Interaction of small molecules with graphene supported on metal

substrates: A first principles study

Mihir Ranjan Sahoo

12PH09008

School of Basic Sciences

IIT Bhubaneswar1

Outline

• Introduction

• Motivation

• Objectives

• Methodology

• Result and Discussion

• Future plans

• References

2

Introduction to Graphene

• One atom thick planarsheet 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

3

Primitive Cell

band structure of graphene

Valence band and conductionband touches at K and K’ inBrillouin zone.

Zero band gap.

Linear energy-momentumrelation.

Mass less fermions- Diracparticles.

K

K’

Brillouin zone4

K

K’

K’

K

• In spite of various novel properties, Graphenehas limitation for using in some applicationssuch as digital electronics, transistors due to itszero band gap.

• For electronic switch high on/off ratio isrequired . For this a material having non zeroband gap is necessary.

5

Inducing bandgap in graphene

• Putting graphene on different substrates

• Adsorption of atoms/molecules on graphenelayer

• By giving mechanical strain.

• By increasing layers of graphene such as bi-layered or trilayered graphene

• Cutting graphene in smaller dimensions suchas nanoribbon.

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• Graphene was reported to be used as highlysensitive gas sensors.

• Sensor property depends upon the change inresistivity by adsorption of molecules ongraphene.

• By adsorption of molecule, charge carrierconcentration can be increased .

• Two-dimensional crystal structure whichhaving surface but no volume enhances effectof surface dopant.

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Objectives• To study electronic structure of

graphene/Ni(111) interface and compare howband gap of the system is different frompristine graphene.

• To study how adsorption of water molecule ongraphene-metal interface affects bindingenergy.

• To know how insulating substrates affectselectronic structure.

8

Methodology• Density functional theory (DFT) is method to

find approximate solution of many bodySchrodinger equation.

• Hence, DFT was employed to perform firstprinciple calculation.

• Vienna Ab-initio Simulation Package (VASP)was used for DFT calculation.

• VASP uses projector augmented wave (PAW)method and pseudopotential for firstprinciples calculation.

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10

N

jiji ij

M

BABA AB

AN

i

M

A iA

AM

AA

N

ii rR

ZZ

r

ZH

,,1 11

2

1

2 1

2

1

2

1 B

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

^

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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

• Electron-nuclear potential acts as external potential.

0constant

eeNe

N

jiji ij

N

i

M

A iA

AN

iielec VVT

rr

ZH

,1 11

2 1

2

1

Electronic Hamiltonian

^

Background of DFT

• Electron density states all physical properties of many body system instead of wavefunction.

• Electron density n(r) :

• 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.

𝒏 𝒓 = 𝒅𝟑𝒓𝟐 𝒅𝟑𝒓𝟑 ……… 𝒅𝟑𝒓𝑵 𝜳( 𝒓, 𝒓𝟐, 𝒓𝟑 …𝒓𝑵) 𝟐

12

13

Kohn-Sham Approach

• Interacting Non-Interacting

• Kohn-Sham Schrodinger equation

• Kohn-Sham Density

−ℏ𝟐

𝟐𝐦𝛁𝟐 + 𝐕 𝐫 + 𝐕𝐇 𝐫 + 𝐕𝐗𝐂 𝐫 𝚿𝐢 𝐫 = ℇ𝐢𝚿𝐢(𝐫)

𝒏 𝒓 = |𝜳𝒊(𝒓)|𝟐𝑵

𝒊=𝟏

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Functional

• The functional described in Hohenberg-Kohn theorem

• Known term

𝑬 𝜳𝒊 = 𝑬𝒌𝒏𝒐𝒘𝒏 𝜳𝒊 + 𝑬𝑿𝑪[{𝜳𝒊}]

𝑬 𝒏 = 𝑻𝒔 𝒏 + 𝑽𝑯 𝒏 + 𝑽𝒆𝒙𝒕 𝒏 + 𝑬𝒙𝒄[𝒏]

• Hence total energy functional

𝑬𝒌𝒏𝒐𝒘𝒏 𝜳𝒊 = −ℏ𝟐

𝟐𝒎 𝜳𝒊

∗𝜵𝟐𝜳𝒊𝒅𝟑𝒓𝒊 +

𝑽 𝒓 𝒏(𝒓)𝒅𝟑𝒓 +𝒆𝟐

𝟐

𝒏 𝒓 𝒏(𝒓′)

|𝒓−𝒓′ |𝒅𝟑𝒓𝒅𝟑𝒓’+𝑬𝒊𝒐𝒏

Exchange and Correlation• Local Density Approximation(LDA) :

• Depends on Local density and derived from Homogeneous electron gas model.

• Generalized Gradient Approximation(GGA):

• Depends on local density and its gradient.

𝑬𝑿𝑪𝑳𝑫𝑨 𝒏 = 𝒏 𝒓 ℇ𝒙𝒄(𝒏) 𝒅𝒓

𝑬𝑿𝑪𝑮𝑮𝑨 𝒏 = ℇ𝒙𝒄(𝒏)𝜵𝒏𝒅𝒓

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Procedure for Self-Consistence Calculation

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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

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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.

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Results and Discussions

• Binding energy of graphene-Ni interface :

• Adsorption energy of water :

• For graphene-nickel interface:

𝑬𝑮−𝑴 = 𝑬𝒕𝒐𝒕[𝑮 𝑴 ] − 𝑬𝒕𝒐𝒕[𝑴] − 𝑬𝒕𝒐𝒕[𝑮]

𝑬𝒂𝒅𝒔 = 𝑬𝒕𝒐𝒕 𝑯𝟐𝑶 − 𝑮 𝑴 − 𝑬𝒕𝒐𝒕 𝑮 𝑴 − 𝑬𝒕𝒐𝒕[𝑯𝟐𝑶]

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

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Graphene on Nickel(111)

top-fcc top-hcp fcc-hcp

Ni atom

C atom

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Band Structure: (For only graphene)

Energy

(eV)

Fermi energy

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Band Structure: (For only Ni(111))

Energy(eV)

Fermi energy

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Band structure: (for graphene/Ni(111))

Energy

(eV)

ΔE=0.35 eV

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Up

down

pointing

parallel

O atom

C atom

H atom

Water on Graphene

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

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26Pristine Graphene Water on graphene

Band Structure

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 wateris 6.18 eV.

• Larger dipole moment associated with water molecules able to modify electronic properties of graphene.

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6.05 eV

Water on Graphene/Ni interface

• Graphene-nickel is arranged in top-fccposition.

• Water lies above graphene surface on thecentre of honeycomb structure and inpointing orientation.

orientation Height of O atom(Å) Adsorptionenergy(meV)

Top-fcc with centre-pointing

3.50 504

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Future Plans

• To study electronic structure modification ofgraphene on different substrates includinginsulating substrate.

• To study how graphene coated materialscontrol corrosion.

• To study the electronic structure of metalssuch as aluminium and copper adsorbed ongraphene.

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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.

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Acknowledgement

• School of Basic Sciences, IIT Bhubaneswar.

• DSC members.

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