The equilibrium structures of the 90 degrees partial dislocation in silicon

Abstract

We consider the free energies of the single-period (SP) and double-period (DP) core reconstructions of the straight 90 degrees partial dislocation in silicon. The vibrational contributions are calculated with a harmonic model. It is found that it leads to a diminishing difference between the free energies of the two core reconstructions with increasing temperature. The question of the relative populations of SP and DP reconstructions in a single straight 90 degrees partial dislocation is solved by mapping the problem onto a one-dimensional Ising model in a magnetic field. The model contains only two parameters and is solved analytically. It leads to the conclusion that for the majority of the published energy differences between the SP and DP reconstructions the equilibrium core structure is dominated by the DP reconstruction at all temperatures up to the melting point. We review whether it is possible to distinguish between the SP and DP reconstructions experimentally, both in principle and in practice. We conclude that aberration corrected transmission electron microscopy should be able to distinguish between these two core reconstructions, but published high resolution micrographs do not allow the distinction to be made.