Developments in the dynamical theory of high energy electron reflection.

Area of Science:

• Surface science
• Condensed matter physics
• Materials science

Background:

• High energy electron reflection (HEER) is crucial for surface structure and electronic state analysis.
• Techniques like RHEED, REM, and EEL have highlighted HEER's utility.
• A stationary dynamical solution for arbitrary surfaces in HEER has been lacking.

Purpose of the Study:

• To review recent developments in the dynamical theory of HEER.
• To introduce novel methods for achieving stationary dynamical solutions.
• To address limitations in existing HEER theoretical models.

Main Methods:

• Introduction of current flow concept for semi-infinite crystal models.
• Development of the Bloch wave + Multislice Combined for Reflection (BMCR) method.
• Emergence of the Edge Patching method in Multislice-mode-Only (EPMO) for arbitrary surfaces.

Main Results:

• Clarified wave point behavior in band gaps using current flow.
• Validated current flow and BMCR method through consistency with Bloch wave and multislice in the Bragg case.
• Identified limitations of Bloch Wave-Only (BWO) solutions on Au (110) surfaces.
• EPMO method yields an infinitely convergent stationary dynamical solution for arbitrary surfaces.

Conclusions:

• Recent theoretical advancements have significantly improved understanding of HEER dynamics.
• The BMCR method offers a valid approach, highlighting potential issues with previous BWO solutions.
• The EPMO method represents a breakthrough, enabling accurate dynamical solutions for any surface in HEER.