Constraints on the effective electron energy spectrum in backscatter Kikuchi diffraction

Electron backscatter diffraction (EBSD) is a technique to obtain microcrystallographic information from materials by collecting large-angle Kikuchi patterns in the scanning electron microscope (SEM). An important fundamental question concerns the scattering-angle dependent electron energy distribution, which is relevant for the formation of the Kikuchi diffraction patterns. Here we review the existing experimental data and explore the effective energy spectrum that is operative in the generation of backscatter Kikuchi patterns from silicon. We use a full pattern comparison of experimental data with dynamical electron diffraction simulations. Our energy-dependent cross-correlation based pattern matching approach establishes improved constraints on the effective Kikuchi pattern energy spectrum, which is relevant for high-resolution EBSD pattern simulations and their applications.

Figure 1

EBSD scattering geometry and raw diffraction pattern with key features. For a specific point on the phosphor screen, the angle $\alpha$ indicates the scattering angle relative to the primary beam, with ${30}^{\circ }⪅\alpha ⪅{130}^{\circ }$ for typical EBSD patterns.

Figure 2

(Top) Experimental raw EBSD pattern from silicon, $E_0=15\mathrm{keV}$. (Bottom) Background-processed silicon Kikuchi pattern. The dashed rectangles mark the regions of interest corresponding to different ranges of scattering angles. Projection center: (0.5024, 0.1555, 0.7751) [22], capture angles: horizontally: ${81}^{\circ }$, vertically: ${59}^{\circ }$.

Figure 3

Analysis of the experimental upper ROI. (Top) Simulation for 13.0 keV ($r=0.839$) with indicated features for comparison to the experiment. (Middle) Experimental ROI. (Bottom) Best fit ROI simulation for 14.0 keV central energy ($r=0.850$), features indicated in the upper panel fit better at 14 keV.

Figure 4

Analysis of the experimental middle ROI. (Top) Simulation for 13.0 keV ($r=0.811$) with indicated features for comparison to the experiment. (Center) Experimental middle ROI. (Bottom) Best fit ROI simulation for 14. keV central energy ($r=0.844$), features indicated in the upper panel fit better at 14 keV.

Figure 5

Analysis of the experimental lower ROI. (Top) Simulation for 13.5 keV ($r=0.766$) with indicated features for comparison to the experiment. (Center) Experimental middle ROI. (Bottom) Best fit ROI simulation for 14.5 keV central energy (bottom, $r=0.792$), features indicated in the upper panel fit better at 14.5 keV.

Figure 6

Energy-dependent NCC $r$-values for all ROIs and the full Si pattern as shown in Fig. 2. Lines are guides to the eye.

Figure 7

Comparison of (110) band profiles extracted from two Kikuchi patterns of slightly different orientations [(a) and (b)]. The middle panels (c) and (d) show the (110) bands reprojected in a spherical coordinate system $(\theta ,\varphi )$ for quantitative bandwidth comparison. Bottom [(e) and (f)] Averaged (110) band profiles within $5^{\circ }$ of the top and bottom of (c) and (d). The vertical lines indicate the geometrical Bragg angles for the 220 reflection in Si ($a_{\mathrm{Si}}=5.4307\AA , d_{220}=1.920\AA$) for energies of 15 (solid), 14 (dashed), and 11 keV (dash-dotted).

Figure 8

(Top) Kikuchi pattern measured at 12 K from ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, primary beam voltage 20 keV.

(Bottom) Best fit dynamical simulation for 20 keV. The viewing angles are ${89}^{\circ }$ horizontally, and ${74}^{\circ }$ vertically.

Figure 9

Energy-dependent NCC $r$ values for all ROIs and the full ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ pattern as shown in Fig. 8. Lines are guides to the eye.