With the continuously shrinking lithography process nodes, new materials, and technologies are constantly introduced, which exerts different effects on the mark in the lithography machine alignment system. Therefore, improving the robustness of alignment marks is crucial for high-precision alignment. It takes extensive time and cost to verify the robustness of alignment marks based on experimental methods. The industry tends to adopt simulation experiments to improve research efficiency and economy. The theory of alignment mark simulation can be divided into scalar diffraction theory and vector diffraction theory. For alignment marks with small periods or complex structures, the rigorous coupled wave method in vector diffraction theory has good computational accuracy and speed. For the alignment mark simulation with complex structures, a robustness analysis method of alignment marks is proposed by combining the rigorous coupled wave method and the layered approximation method. The robustness of marks is analyzed by this method, and the lithography strategy of improving the process adaptability of the mark is clarified with the analysis results. The proposed method and the given process adaptability strategy show theoretical significance and application value for the alignment mark design and alignment accuracy of scanners.

For the ideal mark with the standard surface, a vector diffraction simulation model can be built by the rigorous coupled wave method. For alignment marks with sidewall deformation due to process influence, it is difficult to directly establish the surface function, as the surface is non-standard anymore. Therefore, a robust analysis method of alignment marks is proposed by combining the rigorous coupled wave method and the layered approximation method to meet the requirements. The alignment mark with sidewall deformation is divided into multiple layers with equal thickness. When the number of layers is large enough, each layer can be approximated as a rectangular structure. The alignment mark with complex structure can be replaced by a whole composed of multiple rectangular structures. The rectangular structure in each layer is analyzed according to the rectangular grating method. Then the Maxwell equations and boundary conditions of each layer and region are combined. Finally, the diffraction efficiency of the alignment mark with complex structure is calculated. Wafer quality (WQ), signal-to-noise ratio (SNR), and alignment error are three important factors affecting measurement accuracy, which are employed as evaluation functions to study the robustness of alignment marks.

With WQ and SNR as the evaluation functions, the effects of the changes in groove depth, groove width, film thickness, and sidewall symmetry deformation on mark robustness are studied. The changes in groove depth, groove width, and film thickness cause the WQ and SNR to change approximately and periodically. The period is positively correlated with the measured optical wavelength. Under different wavelengths, the WQ and SNR show different peaks and valleys along with these parameter changes (Figs. 4-7). Therefore, the problem that these changes affect WQ and SNR can be solved by increasing the number of measurement wavelengths of the alignment system and selecting the signal channel with WQ and SNR as the measurement signal to improve the process adaptability of the alignment system. Symmetrical sidewall deformation shows little impact on the WQ and SNR of the mark, making it unnecessary to take targeted process adaptation strategies (Figs. 11-14). With the alignment error as the evaluation function, the robustness of the sidewall asymmetric deformation mark is studied. The diffraction efficiency of positive and negative order measurement signals of this mark is different, indicating that the alignment error is introduced (Table 2). With an aim to reduce the alignment error, on one hand, the asymmetric deformation is minimized through process optimization. On the other hand, the correct alignment position in the presence of deformation is obtained by solving the weights under multiple wavelengths. Finally, the correctness of the model is verified by the VirtualLab commercial software, and the marks are set up on the scanner for experimental testing. The simulation results are consistent with the experimental results, thus verifying the effectiveness and accuracy of the proposed method.

In this study, a robustness analysis method of alignment marks is proposed by combining the rigorous coupled wave method and the layered approximation method based on the simulation requirements of alignment marks for complex structures. The simulation model is built by this method. This paper analyzes the effects of groove depth, groove width, film thickness, and sidewall deformation on mark robustness. The changes in groove depth, groove width, and film thickness cause the WQ and SNR to change approximately and periodically. Additionally, the period is positively correlated with the measured optical wavelength. Under different wavelengths, the WQ and SNR show different peaks and valleys along with these parameter changes. Symmetrical sidewall deformation shows little impact on the WQ and SNR of the mark, whereas the mark deformation of asymmetric deformation introduces alignment error. The lithography strategy of improving the process adaptability of the mark is clarified with the analysis results. With the assistance of VirtualLab commercial software and the experimental platform, the validity and accuracy of the analysis method are verified. The research results in this paper show theoretical significance and application value for the alignment mark design and the alignment accuracy of scanners.