Reaction-diffusion modeling and simulations in positive deep ultraviolet resists

This article examines the effects of acid diffusion in APEX-E through the quantitative modeling of resist top loss in unexposed samples due to acid diffusion from a top-to-top contact bake with an exposed sample. Top-loss measurements are reported for 90 and 95 °C postexposure bake (PEB) temperatures ranging from 60 to 360 s bake times, resulting in 0.12 and 0.29 μm top loss, respectively, after 360 s PEB times. Results of systematically changing the diffusion constant, the kinetic reaction rates, and the deprotection level for dissolution in a Fickean diffusion model show that this model cannot account for the experimental observations. A better fit of the data and a near linear top-loss dependence with bake time are obtained with a deprotection dependent diffusion model, suggesting nonlinear diffusion mechanisms are important in modeling lithographic performance in positive deep ultraviolet resists.