Direct Observation of Depth-Dependent Atomic Displacements Associated with Dislocations in Gallium Nitride

J. G. Lozano, H. Yang, M. P. Guerrero-Lebrero, A. J. D’Alfonso, A. Yasuhara, E. Okunishi, S. Zhang, C. J. Humphreys, L. J. Allen, P. L. Galindo, P. B. Hirsch, and P. D. Nellist

Phys. Rev. Lett. 113, 135503 – Published 24 September 2014

Abstract

We demonstrate that the aberration-corrected scanning transmission electron microscope has a sufficiently small depth of field to observe depth-dependent atomic displacements in a crystal. The depth-dependent displacements associated with the Eshelby twist of dislocations in GaN normal to the foil with a screw component of the Burgers vector are directly imaged. We show that these displacements are observed as a rotation of the lattice between images taken in a focal series. From the sense of the rotation, the sign of the screw component can be determined.

Received 10 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.135503

Authors & Affiliations

J. G. Lozano¹, H. Yang¹, M. P. Guerrero-Lebrero², A. J. D’Alfonso³, A. Yasuhara⁴, E. Okunishi⁴, S. Zhang⁵, C. J. Humphreys⁵, L. J. Allen³, P. L. Galindo², P. B. Hirsch¹, and P. D. Nellist¹

¹Department of Materials, University of Oxford, OX1 3PH Oxford, United Kingdom
²Departamento de Ingeniería Informática, CASEM, Universidad de Cadiz, Polígono Rio San Pedro s/n, 11510 Puerto Real (Cadiz), Spain
³School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
⁴JEOL Ltd., 1-2 Musashino 3-Chome, Akishima, 196-8558 Tokyo, Japan
⁵Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, CB3 0FS Cambridge, United Kingdom

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Vol. 113, Iss. 13 — 26 September 2014

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Images

Figure 1
Atomic displacement maps from simulated images, using the $μ$ stem software [16], where the magnitude of the arrows is calculated as the difference between the position of the intensity peaks at focus values (a) $- 2.5 nm$ , (b) $- 5 nm$ , and (c) $- 7.5 nm$ for a GaN crystal with a screw dislocation normal to the foil with the Eshelby twist, and the atomic positions at the entrance surface (zero defocus). For better visualization, a factor of 5 has been applied to the magnitude of these displacements. The core of the dislocation is at the origin. Variations in the height of the atoms in the entrance and exit surface layers due to the screw displacements lead to an asymmetry in the Eshelby displacements with respect to the dislocation core. (d) Displacement of the atomic columns due to the Eshelby twist averaged over an 8.4 nm depth of field as a function of the distance from the core for $z_{1} = 0 nm$ (entrance surface). The field of view in the experimental images of a screw dislocation is marked with a dashed line.
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Figure 2
(a),(b) show two HRSTEM micrographs of a pure screw dislocation, part of a focal series, taken at defocus values 2.4 nm apart. The position of the core of the dislocation is marked with a white cross. (c),(d) are the Radon transformation maps calculated from the upper area in the micrographs marked with a red rectangle in (a),(b). An area symmetrically opposite (also shown with red boxes in the lower area of the micrographs) showed a consistent rotation and was also used in the measurement of the lattice rotation by taking an average of the two values. (e),(f) represent the variance of each intensity profile in the area between the dashed lines in the Radon maps in (c),(d).
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Figure 3
Rotation angle as a function of the focus value for the experimental (red curve) and simulated (green and blue curves) HAADF focal series of a 10 and 20 nm thick GaN crystal including a right-handed screw dislocation and the Eshelby twist under the experimental conditions. The zero focus value corresponds to the entrance surface. The highest contrast experimental image in the focal series was assigned to a defocus of $- 1.2 nm$ (indicated by a dashed red circle in the experimental curve) as described in the text.
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Figure 4
HRSTEM micrographs part of a complete focal series of (a),(b) two neighboring mixed dislocations and (c) a pure edge dislocation. The position of the dislocation cores are marked with white crosses. (d) The experimentally measured rotation angle as a function of defocus for these three dislocations. The rotation is clockwise for one of the mixed dislocations and anticlockwise for the other. No significant rotation is observed for the case of the pure edge dislocation.
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