Low-energy electron diffraction

Low-energy electron diffraction is a technique for the determination of the surface structure of single-crystalline materials by bombardment with a collimated beam of low-energy electrons and observation of diffracted electrons as spots on a fluorescent screen.
LEED may be used in one of two ways:

Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions gives information on the symmetry of the surface structure. In the presence of an adsorbate the qualitative analysis may reveal information about the size and rotational alignment of the adsorbate unit cell with respect to the substrate unit cell.
Quantitatively, where the intensities of diffracted beams are recorded as a function of incident electron beam energy to generate the so-called I–V curves. By comparison with theoretical curves, these may provide accurate information on atomic positions on the surface at hand.
Historical perspective

An electron-diffraction experiment similar to modern LEED was the first to observe the wavelike properties of electrons, but LEED was established as a ubiquitous tool in surface science only with the advances in vacuum generation and electron detection techniques.

Davisson and Germer's discovery of electron diffraction

The theoretical possibility of the occurrence of electron diffraction first emerged in 1924, when Louis de Broglie introduced wave mechanics and proposed the wavelike nature of all particles. In his Nobel-laureated work de Broglie postulated that the wavelength of a particle with linear momentum p is given by h/''p, where h'' is the Planck constant.
The de Broglie hypothesis was confirmed experimentally at Bell Labs in 1927, when Clinton Davisson and Lester Germer fired low-energy electrons at a crystalline nickel target and observed that the angular dependence of the intensity of backscattered electrons showed diffraction patterns. These observations were consistent with the diffraction theory for X-rays developed by Bragg and Laue earlier. Before the acceptance of the de Broglie hypothesis, diffraction was believed to be an exclusive property of waves.
Davisson and Germer published notes of their electron-diffraction experiment result in Nature and in Physical Review in 1927. One month after Davisson and Germer's work appeared, Thompson and Reid published their electron-diffraction work with higher kinetic energy in the same journal. Those experiments revealed the wave property of electrons and opened up an era of electron-diffraction study.

Development of LEED as a tool in surface science

Though discovered in 1927, low-energy electron diffraction did not become a popular tool for surface analysis until the early 1960s. The main reasons were that monitoring directions and intensities of diffracted beams was a difficult experimental process due to inadequate vacuum techniques and slow detection methods such as a Faraday cup. Also, since LEED is a surface-sensitive method, it required well-ordered surface structures. Techniques for the preparation of clean metal surfaces first became available much later.
Nonetheless, H. E. Farnsworth and coworkers at Brown University pioneered the use of LEED as a method for characterizing the absorption of gases onto clean metal surfaces and the associated regular adsorption phases, starting shortly after the Davisson and Germer discovery into the 1970s.
In the early 1960s LEED experienced a renaissance, as ultra-high vacuum became widely available, and the post acceleration detection method was introduced by Germer and his coworkers at Bell Labs using a flat phosphor screen. Using this technique, diffracted electrons were accelerated to high energies to produce clear and visible diffraction patterns on the screen. Ironically the post-acceleration method had already been proposed by Ehrenberg in 1934. In 1962 Lander and colleagues introduced the modern hemispherical screen with associated hemispherical grids. In the mid-1960s, modern LEED systems became commercially available as part of the ultra-high-vacuum instrumentation suite by Varian Associates and triggered an enormous boost of activities in surface science. Notably, future Nobel prize winner Gerhard Ertl started his studies of surface chemistry and catalysis on such a Varian system.
It soon became clear that the kinematic theory, which had been successfully used to explain X-ray diffraction experiments, was inadequate for the quantitative interpretation of experimental data obtained from LEED. At this stage a detailed determination of surface structures, including adsorption sites, bond angles and bond lengths was not possible.
A dynamical electron-diffraction theory, which took into account the possibility of multiple scattering, was established in the late 1960s. With this theory, it later became possible to reproduce experimental data with high precision.

Experimental setup

In order to keep the studied sample clean and free from unwanted adsorbates, LEED experiments are performed in an ultra-high vacuum environment.

