Theory of Defects in One-Dimensional Systems: Application to Al-Catalyzed Si Nanowires

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 applying the bulk formalism and the possible passivation of the surface. We also develop a formula for the Madelung correction for general dielectric tensors. We apply this formalism to the technologically Important case of Al-nanoparticle-catalyzed Si nanowires, obtaining Al concentrations significantly larger than In their bulk counterparts and predicting the fast consumption of the nanoparticles when the wires are grown on n-type substrates.