Modeling of bottom antireflection layers: sensitivity to optical constants

Bottom anti-reflective layers provide a number of benefits including significant reduction in swing curve amplitude and reflective notching. The key to understanding how a bottom antireflective layer improves lithography lies in the interaction of the thin film system with the exposing radiation. Bottom antireflective layers function primarily via their absorption which is significantly larger than that of the overlying photoresist at the actinic wavelength. In the simplest physical picture, a bottom antireflective layer must be thick enough to effectively extinguish radiation that has passed through it twice, with the turning point being at the substrate/bottom antireflective layer interface. It might therefore seem that the larger the bottom antireflective layer absorption coefficient, the better the performance. More precise studies show that this simplistic view is incorrect. We have modeled the general photoresist/bottom antireflective layer/substrate film stack using the standard theory of thin film optics. It follows from the complete mathematical model that at very high absorption coefficients, bottom antireflective layers may act as mirror elements of their own. Reflection from the bottom antireflective layer/photoresist interface comes both from differences in the absorption coefficients of the two materials (the dominant effect), as well as from differences in the refractive indices. Theory therefore predicts an optimum set of optical constants for every desired film thickness range, a relationship which can be summarized in simple contour diagrams.