Convexity constraints on linear background models for electron energy-loss spectra

Area of Science:

• Materials Science
• Spectroscopy
• Computational Chemistry

Background:

• Electron energy loss spectroscopy (EELS) is crucial for material analysis.
• Accurate background modeling is essential for reliable elemental quantification in EELS.
• Conventional power-law fitting methods can be slow and require initial parameters.

Purpose of the Study:

• To develop a novel, linear background model for EELS.
• To improve the accuracy of elemental quantification in EELS.
• To reduce user dependency in spectral analysis.

Main Methods:

• Derivation of convexity constraints for a linear EELS background model.
• Implementation of quadratic programming for fitting the constrained model.
• Comparison with conventional power-law fitting on experimental and simulated data.

Main Results:

• The linear model outperforms power-law fitting, especially over wide energy ranges.
• Quadratic programming ensures high-speed fitting with a guaranteed unique solution.
• Reduced need for user input facilitates unsupervised analysis of large EELS datasets.

Conclusions:

• The proposed linear background model with convexity constraints enhances EELS elemental quantification.
• The method offers significant advantages in speed, uniqueness, and automation.
• Demonstrated effectiveness on complex semiconductor device samples highlights its practical utility.