BEAM_INCIDENCE

BEAM_INCIDENCE defines the incidence angles (in degrees) of the electron beam on the surface. The polar angle theta is measured from the surface normal, the azimuthal angle phi is positive counterclockwise when looking at the solid from vacuum, with phi=0 corresponding to the positive x axis, as defined in the POSCAR file. See also the diagram shown in Fig. 22. ViPErLEED considers the incident wave vector to be in direction from the electron gun towards the surface, i.e.

\[\mathbf{k} = |\mathbf{k}|(-\cos(\phi)\sin(\theta)\hat{u}_x - \sin(\phi)\sin(\theta)\hat{u}_y - \cos(\theta) \hat{u}_z) .\]

Default: BEAM_INCIDENCE = THETA 0, PHI 0

Syntax:

BEAM_INCIDENCE = THETA 0.3, PHI 10.1
BEAM_INCIDENCE = 0.3 10.1

Acceptable values: -90 \(\leq\) theta \(\leq\) 90, 0 \(\leq\) phi < 360. All numbers are considered floats. Negative values for theta will internally be corrected to positive by adding or subtracting 180° from phi.

theta and phi represent tilt and azimuthal angles, respectively, in degrees. Notice that if the flags THETA and PHI are not specified, only the first two floats are considered: the first is taken as the polar angle theta, the second as the azimuth phi.

../../../_images/theta_and_phi.svg

Fig. 22 Definition of angles theta (\(\theta\)) and phi (\(\phi\)) relative to the coordinate system of the POSCAR file.

Hint

  • In general, unless the experiment was performed at large off-normal incidence (>2°), keeping the default value should lead to the correct optimized geometry, but the \(R\) factor will be worse than for an experiment at normal incidence. In case the incidence angle is significantly off, one needs to measure a simple system (clean, unreconstructed metal) with the same experimental settings, to determine first the correct angle of incidence to be used for more complicated situations.

  • Beam incidence optimization is commonly one of the last refinement steps of the LEED fit.

  • Even for normal incidence, during the last polishing one can even use a purposely off-normal BEAM_INCIDENCE (theta different from zero) and average the resulting almost-equivalent beams in order to account for the fact that the electron beam has a finite aperture angle. (For averaging, see the AVERAGE_BEAMS parameter). This commonly leads to theta values in the order of 0.3–0.5°. This option makes sense only if the \(R\) factor is very low and the surface has sufficiently high symmetry (at least threefold rotation symmetry or mirror/glide planes in two directions), so that averaging simulates incoming beams from several azimuthal directions. The azimuth phi of the incoming beam should be chosen such that it is midway between the azimuth values of two beams that are symmetry-equivalent at normal incidence.