Modeling of alignment errors induced by secondary reflection stray light and suppression based on angular spectrum...

Area of Science:

• Optical Engineering
• Metrology
• Semiconductor Manufacturing

Background:

• Secondary reflection stray light is a primary source of measurement errors in wafer alignment systems.
• Current methods to reduce coherence length can broaden spectral width, causing chromatic dispersion and reducing signal-to-noise ratio.
• Existing stray light models often oversimplify by considering only single stray light beams, neglecting cumulative interference effects.

Purpose of the Study:

• To develop a quantitative model for understanding the relationship between coherence length and wafer alignment errors.
• To introduce a novel method for controlling longitudinal coherence length without compromising spectral width.
• To experimentally validate the effectiveness of the proposed method in reducing stray light-induced alignment errors.

Main Methods:

• Developed a "signal light-multiple stray light-complex coherence degree" superposition model incorporating statistical stray light characteristics.
• Integrated partial coherence theory with Monte Carlo analysis for quantitative mapping of coherence length and alignment error.
• Employed angular spectrum expansion to tune longitudinal coherence length, preserving spectral width.

Main Results:

• The developed model provides a theoretical basis for optimizing coherence length in wafer alignment.
• Angular spectrum expansion successfully reduced coherence length from 3 m to 195 µm without increasing spectral width.
• Experimental perturbations showed a decrease in alignment error standard deviation from 1.7 nm to 1.4 nm and a narrowed variation range from 7.8 nm to 1.9 nm.

Conclusions:

• The study establishes a theoretical framework and practical method for managing longitudinal coherence length in wafer alignment.
• The novel angular spectrum expansion technique effectively suppresses stray light errors without introducing chromatic dispersion.
• This research addresses a critical gap in coherence control for advanced semiconductor manufacturing processes.