# Electron backscatter diffraction (EBSD)

In the development and study of new materials, the understanding of their crystal structure plays a crucial rule. Electron backscatter diffraction (EBSD), also known as backscatter Kikuchi diffraction (BKD), is a technique used to obtain accurate crystallographic information from bulk materials, thin films and nanostructures with high spatial resolution [bibcite key=Schwarzer2009] (of order 20 nm). Typical materials which can be investigated by EBSD include metals, rocks, ceramics and semiconductors. The technique allows the identification of individual grain orientations, grain boundaries and phase identification [bibcite key=Schwarzer2009,Goldstein2003]. It is also used to study processes like recrystallization and grain growth, and it is a very powerful tool in the study of strain fields in crystals [bibcite key=Wilkinson2000JEM49].

EBSD patterns were first observed by Nishikawa and Kikuchi in 1928, in both backscattering and transmission modes, using electron-sensitive film [bibcite key=Nishikawa1928PIA4]. The technique was developed further by Alam et al in the 1950s [bibcite key=Alam1954PRSA221], and later by Venables and Harland (1973) and by Venables and Bin-Jaya (1977) [bibcite key=Venables1973PM27,Venables1977PM35]. In 1984 the first commercial system was produced by Moon and Harris, exploiting the work of Dingley at the University of Bristol [bibcite key=Wright2000]. In the 1990s fully automated EBSD systems in the SEM had been developed by Adams et al [bibcite key=Adams1993MTA24] and Krieger Lassen et al [bibcite key=KriegerLassen1992SM6,KreigerLassen1998JM190]. The capability to automatically index EBSPs and map the spatial distribution of crystal orientation led to EBSD becoming a good alternative to X-ray pole figure analysis of texture, and so opened up new horizons in quantitative orientation mapping and grain boundary studies [bibcite key=Schwarzer2009].

Figure 1: Illustration of the EBSD detection geometry and a conventional EBSD detector.

Experimentally, EBSD is conducted in a scanning electron microscope (SEM) equipped with an EBSD detector. Commercial EBSD detectors consist of an electron sensitive screen (a phosphor or a scintillator) placed in front of the specimen which is usually tilted by approximately 70° to the normal of the exciting electron beam. A digital camera is used to acquire an image of the diffraction pattern formed by the backscattered electrons impinging on the screen [bibcite key=Schwarzer2009,Day2009]; this is illustrated in Figure 1.

An electron backscatter diffraction pattern (EBSP) is shown in Fig. 1 (b). A detailed description of the intensities in EBSPs is possible using a Bloch wave approach to the dynamical theory of electron diffraction [bibcite key=Winkelmann2007UM107,Wikelmann2009]; however, the geometry of the EBSP can be described, to a first approximation, by considering the angular position of electrons which have been Bragg reflected from the lattice planes of the crystal specimen. On penetrating the specimen, the electrons of the impinging beam are both elastically and inelastically scattered. This creates a diverging source of electrons with a broad range of energies [bibcite key=Goldstein2003,Winkelmann2010NJP12,Wells1999Scanning21,Matsukawa1974JPD7,Lloyd1987MinMag51,Yubero2008PRB77,Winkelmann2013MM19,Zaefferer2014AM75]. The elastically scattered electrons and quasi-elastically scattered electrons (those electrons which have lost only a relatively small amount of energy through phonon or plasmon scattering) may travel in such a way that their energy and direction satisfy the Bragg condition, $2d\sin{\theta} = n\lambda$, for a set of planes and undergo diffraction, where $d$ is the spacing between planes, $\theta$ is the Bragg angle, $\lambda$ the wavelength of the electron and $n$ the order of diffraction. Because of the cylindrical symmetry of the Bragg reflection condition with respect to the lattice plane normal, diffraction cones (Kossel cones) are formed. When these cones intersect the phosphor screen, Kikuchi lines are observed in a gnomonic projection: see Fig. 1. The Kikuchi lines appear as almost straight lines because the cones are very shallow, as the Bragg angle $\theta$ is of order 1°. The Kikuchi lines are superimposed on a diffuse background which is produced predominantly by lower energy inelastically scattered electrons which have not been Bragg scattered. As each Kikuchi band (pair of Kikuchi lines) is effectively fixed to the plane from which it is formed, an EBSD pattern provides a direct measurement of a sample’s orientation. Rotation of a crystal will produce a rotation of the EBSP; a tilt of a crystal will produce a shift in the EBSP (see Fig. 2). EBSPs acquired from a mesh of points on a sample can be used to produce a map of tilt or rotations in that sample [bibcite key=Schwarzer2009] (see Fig. 3).

Figure 2: Effect of the rotation and tilt of single crystal silicon on the EBSD pattern: (a) Si (100), (b) crystal rotated by 10°, (c) crystal tilted by 10°. The inset placed on the right side of each picture shows the 3D spherical Kikuchi pattern and the corresponding real space views of the crystal structure. (Patterns were simulated using the trial version of Bruker’s ESPRIT DynamicS software)

Figure 3. Orientation map of a nickel sample (courtesy of Ken Mingard, NPL, Teddington)

An EBSP contains a large amount of crystallographic information from which it is possible to deduce the phase of the material under study. The space group may be determined by analysing the symmetry exhibited by the pattern. An unknown phase may be identified by a comparison of the observed symmetry with the symmetry of a list of known phases contained in a database until it is correctly identified [bibcite key=Michael2000].

Our EBSD research at Strathclyde is mainly focused on the development of new direct electron detectors [bibcite key=Vespucci2015]. We are using the Timepix detector [bibcite key=Llopart2007NIMA581,Llopart2002IEEETNS49], which belongs to the CMOS hybrid pixel detectors family. It is one of the outcomes of an international collaboration (Medipix) hosted at CERN, established to provide a solution for a range of problems in X-ray and gamma-ray imaging in hostile conditions. Using the Timepix allows digital direct electron detection and energy filtering; it enables EBSPs to be acquired with reduced noise and increased contrast, and an unprecedented increase in detail is observed in the patterns (see Fig. 4).

Figure 4: Experimental and simulated EBSPs from diamond (a, d, g), Si (b, e, h) and GaN (c, f, i) for an incident beam energy of 20 keV and a probe current of ~10 nA. (a–c) were acquired with a high pass energy filter of 4.6 keV, (d–f) were acquired with a high pass energy filter of 19.4 keV, and (g–i) are simulations (courtesy of Aimo Winkelmann, Bruker Nano, Berlin). The insets are 2D fast Fourier transforms of each image.

## References

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