Theory of defects in one-dimensional systems: the case of Al in Si nanowires

TL;DR

This paper develops a formalism to calculate defect formation energies in one-dimensional nanostructures, addressing surface passivation and dielectric effects, and applies it to aluminum impurities in silicon nanowires, revealing higher impurity concentrations than in bulk silicon.

Contribution

It introduces a new method for calculating defect formation energies in 1D nanostructures, overcoming previous challenges related to chemical potentials and surface passivation.

Findings

Higher formation energies of Al impurities in nanowires compared to bulk silicon.

The formalism includes a generalized Madelung correction for dielectric anisotropy.

Application demonstrates increased impurity concentrations in nanowires.

Abstract

The energetic cost of creating a defect within a host material is given by the formation energy. Here we present a formulation allowing the calculation of formation energies in one-dimensional nanostructures, which overcomes the difficulties involved in defining the chemical potential of the constituent species and the possible passivation of the surface. We also develop a formula for the Madelung correction for general dielectric tensors and computational cell shapes. We apply this formalism to the formation energies of charged Al impurities in silicon nanowires, obtaining concentrations significantly larger than in their bulk counterparts.