Weakly guiding approximation of a three-dimensional waveguide model for extreme ultraviolet lithography simulation

Area of Science:

• Computational physics
• Nanotechnology
• Semiconductor manufacturing

Background:

• Extreme ultraviolet (EUV) lithography is crucial for advanced semiconductor fabrication.
• Accurate simulation of EUV lithography requires solving complex electromagnetic equations.
• Existing methods like rigorous coupled-wave analysis can be computationally intensive.

Purpose of the Study:

• To develop a computationally efficient three-dimensional (3D) waveguide model for EUV lithography simulations.
• To simplify Maxwell's equations for simulating EUV light propagation through lithographic masks.
• To reduce simulation time without sacrificing accuracy.

Main Methods:

• Developed a 3D waveguide model using two components of the vector potential (A_x and A_y) to represent two polarizations.
• Applied the weakly guiding approximation, commonly used in optical fiber theory, to the model.
• Decoupled the coupled vector wave equations into two independent scalar wave equations.

Main Results:

• The 3D waveguide model effectively simulates EUV lithography, equivalent to rigorous coupled-wave analysis but with fewer field components.
• The weakly guiding approximation significantly simplifies the governing equations.
• Simulation time using the weakly guiding approximation was reduced to approximately 1/5 of the original 3D model's computation time.

Conclusions:

• The simplified 3D waveguide model offers a faster and efficient approach for EUV lithography simulations.
• The weakly guiding approximation is a valid and effective technique for reducing computational load in EUV lithography.
• This method accelerates the design and optimization process for EUV lithographic masks and systems.