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Silicon fullerenes Vijay Kumar 1,2 and Yoshiyuki Kawazoe 1 1 Institute for Materials Research Tohoku University, Sendai & 2 VKF, Chennai In Collaboration with C. Majumder, T. M. Briere, A. K. Singh, Q. Sun, Q. Wang, and P. Jena, M.W. Radny, and H. Kawamura

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Plan Introduction Novel structures of silicon with metal encapsulation Silicon Fullerenes and other forms Metal encapsulated clusters of Germanium Hydrogenated silicon fullerenes Metal encapsulated nanotubes of silicon

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Introduction Nanoforms of silicon for atomic-scale engineering - miniature devices Bright luminescence from nanoparticles of Si. Porous Si, hydrogenated Si clusters Bulk Si poor emitter of light. Si laser, integration of photonics and electronics leading to microphotonics integrated circuits.

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Bright colors from Hydrogen capped Silicon particles Belomoin et al. Appl. Phys. Lett. 80, 841 (2002)

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Elemental silicon clusters Clusters with N ~ 15-25 atoms prolate, N > 25 → 3D fullerene-like, experiments on H or O passivated nanoparticles or embedded in a matrix, quantum confinement → PL No strong magic behavior except for Si 10. Often in experiments a distribution of different sizes

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Clusters of Elemental Silicon L. Mitas et al. PRL 84, 1479 (2000) Si 10 Si 25 Si 20 A similar isomer for Si 25

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Materials with clusters as superatoms Clusters with their unique properties can be assembled to develop novel materials with desired properties Large abundance, stability and size selection important.

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Metal encapsulation - a novel approach A new cluster of silicon: Si 12 W, hexagonal prism open structure with W at the center. Stability: 18 valence electron rule? Large abundances of Si 15 M and Si 16 M (M = Cr, Mo, and W) reported more than a decade ago. Nucleation conditions play an important role.

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Si 12 W Hexagonal prism with W at the center Hiura et al. PRL 86, 1733 (2001) Atomic radius of W larger than Si → open Structure Magnetic moment of M completely quenched Similar behavior for Cr and Mo Interaction of SH 4 with M monomers and dimers ions

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S.M. Beck, J. Chem. Phys. 90, 6306 (1989) Large abundance of Si 15 M and Si 16 M (M = Cr, Mo, and W) and little intensity for other M doped clusters, in particular Si 12 M Possibilities of size selection like for C 60 About a decade ago experiments by laser evaporation of Si and addition of metal carbonates Also by Bergeron & Castleman, Jr.

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We find from computer experiments High symmetry M encapsulated caged fullerene-like, Frank-Kasper polyhedral and cubic Si clusters M@Si n (n=14-16) Exceptionally large gap of up to 2.36 eV. Hydrogenated silicon fullerenes with ~2.8 eV gap, photoluminescence ?

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Computational Method Ab initio plane wave ultrasoft pseudopotential method Generalized gradient approximation for the exchange-correlation energy Spin-polarized calculations Optimizations by conjugate gradient method Successive cage shrinkage and atom(s) removal method Dynamic stability of clusters is checked by calculating frequencies using Gaussian program

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The Cage Shrinkage Approach for M@Si n (M = Ti, Zr, Hf) – silicon fullerene Kumar and Kawazoe, PRL 87, 045503 (2001). M@Si 16

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ISSPIC-11 Strasbourg Sept. 2002

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Silicon fullerene 8 pentagons and 2 squares, each Si tri-coordinated like in C 60 §Short bonds 2.25 (double), 2.28 (single), and 2.34 Å (single) §sp 2 -sp 3 bonding (double bonds in Si) Small charge transfer from M to Si cage, covalent p-d bonding §Possibilities of producing such clusters uniquely in large abundance Kumar, Majumder and Kawazoe, CPL 363, 319 (2002)

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Frank-Kasper Polyhedral structure M@Si 16 Exceptionally large gap (~2.36 eV) in optical region M = Ti & Hf ~3e charge transfer from M to Si cage Large Polarizability About 482 a.u. Si-Si bonds 2.45 – 2.66 Å Tetrahedral symmetry Normally in metal alloys Different bonding from fullerene isomer

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Superatom behavior of clusters Cluster IP (eV) EA (eV) Gap (eV) f-Zr@Si 16 7.29 2.61 1.58 FK-Ti@Si 16 7.39 1.9 2.36 Expt. ~ 1.8eV (green) ↓ True gap ~ 3.2 (eV) Large IPs and low EAs → Superatom

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M@Si 15 and M@Si 16 a)Si 16 M, M= Cr, Mo, and W. The f Cage shrinks b) f-M@Si 15 obtained from a) c) Lowest energy isomer M@Si 15, M = Cr, Mo, and W d) Lowest Energy isomer of M@Si 15, M = Ti, Zr, Hf, Ru, Os Kumar and Kawazoe, Phys. Rev. B 65, 073404 (2002) Magnetic moment of M quenched

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Cubic and Fullerenelike M@Si 14 Kumar and Kawazoe, PRL 87, 045503 (2001) a)Shrinkage of f cage c) Cubic for M = Fe, Ru, Os, Ni, Pd, Pt b) Fullerene M = Ru, Os, Cr, Mo, W d) Fullerene M = Os All Si 3-fold coordinated

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Charge density surfaces of M@Si 16 and M@Si 14

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Binding and Embedding Energies Large binding energy of M encapsulated Si clusters ~ 4 eV/atom as compared to about 3.5 eV/atom for elemental Si clusters High embedding energy (EE) (~ 12 – 14 eV) of M atom in the cage. For Fe and Cr, it is significantly lower due to quenching of moments EE significantly low for M = Pd and Pt presumably due to filled d shell.

