Theoretical calculation of the dislocation width and Peierls barrier and stress for semiconductor silicon

The dislocation width and Peierls barrier and stress have been calculated by the improved Peierls-Nabarro (PN) theory for silicon. In order to investigate the discreteness correction of a complex lattice quantitatively, a simple dynamics model has been used in which interaction attributed to a variation of bond length and angle has been considered. The results show that the dislocation core and mobility will be corrected significantly by the discrete effect. Another improvement is considering the contribution of strain energy in evaluating the dislocation energy. When a dislocation moves, both strain and misfit energies change periodically. Their amplitudes are of the same order, but phases are opposite. Because of the opposite phases, the misfit and strain energies cancel each other and the resulting Peierls barrier is much smaller than that given by the misfit energy conventionally. Due to competition between the misfit and strain energies, a metastable state appears separately for glide 90° and shuffle screw dislocations. In addition, from the total energy calculation it is found that besides the width of dislocation, the core of a free stable dislocation may be different according to where the core center is located. The exact position of the core center can be directly verified by numerical simulation, and provides a new prediction that can be used to verify the validity of PN theory. It is interesting that after considering discrete correction the Peierls stress for glide dislocation coincides with the critical stress at low temperature, and the Peierls stress for shuffle dislocation coincides with the critical stress at high temperature. The physical implication of the results is discussed.