Secondary electron topographical contrast formation in scanning transmission electron microscopy

TL;DR

This work addresses the challenge of interpreting secondary-electron topographic contrast in STEM by introducing a forward analytical model that integrates SE emission physics with the magnetic-field interaction in the objective lens. The key contribution is a closed-form expression for SE yield that depends on local thickness $t$ and surface inclination $\alpha$, enabling realistic SE-STEM image simulations from 3D data and electron tomography reconstructions. The results show qualitative agreement with experimental SEEBIC images and highlight the model’s utility for understanding topographic contrast and guiding potential 3D surface reconstruction, while detailing limitations (e.g., magnetic mirror effects, support SE re-absorption) and future improvements (ray tracing). The approach provides a principled framework for more reliable SE-STEM interpretation and could underpin rapid 3D morphology analyses in nanomaterials research.

Abstract

Secondary electron (SE) imaging offers a powerful complementary capabilities to conventional scanning transmission electron microscopy (STEM) by providing surface-sensitive, pseudo-3D topographic information. However, contrast interpretation of such images remains empirical due to complex interactions of emitted SE with the magnetic field in the objective field of TEM. Here, we propose an analytical physical model that takes into account the physics of SE emission and interaction of the emitted SEs with magnetic field. This enables more reliable image interpretation and potentially lay the foundation for novel 3D surface reconstruction algorithms.

Figures (6)

• Figure 1: (a) Dependence of SE yield $\delta$ on the surface inclination angle $\alpha$ relative to electron beam incidence in STEM expressed as $\left| \sec{(\alpha)} \right|$. (b-d) Schematic showing the length of the primary electron beam $L$ (highlighted in blue color) within SE escape depth $t_{SE}$ at different surface inclination angles $\alpha$: (b) $\alpha = 0$, (c) $0 < \alpha < \frac{\pi}{2}$, (d) $\alpha = \frac{\pi}{2}$, (e) $\frac{\pi}{2} < \alpha < \pi$.
• Figure 2: (a) Schematic representation of the imposed problem. (b) Emission of SEs according to Lambert’s law. The lengths of the red arrows in panel (b) are proportional to the number of SEs emitted in their direction, black arrows indicate the surface normals $\vec{n}$. (c) The spherical coordinate system used in the problem solution.
• Figure 3: Dependence of SE yield $\delta$ on surface inclination angle $\alpha$ and local thickness $t$ in STEM for gold ($t_{SE}$ = 0.5 nm lin2005) according to Equation \ref{['eq:Equation 11']}.
• Figure 4: (a) Experimental SEEBIC and (b-c) simulated SE-STEM images of Au nanorod using (b) voxelized and (c) mesh representation of 3D object. (d) Line profile taken across the long axis of the nanorod for experimental and simulated SEEBIC images. Black arrow in panel (d) shows a sharp transition of the contrast between the nanorod and the background. Scale bar is 20 nm.
• Figure 5: (a, d) 3D triangular meshes obtained from electron tomography reconstruction and corresponding (b, e) simulated SE-STEM and (c, f) experimental SEEBIC images of (a-c) gold Ino decahedron ino1969 and (d-f) gold nanotriangle scarabelli2014.