Determination of Burgers Vectors of Dislocations
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The determination of the Burgers vectors (b) of dislocations is not a straightforward operation. The common method is that in conventional electron diffraction contrast TEM imaging, the Burgers vector is extracted by the images obtained under two-beam diffraction conditions. The Burgers vector of a perfect dislocation is represented by a full lattice translation vector in the close packed direction and on the close packed plane of the crystal, resulting in an integer value of g·b. Regardless of whether the dislocations are of edge- or screw-type, based on the invisibility criterion, the dislocations are invisible at g·b = 0 or exhibit a so-called "residual" contrast for edge dislocations when the dislocations are out of contrast [1], the dislocations are visible in the other cases.

Figure 3463a shows three two-beam TEM images taken from the same area of a GaN thin film grown by MOCVD on N-face of a GaN bulk single crystal substrate. The images present three types (D1, D2, and D3) of dislocations. The conventional diffraction contrast analysis suggested that the dislocations have the Burgers vectors listed in Table 3463.

TEM images taken from the cross-section of a GaN homoepitaxial film showing a variety of dislocations

Figure 3463a. TEM images taken from the cross-section of a GaN homoepitaxial film showing a variety of dislocations: (a) Bright field with g1 = [0002]; (b) Dark-field image with g4 = [01-10]; and (c) Dark-field image with g5 = [1-102]. Adapted from [6]

Table 3463. Standard g·b analysis obtained by observing the dislocation image strength in dark-field and bright-field images in Figure 3463a. Based on the invisibility criterion, a specific dislocation may or may not display in a image. For instance, the two-beam bright-field TEM image in Figure 3463a (a) can not show D2 because g1·b = 0 as indicated in Table 3463.

Table 3463. Standard g·b analysis. Here, s stands for strong contrast, w for
weak contrast, r for residual contrast, and i for invisible contrast.

Dislocation D1 D2 D3
b [000-1] 1/3[1-2-10]
1/3[-1-1-23]
Imaging reflection Image g·b Image
g·b Image g·b
g1 = [0002]
s
≠0
i
0
s
≠0
g2 = [10-10]
i
0
r
0
s
≠0
g3 = [11-20]
i
0
s
≠0
s
≠0
g4 = [01-10]
i
0
s
≠0
s
≠0
g5 = [1-102]
s
≠0
w
≠0
s
≠0

Even though the invisibility criterion described above gives the direction of b, its magnitude and sign is still a question. To draw an unambiguous conclusion, in many cases a combination of different techniques is applied in the Burgers vector investigations. For instance, LACBED (large angle convergent beam electron diffraction) can provide more information on the properties of Burgers vectors. It had been suggested that when a LACBED Bragg line intersects a dislocation, displacement and splitting of the Bragg line may occur [2], from which the sign and magnitude of b can be obtained. [3 - 5] This method is called Cherns–Preston rules. These rules give the magnitude of b by g·b = m+1, where m is the number of subsidiary maxima in between the main peaks obtained in a dark-field image. For instance, Figure 3463b shows the dark-field contour of D1, taken by g = [0006], has m = 5 corresponding to g·b = 6. After applying the rules for the sign of b, [7] the Burgers vector is given by b = - c = [000-1] as listed in Table 3463. Note that the intensity and position of the subsidiary fringes vary with the dislocation character and depth in the TEM sample.

Dark-field LACBED pattern

Figure 3463b. (a) Bright field image and (b) Dark-field LACBED pattern (g = [0006])
taken from dislocation D1 in Figure 3463a. Adapted from [6]

A practical determination procedure of Burgers vector b of a dislocation is given below:
        i) Find the proper g·b table for the crystal structure in your experiment at page1995. The bs in the tables are the possible Burgers vectors for the dislocation, which are usually the shortest lattice vectors.
        ii) In order to know which zone axis should be tilted in and which two-beam condition is needed to obtain two specific conditions having g·b = 0, a Kikuchi map and zone-axis diffraction patterns should be investigated.
        iii) Tilt the specimen to those zone axes along the Kikuchi bands to confirm they are the ones needed.
        iv) Tilt out from the zone axis a few degrees along the bands to a proper two-beam condition, record an image and a diffraction pattern, and then determine the g·b. Note that, in general, by considering the various values of g·b in the proper table at page1995, two non-collinear values of g with g·b = 0 are sufficient to make a unique determination of the direction of b. For instance, for an fcc structure, zone axes like [110] (see page3915) are especially useful because the accessible g vectors include (002), (1-11), (1-1-1), (2-20), (1-13) and their opposites, and the defects (e.g. dislocations here) usually lie on {111} planes. As an example, if we found g1·b = 0 at g1 = [1 1 -1] and g2·b = 0 at g2 = [0 0 2], and then we can determine b = 1/2[1 -1 0] as indicated at page1815.


 

 

 

 

[1] Hirsch, P., Howie, A, Nicholson, R.B., Pashley, D.W. and Whelan, M.J., 1977, Electron Microscopy of Thin Crystals, Krieger, New York, p. 181.
[2] D. Cherns and A. R. Preston, Proceedings of the 11th International Congress on Electron Microscopy (Japan Society of Electron Microscopy, Kyoto, 1986), p. 721.
[3] D. Cherns and J. P. Morniroli, Ultramicroscopy 53, 167 (1994).
[4] J. P. Morniroli, F. Strzelczyk, A. Redjaı¨mia, and D. Cherns, Proceedings of the 13th International Congress on Electron Microscopy, Les Ulis, Les Editions de Physique, Paris, 1994!, Vol. 1, p. 901; J. P. Morniroli and D. Cherns, Ultramicroscopy 62, 53 (1996).
[5] P. Cordier, J. P. Morniroli, and D. Cherns, Philos. Mag. A 72, 1421 (1995).
[6] F. A. Ponce, D. Cherns, W. T. Young, and J. W. Steeds, Characterization of dislocations in GaN by transmission electron diffraction and microscopy techniques, Appl. Phys. Lett. 69 (6), (1996) 770.
[7] P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals (Krieger, New York, 1977).

 

 

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