here we study how band structure changes in graphene on Ni(111) substrate and also binding energy of water on graphene/metal interface.

1. Interaction of small molecules with
graphene supported on metal
substrates: A first principles study
Mihir Ranjan Sahoo
12PH09008
School of Basic Sciences
IIT Bhubaneswar
1

2. Outline
• Introduction
• Motivation
• Objectives
• Methodology
• Result and Discussion
• Future plans
• References
2

3. Introduction to Graphene
• One atom thick planar
sheet of carbon atoms
• Honeycomb like structure
• C-C bond length 1.42 Å
• Thinnest, lightest and
strongest material
• Zero band gap leads to
highly conductive.
• High electron mobility
• High Mechanical Strength
Primitive
Cell
3

4. band structure of graphene
 Valence band and conduction
band touches at K and K’ in
Brillouin zone.
 Zero band gap.
 Linear energy-momentum
relation.
 Mass less fermions- Dirac
particles.
K
K’
Brillouin zone
4
K
K’
K’
K

5. • In spite of various novel properties, Graphene
has limitation for using in some applications
such as digital electronics, transistors due to its
zero band gap.
• For electronic switch high on/off ratio is
required . For this a material having non zero
band gap is necessary.
5

6. Inducing bandgap in graphene
• Putting graphene on different substrates
• Adsorption of atoms/molecules on graphene
layer
• By giving mechanical strain.
• By increasing layers of graphene such as bi-layered
or trilayered graphene
• Cutting graphene in smaller dimensions such
as nanoribbon.
6

7. • Graphene was reported to be used as highly
sensitive gas sensors.
• Sensor property depends upon the change in
resistivity by adsorption of molecules on
graphene.
• By adsorption of molecule, charge carrier
concentration can be increased .
• Two-dimensional crystal structure which
having surface but no volume enhances effect
of surface dopant.
7

8. Objectives
• To study electronic structure of
graphene/Ni(111) interface and compare how
band gap of the system is different from
pristine graphene.
• To study how adsorption of water molecule on
graphene-metal interface affects binding
energy.
• To know how insulating substrates affects
electronic structure.
8

9. Methodology
• Density functional theory (DFT) is method to
find approximate solution of many body
Schrodinger equation.
• Hence, DFT was employed to perform first
principle calculation.
• Vienna Ab-initio Simulation Package (VASP)
was used for DFT calculation.
• VASP uses projector augmented wave (PAW)
method and pseudopotential for first
principles calculation.
9

10. 10
Z Z
Z
1 1
2
B
   A
 
     
i j ij
A B AB
 
   
N
i j
M
A B
A
N
i
M
A iA
M
A
A
N
i
i r
R r
H
1 1 1 , ,
1
2 1
2
2
Many electron system
 Time independent Schrӧdinger equation
Ĥѱ(r1,r2..ri…rN,RA,RB…..RM)=
Eѱ(r1,r2,…ri…rN,RA,RB…..RM)
 The full molecular Hamiltonian
^

11. 11
Born-Oppenheimer Approximation
• Mass of Nucleus is much larger than mass of electron. i.e.
Mn>>me
• Freeze the motion of nuclei.
Nuclear Kinetic Energy
Nuclear-nuclear Interaction
0
constant
• Electron-nuclear potential acts as external potential.
Z
Electronic Hamiltonian
^
2 1
1
H        
elec i T V V
Ne ee
N
i j ij
1 1 1 ,
i j
N
i
M
A
A iA
N
i
r r

2

12. Background of DFT
• Electron density states all physical properties of
many body system instead of wavefunction.
• Electron density n(r) :
풏 풓 = 풅ퟑ풓ퟐ 풅ퟑ풓ퟑ … … … 풅ퟑ풓푵 휳( 풓, 풓ퟐ, 풓ퟑ … 풓푵) ퟐ
• Hohenberg-Kohn Theorem:
1. The ground state energy is a unique functional
of electron density.
2. The electron density that minimizes overall
functional is the true electron density.
12

13. 훁ퟐ + 퐕 퐫 + 퐕퐇 퐫 + 퐕퐗퐂 퐫 횿퐢 퐫 = ℇ퐢횿퐢(퐫)
13
Kohn-Sham Approach
• Interacting Non-Interacting
• Kohn-Sham Schrodinger equation
−
ℏퟐ
ퟐ퐦
• Kohn-Sham Density
푵
풏 풓 = |휳풊(풓)|ퟐ
풊=ퟏ

14. 14
Functional
• The functional described in Hohenberg-Kohn
theorem
푬 휳풊 = 푬풌풏풐풘풏 휳풊 + 푬푿푪[{휳풊}]
• Known term
푬풌풏풐풘풏 휳풊 = −
ℏퟐ
ퟐ풎
∗휵ퟐ휳풊풅ퟑ 풊 풓 +
휳풊
푽 풓 풏(풓)풅ퟑ풓 +
풆ퟐ
ퟐ
풏 풓 풏(풓′)
|풓−풓′ |
• Hence total energy functional
풅ퟑ풓풅ퟑ풓’+푬풊풐풏
푬 풏 = 푻풔 풏 + 푽푯 풏 + 푽풆풙풕 풏 + 푬풙풄[풏]

