�LOW ENERGY ELECTRON DIFFRACTION (LEED)��

SALONI SHARMA

DEPTT. OF PHYSICS

Low-energy electron diffraction (LEED)

It is a technique for the determination of the surface structure of single- crystalline materials by bombardment with a collimated beam of low-energy electrons having energies ranging between 20–200 eV and observation of diffracted electrons as spots on a fluorescent screen.

It is widely used in materials science research to study surface structure, bonding and the effects of structure on surface processes. Its high surface sensitivity is due to the use of electrons with energies between 20-200 eV, which have wavelengths equal to 2.7 – 0.87 Å (comparable to the atomic spacing). Therefore, the electrons can be elastically scattered easily by the atoms in the first few layers of the sample.

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Its features, such as little penetration of low– energy electrons 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.

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�History: Davisson and Germer Experiment�

• In 1924 Louis de Brogile postulated that all forms of matter, such as electrons, have a dual wave-particle nature.
• Three years later after this postulate, the American physicists Clinton J. Davisson and Lester H. Germer proved experimentally the wave nature of electrons while investigating the distribution-in-angle of the elastically scattered electrons from the (111) face of a polycrystalline nickel, material composed of many randomly oriented crystals.

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• The experiment consisted of a beam of electrons from a heated tungsten filament directed against the polycrystalline nickel and an electron detector, which was mounted on an arc to observe the electrons at different angles. During the experiment, air entered in the vacuum chamber where the nickel was, hence producing an oxide layer on its surface.

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• Davisson and Clinton reduced the nickel by heating it at high temperature. They did not realize that the thermal treatment changed the polycrystalline nickel to a nearly mono-crystalline nickel, material composed of many oriented crystals.
• When they repeated the experiment, it was a great surprise that the distribution-in-angle of the scattered electrons manifested sharp peaks at certain angles. They soon realized that these peaks were interference patterns, in analogy to X-ray diffraction, the arrangement of atoms and not the structure of the atoms was responsible for the pattern of the scattered electrons.

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• Although the discovery of low-energy electron diffraction was in 1927, it became popular in the early 1960’s, when the advances in electronics and ultra-high vacuum technology made possible the commercial availability of LEED instruments.
• At the beginning, this technique was only used for qualitative characterization of surface ordering.
• Years later, the impact of computational technologies allowed the use of LEED for quantitative analysis of the position of atoms within a surface. This information is hidden in the energetic dependence of the diffraction spot intensities, which can be used to construct a LEED I-V curve.

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�Experimental Details�

• The LEED experiment uses a beam of electrons of a well-defined low energy (typically in the range 20 - 200 eV) incident normally on the sample. The sample itself must be a single crystal with a well-ordered surface structure in order to generate a back-scattered electron diffraction pattern. A typical experimental set-up is shown below:

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• Only the elastically-scattered electrons contribute to the diffraction pattern; the lower energy (secondary) electrons are removed by energy-filtering grids placed in front of the fluorescent screen that is employed to display the pattern.

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Components of a LEED Instrument

• The main components of a LEED instrument are:
• Electron Gun
• High Pass Filter
• Flourescent Screen
• Sample
• Detector

Electron Gun

• It is a device from which monochromatic electrons are emitted by a cathode filament which 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 (HOPG) are sufficient.

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High Pass FILTER

• 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 third 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.

Flourescent screen

• 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.

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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 (ultra high vacuum) 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 which 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.

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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.