LEED optics

The main components of a LEED instrument are:

An electron gun from which monochromatic electrons are emitted by a cathode filament that is at a negative potential, typically 10–600 V, with respect to the sample. The electrons are accelerated and focused into a beam, typically about 0.1 to 0.5 mm wide, by a series of electrodes serving as electron lenses. Some of the electrons incident on the sample surface are backscattered elastically, and diffraction can be detected if sufficient order exists on the surface. This typically requires a region of single crystal surface as wide as the electron beam, although sometimes polycrystalline surfaces such as highly oriented pyrolytic graphite are sufficient.
A high-pass filter for scattered electrons in the form of a retarding field analyzer, which blocks all but elastically scattered electrons. It usually contains three or four hemispherical concentric grids. Because only radial fields around the sampled point would be allowed and the geometry of the sample and the surrounding area is not spherical, the space between the sample and the analyzer has to be field-free. The first grid, therefore, separates the space above the sample from the retarding field. The next grid is at a negative potential to block low energy electrons, and is called the suppressor or the gate. To make the retarding field homogeneous and mechanically more stable another grid at the same potential is added behind the second grid. The fourth grid is only necessary when the LEED is used like a tetrode and the current at the screen is measured, when it serves as screen between the gate and the anode.
A hemispherical positively-biased fluorescent screen on which the diffraction pattern can be directly observed, or a position-sensitive electron detector. Most new LEED systems use a reverse view scheme, which has a minimized electron gun, and the pattern is viewed from behind through a transmission screen and a viewport. Recently, a new digitized position sensitive detector called a delay-line detector with better dynamic range and resolution has been developed.
Sample

The sample of the desired surface crystallographic orientation is initially cut and prepared outside the vacuum chamber. The correct alignment of the crystal can be achieved with the help of X-ray diffraction methods such as Laue diffraction. After being mounted in the UHV chamber the sample is cleaned and flattened. Unwanted surface contaminants are removed by ion sputtering or by chemical processes such as oxidation and reduction cycles. The surface is flattened by annealing at high temperatures.
Once a clean and well-defined surface is prepared, monolayers can be adsorbed on the surface by exposing it to a gas consisting of the desired adsorbate atoms or molecules.
Often the annealing process will let bulk impurities diffuse to the surface and therefore give rise to a re-contamination after each cleaning cycle. The problem is that impurities that adsorb without changing the basic symmetry of the surface, cannot easily be identified in the diffraction pattern. Therefore, in many LEED experiments Auger electron spectroscopy is used to accurately determine the purity of the sample.

Using the detector for Auger electron spectroscopy

LEED optics is in some instruments also used for Auger electron spectroscopy. To improve the measured signal, the gate voltage is scanned in a linear ramp. An RC circuit serves to derive the second derivative, which is then amplified and digitized. To reduce the noise, multiple passes are summed up. The first derivative is very large due to the residual capacitive coupling between gate and the anode and may degrade the performance of the circuit. By applying a negative ramp to the screen this can be compensated. It is also possible to add a small sine to the gate. A high-Q RLC circuit is tuned to the second harmonic to detect the second derivative.

Data acquisition

A modern data acquisition system usually contains a CCD/CMOS camera pointed to the screen for diffraction pattern visualization and a computer for data recording and further analysis. More expensive instruments have in-vacuum position sensitive electron detectors that measure the current directly, which helps in the quantitative I–V analysis of the diffraction spots.

Theory

Surface sensitivity

The basic reason for the high surface sensitivity of LEED is that for low-energy electrons the interaction between the solid and electrons is especially strong. Upon penetrating the crystal, primary electrons will lose kinetic energy due to inelastic scattering processes such as plasmon and phonon excitations, as well as electron–electron interactions.
In cases where the detailed nature of the inelastic processes is unimportant, they are commonly treated by assuming an exponential decay of the primary electron-beam intensity I₀ in the direction of propagation:
Here d is the penetration depth, and denotes the inelastic mean free path, defined as the distance an electron can travel before its intensity has decreased by the factor 1/e. While the inelastic scattering processes and consequently the electronic mean free path depend on the energy, it is relatively independent of the material. The mean free path turns out to be minimal in the energy range of low-energy electrons. This effective attenuation means that only a few atomic layers are sampled by the electron beam, and, as a consequence, the contribution of deeper atoms to the diffraction progressively decreases.