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Robust overlay metrology with differential Mueller matrix calculus.

Xiuguo Chen, Honggang Gu, Hao Jiang

    Optics Express
    |April 26, 2017
    PubMed
    Summary

    Differential Mueller matrix calculus reveals linear birefringence and dichroism (LB

    Area of Science:

    • Optical Metrology
    • Semiconductor Manufacturing
    • Nanotechnology

    Background:

    • Precise overlay control is critical for semiconductor device performance.
    • Existing metrology methods face challenges in accurately measuring overlay displacements.
    • Mueller matrix calculus offers a potential avenue for advanced optical analysis.

    Purpose of the Study:

    • To introduce differential Mueller matrix calculus for analyzing double-patterned gratings.
    • To identify robust optical properties sensitive to overlay displacements.
    • To establish a more reliable indicator for diffraction-based overlay metrology.

    Main Methods:

    • Applied differential Mueller matrix calculus to investigate Mueller matrices of gratings with overlay displacements.

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  • Analyzed six elementary optical properties derived from the Mueller matrices.
  • Evaluated the response of these properties to overlay displacement under various mounting conditions.

    • Main Results:

    • Identified linear birefringence (LB') and linear dichroism (LD') along the ± 45° axes as linearly responsive to overlay displacement.
    • Demonstrated that LB' and LD' are zero when overlay displacement is absent, irrespective of conical mounting.
    • Showcased LB' and LD' as more robust indicators than off-diagonal Mueller matrix elements, especially under non-ideal mounting conditions.

    Conclusions:

    • Differential Mueller matrix calculus effectively reveals key optical properties in gratings.
    • LB' and LD' along the ± 45° axes are superior, robust indicators for overlay metrology.
    • This method enhances precision in semiconductor overlay control and device performance.