momento telefonica

Grafeno: a folha mais fina do mundo

Tatiana G. RappoportInstituto de Física - UFRJhttp://tinyurl.com/rappoport@tgrappoport

1

1Wednesday, January 19, 2011

http://tinyurl.com/rappoport

http://tinyurl.com/rappoport

Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

O que é?Porque os físicos se

interessam tanto

Para que serve?

Grafeno

2



Outubro de 2010

3



Outubro de 2010

3

Big Bang Theory S3E1402/10

The Einstein Approximation



Outubro de 2010

3



Mas nossa estória começa em 2000...Andre Geim ganhava o Ig Nobel de Física por levitar um sapo

4



Experimentos de 6a à noite

5

Experimentos simples, novos e sem compromisso em áreas de pesquisa diferentes da que normalmente trabalhamos



Experimentos de 6a à noite

5

Experimentos simples, novos e sem compromisso em áreas de pesquisa diferentes da que normalmente trabalhamos

2002-E o grafite? Conhecemos há tantos anos mas não sabemos nada sobre camadas bem finas desse material



Como obter folhas finas de grafite?

Em vez de tentar fabricar folhas finas, arrancar folhas finas de um pedaço de grafite

6



O que são grafite e grafeno?

7

➡Cristais feitos de átomos de Carbono

Grafite



O que são grafite e grafeno?

7

➡Cristais feitos de átomos de Carbono

Grafite

Grafeno: uma única folha



Escala e visibilidade

8

1m

1mm

1µm

1nm

-Eu 1,62 m

-Formiga ~5 mm

-cabelo ~100 μm

-DNA ~2 nm

-molécula de água ~0.3 nm

OH

MO

ME



Escala e visibilidade

8

1m

1mm

1µm

1nm

1mm= 10-3m

1µm= 10-6m

1mm= 10-9m

-Eu 1,62 m

-Formiga ~5 mm

-cabelo ~100 μm

-DNA ~2 nm

-molécula de água ~0.3 nm

OH

MO

ME



Do grafite pro grafeno: método do durex

9



Do grafite pro grafeno: método do durex

9

Ozyilmaz' Group, Graphene Research, National University of Singapore



Do grafite para o grafeno

10



Do grafite para o grafeno

10

0.1 mm



Sobre óxido de silício

Espessura relacionada à cor

11

0.1 mm

microscópio ótico

1-5 camadas

100 camadas

10-30 camadas

Imagem Grupo de Manchester



Achando o grafeno

12

0.1 mm

1 µm = 0.001 mm

1 µm

2004



Grafeno em detalhes

13

2 µm

Microscópio ótico



Grafeno em detalhes

13

2 µm

Microscópio ótico

2 µm

Microscópio eletrônico de varredura



Grafeno em detalhes

13

2 µm

Microscópio ótico

2 µm


!

"#$%&!!'()*#'+,)!!-.#/01#&)!2343!

!

!"#$%&'()*+,+%-,%&'()*./+%

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

Sample bias (mV)

0.0 T

dI/dV

(a.u

.)

topography B=0 spectroscopy B>0 spectroscopy

skip

Landau levels Linear DOS

1 nm1nm= 0.001µm

Microscópio eletrônico de tunelamento



Grafeno em detalhes

13

2 µm

Microscópio ótico

2 µm


!

"#$%&!!'()*#'+,)!!-.#/01#&)!2343!

!

!"#$%&'()*+,+%-,%&'()*./+%

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

Sample bias (mV)

0.0 T

dI/dV

(a.u

.)


skip


1 nm1nm= 0.001µm

!

"#$%&!!'()*#'+,)!!-.#/01#&)!2343!

!

!"#$%&'()*+,+%-,%&'()*./+%

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

Sample bias (mV)

0.0 T

dI/dV

(a.u

.)


skip


Microscópio eletrônico de tunelamento

Imagem Grupo de Rutgers



Outras formas

14

Grafeno



Outras formas

14

Fulereno

R.F. Curl, H.W. Kroto, R. E Smalley 1985Prêmio Nobel 1996

Grafeno



Outras formas

14

Fulereno

R.F. Curl, H.W. Kroto, R. E Smalley 1985Prêmio Nobel 1996

Nanotubo

Sumio Iijima 1991

Grafeno


http://en.wikipedia.org/wiki/Sumio_Iijima

http://en.wikipedia.org/wiki/Sumio_Iijima

Mas por que os físicos se interessaram tanto?

15


Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 16

Propriedades físicas muito interessantes

O que medir? Como medir?





