Inverse scattering with a parametrized spatial spectral volume integral equation for finite scatterers

Area of Science:

• Semiconductor manufacturing
• Optical metrology
• Computational electromagnetics

Background:

• Wafer metrology relies on approximate information from photomasks and deposition processes.
• Precise characterization of 3D structures and material properties is crucial for semiconductor fabrication.

Purpose of the Study:

• To demonstrate the Gauss-Newton method for precise, noise-robust reconstruction of wafer structures.
• To evaluate the method's performance without additional inverse problem regularization.

Main Methods:

• Modeling structures as 3D finite dielectric scatterers with polygonal cross-sections.
• Employing continuous parametrization for permittivity and polygon vertices.
• Utilizing a spatial spectral Maxwell solver with a Gabor frame and consistent parametrization.

Main Results:

• Achieved noise-robust parameter reconstruction with geometrical errors below λ/7 at -3 dB SNR.
• Reconstructed geometrical parameters with errors of ~λ/60 and material properties with ~0.03% error at 10 dB SNR.
• Demonstrated superior performance compared to traditional imaging methods.

Conclusions:

• The Gauss-Newton method enables accurate wafer structure reconstruction using prior information.
• Continuity properties of the Maxwell solver and parametrization are key to the method's success.
• This technique enhances precision and noise robustness in wafer metrology.