Alejandro López Bezanilla – CEA-Grenoble/INAC PhD defense - November 2009 Effect of the Chemical Functionalization on Charge Transport in Carbon-based

Alejandro López Bezanilla – CEA-Grenoble/INAC

PhD defense - November 2009

Effect of the Chemical Functionalization on Charge Transport in Carbon-based materials

at the Mesoscopic Scale

Alejandro López Bezanilla

Institut des Nanosciences et Cryogénie (INAC)

CEA Grenoble, France

Examiners:· Prof. Mark Casida (UJF) Président du Jury· Prof. Juan José Sáenz (UAM) Rapporteur· Prof. Alain Rochefort (EPM) Rapporteur· Dr. Xavier Blase (CNRS) · Dr. Pablo Ordejón (CIN2)

Encadrants:· Dr. Stephan Roche (CEA) Encadrant· Dr. Pascale Maldivi (CEA) Co-encadrante (Grenoble)· Dr. Vincent Derycke (CEA) Co-encadrant (Saclay)



ChimTroniqueTransversal axesSaclay (S. Palacin)

Grenoble (R. Baptist)



Outline

→ Motivations

→ Electronic properties of CNTs and GNRs

· Functionalization

→ Decimation method

· Green´s function technique

→ Results

· Functionalized nanotubes

·Functionalized nanoribbons

·Edge defects in nanoribbons



~ 2D (sp2)Graphene

~ 3D (sp3)Diamond

Carbon atom

Carbon atom

Valence electron orbitals:

interactions between pz orbitals

(bonds/bands )

Hybrid Molecular OrbitalsHybrid Molecular OrbitalsCohesionElectronic properties in the vicinity of EF



-effective model

1

1

1

2

2

2

1

1

21

2

2 atoms/ cell nearest neighbor orbital overlap



Periodic Boundary conditions

EF

Nanotubes electronic properties

Armchair ZigzagEF=0



What would it happen

if we alter these properties ?

Summarizing



→ Selective electrical signals of molecular adsorption events.

→ Protein interaction. → Virus detection.

Bio-, photo-sensors

Zhou et al. Nano Letters 9, 1028 (2009)



Left lead

Right lead

300 nm

→ Transmission after photoactive molecule functionalization.

→ Properties of the linker.

Photoactive molecules:

Phtalocyanine …

hv

e-

Bio-, photo-sensors

S. Campideli et al.J. Am. Chem. Soc. 2008, 130, 11503



· MOSFETs : clean GNR-FET with ~ 3nm are necessary !!!

· Ribbons down to ~ 10 nm width P. Kim et al (Columbia Univ. USA)

Using top-down lithography to fabricate GNRs…

E. Dujardin (CEMES, France) Ph. Avouris et al. (IBM, USA)

X. Wang et al., PRL 100, 206803 (2008)X. Li et al., Science 319, 1229 (2008)

W 2 nm !

Towards graphene nanoribbon transistor



A graphene-based electrochemical switch(M. Lemme & A. Geim)

Functionalizing graphene

2D Graphene and Graphene ribbons

Goal: how to create or enlarge energy/conduction band gaps



Hybrid Carbon Based Materials

Is sp2 bonding broken/preserved?



sp2 sp3

Armchair

nanotube

axis

sp2 vs sp3 functionalization

CH2 chemisoption

Zigzagnanotube

axis



sp3

Tube axis

sp2 vs sp3 functionalization

Phenyl chemisoption



Energy bands

Electronic statesLDoS (0.6 eV)

carbene 2 phenyls carbene

2 phenyls

X Γ X Γ

sp3

sp2



→ Efficient tool for first-principles calculations (geometrical relaxation,…)

→ Local atomic-like orbitals basis set:

· no coupling beyond a cutoff distance,

· sparse Hamiltonian.

→ No fittings, no adjustable parameters.

SIESTA: an ab initio approach

s-orbital p-orbital sp-hybrid orbital



Size : ~ 500 atoms

Building block

1.3 nm

3 nm

→ SWCNT (10,10)

→ phenyl groups

Description of the system



Order N method :

only Hamiltonian - Vector productsallows big systems simulations

No contacts

Intrinsic properties

Quantum diffusion mechanism

Mean free path, scattering time, mobility

Kubo-Greenwood

Order power N method :

inversion of Hamiltonian limites size of systems simulations

Accuracy

Transmission and reflexion probability

Localization length, conductance

Landauer-Büttiker

Transport formalisms



Problem definition&

Decimation technique

Problem statement



Non-interacting electrons

Scattering free leads (perfect electrodes)

No backscattering at lead - reservoir interface

Incident electrons are in thermal equilibrium with reservoirs

Problem definition

Left lead

Right leadChannel



Problem definition

Left

lead

Right

lead

channel

channel

Right leadLeft lead

Nanotubes

Nanoribbons



Conductance from Green´s function

T(E) = Tr [ ΓLGC ΓRGC ](r) (a)

