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Semi-implicit level set formulation for lithographic source and mask optimization.

Yijiang Shen, Fei Peng, Zhenrong Zhang

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    |November 6, 2019
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    Summary
    This summary is machine-generated.

    This study introduces a new method for lithographic source and mask optimization (SMO) that overcomes stability limitations. The approach enhances convergence speed for advanced semiconductor manufacturing processes.

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    Area of Science:

    • Semiconductor Manufacturing
    • Computational Lithography
    • Optimization Algorithms

    Background:

    • Gradient-based Source and Mask Optimization (SMO) methods face stability issues.
    • The explicit Euler-forward scheme imposes restrictive time-step limitations, hindering convergence.
    • Existing methods struggle with the Courant-Friedrichs-Lewy (CFL) condition.

    Purpose of the Study:

    • To develop a more stable and efficient SMO approach.
    • To overcome the convergence limitations imposed by the CFL condition in lithographic processes.
    • To improve the speed and reliability of source and mask pattern optimization.

    Main Methods:

    • Utilized a distance level-set regularized reformulation of SMO.
    • Discretized stability-relevant terms implicitly for enhanced numerical stability.
    • Applied operator splitting to update source and mask patterns independently.
    • Solved linear systems using the Thomas method for tridiagonal systems.

    Main Results:

    • The proposed SMO approach demonstrates superior convergence properties.
    • Successfully overcame the stability constraints of the Courant-Friedrichs-Lewy (CFL) condition.
    • Achieved faster and more stable optimization compared to explicit schemes.

    Conclusions:

    • The implicit discretization and operator splitting method offers a robust solution for SMO.
    • This technique significantly improves convergence speed and stability in lithographic optimization.
    • The proposed method is a promising advancement for efficient semiconductor manufacturing.