Model for polymerization and self-deactivation in two-photon nanolithography

A mathematical model is developed to describe the photochemical processes in two-photon nanolithography, including two-step absorption leading to initiation and self-deactivation of the photoinitiator by laser irradiance, polymer chain propagation, termination, inhibition, and inhibitor and photoinitiator diffusion. This model is solved numerically to obtain the concentrations of the reaction species as a function of time and space as a laser beam is scanned through a volume of photoresist, from which a voxel size or linewidth is determined. The most impactful process parameters are determined by fitting the model to experimentally measured linewidths for a range of laser powers and scanning speeds, while also obtaining effective nonlinearities that are similar to previously measured values. The effects and sensitivities of the different process parameters are examined. It is shown that the photopolymerization process is dominated by diffusion of photoinitiators and oxygen inhibitors, and that self-deactivation can lead to higher effective nonlinearities in two-photon nanolithography.