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Force Field Development for Silicon Carbides, Bulk Silicon and Oxidized Silicon surfaces with Graphite

Force Field Development for Silicon Carbides, Bulk Silicon and Oxidized Silicon surfaces with Graphite. Santiago Solares, Adri van Duin and William A. Goddard III California Institute of Technology. Objectives. To study graphite-silicon systems (vdw interactions and reactions)

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Force Field Development for Silicon Carbides, Bulk Silicon and Oxidized Silicon surfaces with Graphite

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  1. Force Field Development for Silicon Carbides, Bulk Silicon and Oxidized Silicon surfaces with Graphite Santiago Solares, Adri van Duin and William A. Goddard III California Institute of Technology

  2. Objectives • To study graphite-silicon systems (vdw interactions and reactions) • To optimize Reax FF for silicon carbide systems (molecular and bulk systems) • To optimize Reax FF for all-carbon systems (including free radicals and resonant structures) • To compile a bonded force field to be used in mechanical systems under high stresses

  3. 5.5 nm 40 nm Full Width 3.1 nm, Height 1.9 nm Resolution = 1.2 nm AFM Microscopy

  4. AFM Microscopy

  5. Bonds: Si-C Regular bond in H3SiCH3 Simultaneous breaking of 2 bonds in Si2H4-C2H4 Si=C H2Si=CH2 Angles: C-Si-Si C-C-Si C-Si-C Si-C-Si Si-C-H C-Si-H Future work: angles involved in double bonds Interactions to be optimized in Reax

  6. Parameter Optimization Procedure

  7. Reax Fit Results

  8. Reax Fit Results

  9. Reax Fit Results

  10. Reax Fit Results

  11. Reax Fit Results

  12. Reax Fit Results

  13. Reax Fit Results

  14. Reax Fit Results

  15. Reax FF Crystal Fits (in progress) DESIRED RANGE USEFUL RANGE Future calculations: Crystal cohesive energy Also available: Diamond crystal

  16. Bond formation between two C20-dodecahedrons Energy (kcal/mol) Energy (kcal/mol) C-C distance (Å) - ReaxFF properly describes the coalescence reactions between C20-dodecahedrons

  17. Diamond to graphite conversion Calculated by expanding a 144 diamond supercell in the c-direction and relaxing the a- and c axes QC-data: barrier 0.165 eV/atom (LDA-DFT, Fahy et al., PRB 1986, Vol. 34, 1191) graphite DE (eV/atom) diamond c-axis (Å) • ReaxFF gives a good description of the diamond-to-graphite reaction path

  18. Relative stabilities of graphite, diamond, buckyball and nanotubes a: Experimental data; b: data generated using graphite force field (Guo et al. Nature 1991) • ReaxFF gives a good description of the relative stabilities of these structures

  19. Bonded Force Field Remarks • Silicon force field (Hessian-Biassed Method) • LJ 6-12 (vdw), Morse (bond), cosine harmonic (angle), dihedral (torsion), r-cosine (stretch-bend-stretch), r-r (stretch-stretch), cosine2 (bend-bend), coulomb, 2-center Ang-Ang (not available in Cerius2) • Graphite force field (optimized for graphite and CNT’s) • Morse (vdw and C-C bond), cosine harmonic (angle), dihedral (torsion), no inversion, r-cosine (stretch-bend-stretch – not used for CNT’s), r-r (stretch-stretch – not used for CNT’s), coulomb • Vdw Cross Terms (C-O, C-Si, C-H) – Bonds not considered • Bond length: arithmetic combination rule • Well depth: geometric combination rule • Used LJ_6-12 function (instead of Morse Potential)

  20. Force Field Energy Terms • LJ 6-12: E = Ar-12 – Br-6 • Morse: E = Do { (1 – e-B(r-ro))2 – 1} • Cosine harmonic: E = 0.5 Kq ( cos q – cos qo )2 • Dihedral: E = Sj 0.5 Bj ( 1 – Dj cos (njf) ) • Cosine-2: E = Kbb (q jil – qjilo) (qkil – qkilo) • r-r: E = Kss (Rij – Rijo) (Rjk – Rjko) • r-cosine: E = (cos q – cos qo) [Cij (Rij – Rijo) + Cjk (Rjk - Rjko)] • 2-center Ang-Ang: E = Faa (cos ijk – cos ijko) ( cos ikl – iklo)(1 – 2 cosf)/3 • Coulomb: E = C q1 q2 / (r12)2

  21. LJ6-12 Vs. Morse Potential LJ Energy = Ar-12-Br-6 Morse Energy = Do{ [1 – e-B(r-ro)]2 –1}

  22. LJ6-12 Vs. Morse Potential E,F  Infinity E,F finite LJ Energy = Ar-12-Br-6 Morse Energy = Do{ [1 – e-B(r-ro)]2 –1}

  23. AFM Tip Equation of Motion m z” = -k z – (m wo / Q) z’ + Fts + Focos(w t) m = mass k = harmonic force constant z = tip-sample separation wo = cantilever resonance frequency Q = cantilever quality factor Fts= tip-sample interaction force Focos(w t) = external force

  24. 35,200 total atoms 30,30 CNT on Si(100)-OH surface CNT diameter = 40.69 Ang Tip length = 40 nm ~145 hours of computer time 30,30 CNT AFM Tip (vertical)

  25. CNT Tip on CNT (20,20)

  26. Energy Vs. Position Curve

  27. Force Vs. Position Curve

  28. Interpretation and prediction of AFM Behavior Selective Phase Angle Inversion Initial conditions Surface = CNT on Si Tip = Ntb tip DF = 59.45 KHz ASP =1.440 Sensitivity = 21.82 nm / V Q 148 Rp = Asp/DA = 0.6 DA= 653.2 mV ASP=0.1V (small value implies oscillation close to the surface)

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