Strain Induced Deep Electronic States around Threading Dislocations in GaN

Combining through-focus high-resolution transmission electron microscopy and hierarchical multiscale simulations consisting of density-functional theory, analytical empirical potentials, and continuum elastic theory we demonstrate the existence of a new dislocation type in GaN. In contrast with all previously identified or suggested dislocation structures in GaN, all core atoms are fully coordinated; i.e., no broken bonds occur, implying that the dislocation should be electrically inactive. However, as we show, the giant local strain-field around the dislocation core, in combination with the small lattice constant of GaN, causes deep defect states and thus electrically active edge dislocations independent on the specific core structure.

Figure 1

Threading dislocation in GaN at defocus values $\Delta f=-23$ and $\Delta f=-63\mathrm{n}\mathrm{m}$ (unfiltered HR-TEM) (a),(e). Image simulations for the four-core structure (b),(f), full-core structure (c),(g), and the open structure (d),(h). The upper (lower) panel shows defocus values $\Delta f=-23\mathrm{n}\mathrm{m}$ ($\Delta f=-63\mathrm{n}\mathrm{m}$). For additional experimental micrographs, see 11.

Figure 2

Contour plots of dislocation induced deep electronic states for the (a) four-core, (b) full-core, and (c) open-core structures. Large (small) balls correspond to Ga (N) atoms.

Figure 3

Relative formation energies per dislocation as a function of dislocation separation (lower axis) and dislocation density (upper axis). The formation energy of the full-core structure has been used as reference energy. The symbols mark the calculated energies: ab initio calculations (cycles), shifted (squares), and unshifted empirical potentials (triangles). The open and filled diamonds give the relative formation energy if the dislocations are formed in a strained host. The value $\epsilon$ gives the corresponding strain (positive/negative values indicate compressive/tensile strain). The vertical solid lines separate the four zones discussed in the text. Alignment shows the cell size for which the ab initio and the empirical potential calculations have been aligned.