Electron backscatter diffraction
Electron backscatter diffraction is a scanning electron microscopy technique used to study the crystallographic structure of materials. EBSD is carried out in a scanning electron microscope equipped with an EBSD detector comprising at least a phosphorescent screen, a compact lens and a low-light camera. In the microscope an incident beam of electrons hits a tilted sample. As backscattered electrons leave the sample, they interact with the atoms and are both elastically diffracted and lose energy, leaving the sample at various scattering angles before reaching the phosphor screen forming Kikuchi patterns. The EBSD spatial resolution depends on many factors, including the nature of the material under study and the sample preparation. They can be indexed to provide information about the material's grain structure, grain orientation, and phase at the micro-scale. EBSD is used for impurities and defect studies, plastic deformation, and statistical analysis for average misorientation, grain size, and crystallographic texture. EBSD can also be combined with energy-dispersive X-ray spectroscopy, cathodoluminescence, and wavelength-dispersive X-ray spectroscopy for advanced phase identification and materials discovery.
The change and sharpness of the electron backscatter patterns provide information about lattice distortion in the diffracting volume. Pattern sharpness can be used to assess the level of plasticity. Changes in the EBSP zone axis position can be used to measure the residual stress and small lattice rotations. EBSD can also provide information about the density of geometrically necessary dislocations. However, the lattice distortion is measured relative to a reference pattern. The choice of reference pattern affects the measurement precision; e.g., a reference pattern deformed in tension will directly reduce the tensile strain magnitude derived from a high-resolution map while indirectly influencing the magnitude of other components and the spatial distribution of strain. Furthermore, the choice of EBSP0 slightly affects the GND density distribution and magnitude.
Pattern formation and collection
Setup geometry and pattern formation
For electron backscattering diffraction microscopy, a flat polished crystalline specimen is usually placed inside the microscope chamber. The sample is tilted at ~70° from Scanning electron microscope flat specimen positioning and 110° to the electron backscatter diffraction detector. Tilting the sample elongates the interaction volume perpendicular to the tilt axis, allowing more electrons to leave the sample providing better signal. A high-energy electron beam is focused on a small volume and scatters with a spatial resolution of ~20 nm at the specimen surface. The spatial resolution varies with the beam energy, angular width, interaction volume, nature of the material under study, and, in transmission Kikuchi diffraction, with the specimen thickness; thus, increasing the beam energy increases the interaction volume and decreases the spatial resolution.The EBSD detector is located within the specimen chamber of the SEM at an angle of approximately 90° to the pole piece. The EBSD detector is typically a phosphor screen that is excited by the backscattered electrons. The screen is coupled to lens which focuses the image from the phosphor screen onto a charge-coupled device or complementary metal–oxide–semiconductor camera.
In this configuration, as the backscattered electrons leave the sample, they interact with the Coulomb potential and also lose energy due to inelastic scattering leading to a range of scattering angles. The backscattered electrons form Kikuchi lines – having different intensities – on an electron-sensitive flat film/screen, gathered to form a Kikuchi band. These Kikuchi lines are the trace of a hyperbola formed by the intersection of Kossel cones with the plane of the phosphor screen. The width of a Kikuchi band is related to the scattering angles and, thus, to the distance between lattice planes with Miller indexes h, k, and l. These Kikuchi lines and patterns were named after Seishi Kikuchi, who, together with Shoji Nishikawa, was the first to notice this diffraction pattern in 1928 using transmission electron microscopy which is similar in geometry to X-ray Kossel pattern.
The systematically arranged Kikuchi bands, which have a range of intensity along their width, intersect around the centre of the regions of interest, describing the probed volume crystallography. These bands and their intersections form what is known as Kikuchi patterns or electron backscatter patterns. To improve contrast, the patterns' background is corrected by removing anisotropic/inelastic scattering using static background correction or dynamic background correction.
EBSD detectors
EBSD is conducted using an SEM equipped with an EBSD detector containing at least a phosphor screen, compact lens and low-light charge-coupled device or complementary metal–oxide–semiconductor camera., commercially available EBSD systems typically come with one of two different CCD cameras: for fast measurements, the CCD chip has a native resolution of 640×480 pixels; for slower, and more sensitive measurements, the CCD chip resolution can go up to 1600×1200 pixels.The biggest advantage of the high-resolution detectors is their higher sensitivity, and therefore the information within each diffraction pattern can be analysed in more detail. For texture and orientation measurements, the diffraction patterns are binned to reduce their size and computational times. Modern CCD-based EBSD systems can index patterns at a speed of up to 1800 patterns/second. This enables rapid and rich microstructural maps to be generated.
Sample preparation
The sample should be vacuum stable. It is typically mounted using a conductive compound, which minimises image drift and sample charging under electron beam irradiation. EBSP quality is sensitive to surface preparation. Typically the sample is ground using SiC papers from 240 down to 4000 grit, and polished using diamond paste then in 50 nm colloidal silica. Afterwards, it is cleaned in ethanol, rinsed with deionised water, and dried with a hot air blower. This may be followed by ion beam polishing, for final surface preparation.Inside the SEM, the size of the measurement area determines local resolution and measurement time. Usual settings for high-quality EBSPs are 15 nA current, 20 kV beam energy, 18 mm working distance, long exposure time, and minimal CCD pixel binning. The EBSD phosphor screen is set at an 18 mm working distance and a map's step size of less than 0.5 μm for strain and dislocations density analysis.
