Imaging screw dislocations at atomic resolution by aberration-corrected electron optical sectioning

Abstract

Screw dislocations play an important role in materials' mechanical, electrical and optical properties. However, imaging the atomic displacements in screw dislocations remains challenging. Although advanced electron microscopy techniques have allowed atomic-scale characterization of edge dislocations from the conventional end-on view, for screw dislocations, the atoms are predominantly displaced parallel to the dislocation line, and therefore the screw displacements are parallel to the electron beam and become invisible when viewed end-on. Here we show that screw displacements can be imaged directly with the dislocation lying in a plane transverse to the electron beam by optical sectioning using annular dark field imaging in a scanning transmission electron microscope. Applying this technique to a mixed [a+c] dislocation in GaN allows direct imaging of a screw dissociation with a 1.65-nm dissociation distance, thereby demonstrating a new method for characterizing dislocation core structures.

Figure 1. Depth-dependent screw displacements in a GaN c-type screw dislocation.

The positions of the Ga atoms in single layers of planes at various depths in a structure model of a GaN c-type screw dislocation (left) and simulated ADF focal series images (right). The screw dislocation is along [0001] and located at a depth of −5 nm, and the single layers are located at a 0, c−2.5, e−5.0, g−7.4 and i−9.6 nm below the top surface, respectively. In this work depths into the crystal are given by negative values and are measured relative to the entrance surface. Similarly, negative defocus denotes under focusing so that the focal plane moves below the entrance surface into the crystal. Dashed lines show the shearing of planes due to the screw. In e, the two planes immediately above and below the dislocation line are overlaid and indicated by different colours. Owing to a channelling pre-focusing effect, each simulated focal series image on the right (b,d,f,h,j) has a focus set ∼2 nm lower in depth than the corresponding layer of model on the left. The scale bar, 0.5 nm.

Figure 2. Schematic illustration of the image contrast in focal series ADF images of a screw dislocation.

The electron probe is focused at different depths and positions relative to a column, which has an arctangent shape due to the screw displacements. When the probe is focused at (a–c) −3 nm, (d–f) −5 nm and (g–i) −7 nm below the specimen entrance surface, different sections of the column are located close to the brightest part of the probe (atoms indicated by yellow colour). The peak image intensity occurs when the largest number of atoms lie in the most intense region of the elongated probe, as shown from the intensity line profiles of simulated focal series ADF images. This suggests that, despite the effects of dynamical scattering and channelling, the image contrast in focal series images are intuitively interpretable for identifying column locations and measuring screw displacements.

Figure 3. Experimental and simulated ADF image of a dissociated dislocation lying perpendicular to the electron beam.

The experiment STEM ADF image is the average of 64 images (see Supplementary Note 4). The screw displacements associated with each of the partial dislocations can be observed, as indicated by the overlaid solid and dashed lines following the closer-to-focus stronger-intensity peaks and further-from-focus weaker-intensity peaks, respectively. A simulated image (inset) of the isotropic elastic model of a ½[a+c]+½[a+c] dissociated dislocation with a 1.65-nm dissociation distance is overlaid. The simulation was performed with the beam focused at 5 nm below the top entrance surface of a 10-nm-thick foil. The scale bar, 1 nm.

Figure 4. The structure model and simulated focal series images of the dissociated dislocation.

(a) The dots represent the positions of the mixed Ga and N columns viewed along [0001]. The core positions of the two partials are located as indicated, and result in an atomic structure, shown in b, that matches the image shown in Fig. 2 of ref. . The resulting fault has a 4/8/4/8/4-ring structure, similar to the Drum fault, and a 1.65-nm dissociation distance. Simulated focal series ADF images of the dissociated ½[a+c]+½[a+c] and the undissociated [a+c] model viewed along are shown in c,d, respectively. The scale bar in the simulated image, 0.5 nm.

Figure 5. Determining screw dissociation through quantitative analysis of screw displacements near the dislocation.

(a) The images in the fault region consist of pairs of closely spaced peaks whose relative positions correlate with the amount of screw displacement. A Radon transform is used to measure changes in the column pair angles across the dislocation (see Supplementary Note 5). (b) The column pair angles have been measured for both the experimental and simulated images of dissociated screw (1.65-nm dissociation distance) and undissociated screw dislocations, and a good match is found between experiment and the dissociated screw column pair angles, confirming the experimental observation of a dissociated screw. The error bar in b corresponds to the s.d. of multiple measurements from the entire experiment image shown in Fig. 3. (c) The rate of angle change across the dislocation depends on the dissociation distance; therefore, by fitting sigmoid functions to the angle plots, and comparing the fitted slope-controlling parameter in the sigmoid functions of the experimental image with those of simulated images of different possible dissociation distances, the dissociation distance of 1.65 nm clearly gives the best agreement. The robustness of this quantification method against probe defocus and source size is examined across all four dissociation distances, and in the case of 1.65-nm dissociation distance, results of different specimen thicknesses and dislocation depths inside the crystals are also included in the plot in c. The legend in c shows the value of the parameters, for example, ‘df=−4 nm, s=0.6A, (10, −5)' means defocus −4 nm, source size 0.6 Angstrom, (10, −5) means the specimen thickness being 10 nm and the depth of dislocation below the top entrance surface being −5 nm. The scale bar in a, 0.5 nm.