Information theoretical computational lithography based on pattern density statistics.

Area of Science:

• Semiconductor Manufacturing
• Optical Engineering
• Information Theory

Background:

• Computational lithography enhances optical lithography resolution and fidelity.
• Existing information theoretical models rely on uniform pattern density assumptions, leading to inaccurate error bounds.
• A more accurate model is needed to reflect real-world pattern variations.

Purpose of the Study:

• To improve the accuracy of information theoretical models for computational lithography.
• To establish a more precise lower bound for lithography imaging error.
• To derive a more realistic theoretical limit for lithography image fidelity.

Main Methods:

• Introduced a statistical approach to pattern density using a density classification rule (DCR).
• Formulated the information transfer function between mask and print images under DCR constraints.
• Derived optimal information transfer (OIT) and theoretical limits using numerical optimization with mask regularization.

Main Results:

• The proposed statistical model significantly improves the accuracy of lithography image fidelity limits.
• Demonstrated analytically and experimentally that the new model outperforms conventional approaches.
• The DCR provides a more realistic constraint for information transfer in lithography.

Conclusions:

• The statistical pattern density approach offers a superior method for modeling computational lithography.
• This work provides a more accurate theoretical framework for understanding and optimizing lithography processes.
• The findings are crucial for advancing semiconductor manufacturing and achieving higher resolution imaging.