Atomic structure of dislocations and dipoles in silicon

Abstract

Dislocations of the a/2〈110〉 Burgers vector lying in {001} and {111} planes in the form of cross-grids are often observed in ion-implanted and thermally annealed specimens of diamond cubic materials. In order to assess the mechanism of formation of these dislocations, we have calculated the energies and determined the atomic core structures of a/2〈110〉{001} edge dislocations and their dipoles, and of a/2〈110〉{111} dislocations in silicon by minimizing the total configurational energy. The calculations were made using Keating (1966) potentials and these results are compared with those obtained using more recent ideas (Baraff, Kane and Schluter 1980). The initial displacements of individual atoms were calculated using isotropic elasticity theory, and then the structure was relaxed to minimize its strain energy by incorporating bond-bending and stretching effects. A computational cell containing about sixteen-hundred atoms was chosen for the present calculations. In order to eliminate dangling bonds, atomic displacements in the direction (z) of the dislocation line were needed for certain core structures such as those associated with the a/2〈110〉{111} dislocation in the 〈112〉 direction. It should be noted, however, that there was no net displacement in the z direction. The core energy and radius of an a/2〈110〉{001} dislocation was determined, using Keating (1966) potentials, to be 0·62 eV Å⁻¹ and 5 Å, respectively, compared to 1·0eV Å⁻¹ and 5 Å, respectively, for an a/2〈110〉{111} dislocation. The core energies for {001} and {111} dislocations, using the constants of Baraff et al. (1980) were found to be 0·26 eV Å⁻¹ and 0·47 eV Å⁻¹, respectively. The present calculations clearly indicate the directional dependence of dislocation core energy in the diamond-cubic lattice. The coefficient of the logarithmic term of the energy outside the core for both dislocations was determined to be about 0·69 eV Å⁻¹ which was in agreement with the value obtained from well known continuum expressions. Using current ideas, the energy of a/2〈110〉{001} dislocation dipoles was calculated in order to assess the mechanism of condensation of point defects into dislocations and dipoles. The energy of a condensed intermediate-configuration defect was found to be lower than that associated with all the single defects involved. Also the energy of a dipole was found to increase with increasing separation between dislocations. These results indicated that non-equilibrium effects must prevail during the formation of observed dislocation dipoles.