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) 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 Full Width 3.1 nm, Height 1.9 nm Resolution = 1.2 nm 5.5 nm 40 nm

AFM Microscopy

Interactions to be optimized in Reax Bonds: Si-C –Regular bond in H 3 SiCH 3 –Simultaneous breaking of 2 bonds in Si 2 H 4 -C 2 H 4 Si=C –H 2 Si=CH 2 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

Parameter Optimization Procedure

Reax Fit Results

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

C-C distance (Å) Energy (kcal/mol) Bond formation between two C 20 -dodecahedrons - ReaxFF properly describes the coalescence reactions between C 20 -dodecahedrons

c-axis (Å)  E (eV/atom) diamond graphite 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 eV/atom (LDA-DFT, Fahy et al., PRB 1986, Vol. 34, 1191) -ReaxFF gives a good description of the diamond-to-graphite reaction path

Relative stabilities of graphite, diamond, buckyball and nanotubes CompoundE Ref (kcal/atom)E ReaxFF Graphite0.00 a 0.00 Diamond0.8 a 0.52 Graphene1.3 a _10 nanotube2.8 b _0 nanotube2.84 b _8 nanotube2.78 b _2 nanotube2.82 b 2.82 C 60 -buckyball11.5 a 11.3 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 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 LJ 6-12:E = Ar -12 – Br -6 Morse:E = Do { (1 – e-B(r-r o ) ) 2 – 1} Cosine harmonic: E = 0.5 K  ( cos  – cos  o ) 2 Dihedral: E =  j 0.5 B j ( 1 – D j cos (n j  ) ) Cosine-2:E = K bb (  jil –  jil o ) (  kil –  kil o ) r-r: E = K ss (R ij – R ij o ) (R jk – R jk o ) r-cosine:E = (cos  – cos  o ) [C ij (R ij – R ij o ) + C jk (R jk - R jk o )] 2-center Ang-Ang: E = F aa (cos ijk – cos ijk o ) ( cos ikl – ikl o )(1 – 2 cos  )/3 Coulomb:E = C q 1 q 2 / (r 12 ) 2

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

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

AFM Tip Equation of Motion m z” = -k z – (m w o / Q) z’ + F ts + F o cos(w t) m = mass k = harmonic force constant z = tip-sample separation w o = cantilever resonance frequency Q = cantilever quality factor F ts = tip-sample interaction force F o cos(w t) = external force

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

CNT Tip on CNT (20,20)

Energy Vs. Position Curve

Force Vs. Position Curve

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