É preciso nanotecnologia





Propriedades elétricas

É preciso nanotecnologia



Fazendo os contatos elétricos

Imagem de microscópio eletrônico de varredura (MEV)

17

2 µm





Design

18

2 µm





Design

Dispositivo

19

2 µm



Dispositivo

20

contatos de Ouro

SiO2

Si

grafeno



Elétrons no grafeno

21




Grafeno conduz muito bem (como um metal)

21





Mas cargas podem ser controladas como num semicondutor

21






Mobilidade recorde de 1000000 cm2/(V·s) em grafeno suspenso a baixa temperatura

21


http://en.wikipedia.org/wiki/Square_centimetre


http://en.wikipedia.org/wiki/Volt


http://en.wikipedia.org/wiki/Second






Mobilidade recorde de 1000000 cm2/(V·s) em grafeno suspenso a baixa temperatura

Mobilidade de 50000 cm2/(V·s) a temperatura ambiente

21

Maior que em qualquer semicondutor

Si: < 2000 cm2/(V·s)






















22




Em materiais, elétrons podem se comportar como se tivessem massa maior ou menor do que a que eles tem quando livres

22




Em materiais, elétrons podem se comportar como se tivessem massa maior ou menor do que a que eles tem quando livres

No grafeno, eles se comportam como se não tivessem massa

Partículas relativísticas sem massa

Férmions de Dirac

Neutrinos são Férmions de Dirac

Neutrinos viajam a v=c, elétrons no grafeno têm v menor

22



Como sabemos?

23

http://www.magnet.fsu.edu/education/tutorials/java/index.html

Efeito Hall

1879 Edwin H. Hall





Efeito Hall

24

Elétrons em semicondutores e metais

ρxy

B(T)Inclinação da curva nos fornece número de elétrons/Volume

Usado para caracterizar semicondutores



Efeito Hall quântico

25

T=-270oC

ρxy=h/(e2N)

N é um número inteiro!

h e e são constantes

mas a baixa T e em 2D...




25

T=-270oC

ρxy=h/(e2N)




! 12

he2

! 13

he2




25

Descoberto em 81 por Klaus von Klitzing, Nobel em 85

Resistividade é quantizada!

Usado em metrologia como medida padrão

T=-270oC

ρxy=h/(e2N)



Efeito Quântico!


! 12

he2

! 13

he2




26

Elétrons em semicondutores

ρxy=h/(e2N)

T=-270oC

! 12

he2

! 13

he2




26


ρxy=h/(e2N)

16 Z. Jiang et al. / Solid State Communications 143 (2007) 14–19

Fig. 2. Quantized magnetoresistance and Hall resistance of a graphene devicewhere n ! 1012 cm"2 and T = 1.6 K. The horizontal lines correspond to theinverse of the multiples e2/h. The QHE in the electron gas is demonstrated byat least two quantized plateaus in Rxy with vanishing Rxx in the correspondingmagnetic field regime.

where the QHE manifests itself. Fig. 2 shows Rxy and Rxxof a typical high mobility (µ > 10,000 cm2/V s) graphenesample as a function of magnetic field B at a fixed gatevoltage Vg > VDirac. The overall positive Rxy indicates that thecontribution is mainly from electrons. At high magnetic field,Rxy(B) exhibits plateaus and Rxx is vanishing, which are thehallmark of the QHE. At least two well-defined plateaus withvalues (2e2/h)"1 and (6e2/h)"1, followed by a developing(10e2/h)"1 plateau, are observed before the QHE featurestransform into Shubnikov–de Haas (SdH) oscillations at lowermagnetic field. We observed the equivalent QHE features forholes Vg < VDirac with negative Rxy(B) values.

Alternatively we can access the QH plateaus by tuning theelectron density by adjusting Vg at a fixed magnetic field.Fig. 3 shows Rxy of the sample of Fig. 2 as a function ofgate voltage Vg at B = 9 T. A series of fully developed QHstates, i.e., plateaus in h/(e2!) quantized to values with aninteger filling factor !, are observed, which are the hallmarkof the QHE. Well-defined ! = ±2, ±6, ±10, ±14 QH statesare clearly seen, with quantization according to

R"1xy = ±4

!n + 1

2

"e2

h(1)

where n is a non-negative integer, and +/" stands for electronsand holes respectively. This quantization condition can betranslated into the quantized filling factor ! = ±4(n +1/2) in the usual QHE language. While the QHE has beenobserved in many 2D systems, the QHE observed in grapheneis distinctively different from those ‘conventional’ QHE’s sincethe quantization condition Eq. (1) is shifted by a half integer.

