#### 2.2. TEM Analysis

A TEM investigation has been conducted on a (001)-oriented GaAs sample, 500 μm thick, treated with a sandpaper P400 for 10 min which permitted to obtain a curvature radius R = 2.8 m.

The sample cross section, parallel to the (110) planes of the crystal, was mechanically polished down to ca. 300 μm. The resulting foils were ion-sputtered with a Gatan^{®} DuoMill TM model 600 (Gatan, Pleasanton, CA, USA), to reach electron transparency. The final sample thickness was estimated to be between 70 and 120 nm, as evaluated by the extinction length of the electron beam in the GaAs lamella. A final gentle ion milling procedure was applied to the cross-section’s thin lamella using a Gatan PIPS installation operated at a 3 kV accelerating voltage and 7° incidence angle.

A series of TEM micrographs recorded from neighboring areas are assembled in the panoramic image of

Figure 1, which illustrates the effect of the treatment on the (001) surface, which is located on the right-hand side of the image. We did not observe defects such as cracks or inclusions in any of the observed samples but only short straight dislocation segments from the surface to ca. 3 μm in depth. We have no evidence of a formation of an amorphous phase near the surface of the sample as observed for instance in TEM specimens prepared by a focused ion beam [

14,

15], even if it is not possible to exclude the local formation of an amorphous layer a few nanometers thick during surface damage treatment.

The near-surface region shows a high defect density that extends for a few hundred nanometers. Below this first layer, the density of dislocations drastically decreases, and the dislocations, which appear as straight dark lines, can be observed singularly.

It is worth noting that two sets of dislocation lines can be identified in

Figure 1b. The two sets are parallel to the (−111) and (1−11) planes, respectively, perpendicular to the (110) surface of the cross-section sample. Looking carefully at the dislocation segments, it appears that many dislocations cross the TEM sample, i.e., the dislocation lines are not parallel to the surface of the cross section.

Two families of parallel dislocations can be identified in

Figure 1a,b. By comparing the micrograph in

Figure 1b with the corresponding diffraction pattern in

Figure 1c, it turns out that the habit planes of the two families of dislocations are (1−11) and (−111).

By tilting the sample in such a way that only the (−111) and (1−11) reflections are excited, the two families of dislocations become respectively extinguished. It follows that, according to the $\overrightarrow{g}\cdot \overrightarrow{b}$ = 0 invisibility criterion, the Burgers vectors of these dislocations are also parallel to the (−111) and (1−11) crystallographic planes, respectively.

Considering the dislocations with lines parallel to the (1−11) planes, based on the orientation-imaging conditions, it turns out that their Burgers vectors are parallel to the same planes. In the cubic structure of GaAs, an easy slip system is of the type {111}<110>, and the most common dislocations are perfect dislocations with Burgers vector a/2<110>. In the following analysis, we will assume only dislocations of this type. This may appear a critical limit of the model, but the assumption is justified by the fact that

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these dislocations have the lowest elastic energy among perfect dislocations in the face-centered-cubic (fcc) crystals;

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non-perfect dislocations are always associated to stacking faults increasing the elastic energy and limiting their mobility;

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these dislocations are typically observed in indented fcc crystals.

It follows that the Burgers vectors may have one of the following six values: a/2[110], a/2[011], a/2[−101], a/2[−1−10], a/2[0−1−1], and a/2[10−1], all of which are contained in the (1−11) plane.

A similar analysis is valid for the other set of dislocations with Burgers vectors lying in the (−111) habit plane. It follows that their Burgers vector may have one of the following six values: a/2[110], a/2[101], a/2[0−11], a/2[01−1], a/2[−1−10], and a/2[−10−1], all of which are contained in the (−111) plane.

The fact that the A and B dislocations are not extinguished simultaneously leads to the conclusion that the Burgers vector cannot be a/2[110] or a/2[−1−10]. In other words, the Burgers vector of the dislocations are not parallel to the electron beam and therefore not parallel to the wafer surface, the (001) plane. The Burgers vectors of the analyzed dislocations are one of the remaining four vectors—a/2[011], a/2[−101], a/2[0−1−1], or a/2[10−1] for the first set and a/2[101], a/2[0−11], a/2[01−1], or a/2[−10−1] for the second set. This means that all the Burgers vectors have a component b^{||} parallel to the (001) surface of the processed wafer and a component b^{□} oriented perpendicular to the surface.