## 4 Discussion  
The dislocations we observe display a similar contrast and are nearly parallel to the c-axis. The threading dislocations parallel to the c-axis in 4H-SiC that have been reported [5; 6] are either screw dislocations or edge dislocations displaying a Burgers vector along \(11\overline{2}0\). We discard the screw dislocation case because it is such that \(\mathbf{h.b}=0\), \(\mathbf{h}\) being the diffraction vector (perpendicular to the \((40\overline{4}0)\) planes) and \(\mathbf{b}\) the Burgers vector (parallel to \(\mathbf{c}\)), and therefore, these dislocations should not be observed because they produce nearly no contrast in the image [16]. The Burgers vectors of the dislocations we observe display an edge component. These dislocations are such that they produce, on the \(\left(40\overline{4}0\right)\) lattice planes, an angular misorientation towards the \(\mathbf{c}\)-axis, as indicated in Figure 4.  
Figure 5 schematically shows the dislocation lines (violet) and the tilt of the \(\left(40\overline{4}0\right)\) lattice planes in the region between dislocation lines of opposite sign. The intersection of the scattering plane (the \(\left(12\overline{1}0\right)\) lattice planes of the crystal matrix) with the distorted \(\left(40\overline{4}0\right)\) lattice planes is shown as green lines. In the region between the pair of dislocations, these lines are rotated by an angle \(\alpha\) with respect to the matrix. For simplicity, for the present discussion, we assume that the weak variation of the angle \(\alpha\) within this region can be neglected and that \(\alpha\) can be approximated by a constant, average angle, as indicated on the right side of Figure 5. Subgrain boundary-like regions (red rectangles in Figure 5) are generated at the boundaries between the regions where the \(\left(40\overline{4}0\right)\) lattice planes exhibit a rotation and the matrix. Let \(\mathrm{E_{d}}\) be the energy per unit length (comprising core and elastic energy) of the dislocation. When the distance \(D\) between the dislocations is large enough, the interaction between dislocations can be neglected, and the misorientation angle \(\alpha\) in the region between the dislocations decays back to zero. In this case, the energy of the dislocation pair is simply the sum of the energies of the two dislocations \(2\cdot t\cdot\mathrm{E_{d}}\), where \(t\) is the thickness of the crystal, i.e., also the length of the dislocation in the crystal. In the case of the pair of dislocations indicated by the red arrow in Figures 2 and 3, the energy of the dislocations is smaller than \(2\cdot t\cdot\mathrm{E_{d}}\) because there is no return to the matrix orientation in between them. This is shown schematically in Figure 6, which shows a truncated distortion field for the dislocations. A  
Figure 5: Schematic drawing indicating the angular deviation of the Bragg diffracting planes (schematised by green lines) in the region lying between the dislocations (violet lines) with opposite Burgers vectors. This region is misoriented by an average angle \(\alpha\) with respect to the matrix. The direction of the diffraction vector \(\mathrm{h}\) is indicated. On the right side of the figure we show the approximation we use for the discussion, where we consider an angle \(\alpha\) constant over the volume lying between the subgrain boundary-like regions, represented by the rectangular volumes in red. zone in between the two dislocations retains a misorientation \(\alpha\) instead of going to zero. We therefore suggest that the energy of the dislocations reduces to \(k\cdot t\cdot E_{d}\) instead of \(2\cdot t\cdot E_{d}\), with \(k<2\). The energy of the dislocations in the case indicated by the red arrow (Figures 2 and 3) can therefore be expressed as \(k\cdot t\cdot E_{d}\), with \(1<k<2\). However, another energy, the one of the two subgrain boundary-like regions, indicated in Figure 5 by the red rectangular volumes, has to be added, in this simple model approximation, to determine the total energy of this configuration.