The 90° partial dislocation in semiconductor silicon: An investigation from the lattice P–N theory and the first principle calculation

Abstract

The 90° partial dislocation in silicon is studied theoretically in the framework of the improved P–N model and the first principle calculation. Instead of the frequently used integro-differential equation, a fully discrete dislocation equation is proposed to determine the core structure (distribution of dislocation density). Furthermore, in order to describe the dislocation structure precisely, the effective interaction γ-surface is generalized to be the γ-potential and the space change induced by the appearance of the dislocation is addressed self-consistently. With the γ-potential calculated from the first-principles, the core structures and the stress field are explicitly obtained through the variational method and the superposition principle. The reconstructions are examined for an isolated dislocation using ab initio combined with the analytical theory. It is found that in the analytical theory there are two types of core structures. One is the stable (ground-state) structure referred to as the B-type dislocation. Another is the unstable structure referred to as the O-type dislocation. The single-period (SP) dislocation originates from the B-type dislocation and the double-period (DP) dislocation originates from the O-type dislocation. The movement of dislocation is realized by transformation from one type to another. The energy difference between different dislocations measures the height of the Peierls barrier. It is observed that the energy difference decreases after the reconstruction and thus the height of the Peierls barrier is reduced by the reconstruction. The results presented are helpful in understanding the effects associated to the details of the dislocation structure such as the brittle–ductile transition and the electronic structure.