Decomposition of gaseous hydrocarbons and also hydrocarbons on the surface of samples by the electron beam inside the microscope results in carbon deposition, which degrades the quality of EBSPs inside the probed area compared to the EBSPs outside the acquisition window. The gradient of pattern degradation increases moving inside the probed zone with an apparent accumulation of deposited carbon. The black spots from the beam instant-induced carbon deposition also highlight the immediate deposition even if agglomeration did not happen.
Depth resolution
There is no agreement about the definition of depth resolution. For example, it can be defined as the depth where ~92% of the signal is generated, or defined by pattern quality, or can be as ambiguous as "where useful information is obtained". Even for a given definition, depth resolution increases with electron energy and decreases with the average atomic mass of the elements making up the studied material: for example, it was estimated as 40 nm for Si and 10 nm for Ni at 20 kV energy. Unusually small values were reported for materials whose structure and composition vary along the thickness. For example, coating monocrystalline silicon with a few nm of amorphous chromium reduces the depth resolution to a few nm at 15 kV energy. In contrast, Isabell and David concluded that depth resolution in homogeneous crystals could also extend up to 1 μm due to inelastic scattering.A recent comparison between reports on EBSD depth resolution, Koko et al indicated that most publications do not present a rationale for the definition of depth resolution, while not including information on the beam size, tilt angle, beam-to-sample and sample-to-detector distances. These are critical parameters for determining or simulating the depth resolution. The beam current is generally not considered to affect the depth resolution in experiments or simulations. However, it affects the beam spot size and signal-to-noise ratio, and hence, indirectly, the details of the pattern and its depth information.
Monte Carlo simulations provide an alternative approach to quantifying the depth resolution for EBSPs formation, which can be estimated using the Bloch wave theory, where backscattered primary electrons – after interacting with the crystal lattice – exit the surface, carrying information about the crystallinity of the volume interacting with the electrons. The backscattered electrons energy distribution depends on the material's characteristics and the beam conditions. This BSE wave field is also affected by the thermal diffuse scattering process that causes incoherent and inelastic scattering – after the elastic diffraction events – which does not, yet, have a complete physical description that can be related to mechanisms that constitute EBSP depth resolution.
Both the EBSD experiment and simulations typically make two assumptions: that the surface is pristine and has a homogeneous depth resolution; however, neither of them is valid for a deformed sample.
Orientation and phase mapping
Pattern indexing
If the setup geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and crystallographic orientation of the material within the electron interaction volume. Each band can be indexed individually by the Miller indices of the diffracting plane which formed it. In most materials, only three bands/planes intersect and are required to describe a unique solution to the crystal orientation. Most commercial systems use look-up tables with international crystal databases to index. This crystal orientation relates the orientation of each sampled point to a reference crystal orientation.Indexing is often the first step in the EBSD process after pattern collection. This allows for the identification of the crystal orientation at the single volume of the sample from where the pattern was collected. With EBSD software, pattern bands are typically detected via a mathematical routine using a modified Hough transform, in which every pixel in Hough space denotes a unique line/band in the EBSP. The Hough transform enables band detection, which is difficult to locate by computer in the original EBSP. Once the band locations have been detected, it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes. Thus, an orientation solution can be determined when the position/angles between three bands are known. In highly symmetric materials, more than three bands are typically used to obtain and verify the orientation measurement.
The diffraction pattern is pre-processed to remove noise, correct for detector distortions, and normalise the intensity. Then, the pre-processed diffraction pattern is compared to a library of reference patterns for the material being studied. The reference patterns are generated based on the material's known crystal structure and the crystal lattice's orientation. The orientation of the crystal lattice that would generate the best match to the measured pattern is determined using a variety of algorithms. There are three leading methods of indexing that are performed by most commercial EBSD software: triplet voting; minimising the 'fit' between the experimental pattern and a computationally determined orientation, and or/and neighbour pattern averaging and re-indexing, NPAR). Indexing then give a unique solution to the single crystal orientation that is related to the other crystal orientations within the field-of-view.
Triplet voting involves identifying multiple 'triplets' associated with different solutions to the crystal orientation; each crystal orientation determined from each triplet receives one vote. Should four bands identify the same crystal orientation, then four votes will be cast for that particular solution. Thus the candidate orientation with the highest number of votes will be the most likely solution to the underlying crystal orientation present. The number of votes for the solution chosen compared to the total number of votes describes the confidence in the underlying solution. Care must be taken in interpreting this 'confidence index' as some pseudo-symmetric orientations may result in low confidence for one candidate solution vs another. Minimising the fit involves starting with all possible orientations for a triplet. More bands are included, which reduces the number of candidate orientations. As the number of bands increases, the number of possible orientations converges ultimately to one solution. The 'fit' between the measured orientation and the captured pattern can be determined.
Overall, indexing diffraction patterns in EBSD involves a complex set of algorithms and calculations, but is essential for determining the crystallographic structure and orientation of materials at a high spatial resolution. The indexing process is continually evolving, with new algorithms and techniques being developed to improve the accuracy and speed of the process. Afterwards, a confidence index is calculated to determine the quality of the indexing result. The confidence index is based on the match quality between the measured and reference patterns. In addition, it considers factors such as noise level, detector resolution, and sample quality.
While this geometric description related to the kinematic solution using the Bragg condition is very powerful and useful for orientation and texture analysis, it only describes the geometry of the crystalline lattice. It ignores many physical processes involved within the diffracting material. To adequately describe finer features within the electron beam scattering pattern, one must use a many-beam dynamical model.