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Alejandro López Bezanilla

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1 Alejandro López Bezanilla
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)

2 ChimTronique Transversal axes Saclay (S. Palacin)
Grenoble (R. Baptist)

3 Outline → Motivations → Electronic properties of CNTs and GNRs
· Functionalization → Decimation method · Green´s function technique → Results · Functionalized nanotubes ·Functionalized nanoribbons ·Edge defects in nanoribbons

4 Carbon atom Hybrid Molecular Orbitals Cohesion
Electronic properties in the vicinity of EF Valence electron orbitals: ~ 2D (sp2)‏ Graphene interactions between pz orbitals (bonds/bands )‏ ~ 3D (sp3)‏ Diamond

5 -effective model 2 atoms/ cell nearest neighbor orbital overlap 1 2

6 Nanotubes electronic properties
Periodic Boundary conditions Armchair Zigzag EF=0 EF

7 if we alter these properties ?
Summarizing What would it happen if we alter these properties ?

8 → Selective electrical signals of molecular adsorption events.
Bio-, photo-sensors → Selective electrical signals of molecular adsorption events. → Protein interaction. → Virus detection. Zhou et al. Nano Letters 9, 1028 (2009)

9 e- Bio-, photo-sensors Photoactive molecules:
Phtalocyanine … → Transmission after photoactive molecule functionalization. → Properties of the linker. hv e- Left lead Right lead 300 nm S. Campideli et al. J. Am. Chem. Soc. 2008, 130, 11503

10 Towards graphene nanoribbon transistor
Using top-down lithography to fabricate GNRs… · Ribbons down to ~ 10 nm width P. Kim et al (Columbia Univ. USA) E. Dujardin (CEMES, France) Ph. Avouris et al. (IBM, USA) · MOSFETs : clean GNR-FET with ~ 3nm are necessary !!! W  2 nm ! X. Li et al., Science 319, 1229 (2008) X. Wang et al., PRL 100, (2008)

11 Functionalizing graphene
2D Graphene and Graphene ribbons Goal: how to create or enlarge energy/conduction band gaps A graphene-based electrochemical switch (M. Lemme & A. Geim) Controlled electrochemical modification of graphene such that its conductance changes by more than six orders of magnitude (reversible bipolar switching devices). :: Chemical reaction of graphene with hydrogen (H+) and hydroxyl (OH-), which are catalytically generated from water molecules in the sub-stochiometric silicon oxide gate dielectric. The reactive species attach to graphene making it nonconductive but the process can subsequently be reversed by short current pulses that cause rapid local annealing.

12 Hybrid Carbon Based Materials
Is sp2 bonding broken/preserved?

13 sp2 vs sp3 functionalization
CH2 chemisoption sp2 sp3 Zigzag nanotube axis Armchair nanotube axis

14 sp2 vs sp3 functionalization
Phenyl chemisoption Tube axis

15 Electronic states sp3 sp2 LDoS (0.6 eV) Energy bands 2 phenyls carbene
X Γ X Γ carbene 2 phenyls carbene

16 SIESTA: an ab initio approach
→ 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. s-orbital p-orbital sp-hybrid orbital

17 Description of the system
Building block → SWCNT (10,10) Size : ~ 500 atoms → phenyl groups 1.3 nm 3 nm

18 Transport formalisms Kubo-Greenwood Landauer-Büttiker Order N method :
only Hamiltonian - Vector products allows big systems simulations No contacts Intrinsic properties Quantum diffusion mechanism Mean free path, scattering time, mobility Order power N method : inversion of Hamiltonian limites size of systems simulations Accuracy Transmission and reflexion probability Localization length, conductance

19 Problem definition & Decimation technique
Problem statement Problem definition & Decimation technique

20 Problem definition Channel Non-interacting electrons
Left lead Right lead Channel Non-interacting electrons Scattering free leads (perfect electrodes)‏ No backscattering at lead - reservoir interface Incident electrons are in thermal equilibrium with reservoirs

21 Problem definition Nanotubes Left lead Right lead channel Nanoribbons

22 Conductance from Green´s function
Fisher and Lee relation for transmission: T(E) = Tr [ ΓLGC ΓRGC ] (r) (a) Σ L Σ R HC ~ where: ΓL,R = i [ Σ L,R - Σ L,R ] (r) (a) ~ GC = [ E- HC - Σ L- Σ R ] - 1 S. Fisher and P.A. Lee, Phys. Rev. Lett., 23, 6851 (1981) Datta, Electronic transport in mesoscopic system, Cambidge (1995)

