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 Madeiung 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. © 2009 American Chemical Society.