General mathematical model for the period chirp in interference lithography.

Area of Science:

• Optics and Photonics
• Nanofabrication
• Materials Science

Background:

• Laser interference lithography (LIL) and scanning-beam interference lithography (SBIL) are crucial for micro- and nanofabrication.
• Existing models often rely on simplified point source approximations, limiting accuracy for complex setups.
• A unified theoretical framework is needed to accurately predict grating characteristics across different LIL and SBIL configurations.

Purpose of the Study:

• To develop a general analytical model for calculating the spatial distribution of grating periods.
• To unify classical LIL and SBIL into a single theoretical formalism.
• To accurately describe grating formation on arbitrarily shaped substrates using Gaussian beams.

Main Methods:

• Developed a general analytical model considering Gaussian beams instead of point sources.
• The model accounts for both the far-field and near-field of laser beams.
• Applied the formalism to calculate grating period, inclination, and slant for arbitrary substrate geometries.

Main Results:

• Successfully unified LIL and SBIL configurations within a single analytical framework.
• The model accurately predicts grating parameters by considering Gaussian beam properties.
• Demonstrated the capability to calculate grating characteristics on arbitrarily shaped substrates.

Conclusions:

• The proposed Gaussian beam-based model provides a unified and accurate approach for LIL and SBIL.
• This formalism enhances the predictability and control of grating fabrication processes.
• Enables precise design and manufacturing of periodic structures on complex surfaces.