Modeling and simulations of a positive chemically amplified photoresist for x-ray lithography

Abstract

This article presents the results of the experimental and modeling study of a positive tone, chemically amplified photoresist, in application to x-ray lithography. Spectrophotometric titration, Fourier transform infrared spectroscopy (FTIR), and development rate monitor data were acquired and used as inputs for the modeling of the processes and pattern simulations. The exposure model assumes monomolecular decomposition upon radiation and corresponds to Dill’s model for a nonbleaching photoactive compound. The post-exposure bake (PEB) model is based on formal kinetic equations which include a term for photoacid loss (or side reactions) during the post-exposure bake process in a generalized way. The effective kinetic order of the photoacid loss reaction is derived from the FTIR absorbance data obtained for different PEB times and exposure doses. For patterned exposures, a diffusion term for the local photoacid concentration is included. The photoacid and tert-butoxycarbonyloxystyrene concentration profile changes with PEB time have been simulated for a 0.25 μm line and spaces pattern. It is shown that a nonlinear PEB photoacid reaction kinetics, rather than the photoacid diffusion, dominates the linewidth decrease during PEB for the photoresist studied.

Simulation of the Postexposure Bake Process of Chemically Amplified Resists by Reaction–Diffusion Equations

“…The subscripts including i and j and the superscripts including n are the indices of the spatial grids and the temporal steps, respectively. The reaction parameters k a and k D and the diffusion coefficient D (a short-hand notation for D H ) all have superscripts involving n in finite-difference equations (18) (18) to (20) are the reaction orders, not to be confused with the time-step index denoted by the superscript n.…”

“…(4) accounts for the acid loss mechanism which is modeled as a reaction with the reaction parameter k a and the reaction order m [20]. The temperature dependence of the reaction parameters of the acid loss mechanism is given by [20] …”

“…The iterative algorithm utilizing (18) to (20) to solve the reaction-diffusion equations (3) and (4) Equation (18) shows that step 4 for the protection sites is an implicit scheme. Equations (19) and (20) illustrate that steps 5 and 6 for the photoacids are also implicit.…”

“…The reaction is characterized by the reaction parameter k D and the reaction orders p and q associated with the protection sites and the acids, respectively. The deprotection reaction parameter is modeled by the Arrhenius-type relation [20] …”

Measurement of the spatial evolution of the deprotection reaction front with nanometer resolution using neutron reflectometry

“…Differences between the models largely lie in the description of the acid diffusion process and the detail in which the reaction kinetics are incorporated. Predictions from reaction-diffusion models have been compared with the total extent of reaction with FTIR data before development in several systems [7,8,[12][13][14]. Top loss deprotection experiments and comparison with different acid diffusion descriptions showed that Fickian diffusion cannot explain the experimental results [11].…”