![]() Vector G is useful for finding distance between arbitrary planes in the crystal. K i=electron wave vector at any intersection of reciprocal lattice with Ewald sphereĪn arbitrary vector, G, defines the reciprocal lattice vector between the ends of any two k vectors. Therefore, the magnitude of a vector from the origin of the Ewald sphere to the intersection of any reciprocal lattice rods is equal in magnitude to that of the incident beam. Where: λ=wavelength of incident electronsĭiffraction conditions are satisfied where the rods of reciprocal lattice intersect the Ewald sphere. The Ewald sphere is centered on the sample surface with a radius equal to the reciprocal of the wavelength of the incident electrons. These rods originate at the conventional 2D reciprocal lattice points of the sample’s surface. Due to the lack of a third diffracting condition, the reciprocal lattice of a crystal surface is a series of infinite rods extending perpendicular to the sample’s surface. However, only the first few layers of the material contribute to the diffraction in RHEED, so there are no diffraction conditions in the dimension perpendicular to the sample surface. The reciprocal lattices of bulk crystals consist of a set of points in 3D space. The Ewald sphere analysis is similar to that for bulk crystals, however the reciprocal lattice for the sample differs from that for a 3D material due to the surface sensitivity of the RHEED process. The user must relate the geometry and spacing of the spots of a perfect pattern to the Ewald sphere in order to determine the reciprocal lattice of the sample surface. The diffraction pattern at the screen relates to the Ewald sphere geometry, so RHEED users can directly calculate the reciprocal lattice of the sample with a RHEED pattern, the energy of the incident electrons and the distance from the detector to the sample. Ewald spheres show the allowed diffraction conditions for kinematically scattered electrons in a given RHEED setup. RHEED users construct Ewald spheres to find the crystallographic properties of the sample surface. RHEED users also analyze dynamically scattered electrons with complex techniques and models to gather qualitative from RHEED patterns. These electrons account for the high intensity spots or rings common to RHEED patterns. Users extract non-qualitative data from the kinematically diffracted electrons. Dynamic scattering occurs when electrons undergo multiple diffraction events in the crystal and lose some of their energy due to interactions with the sample. Some incident electrons undergo a single, elastic scattering event at the crystal surface, a process termed kinematic scattering. Two types of diffraction contribute to RHEED patterns. Users characterize the crystallography of the sample surface through analysis of the diffraction patterns. Some of the electron waves created by constructive interference collide with the detector, creating specific diffraction patterns according to the surface features of the sample. The diffracted electrons interfere constructively at specific angles according to the crystal structure and spacing of the atoms at the sample surface and the wavelength of the incident electrons. Atoms at the sample surface atoms diffract (scatter) the incident electrons due to the wavelike properties of electrons. The glancing angle of incident electrons prevents them from escaping the bulk of the sample and reaching the detector. In the RHEED setup, only atoms at the sample surface contribute to the RHEED pattern. Figure 1 shows the most basic setup of a RHEED system. The electrons interfere according to the position of atoms on the sample surface, so the diffraction pattern at the detector is a function of the sample surface. Incident electrons diffract from atoms at the surface of the sample, and a small fraction of the diffracted electrons interfere constructively at specific angles and form regular patterns on the detector. The electron gun generates a beam of electrons which strike the sample at a very small angle relative to the sample surface. Low energy electron diffraction (LEED) is also surface sensitive, but LEED achieves surface sensitivity through the use of low energy electrons.Ī RHEED system requires an electron source (gun), photoluminescent detector screen and a sample with a clean surface, although modern RHEED systems have additional parts to optimize the technique. Transmission electron microscopy, another common electron diffraction method samples the bulk of the sample due to the geometry of the system. ![]() RHEED systems gather information only from the surface layer of the sample, which distinguishes RHEED from other materials characterization methods that rely on diffraction of high-energy electrons. Reflection high-energy electron diffraction (RHEED) is a technique used to characterize the surface of crystalline materials. ![]()
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