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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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slide1

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
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
afm microscopy

5.5 nm

40 nm

Full Width 3.1 nm, Height 1.9 nm

Resolution = 1.2 nm

AFM Microscopy
interactions to be optimized in reax
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
reax ff crystal fits in progress
Reax FF Crystal Fits (in progress)

DESIRED RANGE

USEFUL RANGE

Future calculations: Crystal cohesive energy

Also available: Diamond crystal

slide16

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

slide17

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
slide18

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
bonded force field remarks
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)
force field energy terms
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
lj6 12 vs morse potential
LJ6-12 Vs. Morse Potential

LJ Energy = Ar-12-Br-6

Morse Energy = Do{ [1 – e-B(r-ro)]2 –1}

lj6 12 vs morse potential1
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}

slide23
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

30 30 cnt afm tip vertical
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)
slide28

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)