Fast nonlinear compressive sensing lithographic source and mask optimization method using Newton-IHTs algorithm.

Area of Science:

• * Lithography and semiconductor manufacturing
• * Computational imaging and signal processing
• * Applied mathematics

Background:

• * Source and Mask Optimization (SMO) is crucial for enhancing lithography imaging fidelity.
• * Current SMO methods face computational inefficiency, limiting their application to clip-level tasks.
• * Addressing this bottleneck is essential for advancing semiconductor fabrication processes.

Purpose of the Study:

• * To apply fast nonlinear compressive sensing (CS) theory to the nonlinear inverse reconstruction problem in SMO.
• * To develop a computationally efficient SMO method that maintains high imaging fidelity.
• * To accelerate the SMO procedure for broader applicability in lithography.

Main Methods:

• * Formulation of SMO as a nonlinear CS reconstruction problem by leveraging sparsity assumptions.
• * Utilization of space basis and 2D Discrete Cosine Transform (DCT) basis for source and mask patterns.
• * Innovation of a Newton-iteration hard thresholding (Newton-IHTs) algorithm incorporating second derivative information for accelerated convergence.

Main Results:

• * The proposed nonlinear CS-SMO method effectively reduces computation complexity by downsampling layout patterns.
• * The Newton-IHTs algorithm achieves high imaging fidelity in nonlinear CS-SMO.
• * Significant acceleration achieved: 9.31x over gradient-based methods and 7.39x over IHTs-based methods.

Conclusions:

• * Nonlinear compressive sensing provides an efficient framework for solving the SMO inverse problem.
• * The developed Newton-IHTs algorithm offers a substantial speedup for SMO while preserving imaging quality.
• * This advancement has the potential to enable full-chip SMO applications, improving overall lithography performance.