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)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
ChimTroniqueTransversal axesSaclay (S. Palacin)
Grenoble (R. Baptist)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Outline
→ Motivations
→ Electronic properties of CNTs and GNRs
· Functionalization
→ Decimation method
· Green´s function technique
→ Results
· Functionalized nanotubes
·Functionalized nanoribbons
·Edge defects in nanoribbons
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
~ 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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
-effective model
1
1
1
2
2
2
1
1
21
2
2 atoms/ cell nearest neighbor orbital overlap
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Periodic Boundary conditions
EF
Nanotubes electronic properties
Armchair ZigzagEF=0
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
What would it happen
if we alter these properties ?
Summarizing
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
→ Selective electrical signals of molecular adsorption events.
→ Protein interaction. → Virus detection.
Bio-, photo-sensors
Zhou et al. Nano Letters 9, 1028 (2009)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
· 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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Hybrid Carbon Based Materials
Is sp2 bonding broken/preserved?
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
sp2 sp3
Armchair
nanotube
axis
sp2 vs sp3 functionalization
CH2 chemisoption
Zigzagnanotube
axis
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
sp3
Tube axis
sp2 vs sp3 functionalization
Phenyl chemisoption
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Energy bands
Electronic statesLDoS (0.6 eV)
carbene 2 phenyls carbene
2 phenyls
X Γ X Γ
sp3
sp2
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
→ 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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Size : ~ 500 atoms
Building block
1.3 nm
3 nm
→ SWCNT (10,10)
→ phenyl groups
Description of the system
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Problem definition&
Decimation technique
Problem statement
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Problem definition
Left
lead
Right
lead
channel
channel
Right leadLeft lead
Nanotubes
Nanoribbons
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
~
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Hamiltonian: Wavefunction:
Energy spectrum:Eigenvalue equation:
Eigenvalues:
Decimation: 2-site model
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Decimation: 2-site model
is an effective potential that corrects the non-interacting on-site energy
Self-energy
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Decimation: 3-site model
→ A method to reduce the dimension of the Hamiltonian basis function space
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Decimation: N-site model
H1 H2 H3 H4 H1
~H4
~
V1,2 V2,3 V3,4
V1,4
~
V4,1
~
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Long channel decimation
Left lead
Right lead
Buildingblock
3
Buildingblock
2
Pristineblock
Linear scaling with length: method of N order
Buildingblock
1
Buildingblock
1
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Semi-infinite systems
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Finite system
Right leadChannelLeft lead
H =
HL
HC
HR
VLC
VCL
VRC
VCR
0
0~
~
~
NRorbNL
orb NCorb
→ Finite size Hamiltonian
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Functionalized CNTs
Results
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Quasi-ballistic
Diffusive
Localized
Transport regimes
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
phenyls in 300 nmDiffusive regime
Metallic CNTs
200 configurations
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Carbenes in 1000 nm Quasi-ballistic regime
Metallic CNTs
200 configurations
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
→ Small radius: quasi-ballistic
→ Large radius: diffusive !!!
Semiconducting CNTs
1000 nm
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
→ sp3 signature in “metallic” tubes
→ CH2 vs 2H
Semiconducting CNTs
Parallel orientation
2 Hydrogens
CH2
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Functionalized GNRs
Results
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
OH/H vs phenyls→ sp3 rehybridization signature
→ T(E) is independent of functional group
4 nm wide
2 nm wide
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
OH/H functionalization
→ Backscattering supression for edge functionalization
→ Conductance dips
→ Quantum mechanical interferences
A. L. Bezanilla, F. Triozon, S.RocheNano Letters 9, 2737 (2009)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Long nanoribbons (large gap)
Mean free path4 nm wide
A. L. Bezanilla, F. Triozon, S.RocheNano Letters 9, 2737 (2009)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Long nanoribbons (small gap)
Mean free path4 nm wide
A. L. Bezanilla, F. Triozon, S.RocheNano Letters 9, 2737 (2009)
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Edge defects in GNRs
Results
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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).
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Benzenoid defects
S.Dubois, A. L.-Bezanilla et al.Submitted to PRL
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Doping defects
Acceptor
Donor sp3-like
Passivated
Radical passivation
Backscattering suppression
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
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
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Coworkers
Merci! ¡Gracias!Grazie!Tack!
Merci! ¡Gracias!Grazie!Tack!
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Thanks
for your
attentio
n
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Alejandro López Bezanilla – CEA-Grenoble/INAC
PhD defense - November 2009
Conductance suppresion
sp3 barrier
High coverage-functionalization
D.C. Elias et al., Science 323, 610 (2009)
Insulating regime : (towards GRAPHANE)
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