Combining model-based measurement results of critical dimensions from multiple tools

Area of Science:

• Metrology and Measurement Science
• Computational Physics
• Materials Science

Background:

• Model-based measurement techniques integrate experimental data with physics simulations for quantitative analysis.
• Uncertainty in these estimates arises from data variability, model parameter sensitivity, and parameter correlations.

Purpose of the Study:

• To demonstrate that combining multiple model-based techniques and employing Bayesian approaches optimally minimizes measurement uncertainties.
• To present hybrid metrology as a superior method for achieving high-precision measurements.

Main Methods:

• Utilizing parametric models of specimens to extract measurands from experimental data and simulations.
• Combining regression analyses from complementary techniques, such as critical-dimension small-angle X-ray scattering (CD-SAXS) and scanning electron microscopy (SEM).
• Applying Bayesian inference to integrate information and reduce uncertainty.

Main Results:

• The combination of techniques and Bayesian methods yields the lowest possible uncertainties in parameter estimation.
• Hybrid metrology successfully measured sub-14 nm lines in semiconductor manufacturing with enhanced precision.
• Demonstrated significant uncertainty reduction compared to individual measurement techniques.

Conclusions:

• Hybrid metrology, integrating multiple model-based techniques, is optimal for minimizing measurement uncertainty.
• This approach provides state-of-the-art precision for critical metrology applications, particularly in advanced manufacturing.
• The synergy between different physical models and data sources enhances the reliability of quantitative measurements.