ΓL,R = i [ Σ L,R - Σ L,R ](r) (a)

where:

Fisher and Lee relation for transmission:

Σ L Σ R

HC

~

S. Fisher and P.A. Lee, Phys. Rev. Lett., 23, 6851 (1981)Datta, Electronic transport in mesoscopic system, Cambidge (1995)

GC = [ E- HC - Σ L- Σ R ] - 1

~



Problem definition

Left lead

Right lead

...... Channel

HC HRHL

H =

HL

HC

HR

VLC

VCL

VRC

VCR

0

0

VLC VCR

HL HRHC

Norb

Semi-infinite leads+

Long channel (~ 100.000 orbitals)

Decimation techniques



Hamiltonian: Wavefunction:

Energy spectrum:Eigenvalue equation:

Eigenvalues:

Decimation: 2-site model




is an effective potential that corrects the non-interacting on-site energy

Self-energy




→ A method to reduce the dimension of the Hamiltonian basis function space



Decimation: N-site model

H1 H2 H3 H4 H1

~H4

~

V1,2 V2,3 V3,4

V1,4

~

V4,1

~



Long channel decimation

Left lead

Right lead

Buildingblock

3

Buildingblock

2

Pristineblock

Linear scaling with length: method of N order

Buildingblock

1

Buildingblock

1



Semi-infinite systems



Finite system

Right leadChannelLeft lead

H =

HL

HC

HR

VLC

VCL

VRC

VCR

0

0~

~

~

NRorbNL

orb NCorb

→ Finite size Hamiltonian



Green´s function techniqueSystem Green´s function:

GC

GLC

GCL

GRC

GCR ·

VLC

VCL

VRC

VCR

0

0E-HL

~

E-HR

~

E-HC

~1

1

0

0

0

0

1 0

0

=

where:

GCL (E-HL) + GC VCL = 0~

GC VCR + GCR (E-HR) = 0

GCL VLC + GC (E-HC) + GCRVRC = 1~

~

(1)

(2)

(3)



Green´s function techniqueSystem Green´s function:

GCL (E-HL) + GC VCL = 0~

GC VCR + GCR (E-HR) = 0

GCL VLC + GC (E-HC) + GCRVRC = 1~

~

GCL = -GC VCL gL

GCR = -GC VCR gR

GC = [ E-HC - Σ L- Σ R ] - 1

(1)

(2)

(3)

where:

gL= [ E- HL ]-1

gC = [ E- HC]-1

~

Σ L Σ R

HC

~

Left & Right leadself-energies



Functionalized CNTs

Results



Quasi-ballistic

Diffusive

Localized

Transport regimes



phenyls in 300 nmDiffusive regime

Metallic CNTs

200 configurations



Carbenes in 1000 nm Quasi-ballistic regime

Metallic CNTs

200 configurations



→ Small radius: quasi-ballistic

→ Large radius: diffusive !!!

Semiconducting CNTs

1000 nm



→ sp3 signature in “metallic” tubes

→ CH2 vs 2H

Semiconducting CNTs

Parallel orientation

2 Hydrogens

CH2



Functionalized GNRs

Results



OH/H vs phenyls→ sp3 rehybridization signature

→ T(E) is independent of functional group

4 nm wide

2 nm wide



OH/H functionalization

→ Backscattering supression for edge functionalization

→ Conductance dips

→ Quantum mechanical interferences

A. L. Bezanilla, F. Triozon, S.RocheNano Letters 9, 2737 (2009)



Long nanoribbons (large gap)

Mean free path4 nm wide




Long nanoribbons (small gap)

Mean free path4 nm wide




Edge defects in GNRs

Results



Edge defects

Experimental evidences

→ Z. Liu, K. Suenaga, P.J.F. Harris, S. Iijima, Phys. Rev. Lett. 102, 015501 (2009)

→ P. Koskinen, S. Malola, H. Hakkinen, Phys. Rev. Lett. 101, 115502 (2008).



Benzenoid defects

S.Dubois, A. L.-Bezanilla et al.Submitted to PRL



Doping defects

Acceptor

Donor sp3-like

Passivated

Radical passivation

Backscattering suppression



Conclusions

→ Full ab initio transport studies: SIESTA +TB_Sim

→ sp2 vs sp3 functionalization

→ Chemical modification leads to diffusive transport

→ Benzenoid edge defects are not critical in electronic transport properties

→ Mind the radicals!

→ sp3 defects induce backscattering

Graphene Nanoribbons

Carbon Nanotubes

Decimation technique



Coworkers

Merci! ¡Gracias!Grazie!Tack!

Merci! ¡Gracias!Grazie!Tack!



Thanks

for your

attentio

n





Conductance suppresion

sp3 barrier

High coverage-functionalization

D.C. Elias et al., Science 323, 610 (2009)

Insulating regime : (towards GRAPHANE)

Documents

Alejandro López Bezanilla – CEA-Grenoble/INAC PhD defense - November 2009 Effect of the Chemical Functionalization on Charge Transport in Carbon-based