# Low Energy Electron Diffraction

The English term Low Energy Electron Diffraction (LEED, dt " low energy electron diffraction at surfaces " ) refers to a physical method for the study of the arrangement of atoms at surfaces and in thin films. Here one takes advantage of the basic effect of the interference of waves, resulting in the formation of diffraction patterns, which are displayed on a viewing screen. The first evidence of the wave nature of the electron radiation Davisson and Germer succeeded in 1927 on a nickel single crystal at Bell Laboratories.

In LEED electron waves are used, the de Broglie wavelength is in the range of about 0.1 nm ( 1 Å). This is equivalent in magnitude to the distances of the atoms in the crystal lattice. The relationship with the adjustable on the control electronics energy of the electron is

The surface sensitivity of the method is caused by the low penetration depth of elastically scattered electrons, which is in the range of 0.5 to 1 nm. For surface studies with the LEED method to ultra-high vacuum (UHV ) reign with pressures of less than 10-8 Pa, so that the sample surface impurities remain free long enough and interactions of the electrons can be avoided with gas molecules.

## The LEED apparatus

From a hot filament, electrons are emitted and accelerated by an anode in the direction of sample. By an electrostatic lens system of the electron beam is focused. After the electrons have been scattered in the sample to pass the diffracted electrons of the way in the direction of the fluorescent screen, a retarding grid which serves as a high pass filter in the spectrum of the diffracted electron select the elastic peak. On the screen of light is illuminated at the locations of the impinging electrons, making the diffraction pattern visible.

## LEED diffraction pattern

LEED pattern is in the ideal case of sharp points, which are symmetrically arranged. Very often, the electron gun is mounted in front of the screen and therefore obscures the very bright lens 0th order. From the symmetry of the pattern can be close to the symmetry of the crystal surface. Since in addition to the substrate via structures to be imaged, different diffraction patterns are observed depending on the preparation. From the diffraction pattern, different arrangements of atoms on the surface can be determined. The pictures are an example of a LEED diffraction pattern.

LEED diffraction pattern with a CO covered platinum -rhodium (100 ) ( Miller indices ) surface of single crystal. The picture is taken in high vacuum; eV at 94.

## Medium energy electron diffraction

At the medium -energy electron diffraction ( MEED ) observing the multilayer surface growth as a function of time with the electron diffraction. Grow the layers monolayer for monolayer on the surface ( Frank - van der Merve growth), then the order of the surface changes periodically. When fully completed documents is the long-range order is greatest, ie, the intensity of the reflection. This gives at intervals greater or less reflections, suggesting the monolayer growth as a function of time.

## Video - LEED

In order to investigate the dynamics of structural changes, you can record the LEED pattern with a camera. This allows the structure-determining parameter varies and so their influence will be determined during the LEED measurement.

## Conversion of the lattice vectors between local and k-space

The captured image corresponds to a projection of the surface in the k-space, which is also called reciprocal space. To get the actual sites of the diffraction centers in the spatial domain, the image of the Fluoreszenschirms into the spatial domain must be transformed back.

### Generally

The conversion of the basis vectors of the local area ai and aj in the reciprocal space and ai * aj * done via the following rules:

The angle between ai and aj. That is, it changes with the change of basis, only the length of the individual vectors; Longer vectors are shorter, shorter longer.

Furthermore, applies

So that each vector is in k-space to the other vertically in the spatial domain. It also follows that the angle in reciprocal space between ai and aj * appears *.

### Example: square surface grid in the spatial domain

The surface of a single crystal have a square surface lattice (eg (100 ) face of a fcc crystal ) that can be observed, for example, directly by scanning tunneling microscopy. The gratings in the spatial domain is defined by the vectors

And

Described. The lengths of the reciprocal vectors, which are measured with LEED, calculated according to the above formula

Furthermore, it follows that

From this it can be constructed first points of the LEED image. Other issues arise from other periodicities of the grating.