A maximum likelihood approach to the inverse problem of scatterometry

Area of Science:

• Optical metrology
• Nanotechnology
• Data analysis

Background:

• Scatterometry is a key non-imaging technique for determining critical dimensions (CD) of nanostructures.
• Extreme Ultraviolet (EUV) scatterometry, using 13-14 nm wavelengths, is a promising advancement.
• Current methods often rely on least squares (LSQ) minimization for CD reconstruction.

Purpose of the Study:

• Introduce Maximum Likelihood Estimation (MLE) as an alternative to LSQ for scatterometry.
• Directly determine statistical error model parameters from measurement data.
• Enhance the accuracy and reliability of nanostructure CD measurements.

Main Methods:

• Developed and applied a Maximum Likelihood Estimation (MLE) approach.
• Utilized simulation data to validate the MLE method against LSQ.
• Applied MLE to both Extreme Ultraviolet (EUV) and Deep Ultraviolet (DUV) scatterometry measurement data.

Main Results:

• MLE corrects systematic errors inherent in LSQ methods, leading to improved scatterometry accuracy.
• MLE analysis of EUV scatterometry data resolves discrepancies with Scanning Electron Microscopy.
• Consistent results are achieved for DUV scatterometry using the MLE approach.

Conclusions:

• MLE provides a more robust statistical framework for scatterometry data analysis.
• This method enhances the precision and agreement of critical dimension measurements.
• MLE represents a significant improvement for nanostructure metrology, particularly in EUV applications.