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Methods & Techniques

LEED / RHEED

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LEED

Low Energy Electron Diffraction (LEED) is a state ot the art technique for characterizing the surface structure of crystalline solids. If a crystal is cut along a certain plane, then the atoms near the surface may well be disturbed from their equilibrium positions in the bulk. This leads to changes in the relative positions of the surface and near surface atoms (surface reconstruction). Such changes can be explored with LEED. The surface crystallographic structure can be determined by bombarding the surface with low energy electrons (approx. 10-200 eV) and observe diffracted electrons as spots on a phosphorescent screen. The relative position of the spots on the screen shows the surface crystallographic structure. The diffracted spots will move as the energy of the incident electrons changes, and the intensity of the spots as a function of incident electron energy reveals much about surface reconstructions. In order to determine the true surface structure, much computer analysis needs to be done.
 

Reflection High Energy Electron Diffraction (RHEED)

Reflection High-Energy Electron Diffraction (RHEED) is a versatile analytical tool for characterizing thin films during growth by molecular beam epitaxy, since it is very sensitive to surface structure and morphology. RHEED is particularly suited to this application as it does not block the direction vertical to the surface of the crystal which is observed, and is particularly sensitive to surface roughness, down to monolayer sensitivity. This allows the growth rate of layers of atoms on the surface to be monitored, by analysing the periodic variations of the RHEED intensity during growth, the so called RHEED oscillations. By knowing both the distance from the sample to the screen or recording medium and the energy of the electron source, it is possible to calculate the lattice spacings of the sample analysed. The WMI operates a special "high pressure RHEED system" suitable for monitoring the growth of oxide thin films at large background pressure (up to 1 mbar) in laser molecular beam epitaxy (L-MBE).

Operation Principle of RHEED

RHEED is based on the reflection of electrons with high kinetic energy (typically in the 5-100 keV regime) and low impact angle 8 (typically less than 5°) from the surface of a solid. Below we give a brief illustration of the operation principle of RHEED for a sample with a cubic lattice. The incoming electrons with a momentum of k0 have a very small incident angle with respect to the sample surface. Therefore, they will only be scattered from the top layer of atoms of the sample. In the figure (right, top), the surface of the sample is shown in reciprocal space. This reciprocal lattice builds a surface with a quadratic array of atoms. Assuming elastic scattering no energy transfer is allowed from the electrons to the sample. So the scattered wave vector kij lies on the surface of the sphere of constant energy, the so-called Ewald sphere. The side view is shown at the bottom. In reciprocal space, the two-dimensional array of the surface atoms turns into vertical lines, the reciprocal rods. Whereever these rods cross the Ewald sphere, the condition for constructive interference of the elastically scattered electron beams from the surface is fulfilled. Therefore, these crossing points in k-space determine the directions of constructive interference for the elctrons in real space.

The 3D sketch (bottom figure) shows the directions of the elastically scattered electrons in real space. These scattered electron beams hit a fluorescent RHEED screen in certain RHEED spots, lying on so-called Laue circles which are numbered starting from zero. The figure shows the Laue circles no. 0 in red and no. 1 in cyan. The spots form a characteristic RHEED pattern depend on the morphology and roughness of the sample surface. Therefore, RHEED is a powerful tool for in-situ analysis of thin film deposition. As the RHEED intensity depends on the film roughness, the growth process leads to characteristic intensity oscillations of the RHEED spots during the growth process with a single oscillation usually corresponding to the completion of a single monolayer.
RHEED - top and side view (jpeg, 24k)
 
RHEED - 3D view (jpeg, 40k)
[Figures taken from: Jürgen Klein, Epitaktische Heterostrukturen aus dotierten Manganaten, PhD Thesis, University of Cologne (2001)]

 

RHEED Patterns

RHEED patterns (jpeg, 35k)