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Working

• The low energy electron diffraction technique operates by sending a beam of electrons from an electron gun to the surface of the sample being tested. An electron gun consists of a heated cathode and a set of focusing lenses which sends the electrons between 20-300keV. As the electrons collide with the surface of the sample, they diffract in numerous directions depending on the surface crystallography.
• Once the electrons diffract, they head back towards three girds followed by a phosphor covered screen. The first grid is grounded and basically serves as a shield which protects the second grid as a result of its negative potential. The second grid acts as filter by allowing only the electrons with higher energies to pass through. The lower energy electrons are blocked out due to the fact that they disorder the image creating a clouded image. Once the electrons pass through the second grid, they come to third and final grid. This grid separates the pervious negative grid from the phosphor screen which carries a positive charge. As the electrons land on the phosphor screen they create a phosphor glow. The intensity of the glow depends on the intensity of the electron. The pattern of these glows is the pattern of the atoms on the surface of the crystal structure. These are the images produced by LEED.
• For analyzing these diffraction patterns photographs were scanned and digitized and the computer ran a program to do the analysis thus saving some time on the experimentalist's part. Later a design was constructed such that the electrons were diffracted directly into a special camera and computer with an imaging software which immediately digitized and analyzed the pattern.

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�Basic Theory of LEED�

• The range of wavelengths of electrons employed in LEED experiments is seen to be comparable with atomic spacings, which is the necessary condition for diffraction effects associated with atomic structure to be observed.
• Consider, first, a one dimensional (1-D) chain of atoms (with atomic separation a ) with the electron beam incident at right angles to the chain. This is the simplest possible model for the scattering of electrons by the atoms in the topmost layer of a solid; in which case the diagram below would be representing the solid in cross-section with the electron beam incident normal to the surface from the vacuum above.

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• If we consider the backscattering of a wavefront from two adjacent atoms at a well-defined angle, θ, to the surface normal then it is clear that there is a "path difference" (d) in the distance the radiation has to travel from the scattering centres to a distant detector (which is effectively at infinity) - this path difference is best illustrated by considering two "ray paths" such as the right-hand pair of green traces in the above diagram.
• The size of this path difference is a sin θ and this must be equal to an integral number of wavelengths for constructive interference to occur when the scattered beams eventually meet and interfere at the detector i.e. d=asinθ=nλ; where λ=wavelength, n= integer. For two isolated scattering centres the diffracted intensity varies slowly between zero (complete destructive interference ; d = (n + ½) λ ) and its maximum value (complete constructive interference ; d = n λ ) - with a large periodic array of scatterers, however, the diffracted intensity is only significant when the "Bragg condition"

a sinθ = nλ is satisfied exactly.

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• The diagram below shows a typical intensity profile for this case.

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• There are a number of points worth noting from this simple 1-D model
• the pattern is symmetric about θ = 0 (or sin θ = 0)
• sin θ is proportional to 1 / V ^1/2 (since λ is proportional to 1 / V ^1/2 )
• sin θ is inversely proportional to the lattice parameter, a
• All surface diffraction patterns show a symmetry reflecting that of the surface structure, are centrally symmetric, and of a scale showing an inverse relationship to both the square root of the electron energy and the size of the surface unit cell.

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LEED pattern from FCC

• Consider the LEED pattern from an fcc (110) surface. The surface atomic structure is shown on the left in plan view, as viewed from the position of the electron gun in the LEED experiment. The primary electron beam would then be incident normally on this surface as if fired from current viewpoint and the diffracted beams would be scattered from the surface backwards. The diffraction pattern on the right illustrates how these diffracted beams would impact upon the fluorescent screen.

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• The pattern shows the same rectangular symmetry as the substrate surface but is "stretched" in the opposite sense to the real space structure due to the reciprocal dependence upon the lattice parameter. The pattern is also centrosymmetric about the (00) beam - this is the central spot in the diffraction pattern corresponding to the beam that is diffracted back exactly normal to the surface (i.e. the n = 0 case in our 1-D model).
• The above illustration of the diffraction pattern shows only the "first-order" beams i.e. it is representative of the diffraction pattern visible at low energies when only for n = 1 is the angle of diffraction, θ, sufficiently small for the diffracted beam to be incident on the display screen.
• A much better method of looking at LEED diffraction patterns involves using the concept of reciprocal space: more specifically, it can be readily shown that -
• " The observed LEED pattern is a (scaled) representation of the reciprocal net of the pseudo-2D surface structure "