23 Decimation techniques
Problem definition VLC VCR Channel ... Left lead Right lead ... HL HL HC HC HR HR Semi-infinite leads + Long channel (~ orbitals) HL VLC VCL HC VCR H = VRC HR Decimation techniques Norb

24 Decimation: 2-site model
Hamiltonian: Wavefunction: Eigenvalue equation: Energy spectrum: Eigenvalues:

25 Decimation: 2-site model
Self-energy is an effective potential that corrects the non-interacting on-site energy

26 Decimation: 3-site model
→ A method to reduce the dimension of the Hamiltonian basis function space

27 Decimation: N-site model
V1,2 V2,3 V3,4 V1,4 ~ V4,1 ~ H1 ~ H4 ~ H1 H2 H3 H4

28 Long channel decimation
Linear scaling with length: method of N order Left lead Building block 1 Building block 2 Pristine block Building block 3 Building block 1 Right lead

29 Semi-infinite systems

30 Finite system → Finite size Hamiltonian H = HL HC HR VLC VCL VRC VCR ~
~ NRorb NLorb NCorb Right lead Channel Left lead

31 Green´s function technique
System Green´s function: where: GC GLC GCL GRC GCR VLC VCL VRC VCR E-HL ~ E-HR E-HC 1 = ~ (1) GCL (E-HL) + GC VCL = 0 ~ (2) GCL VLC + GC (E-HC) + GCRVRC = 1 ~ (3) GC VCR + GCR (E-HR) = 0

32 Green´s function technique
System Green´s function: ~ (1) GCL (E-HL) + GC VCL = 0 GCL = -GC VCL gL ~ Left & Right lead self-energies ~ GC = [ E-HC - Σ L- Σ R ] - 1 (2) GCL VLC + GC (E-HC) + GCRVRC = 1 ~ (3) GC VCR + GCR (E-HR) = 0 GCR = -GC VCR gR where: Σ L Σ R HC ~ gL= [ E- HL ]-1 gC = [ E- HC]-1

33 Results Functionalized CNTs

34 Transport regimes Quasi-ballistic Diffusive Localized

35 Metallic CNTs Diffusive regime phenyls in 300 nm 200 configurations

36 Quasi-ballistic regime
Metallic CNTs Quasi-ballistic regime Carbenes in 1000 nm 200 configurations

37 Semiconducting CNTs → Small radius: quasi-ballistic
→ Large radius: diffusive !!! 1000 nm

38 Semiconducting CNTs Parallel orientation CH2 2 Hydrogens
→ sp3 signature in “metallic” tubes → CH2 vs 2H 2 Hydrogens

39 Results Functionalized GNRs

40 OH/H vs phenyls → sp3 rehybridization signature
→ T(E) is independent of functional group 2 nm wide 4 nm wide

41 OH/H functionalization
→ Backscattering supression for edge functionalization → Conductance dips → Quantum mechanical interferences A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

42 Long nanoribbons (large gap)
4 nm wide Mean free path A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

43 Long nanoribbons (small gap)
4 nm wide Mean free path A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

44 Results Edge defects in GNRs

45 Edge defects Experimental evidences
→ Z. Liu, K. Suenaga, P.J.F. Harris, S. Iijima, Phys. Rev. Lett. 102, (2009) → P. Koskinen, S. Malola, H. Hakkinen, Phys. Rev. Lett. 101, (2008).

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

47 Doping defects Donor Radical passivation Backscattering suppression
Acceptor Passivated sp3-like Donor Radical passivation Backscattering suppression

48 Conclusions Decimation technique Carbon Nanotubes Graphene Nanoribbons
→ Full ab initio transport studies: SIESTA +TB_Sim Carbon Nanotubes → Chemical modification leads to diffusive transport → sp2 vs sp3 functionalization Graphene Nanoribbons → sp3 defects induce backscattering → Mind the radicals!  → Benzenoid edge defects are not critical in electronic transport properties

49 Coworkers Merci! ¡Gracias! Grazie! Tack!

50 Thanks for your attention

51

52 High coverage-functionalization
sp3 barrier High coverage-functionalization Conductance suppresion Insulating regime : (towards GRAPHANE) D.C. Elias et al., Science 323, 610 (2009) 52


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