skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Theory of bright-field scanning transmission electron microscopy for tomography

Abstract

Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elastic scattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of 300-keV electrons through aluminum foils up to 25 {mu}m thick. For thin films, the theory gives a validity condition for Beer's law. For thick films, a variant of Moliere's theory [V. G. Moliere, Z. Naturforschg. 3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as [t ln(e{sup 1-2{gamma}}t/{tau})]{sup -1} where t is the path length of the beam, {tau} is the mean free path for elastic scattering, and {gamma} is Euler's constant. The Goudsmit-Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elastic scattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elastic scattering cross sections minus a deltamore » function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.« less

Authors:
 [1]
  1. National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8410 (United States)
Publication Date:
OSTI Identifier:
20665076
Resource Type:
Journal Article
Journal Name:
Journal of Applied Physics
Additional Journal Information:
Journal Volume: 97; Journal Issue: 3; Other Information: DOI: 10.1063/1.1828604; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979
Country of Publication:
United States
Language:
English
Subject:
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; CHROMIUM; COPPER; CROSS SECTIONS; DELTA FUNCTION; ELASTIC SCATTERING; ELECTRON BEAMS; ELECTRON COLLISIONS; IMAGE PROCESSING; KEV RANGE 100-1000; MEAN FREE PATH; MOLIERE THEORY; MULTIPLE SCATTERING; RADIATION TRANSPORT; SCANNING ELECTRON MICROSCOPY; TELLURIUM; THIN FILMS; TOMOGRAPHY; TRANSMISSION ELECTRON MICROSCOPY; TRANSPORT THEORY; ZIRCONIUM

Citation Formats

Levine, Zachary H. Theory of bright-field scanning transmission electron microscopy for tomography. United States: N. p., 2005. Web. doi:10.1063/1.1828604.
Levine, Zachary H. Theory of bright-field scanning transmission electron microscopy for tomography. United States. https://doi.org/10.1063/1.1828604
Levine, Zachary H. 2005. "Theory of bright-field scanning transmission electron microscopy for tomography". United States. https://doi.org/10.1063/1.1828604.
@article{osti_20665076,
title = {Theory of bright-field scanning transmission electron microscopy for tomography},
author = {Levine, Zachary H},
abstractNote = {Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elastic scattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of 300-keV electrons through aluminum foils up to 25 {mu}m thick. For thin films, the theory gives a validity condition for Beer's law. For thick films, a variant of Moliere's theory [V. G. Moliere, Z. Naturforschg. 3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as [t ln(e{sup 1-2{gamma}}t/{tau})]{sup -1} where t is the path length of the beam, {tau} is the mean free path for elastic scattering, and {gamma} is Euler's constant. The Goudsmit-Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elastic scattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elastic scattering cross sections minus a delta function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.},
doi = {10.1063/1.1828604},
url = {https://www.osti.gov/biblio/20665076}, journal = {Journal of Applied Physics},
issn = {0021-8979},
number = 3,
volume = 97,
place = {United States},
year = {Tue Feb 01 00:00:00 EST 2005},
month = {Tue Feb 01 00:00:00 EST 2005}
}