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• The reciprocal net is defined by the reciprocal vectors:
• a₁* & a₂* (for the substrate) and b₁* & b₂* (for the adsorbate)
• Initially we will consider just the substrate. The reciprocal vectors are related to the real space unit cell vectors by the scalar product relations:
• a₁. a₂* = a₁*. a₂ = 0 and a₁. a₁* = a₂. a₂* = 1
• This means that:
• a₁ is perpendicular to a₂*, and a₂ is perpendicular to a₁*
• there is an inverse relationship between the lengths of a₁ and a₁* (and a₂ and a₂* ) of the form:�|a₁| = 1 / ( |a₁*| cos A ) , where A is the angle between the vectors a₁ and a₁*.
• Note that when A = 0 degrees (cos A = 1) this simplifies to a simple reciprocal relationship between the lengths a₁ and a₁*.
• Exactly analogous relations hold for the real space and reciprocal vectors of the adsorbate overlayer structure: b₁, b₁*, b₂ and b₂*.
• To a first approximation, the LEED pattern for a given surface structure may be obtained by superimposing the reciprocal net of the adsorbate overlayer (generated from b₁* and b₂) on the reciprocal net of the substrate (generated from a₁* and a₂*).

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Comparison between low energy electron diffraction and X-ray diffraction.

• Electrons can be considered as a stream of waves that hit a surface and are diffracted by regions with high electron density (the atoms). The electrons in the range of 20 to 200 eV can penetrate the sample for about 10 Å without loosing energy. Because of this reason, LEED is especially sensitive to surfaces, unlike X-ray diffraction, which gives information about the bulk-structure of a crystal due to its larger mean free path.
• Like X-ray diffraction, electron diffraction also follows the Bragg’s law, where λ is the wavelength, a is the atomic spacing, d is the spacing of the crystal layers, θ is the angle between the incident beam and the reflected beam, and n is an integer. For constructive interference between two waves, the path length difference (2a sinθ / 2d sinθ) must be an integral multiple of the wavelength.

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In LEED, the diffracted beams impact on a fluorescent screen and form a pattern of light spots which is a to-scale version of the reciprocal lattice of the unit cell. The reciprocal lattice is a set of imaginary points, where the direction of a vector from one point to another point is equal to the direction of a normal to one plane of atoms in the unit cell (real space).

For example, an electron beam penetrates a few 2D-atomic layers, so the reciprocal lattice seen by LEED consists of continues rods and discrete points per atomic layer.

In this way, LEED patterns can give information about the size and shape of the real space unit cell, but nothing about the positions of the atoms. To gain this information about atomic positions, analysis of the spot intensities is required. For further information about reciprocal lattice and crystals refer to Crystal Structure and an Introduction to Single-Crystal X-Ray Crystallography.

�LEED Applications�

• Study of Adsorbates on the Surface and Disorder Layers:
• One of the principal applications of LEED is the study of adsorbates on catalysts, due to its high surface sensitivity. In order to illustrate the application of LEED in the study of adsorbates. As an example, consider the surface of Cu (100) single crystal, the pristine material. The LEED images at different temperatures are shown below:

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• This surface was cleaned carefully by various cycles of sputtering with ions of argon, followed by annealing. The figure (a) shows the LEED pattern of Cu (100) presents four well-defined spots corresponding to its cubic unit cell.
• Figure (b)shows the LEED pattern after the growth of graphene on the surface of Cu (100) at 800 °C, we can observe the four spots that correspond to the surface of Cu (100) and a ring just outside these spots, which correspond to the domains of graphene with four different primary rotational alignments with respect to the Cu (100) substrate lattice.
• When increasing the temperature of growth of graphene to 900 °C, we can observe a ring of twelve spots as seen in Figure (c), which indicates that the graphene has a much higher degree of rotational order.
• Only two domains are observed with an alignment of one of the lattice vectors to one of the Cu (100) surface lattice vectors, given that graphene has a hexagonal geometry, so that only one vector can coincide with the cubic lattice of Cu (100).

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• Figure below shows the Simulated LEED image for graphene domains with four different rotational orientations with respect to the Cu(100) surface.

