Theory of bright-field scanning transmission electron microscopy for tomography
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8410 (United States)
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.
- OSTI ID:
- 20665076
- Journal Information:
- Journal of Applied Physics, Vol. 97, Issue 3; Other Information: DOI: 10.1063/1.1828604; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
- Country of Publication:
- United States
- Language:
- English
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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