Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography

• Main Author: Tan, Chin Boon
• Other Authors: Yeo Swee Hock
• Format: Theses and Dissertations
• Language: English
• Published: 2009
• Subjects: DRNTU::Engineering::Manufacturing; DRNTU::Engineering::Electrical and electronic engineering::Semiconductors; DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
• Online Access: https://hdl.handle.net/10356/15168
• Institution: Nanyang Technological University

Line structures are an essential part in integrated circuit (IC) fabrication. In photolithography, the electromagnetic scattering of line structures is one of the main factors that determine the advancement of the technology node. From the perspective of modeling, a theoretical model to physically understand the scattering phenomenon is necessary for a solid foundation in efficient characterization. When the domain of simulation that needs to be addressed is substantial, an approximate solution is ideal for resource efficient modeling. From the perspective of alignment using line structures, it must meet the stringent overlay budget for new fabrication processes. The robustness of the alignment marks is critical as accurate signal is required to precisely align a masking layer to the previous layer. The key contribution in this research work is the establishment of a new electromagnetic scattering model for line structures based on a ray tracing approach. This electromagnetic ray tracing (ERT) model provides detailed understanding of every physical field that contributes to the scattering solution, which could not be offered by any other photolithography simulators found in the literature. The ERT model is capable of distinguishing all the geometrical optics and diffracted fields. The diffracted field is required to compensate the discontinuities caused by the geometrical optics field. Prior to the establishment of the ERT model for line structures, the diffraction coefficients for both external and internal regions of a wedge were formulated and studied extensively. The external diffraction coefficient was developed by using Maliuzhinets’s impedance approach with the inclusion of higher order in the asymptotic expansion. On the other hand, a heuristic solution was derived for the internal diffraction coefficient by extracting the poles in dual Sommerfeld contour integrals. By exploiting both diffraction coefficients in the ERT model, the electromagnetic field that causes a disturbance in the amplitude profile for the total solution was identified and explained in detail. The accuracy of the ERT model was also verified by comparing with the finite difference time domain (FDTD) solution. For a single polysilicon line structure with width of 1.66 λ (λ is the wavelength) on silicon substrate, the developed ERT model was able to demonstrate amplitude correlation coefficient (ACC) of 0.978 and the maximum amplitude difference, Δ|Ez| of as low as -0.067. The subwavelength line width of 0.4 λ was identified as the limit of the ERT model for the single polysilicon line structure.