Temporal coherence envelope function of field emission in electron microscopy.

Area of Science:

• Electron microscopy
• Optics
• Materials Science

Background:

• Partial electron spatial and temporal coherence negatively impact electron microscopy imaging.
• Previous theoretical treatments of temporal coherence assumed Gaussian energy distributions.
• Modern field emission (FE) sources produce non-Gaussian energy distributions.

Purpose of the Study:

• To update the theoretical treatment of temporal coherence for arbitrary electron energy distributions.
• To investigate the impact of FE sources on image formation in low energy electron microscopy (LEEM).
• To compare the effects in conventional, non-aberration-corrected (NAC), and aberration-corrected (AC) LEEM.

Main Methods:

• Developed an updated theoretical framework for temporal coherence considering arbitrary energy distributions.
• Implemented the updated approach in Fourier optics simulations.
• Simulated image formation in NAC and AC LEEM with FE sources.

Main Results:

• The resolution degradation for FE distributions is only slightly greater than for Gaussian distributions with equivalent energy spread.
• Field emission sources introduce a focus offset in image formation.
• Both resolution degradation and focus offset are less pronounced in AC LEEM compared to NAC LEEM.

Conclusions:

• The updated theory accurately describes temporal coherence effects for FE sources in LEEM.
• FE sources have a manageable impact on image resolution and focus, especially in AC systems.
• Findings are relevant for optimizing aperture selection and analyzing focal series in electron microscopy, and applicable to transmission electron microscopy.