Electronic Structure and van der Waals Interactions in the Stability and Mobility of Point Defects in Semiconductors

We study the role of electronic structure (band gaps) and long-range van der Waals (vdW) interactions on the stability and mobility of point defects in silicon and heavier semiconductors. Density functional theory calculations with hybrid functionals that contain part of the Hartree-Fock exchange energy are essential to achieve a reasonable description of defect electronic levels, leading to accurate defect formation energies. However, these functionals significantly overestimate the experimental migration barriers. The inclusion of screened vdW interactions further improves the description of defect formation energies, significantly changes the barrier geometries, and brings migration barrier heights into close agreement with experimental values. These results suggest that hybrid functionals with vdW interactions can be successfully used for predictions in a broad range of materials in which the correct description of both the electronic structure and the long-range electron correlation is essential.

Figure 1

The crystal structure of the $X$, $H$, $T$, and $V$ defects in Si. For $V$ the most stable JT-distorted configuration is shown. The size of the balls indicates the change in the atomic vdW $C_6$ coefficients [39]. The $C_6$ coefficients increase with increasing size of the balls (in the order $\mathrm{\text{blue}}\mathrm{\text{−}}\mathrm{\text{green}}<\mathrm{\text{blue}}<\mathrm{\text{green}}<\mathrm{\text{red}}$).

Figure 2

Relative energies and migration barriers for different diffusion pathways of interstitials and vacancies in Si. The insets show the geometry of the transition state along the $H\mathrm{\text{−}}X$ pathway, determined with and without including vdW interactions.