Design and application of a relativistic Kramers-Kronig analysis algorithm

Area of Science:

• Materials Science
• Condensed Matter Physics
• Electron Microscopy

Background:

• Low-loss electron energy loss spectroscopy (EELS) in scanning transmission electron microscopes probes valence electron density and optoelectronic properties.
• EELS spectra are typically analyzed within a dielectric theory framework, similar to optical spectroscopies.
• Kramers-Kronig analysis (KKA) is used to retrieve the complex dielectric function from EELS data, but is often affected by spurious contributions.

Purpose of the Study:

• To develop and validate a modified relativistic Kramers-Kronig analysis (KKA) algorithm for low-loss electron energy loss spectroscopy (EELS).
• To address spurious contributions and radiative losses that affect traditional KKA implementations in EELS.
• To improve the accuracy and robustness of dielectric property retrieval from EELS measurements.

Main Methods:

• Developed a relativistic Kramers-Kronig analysis (KKA) algorithm to account for bulk and surface radiative loss contributions in low-loss EELS.
• Implemented modifications to the naive KKA algorithm, including regularization for improved robustness and an efficient numerical integration methodology.
• Utilized a synthetic low-loss EELS model and hyperspectral datasets for algorithm testing and validation.

Main Results:

• The relativistic KKA algorithm successfully accounts for radiative losses, enabling accurate retrieval of dielectric properties from low-loss EELS.
• Algorithm modifications, including regularization, enhance robustness and broaden the applicability of KKA for EELS data analysis.
• Efficient numerical integration allows for timely processing of hyperspectral EELS datasets, with simultaneous processing of multiple spectra yielding improved results.

Conclusions:

• The enhanced relativistic KKA algorithm provides a more accurate method for extracting dielectric information from low-loss EELS data.
• The developed methodology offers improved robustness and efficiency for analyzing complex EELS datasets, including hyperspectral imaging.
• Simultaneous processing of multiple spectra using the improved KKA approach enhances the reliability and accuracy of the retrieved dielectric properties.