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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

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Related Experiment Video

Updated: May 20, 2026

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope
10:25

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope

Published on: September 14, 2018

Minimizing off-axis aberrations in multi-beam electron optical systems: An analytical approach.

Weixia Zhao1, Lingchao Bai2, Lixin Zhang3

  • 1Research Department of Micro-nano Fabrication Technology and Intelligent Electronic Device, Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China.

Ultramicroscopy
|May 18, 2026
PubMed
Summary

Optimizing multi-beam electron optical systems (MBEOS) involves controlling aberrations. This study presents a simplified method to minimize off-axis aberrations, enabling larger usable beamlet areas for high-throughput applications.

Keywords:
Analytical modelMulti-beam electron optical systemOff-axis aberrationOptimization methodScanning electron microscope

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Last Updated: May 20, 2026

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope
10:25

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Published on: September 14, 2018

High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis
07:55

High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis

Published on: September 22, 2017

Area of Science:

  • Electron Optics
  • Materials Science

Background:

  • Multi-beam electron optical systems (MBEOS) are essential for high-throughput applications like electron microscopy and lithography.
  • Performance limitations arise from on-axis and off-axis aberrations, degrading the final electron beam spot size.
  • Systematic aberration control and optimization strategies for MBEOS remain underexplored.

Purpose of the Study:

  • To develop a simplified analytical method for optimizing operating conditions in two-lens demagnification MBEOS.
  • To minimize off-axis aberrations by determining optimal beam deflection angles and field lens strengths.
  • To provide a practical framework for designing high-performance MBEOS.

Main Methods:

  • Extension of M. J. van Bruggen's analytical model for aberration analysis.
  • Rapid determination of optimal beam deflection angle and field lens strength.
  • Investigation of aberration dependence on beamlet radial distance from the optical axis.

Main Results:

  • Minimum total aberration is achieved when beamlets pass near, not through, the second lens center.
  • A non-monotonic relationship exists between off-axis aberration and beamlet radial distance.
  • Spherical and chromatic aberrations dominate after geometric aberrations are minimized.

Conclusions:

  • A practical optimization routine for two-lens demagnification MBEOS is proposed.
  • Achieved a usable beamlet generation area of 480 µm × 480 µm with a 10 nm spot size.
  • The analytical framework facilitates the design of high-performance MBEOS with reduced aberrations.