Reflection high-energy electron diffraction: Difference between revisions

Revision as of 13:34, 11 July 2019

Revision as of 21:57, 2 August 2019

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RHEED users construct [[Ewald's sphere]]s to find the crystallographic properties of the sample surface. Ewald's spheres show the allowed diffraction conditions for kinematically scattered electrons in a given RHEED setup. The diffraction pattern at the screen relates to the Ewald's sphere geometry, so RHEED users can directly calculate the reciprocal lattice of the sample with a RHEED pattern, the energy of the incident electrons and the distance from the detector to the sample. The user must relate the geometry and spacing of the spots of a perfect pattern to the Ewald's sphere in order to determine the reciprocal lattice of the sample surface.

The Ewald's sphere analysis is similar to that for bulk crystals, however the reciprocal lattice for the sample differs from that for a 3D material due to the surface sensitivity of the RHEED process. The reciprocal lattices of bulk crystals consist of a set of points in 3D space. However, only the first few layers of the material contribute to the diffraction in RHEED, so there are no diffraction conditions in the dimension perpendicular to the sample surface. Due to the lack of a third diffracting condition, the reciprocal lattice of a crystal surface is a series of infinite rods extending perpendicular to the sample’ssample's surface.<ref name="oura2001">{{cite book|author=Oura K|author2=Lifshits V G|author3=Saranin A A|author4=Zotov A V|author5=Katayama M|last-author-amp=yes|title=Surface Science: An Introduction|publisher=Springer-Verlag: Berlin|date=2001|pages=59–65|isbn=3-540-00545-5}}</ref> These rods originate at the conventional 2D reciprocal lattice points of the sample’ssample's surface.

The Ewald's sphere is centered on the sample surface with a radius equal to the reciprocal of the wavelength of the incident electrons. The relationship is given by

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[[File:Laue.gif|thumbnail|400px|'''Figure 4'''. Diffraction from a row of atoms a Laue circle on the surface of the Ewald's sphere. The reciprocal lattice rods are so closely space, that they comprise the plane cutting the sphere. Diffraction conditions are fulfilled on the perimeter of the Laue circle. The vectors are all equal to the reciprocal of the incident vector, k.]]

The azimuthal angle affects the geometry and intensity of RHEED patterns.<ref name="oura2001"/> The azimuthal angle is the angle at which the incident electrons intersect the ordered crystal lattice on the surface of the sample. Most RHEED systems are equipped with a sample holder that can rotate the crystal around an axis perpendicular to the sample surface. RHEED users rotate the sample to optimize the intensity profiles of patterns. Users generally index at least 2 RHEED scans at different azimuth angles for reliable characterization of the crystal’scrystal's surface structure.<ref name="oura2001"/> Figure 5 shows a schematic diagram of an electron beam incident on the sample at different azimuth angles.

[[File:Azimuth angles comparison.svg|thumb|400px|'''Figure 5'''. The incident electron beam is incident on an identical surface structure at a different azimuth angles in a) and b). The sample is viewed from the top in the figure, and the points correspond to the reciprocal lattice rods, which extend out of the screen. The RHEED pattern would be different for each azimuth angle.]]