![]() Using this geometry, RHEED provides the unique ability to monitor growth on a surface in real-time whilst the grazing incidence of the electron beam ensures surface specificity. A typical RHEED set-up consists of an electron gun, sample and a phosphor screen and a typical geometry is illustrated on the MBE page. In RHEED electrons of between 8 and 20 keV impinge upon a surface at angles of approximately 1 o - 3 o. RHEED (Reflection High-Energy Electron Diffraction) Through the introduction of the offset voltage, δV, any electrons with an energy equal to or lower than are filtered out and are not detected. Peak (A), centred around the incident electron energy E, is the elastically back-scattered peak and is of interest in LEED studies whereas peak (B) is the secondary electron peak which arises from inelastically scattered electrons and is not of interest. The energy distribution of emitted electrons is shown in Figure (3).įigure (3): Energy distribution of back-scattered electrons in LEED, reproduced from (2). By studying the intensity of a spot and it location over a range of energies, then the position of atoms on the surface can be studied due to their effect on the scattered electrons. This provides a useful tool in the determination of surface structure and atomic positions. A side-effect of the extension of lattice points into rods is that as the incident electron energy is varied spots do not go extinct but instead move. The diffraction pattern then seen is a magnified version of the surface reciprocal lattice.ĭue to the geometry of this arrangement the incident electron wavevector effectively looks 'down' on the Ewald sphere and views the infinitely long rods as spots, giving rise to the characteristic spot patterns seen. The large screen potential provides scattered electrons with a large enough kinetic energy, so that a LEED pattern will be produced. Another earthed grid filters out the large potential of the screen, which is held at +5 kV and accelerates electrons towards a fluorescent screen. This potential filters out electrons who have an energy lower than eV E, the incident electron energy. The central grids are held at the same potential as the electron gun, V E but features an offset δV, which is typically of the order 10 V. The inner grid, closest to the sample, is held at ground and screens the potentials of the outer grids. Electrons back-scattered from the surface travel towards a series of grids. The typical layout of LEED optics, set to operate as a retarding field analyser (RFA), is illustrated in Figure (2). The surface of a crystal is typically only 10 Å thick, with a lattice parameter of approximately 5 Å and so the electrons are well suited for the study of surfaces.įigure (2): Schematic of a typical LEED optics set-up At 20 eV these electrons have mean free paths of approximately 5 Å and wavelengths of around 3 Å. In LEED the electrons used have energies in the range of 20 to 100 eV. Correspondingly, below the line represents forward-scattering into the crystal. a* is the reciprocal lattice vector and k i is the incident electron wavevector, θ D is the diffraction angle. The dashed horizontal line on the 2-D plot represents the surface, electron paths above this are back-scattered. The techniques described below, LEED and RHEED, both view the Ewald sphere in subtly different ways.įigure (1): The Ewald sphere in both two- and three-dimensions showing the change in reciprocal lattice points to rods. However, the loss of periodicity in one dimension, perpendicular to the plane of the surface, causes these spots to elongate into infinitely long rods that extend outwards from the surface as illustrated in Figure (1). For a bulk structure, which has periodicity in three dimensions the solutions to the Ewald sphere result in spots. Note that relativistic effects are ignored here.Īs both LEED and RHEED are surface sensitive techniques note that the Ewald spherechanges. Where is the mass of the electron and U is the electric potential through which the electron is accelerated. an electric potential we see that Equation (1) can be written As the momentum is related to the velocity and, in turn, the velocity is dependent upon the accelerating force i.e. Where h is Planck's constant and p is the electron momentum. In this case, the wavelength of an electron is given by the de Broglie relation, as shown in Equation (1) However, this time we extend from massless particles to those with mass, including the electron and the neutron. The wave-like properties of objects means that we can perform diffraction using them, as with X-ray photons. The wave-particle duality of nature results in particles having both wave-like and particle-like properties. ![]()
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