Low Energy Electron Diffraction (LEED)

Figure 2.13: A diagram of the Ewald sphere intersecting the reciprocal lattice rods in back-scattered geometry.

Like RHEED, the technique of surface electron diffraction by back scattering obeys the modified Bragg’s law 2.4, however in order to do so, the primary energy of the beam is much lower, typically up to 400eV. This means that the diffraction pattern created in LEED is due to the interference of electrons scattered from surface atoms, because the energy of the incident electrons is too low to penetrate into the crystal bulk and even if the electrons could penetrate beyond the first few atomic planes, they would not have sufficient energy to escape the crystal. The De Broglie wavelength [90] of a 100eV electron is ≈ 1.2˚A, so even at low energies, compared to RHEED and electron microscopy techniques, the instrument can resolve atomic distances.

The condition for diffraction from atoms on the the surface in back scattered geometry is described in figure 2.8(a). The electrons incident on the surface have a wave vector, k. Elastically scattered electrons that meet the condition for constructive interference are described by equation 2.4. The Ewald sphere, described in figure 2.13, is a map of all the possible scattering angles and where the sphere intersects a surface reciprocal lattice rod satisfies the condition for constructive interference. This is all discussed for RHEED geometry in section 2.3.1 however, the main difference

in the construction of the LEED pattern is that the radius of the Ewald sphere is much smaller than that for RHEED, due to the reduced beam energy, and as a result, the LEED pattern is an array of spots, rather than streaks, mapping out the surface reciprocal lattice. The experimental setup of the instrument is shown in figure 2.14 where electrons are generated from an electron gun, which has a Lanthanum hexaboride (LaB6) filament on the project system. The advantage of using a LaB6

filament instead of a Tungsten filament is that the energy distribution of the electrons generated is smaller. This is partly due to dimensions of the filament, but is also due to the work function of the filament. The LaB6 filament is shaped to a sharp tip to

approximate conditions for a point source, to reduce energy spread of the beam and thereby minimise inelastic scattering. This filament type also has a longer working lifetime than Tungsten filaments, ideal for UHV conditions so the lowest possible base pressure can be maintained.

Similar to the RHEED system, electrons are filtered by a Wehnelt cylinder and are then focused by electromagnetic lenses to approach parallel beam conditions. Such lenses are the L1, L2 and L3 lenses, the strength of which can be varied to

focus electrons to a point on the sample with ≈100µm beam diameter. The sample is positioned ≈ 10cm from a screen. The screen is biased to 5kV electric potential to uniformly accelerate electrons onto a phosphorescent screen.

Figure 2.14: A schematic of the Low energy electron diffraction system viewed in cross section. The sample is labelled S, the grids focusing the electrons are labelled G1−3, the phosphorescent

screen is labelled F, and the energy of the electron beam is labelled V. Although the sample is drawn with tilt θ, LEED is typically conducted at normal incidence. Image sourced from an article on LEED by Jona et al. [91]

Analysis of a surface by LEED is conducted by varying the primary electron beam energy. Increasing the beam energy results in two outcomes; higher scattering angle and increased sample penetration, although the primary energy will not be high enough to penetrate more than ≈2nm at its maximum. This does make the instru- ment sensitive to both the surface and selvedge of the sample. Due to the interference of elastically scattered electrons, this becomes convoluted and so simulations of the kinematics from the scattering of electrons from different surface structures is required to accurately identify the correct structure. This technique of analysis is Dynamical LEED and will not be considered again in this thesis however the principle of this technique is worth mentioning briefly. The intensity of the spots can be tracked as the energy of the electron beam is increased and decreased. From this, spot intensity vs. beam energy (IV) can be plotted. Simulations of IV curves for scattering of elec- trons from predicted surface structures can be fitted to the empirical data in order to determine the structure of a sample surface. In this thesis, only indexing of the spots and the pattern geometry has been utilised to analyse sample surfaces with reference to the literature.

rocal surface lattice. As the primary energy increases, the angle at which electrons scatter off atoms increases, causing spots on the screen to translate toward a specular reflection of the electron source. As beam energy increases, the scattering angle for higher order diffraction falls within the angular field of view of the screen and higher order spots are observed on the screen. These spots identify surface reciprocal lattice directions relative to the specular reflection and can be indexed with miller indices (hk) for the 2D reciprocal lattice. By analysing spacings between first order and higher order spots, parameters such as lattice spacing and surface reconstruction can be determined alongside features such as specular reflections and surface steps.

The LEED instrument is calibrated in a similar way to the RHEED system; using a well defined reference surface structure, in order to convert distances between spots on the screen into atomic distances. In all diffraction patterns, a longer length in reciprocal space corresponds to a shorter length in real space and vice versa. This is important to consider when deducing the type of surface reconstruction and surface lattice parameter. For the discussion of the heavily reconstructed MgO surface in Chapter 7 it seems pertinent to describe the formation of LEED patterns from faceted surfaces.

Diffraction from flat surfaces with normal incidence exhibit a specular reflection where electrons are scattered directly back into the path of the electron beam. This is the (00) spot. Elastic scattering is also observed from faceted surfaces, where the surface has reconstructed into an ordered array of tilted planes because the surface energy density of these planes is significantly lower than that of frozen bulk or re- constructed surfaces. Since facets are tilted at an angle off normal incidence, the electron beam is reflected off the surface and can be further reflected by surface fea- tures. When coherence of electrons in the primary beam is sustained over multiple reflections, specular reflection spots can be observed on the screen. The spot formed in a diffraction pattern from a specular reflection can be identified by the fact that the position of the spot does not alter with or depend on the primary energy of the electron beam, and the position of a specular spot can only be changed by tilting the sample.