15. Exchange and Correlation
• Local Density Approximation(LDA) :
푳푫푨 풏 = 풏 풓 ℇ풙풄(풏) 풅풓
푬푿푪
• Depends on Local density and derived from
Homogeneous electron gas model.
• Generalized Gradient Approximation(GGA):
푮푮푨 풏 = ℇ풙풄(풏)휵풏 풅풓
푬푿푪
• Depends on local density and its gradient.
15

16. Procedure for Self-Consistence Calculation
16

17. Calculation in VASP
• Spin polarization Calculation
• Exchange-Correlation potential-GGA
• Supercell 2X2
• Energy cutoff 400 eV
• 5X5X1 grid in kpoints for Brillouin zone
sampling
• 5 layers of Ni(111)
• 15 Å vacuum
17

18. Why Ni(111) ?
• Ni(111) surface –Hexagonal structure
• ABC type Arrangement
• Lattice Constant of Ni(111)= 3.52Å
• Nearest C-C atom distance in Graphene =
1.42Å
• Length calculated for C-C distance on Ni(111)
surface = 1.43Å
• 1% lattice mismatch.
18

19. 19
Results and Discussions
• Binding energy of graphene-Ni interface :
푬푮−푴 = 푬풕풐풕[푮 푴] − 푬풕풐풕[푴] − 푬풕풐풕[푮]
• Adsorption energy of water :
푬풂풅풔 = 푬풕풐풕 푯ퟐ푶 − 푮 푴 − 푬풕풐풕 푮 푴 − 푬풕풐풕[푯ퟐ푶]
• For graphene-nickel interface:
Orientation Equilibrium height(Å) Binding energy
(eV)
Top-fcc 2.1 0.317
Top-hcp 2.1 0.287
Fcc-hcp 3.0 0.269

20. 20
Graphene on Nickel(111)
top-fcc top-hcp fcc-hcp
Ni atom
C atom

21. 21
Band Structure: (For only graphene)
Fermi energy
Energy
(eV)

22. 22
Band Structure: (For only Ni(111))
Fermi energy
Energy
(eV)

23. 23
Band structure: (for graphene/Ni(111))
Energy
(eV)
ΔE=0.35 eV

24. 24
Up
down
pointing
parallel
Water on Graphene
C atom
O atom
H atom

25. Adsorption energy and heights for
different geometry
Position Orientation Height in Å Adsorption
Energy (meV)
Centre Up 3.70 36.22
Centre Down 4.02 30
Centre parallel 3.55 36.80
Top Up 3.70 33.87
Top Down 4.05 28.95
Bridge Up 3.70 32.45
Bridge Down 4.05 29.87
Centre Pointing 3.50 54.26
The Adsorption
energy has weaker
orientation
dependence
25

26. 26
Band Structure
Pristine Graphene Water on graphene

27. Band Structure
• Band structure of water on graphene is almost
identical to pristine graphene due to weak
interaction of water with graphene.
• HOMO is located at -5.16 eV
• LUMO is located at 0.89 eV
• HOMO-LUMO gap of Isolated gas phase water
is 6.18 eV.
• Larger dipole moment associated with water
molecules able to modify electronic properties
of graphene.
27
6.05 eV

28. Water on Graphene/Ni interface
• Graphene-nickel is arranged in top-fcc
position.
• Water lies above graphene surface on the
centre of honeycomb structure and in
pointing orientation.
orientation Height of O atom(Å) Adsorption
energy(meV)
Top-fcc with centre-pointing
3.50 504
28

29. Future Plans
• To study electronic structure modification of
graphene on different substrates including
insulating substrate.
• To study how graphene coated materials
control corrosion.
• To study the electronic structure of metals
such as aluminium and copper adsorbed on
graphene.
29

30. References
• Wallace P. R.:”The Band Theory of Graphite”. Phys. Rev. 71,
622, 1947.
• Geim A. K., Novoselov K.S.: “The Rise of Graphene”. Nat.
Matter, 6, p.183. 2007.
• Geim A. K., Science, 324, 5934, 2009.
• Allen M. J., et al., : “Honeycomb Carbon: A Review of
Graphene”. Chem. Rev. 110, 2010.
• Balandin A. A. , “Thermal properties of graphene and
nanostructured carbon materials”, Science ,320 , p. 1308,
2008.
• Boukhvalov D.W., Katsnelson M. I.: “Chemical
functionalization of graphene”. J Phys. Condens. Matter, 21,
p.344205, 2009.
30

31. • Kohn W., Becke A. D. , Parr R. G. , J. Phys. Chem. , 100(31), p.
12974-12980, 1996.
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• Perdew J. P. , Zunger A. , Phys. Rev. B. ,23, 5048, 1981.
• Sham L. J., Kohn W. , Phys. Rev. 145, 561 , 1966.
• Sham L. J., Schluter M. , Phys. Rev. Lett. , 51, p. 1888, 1983.
• Kresse, G. "Software VASP, Vienna, 1999; G. Kresse, J.
Furthmüller." Phys. Rev. B., 54.11, 1996.
• Kresse G., Hafner J., Phys. Rev. B., 47, p. 558 , 1993 .
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32. Acknowledgement
• School of Basic Sciences, IIT Bhubaneswar.
• DSC members.
32

33. 33