Profile Study on Different Patterns in PMMA Bilayer Resist Configurations Under 20 keV Electron Beam Exposure

Electron beam lithography (EBL) using bilayer resists is influenced by electron scattering, proximity effects, resist thickness, pattern density, and exposure dose. Optimization based only on the top-view critical dimension does not capture linewidth variation through the developed resist thickness. This study presents an experimental and theoretical approach to model and optimize the depth-dependent sidewall geometry of bilayer PMMA exposed by a variable-shaped-beam EBL at 20 keV. Bilayers consisting of 950 PMMA A2 and 495 PMMA A6, with total thicknesses of 300 and 550 nm, on SiO₂/Si substrates were fabricated. We investigated isolated lines and line gratings with nominal line/space (L/S) dimensions of 100/500 and 100/700 nm over selected exposure dose ranges. Cross-sectional SEM measurements at five resist depths were used to develop regression models describing linewidth as a function of the exposure dose and resist depth. Two models for mean values and standard deviations were constructed for each of the considered experimental cases to account for external noise not included in the regression models, and the propagated uncertainties are quantified by Monte Carlo simulation. Four linewidth-difference criteria to identify doses producing near-vertical profile segments were introduced and applied. The results demonstrate that the selected optimum dose depends strongly on the bottom-layer thickness, pattern density, and the profile segment considered. The proposed approach provides a quantitative empirical method for predicting, analyzing, controlling, and optimizing EBL resist profiles, and can also be applied, with appropriate experimental calibration, to different resist systems, pattern geometries, exposure dose ranges, beam shot sizes, and acceleration voltages.