Theoretical calculations of the structure and energy of the .SIGMA.=5 tilt grain boundary in silicon.

Abstract

The structure and energy of the ∑=5 (130) symmetrical tilt grain boundary in Si were calculated theoretically. The valence force fields, the bond orbital model, and the semiempirical tight-binding method with the use of the supercell technique were used and the computed results were compared with each other. All the computations have shown that the structural model by Bacmann et al. is more energetically favored than that by Hornstra and that the optimum rigid-body translation of the former model is characterized by a translation of about 1/8a0 along the direction. These results are in good agreement with the experimental observation of a germanium bicrystal. However, there are diferences in the absolute values of calculated boundary energies. The energy values obtained by the valence force potentials with the parameters fitted to the elastic constants and by the bond orbital model are overestimated, although the energy values by the valence force potential with the parameters fitted to the finite wave vector modes of lattice distortions are comparable with those by the semiempirical tight-binding method.