniques are well established for flat surfaces and perpendicular exposure, but for curved and tilted surfaces adjustments are needed as the dose distribution is no longer cylindrically symmetric with respect to the surface normal. A graphical processing unit -accelerated 3D Monte Carlo simulation, based on first-principle scattering models, is used to simulate the asymmetric dose distribution. Based on that, an approximate adjustment is made to an existing high-performance proximity effect correction (PEC) algorithm aimed at the correct exposure of a pattern of nanowires on a 17° tilted surface. It was experimentally verified that using the adjusted PEC indeed leads to a more uniform exposure on tilted surfaces.

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.