Lattice-resolution contrast from a focused coherent electron probe. Part I

Area of Science:

• Materials Science
• Solid-State Physics
• Electron Microscopy

Background:

• Accurate lattice-resolution contrast in electron microscopy is crucial for materials characterization.
• Existing theories often simplify electron probe behavior, limiting analysis of complex crystal structures.

Purpose of the Study:

• To develop a general Bloch wave framework for analyzing lattice-resolution contrast in scanning transmission electron microscopy (STEM).
• To incorporate boundary conditions relevant to electron probes focused within a unit cell.
• To derive equations for both coherent and incoherent contrast applicable to various detector configurations.

Main Methods:

• Development of a Bloch wave theory considering probe distortion and focusing.
• Mathematical derivation of contrast equations for coherent and incoherent scattering.
• Integration of multislice techniques for computational evaluation.
• Inclusion of background contributions and cross-talk effects.

Main Results:

• A general theory for Bloch wave excitation amplitudes as a function of beam position and focus is established.
• Antisymmetric Bloch states are shown to be significantly excited by focused probes, contrary to plane wave assumptions.
• Explicit equations for coherent and incoherent contrast are derived for arbitrary detector setups.
• The framework accounts for mixed dynamic form factors in incoherent scattering and background absorption.

Conclusions:

• The Bloch wave framework provides a comprehensive approach to understanding lattice-resolution contrast in STEM.
• The theory accurately describes the influence of probe characteristics on image formation.
• This framework is essential for advanced materials analysis using electron microscopy techniques.