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Table 1. Binding energy (BE) in eV/atom, embedding energy (EE) in eV and HOMO-LUMO gap (eV) of metal encapsulated silicon clusters. ===================================== Cluster BE EE Gap ===================================== FK-Ti@Si 16 4.135 11.269 2.358 f-Ti@Si 16 4.089 12.733 1.495 f-Zr@Si 16 4.162 13.965 1.580 f-Hf@Si 16 4.175 14.176 1.576 FK-Hf@Si 16 4.171 12.399 2.352 f-Si 16 Cr 3.934 8.817 1.244 f-Si 16 Mo 4.131 12.091 1.195 f-Si 16 W 4.246 14.053 1.208 f-Si 16 Fe 4.010 9.426 1.294 f-Si 16 Ru 4.188 12.445 1.230 f-Si 16 Os 4.252 13.551 1.246 ======================================

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HOMO-LUMO gaps for pure and M doped Si and Ge clusters Clusters with more than 2 eV GGA gap may exhibit visible luminescence GGA

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Cluster-cluster interaction between M@Si 16 Fullerene Frank-Kasper B.E. =1.345 eV Gap = 0.673 eV B.E. = 0.048 eV Gap = 2.211 eV Self-assembly of clusters, polymerized forms

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Stabilization of Si 20 fullerene cage All structures dynamically stable. There are distortions, but it is least with Ba. Clathrate compounds of Si with Ba and Na with such cages Q. Sun, Q. Wang, T.M. Briere, V. Kumar, Y. Kawazoe, and P. Jena, Phys. Rev. B65, 235417 (2002) Low binding energies Importance of d electrons

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Growth behavior Of Si n M clusters M = Cr, Mo, and W N = 15 and 16 are Magic Competing f and FK growths

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Metal encapsulated clusters of Ge with Large Gaps 1615 14 Cubic 14 pentagons 14 another view 14 different capping M = Ti, Hf, Zr, Cr, Mo, W, Fe, Ru, Os, Pb Kumar + Kawazoe, PRL 88, 235504 (2002) HOMO-LUMO Gap 1-2 eV

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Interaction of hydrogen Si 12 M and Si 18 M 2 M = Cr, Mo, W Si 18 M 2 a double prism Binding energy per H About 2.4 eV, H 2 may not dissociate Kumar and Kawazoe PRL (2002), in press Hydrogenated fullerenes

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Hydrogenated silicon fullerenes Empty center 12 16 20

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Hydrogen abundance as a Function of temperature in Si 14 H x + clusters Peaking of the distribution at 1:1 at around 787 K G.A. Rechtsteiner et al. J. Phys. Chem. B105, 4188 (2001)

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Excitation energy (optical gap) for hydrogenated Si clusters Optical gap for the FK-Ti@Si 16 around 3 eV from time dependent density functional theory

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Icosahedral clusters: Zn@Ge 12 and Cd@Sn 12 Perfect icosahedral symmetry and large HOMO-LUMO gaps of about 2.2 eV in the green - blue range V. Kumar and Y. Kawazoe, Appl. Phys. Lett. 80, 859 (2002) Zn@Ge 12 IP = 6.874 eV EA = 1.735 eV Gap = 2.212 eV B3PW91 gap = 2.97 eV Metal like close packing Such an icosahedral cluster of Ge or Sn found for the first time Superatom Similar result for M = Be, Ca, Mg, Be Mn doping 5 µ B Magnetic moment

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Si 12 Be Chair type3-fold planar Icosahedron local minimum but not of lowest energy Assembly of Nanotubes

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Assembly of clusters Nanowires Nanotubes Layers Solids

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Nanowire of f-Si 16 Zr Lattice constant = 14.85 Å Semiconducting gap ~0.53 eV Binding energy = 2.98 eV/cluster

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Finite nanotubes of elemental silicon Distorted

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Assembly of metal encapsulated Si clusters to form nanotubes: Be Carbon nanotubes or silicon? Elemental Si tubes distorted. Metal encapsulation stabilizes nanotubes to quite symmetric forms Singh, Kumar, Briere, and Kawazoe, Nano Lett. 2, 1243 (2002)

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Infinite metal encapsulated Si nanotubes Symmetric, stable, and metallic, could act as nanowires, similar behavior for transition M atoms

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Metallic behavior of metal encapsulated Si nanotubes Si 24 Be 4

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Excess of charge Depletion of charge Infinite Si 24 Be 4 nanotube

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Conclusions Novel forms of Si with M encapsulation: fullerenelike, cubic and Frank-Kasper, high stability. One metal atom changes the structure and properties drastically. Strong bonding of M atom leads to compact cages. The dynamic stability of structures has been studied Size and gap depends upon the M atom. Largest gap of ~ 2.35 eV -> PL. Similar for Ge Highest symmetry icosahedral clusters of M@Ge 12 and M@Sn 12 with ~2 eV gap. Mn@Ge 12 with 5 µ B moment. Magic behavior of M@Si 15 (M = Cr, Mo, and W) agrees with experiments Hydrogenated silicon fullerenes with empty centers Assemblies: predicted Nanotubes and nanowires, …..

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