Mask optimization approaches in optical lithography based on a vector imaging model.

Area of Science:

• Semiconductor Manufacturing
• Computational Lithography
• Electromagnetics

Background:

• Scalar imaging models limit optical proximity correction (OPC) and phase-shifting mask (PSM) optimization to numerical apertures (NA) below 0.4.
• Immersion lithography systems with hyper-NA (NA>1) are critical for 45 nm semiconductor fabrication.
• Existing OPC and PSM methods are inadequate for hyper-NA systems due to their scalar approximations.

Purpose of the Study:

• Develop gradient-based OPC and PSM optimization algorithms for hyper-NA lithography systems.
• Address the limitations of scalar imaging models in advanced semiconductor manufacturing.
• Enhance resolution in immersion lithography through vector imaging models.

Main Methods:

• Formulated a mask optimization framework using an integrative and analytic vector imaging model.
• Employed a gradient-based algorithm for iterative mask optimization.
• Introduced a generalized wavelet penalty to balance mask complexity and convergence errors.
• Developed methods to accelerate algorithm computation.

Main Results:

• Successfully developed pixelated gradient-based OPC and PSM optimization under a vector imaging model.
• The proposed methods are suitable for hyper-NA immersion lithography systems.
• The generalized wavelet penalty effectively manages mask complexity.
• Algorithm acceleration techniques were successfully implemented.

Conclusions:

• The developed vector-based OPC and PSM optimization algorithms are essential for high-resolution patterning in advanced semiconductor lithography.
• These methods overcome the limitations of scalar models, enabling effective mask design for hyper-NA systems.
• The research provides a foundation for future advancements in computational lithography for next-generation integrated circuits.