Statistics of EUV exposed nanopatterns: Photons to molecular dissolutions

For higher computing power of semiconductor integrated circuits, pattern feature sizes below 10 nm are anticipated by introducing extreme ultraviolet (EUV) lithography with high numerical aperture (NA) optics. However, performances of EUV resist processes are not commensurate with its imaging capability or that for its deep UV predecessor. We regard resist processes as a series of chemo-physical events and examine their statistical nature, which bridges chemo-physics and lithography performances. The relationships between statistical characteristics and lithography performances are investigated by first-principle Monte Carlo simulations. We further describe a whole pattern formation as a directional network spatially and hierarchically connecting chemo-physical events. It clarifies that the contrast between exposed and unexposed areas and spatial correlations in event distributions increase with the proceeding event steps from photon absorptions to molecular dissolutions, achieving molecular order precision and high resolution. This is attributed to the averaging effect of multi-photon-induced molecular solubility switching and collaborative molecular dissolutions. Their effectiveness, however, decrease as the pattern size shrinks with changing the exposure systems from deep ultraviolet to high-NA EUV, degrading material-inherent resolution capability and increasing stochasticity. This is because of sparse photon absorptions, localized secondary electron generations, and molecular interaction ranges approaching the pattern sizes. The directional network models using the hierarchical stack of binomial, beta-binomial distributions, and mixed Bernoulli convolution well describe the behaviors of EUV-exposed nanopatterns, opening a path to fully statistical lithography simulations. Controlling the statistical nature is crucial in pushing the EUV resolution down below 10 nm.