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• One possible explanation for the twelve spots observed at 900 ˚C is that when the temperature of all domains is increased the four different domains observed at 800 ˚C, may possess enough energy to adopt the two orientations in which the vectors align with the surface lattice vector of Cu (100). In addition, at 900 ˚C, a decrease in the size and intensity of the Cu (100) spots is observed, indicating a larger coverage of the copper surface by the domains of graphene

• When the oxygen is chemisorbed on the surface of Cu (100), the new spots correspond to oxygen, as shown in figure below.Once graphene is allowed to grow on the surface with oxygen at 900 ˚C, the LEED pattern turns out different: the twelve spots corresponding to graphene domains (figure a) are not observed due to nucleation of graphene domains in the presence of oxygen in multiple orientations (figure b)

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A way to study the disorder of the adsorbed layers is through the LEED–IV curves.In this case, the intensities are in relation to the angle of the electron beam. The spectrum of Cu (100) with only four sharp peaks shows a very organized surface. In the case of the graphene sample growth over the copper surface, twelve peaks are shown, which correspond to the main twelve spots of the LEED pattern. These peaks are sharp, which indicate an high level of order. For the case of the sample of graphene growth over copper with oxygen, the twelve peaks widen, which is an effect of the increase of disorder in the layers.

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Structure Determination

• LEED–IV curves may give us exact information about the position of the atoms in a crystal. These curves are related to a variation of intensities of the diffracted electron (spots) with the energy of the electron beam. The process of determination of the structure by this technique works as ‘proof and error’ and consists of three main parts: the measurement of the intensity spectra, the calculations for various models of atomic positions and the search for the best-fit structure which is determined by an R-factor.
• The first step consists of obtaining the experimental LEED pattern and all the electron beam intensities for every spot of the reciprocal lattice in the pattern. Theoretical LEED–IV curves are calculated for a large number of geometrical models and these are compared with the experimental curves. The agreement is quantified by means of a reliability factor or R–factor. The closest this value to zero is, the more perfect the agreement between experimental and theoretical curves. In this way, the level of precision of the crystalline structure will depend on the smallest R–factor that can be achieved.

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• Pure metals with pure surfaces allow R–factor values of around 0.1. When moving to more complex structures, these values increase. The main reason for this gradually worse agreement between theoretical and experimental LEED-IV curves lies in the approximations in conventional LEED theory, which treats the atoms as perfect spheres with constant scattering potential in between.
• This description results in inaccurate scattering potential for more open surfaces and organic molecules. In consequence, a precision of 1-2 pm can be achieved for atoms in metal surfaces, whereas the positions of atoms within organic molecules are typically determined within ±10-20 pm. The values of the R-factor are usually between 0.2 and 0.5, where 0.2 represents a good agreement, 0.35 a mediocre agreement and 0.5 a poor agreement.

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• The figure below shows an example of a typical LEED–IV curve for Ir (100), which has a quasi-hexagonal unit cell. One can observe the parameters used to calculate the theoretical LEED–IV curve and the best-fitted curve obtained experimentally, which has an R–factor value of 0.144. The model used is also shown.

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• Experimental and theoretical LEED-IV curves for Ir (100) using two different electron beams (left), and the structural parameters using for the LEED-IV theoretical curve (right).

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• Strengths of LEED
• Extremely surface sensitive.
• Overlayer structural symmetry can be determined.
• Surface reconstruction; impurity adsorptions can be identified.
• Strengths of RHEED
• Suitable for in situ analysis.
• Excellent technique for monitoring epitaxial growth mode (island, layer, etc.).
• Patterns are indicative of structural quality.

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• Limitations of LEED:
• Backscattered geometry limits its use for in situ analysis.
• Often, substrate diffraction pattern may also be present, thereby analysis becomes complicated.
• Limitations of RHEED:
• Fixed position of the RHEED optics restricts the geometry of deposition instrumentation.
• May not be suitable for high-pressure deposition chambers.

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