Theoretical study on doping efficiency in silicon nanowires

Abstract

Over the past few decades, silicon nanowires have received much attention because of their unique electronic properties. Due to their low dimensional structures, quantum confinement effect is strong. Moreover their surface has much influence of their properties since they have large surface to volume ratio. Although they are one of the promising material for the building blocks of future devices, achieving high doping concentration is still challenging. In this thesis, we perform first-principles study on structural and electronic properties of silicon nanowires.

First, we investigate the electronic band structure of silicon nanowires. In nanowires, the band structures are folded into the one dimensional Brillouin zone. We develop the band unfolding scheme for nanowires using the simplified localized orbitals as the basis. The unfolded band dispersions are similar to those of the bulk Si. The direct band gap is derived from the unfolded band structure. We relate the unfolded direct band gap and the dielectric tensors of silicon nanowires.

Second, we develop the finite-size correction scheme for charged defects and impurities in silicon nanowires, where the medium is surrounded by vacuum in radial directions. The formation energy of a charged defect converges slowly due to the periodic boundary conditions. The energy correction is obtained by solving the Poisson equation with the macroscopic dielectric constant. We show that the macroscopic dielectric constant and the defect charge distribution can be derived from the electrostatic potential in first-principles calculations. After the electrostatic energy corrections, the formation energies converges rapidly as the supercell expands in either radial and axial directions. We demonstrate the validity of our correction method by calculating the substitutional boron and phosphorus in silicon nanowires. The acceptor and donor levels of the dangling bond defect in silicon nanowires lie in the band gap, while the uncorrected donor levels are below the valence band maximum. We find that the hydrogen interstitial which is known to be negative-$U$ --- the donor level is higher than the acceptor level --- becomes ordinary positive-U in small nanowires because of the reduction of dielectric screening.

Finally, we study structural and electronic properties of oxidized silicon nanowires. To realize the realistic atomic model for $Si/SiO_2$ core-shell nanowires, we generate core-shell models via classical molecular dynamics simulations. We show that B dopants easily segregate to oxide shells. On the other hands, P dopants tend to aggregate near the surface and forms electrically inactive donor-pair defects. The donor-pair defects become more stable under the uniaxial compressive strain.