Practical Electron Microscopy and Database

Electron channeling occurs if the incident beam is parallel to the atom columns of a crystal or a particular crystal defect. In a simplified channeling theory, an expression for the exit wave of a single atom column is expressed as [1 - 3],

       ---------------------- [4151]

where,
          r -- A two-dimensional (2-D) vector in the plane at the exit face of the crystal ( = (x,y)^T ), which is perpendicular to the incident beam direction
          z -- The crystal thickness
          C_1s -- The excitation coefficient for plane wave incidence ()
          E₀ -- The incident electron energy
          λ -- The electron wavelength
          Φ_1s(r) -- The lowest energy bound state of the atom column
          E_1s -- The energy of the lowest energy bound state

[1] D.Van Dyck, H. Lichte, K. D. van der Mast, Sub-angstrom structure characterisation: the Brite–Euram route towards one angstrom, Ultramicroscopy 64 (1996) 1–15.
[2] P. Geuens, D. VanDyck, The S-state model: a work horse for HRTEM, Ultramicroscopy 93 (2002) 179–198.
[3] S. Van Aert, P. Geuens, D. Van Dyck, C. Kisielowski, J. R. Jinschek, Ultramicroscopy 107 (2007) 551–558.