Bulk effects in hyper-numerical aperture optical lithography

To control critical dimension (CD) effectively, bulk effect is studied in hyper-numerical aperture (NA) optical lithography and a novel optimization strategy for resist film stacks is developed to balance bulk effect with appropriate swing effect. Firstly, the incident angle distribution of imaging light is evaluated based on NA and coherence factor σ settings, so that the average energy (φ̄) absorbed per unit volume in the resist at the resist bottom surface is calculated over the whole range of incident angle. Secondly, the analytic relationship between Φ̄ and resist thickness (d) is obtained by fitting with least-squares procedure and the derivative of 3 with respect to d is calculated. Lastly, the resist film stacks are optimized to minimize the derivative of Φ̄. With the optimized thin-film stack structure design, the CD variation with resist thickness is obtained by using commercial software Prolith 9.0. The results show that the optimization strategy can effectively overcome CD variation from the bulk effect over the thickness range of 30-40 nm.