Emf (electro-Magnetic Field) Simulation

EMF (Electromagnetic Field) simulation in lithography is the rigorous computational modeling of how light (electromagnetic waves) interacts with the physical 3D structure of a photomask, based on solving Maxwell's equations. It replaces simplified thin-mask (Kirchhoff) approximations with physically accurate models that account for mask topography effects.

Why EMF Simulation Is Needed

• Thin-Mask Approximation: Traditional lithography simulation treats the mask as a 2D plane — light is either blocked or transmitted. This ignores the 3D structure of the mask absorber.
• Reality: Mask features have finite thickness (50–100 nm absorbers, multilayer stacks for EUV). At advanced nodes, feature sizes approach or are smaller than the absorber thickness, making thin-mask assumptions inaccurate.
• EMF simulation captures the full interaction of light with the mask structure — including shadowing, diffraction from sidewalls, and interference within the absorber stack.

Simulation Methods

• FDTD (Finite-Difference Time-Domain): Discretizes space and time, solving Maxwell's equations on a grid. Versatile but computationally expensive.
• RCWA (Rigorous Coupled-Wave Analysis): Decomposes the mask structure into layers and solves for diffraction orders at each layer. Efficient for periodic structures.
• Waveguide Method: Treats mask features as waveguide sections and calculates mode propagation. Good for certain geometric configurations.
• Boundary Element Method: Solves Maxwell's equations at material boundaries. Efficient for large masks with simple material interfaces.

What EMF Simulation Captures

• Near-Field Effects: How the electromagnetic field is distributed immediately after passing through/reflecting from the mask.
• Polarization Effects: Different polarization states interact differently with mask topography — EMF simulation captures this.
• Phase and Amplitude Distortions: The 3D mask structure modifies both the phase and amplitude of diffracted orders, affecting imaging.
• Angle-Dependent Effects: How the mask response varies with illumination angle — critical for high-NA and off-axis illumination.

EMF in EUV Lithography

• EUV masks are reflective multilayer structures (40+ Mo/Si bilayers) with an absorber on top, illuminated at 6° incidence.
• EMF simulation must model the full multilayer stack plus the absorber — capturing reflection, transmission, and interference within dozens of layers.
• This is essential for accurate EUV OPC and imaging prediction.

Computational Challenge

• Full-chip EMF simulation is prohibitively expensive — a single mask window can take hours of computation.
• In practice, hybrid approaches are used: EMF simulation for critical features or representative patterns, combined with fast approximate models for full-chip applications.

EMF simulation is the gold standard for lithographic accuracy — it provides the ground truth that all approximate models are validated against.