force field development for silicon carbides, bulk silicon and oxidized silicon surfaces with...

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 nmResolution = 1.2 nm

5.5 nm

40 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

Parameter Optimization Procedure

Si-C dissociation curve in H4Si2-C2H4 (for 2 bonds)

0

50

100

150

200

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Radius, Ang

En

erg

y, k

cal/m

ol

singlet

triplet

Reax fit

Reax Fit Results

Si-C Bond Dissociation Curve

in H3Si-CH3

0

50

100

150

200

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Bond Length, Angstrom

En

erg

y, k

ca

l/mo

l

Reax

QM

Reax Fit ResultsSi=C Double Bond Dissociation Curve

in H2Si=CH2

0

50

100

150

200

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Bond Length, Angstroms

En

erg

y, k

cal/

mo

l

Reax

QM

Reax Fit Results

C_C_Si Angle Bend Curvein H3C-CH2-SiH3

0

5

10

15

20

25

30

80 90 100 110 120 130 140 150

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax Fit Results

C_Si_C Angle Bend Curvein H3C-SiH2-CH3

0

5

10

15

20

25

30

75 85 95 105 115 125 135 145 155

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax Fit Results

C_Si_Si Angle Bend Curvein H3CSiH2SiH2

0

5

10

15

20

25

30

75 85 95 105 115 125 135 145 155

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax Fit Results

Si_C_Si Angle Bend Curvein H3SiCH2SiH3

0

5

10

15

20

25

30

75 85 95 105 115 125 135 145 155

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax Fit ResultsSi_C_H Angle Bend Curve

in H3CSiH2CH3

0

5

10

15

20

25

30

75 85 95 105 115 125 135 145 155

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax Fit ResultsC_Si_H Angle Bend Curve

in H3SiCH2SiH3

0

5

10

15

20

25

30

75 85 95 105 115 125 135 145 155

Angle, degrees

En

erg

y, k

cal/m

ol

Reax

QM

Reax FF Crystal Fits (in progress)

Energy Vs. Lattice - Silicon Crystal (periodic PBE)

-20

0

20

40

60

80

100

120

4.0 5.0 6.0 7.0 8.0

Lattice constant, Ang.

En

erg

y, k

cal/m

ol/a

tom

Energy Vs. Lattice - Silicon Carbide Crystal (periodic PBE)

-10

0

10

20

30

40

50

60

70

80

3.5 4.0 4.5 5.0 5.5 6.0 6.5

Lattice constant, Ang.E

ner

gy,

kca

l/mo

l/ato

m

Future calculations: Crystal cohesive energyAlso available: Diamond crystal

USEFUL RANGE

DESIRED RANGE

0

50

100

1.5 2 2.5

DFTReaxFF

0

50

100

1.5 2 2.5

DFTReaxFF

C-C distance (Å)

Ene

rgy

(kca

l/m

ol)

Ene

rgy

(kca

l/m

ol)

Bond formation between two C20-dodecahedrons

- ReaxFF properly describes the coalescence reactions between C20-dodecahedrons

0

0.05

0.1

0.15

0.2

10 15 20

c-axis (Å)

E (

eV/a

tom

)

diamond

graphite

Diamond to graphite conversionCalculated 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)

-ReaxFF gives a good description of the diamond-to-graphite reaction path

Relative stabilities of graphite, diamond, buckyball and nanotubes

Compound ERef (kcal/atom) EReaxFF

Graphite 0.00a 0.00

Diamond 0.8a 0.52

Graphene 1.3a 1.56

10_10 nanotube 2.8b 2.83

17_0 nanotube 2.84b 2.83

12_8 nanotube 2.78b 2.81

16_2 nanotube 2.82b 2.82

C60-buckyball 11.5a 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-ro))2 – 1}• Cosine harmonic:

E = 0.5 K ( cos – cos o )2

• Dihedral: E = j 0.5 Bj ( 1 – Dj cos (nj ) )

• Cosine-2: E = Kbb ( jil – jilo) ( kil – kilo)

• r-r: E = Kss (Rij – Rijo) (Rjk – Rjko)

• r-cosine: E = (cos – cos o) [Cij (Rij – Rijo) + Cjk (Rjk - Rjko)]

• 2-center Ang-Ang:

E = Faa (cos ijk – cos ijko) ( cos ikl – iklo)(1 – 2 cos)/3

• Coulomb: E = C q1 q2 / (r12)2

LJ6-12 Vs. Morse Potential

Comparison of LJ 6-12 and Morse Potentials

-5

0

5

10

2.50 3.50 4.50 5.50 6.50

Interatomic Distance, Ang.

En

erg

y, k

cal/

mo

l

LJ 6-12

Morse

LJ Energy = Ar-12-Br-6

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

LJ6-12 Vs. Morse PotentialComparison of LJ 6-12 and Morse Potentials

(Behavior near r = 0)

-5.E+00

2.E+05

4.E+05

6.E+05

8.E+05

1.E+06

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Interatomic Distance, Ang.

En

erg

y, k

cal/

mo

l

LJ 6-12

Morse

LJ Energy = Ar-12-Br-6

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

E,F Infinity

E,F finite

AFM Tip Equation of Motion

m z” = -k z – (m wo / Q) z’ + Fts + Focos(w t)

m = massk = harmonic force constantz = tip-sample separation

wo = cantilever resonance frequencyQ = 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

CNT Tip on CNT (20,20)

Energy Vs. Position CurveEnergy Vs. Tip Position

30,30 CNT Tip on 30,30 CNT

0

1000

2000

3000

4000

5000

6000

-35 -30 -25 -20 -15 -10 -5 0 5

Tip Position (above CNT), Ang.

En

erg

y,

kc

al/

mo

l

Down

Up

CNT Readjustments

Force Vs. Position CurveForce Vs. Position, 30,30 CNT Tip on 30,30 CNT

-20

-10

0

10

20

30

40

50

60

70

-50 -40 -30 -20 -10 0 10 20

Tip Position (above CNT), ang.

Fo

rce

, n

N

Down

Up

CNT Readjustments

Strong Interaction with the Surface

Interpretation and prediction of AFM BehaviorSelective Phase Angle Inversion

Initial conditionsSurface = CNT on SiTip = Ntb tipDF = 59.45 KHzASP =1.440Sensitivity = 21.82 nm / VQ 148Rp = Asp/DA = 0.6

DA= 653.2 mVASP=0.1V (small value impliesoscillation close to the surface)