This so-called half-integer QHE is unique to graphene.It has been predicted by several theories which combine‘relativistic’ Landau levels (LLs) with the particle–hole

Fig. 3. The Hall resistance as a function of gate voltage at fixed magnetic fieldB = 9 T, measured at 1.6 K. The horizontal lines correspond to the inverse ofinteger multiples of e2/h values.

symmetry of graphene [1–3]. The experimental phenomena canbe understood from the calculated LL spectrum in the Diracspectrum.

As in other 2D systems, application of a magnetic field Bnormal to the graphene plane quantizes the in-plane motion ofcharge carriers into LLs. The LL formation for electrons/holesin graphene has been studied theoretically using an analogy to2 + 1 dimensional Quantum Electro Dynamics (QED) [4], inwhich the LL energy is given by

En = sgn(n)

#2eh̄v2

F |n|B. (2)

Here e and h̄ are electron charge and Planck’s constant dividedby 2" , and the integer n represents an electron-like (n >

0) or a hole-like (n < 0) LL index. In particular, a singleLL with n = 0 also occurs, where electrons and holes aredegenerate. Note that in Eq. (2). we do not consider a spindegree of freedom, assuming the separation of En is muchlarger than the Zeeman spin splitting. Therefore each LL hasa degeneracy gs = 4, accounting for spin degeneracy andsublattice degeneracy. This assumption needs to be changedwhen the magnetic field becomes large as we will discuss inthe next section.

The observed QH sequence can be understood employingthe symmetry argument for the Hall conductivity #xy ="Rxy/(R2

xy + (W/L)2 R2xx ), where L and W are the length and

width of the sample, respectively. With the given LL spectrumin Eq. (2), the corresponding Hall conductance #xy exhibitsQH plateaus when an integer of LLs are fully occupied, andjumps by an amount of gse2/h when the Fermi energy, EF ,crosses a LL. Time reversal invariance guarantees particle–holesymmetry and thus #xy is an odd function in energy acrossthe Dirac point [4]. Here, in particular, the n = 0 LL ispinned at zero energy. Thus the first plateau for electrons(n = 1) and holes (n = "1) are situated exactly at


ρxy=h/(4e2(N+1/2))

T=-270oC

! 12

he2

! 13

he2




26


ρxy=h/(e2N)





R"1xy = ±4

!n + 1

2

"e2

h(1)






En = sgn(n)

#2eh̄v2

F |n|B. (2)







ρxy=h/(4e2(N+1/2))


T=-270oC

Temperatura ambiente!

! 12

he2

! 13

he2

12

he2!

16

he2

110

he2



Efeito Hall quântico no grafeno

27





R"1xy = ±4

!n + 1

2

"e2

h(1)






En = sgn(n)

#2eh̄v2

F |n|B. (2)







Temperatura ambiente!

Efeito Quântico!Einstein Bohr



Não aguento mais toda essa física! Que sono..

Pra que serve esse tal de grafeno?


Outras propriedades

29



É transparente

30



É transparente

30

Imagem Y. P. Chen, Purdue University



É flexível

31

Camada de grafeno depositada em polímero flexível

Imagem Rutgers



É flexível

31

Camada de grafeno depositada em polímero flexível

Imagem SKKU KoreaImagem Rutgers



Pode ser dobrado e esticado

32

21



Pode ser dobrado e esticado

32

21

Imagem Manchester



Grafeno

33

É excelente condutorÉ transparenteÉ ultra-resistenteÉ flexível

Para que serve?



Grafeno

33

E quais são as limitações


Para que serve?



Transistores na eletrônica

Feitos de semicondutores

Fundamentais em todos os circuitos eletrônicos

34

Amplificação

Chaveamento (liga-desliga)

Porta controla corrente entre entrada (fonte) e saida (dreno)

F

DP



A vida antes do transistor

35

ENIAC 1946



A vida antes do transistor

35

ENIAC 1946

Bell Labs 1948Prêmio Nobel de Física 1956Shockley, Bardeen, Brattain



Permitiu grande revolução na eletrônica

Circuitos desenhados em um único semicondutor

Circuitos integrados

36



Permitiu grande revolução na eletrônica

Circuitos desenhados em um único semicondutor


36

1958 Texas Instruments Prêmio Nobel de Física 2000

J. S. Kilby



Fazendo um chip

37

http://nobelprize.org/educational/physics/integrated_circuit/history/index.html





Método do durex não pode ser usado em larga escalae produz folhas pequenas

Novos métodos de fabricação



Método do durex não pode ser usado em larga escalae produz folhas pequenas


Deposição Química de Vapores (CVD)

Epitaxia por feixe molecular

Outros




39

Co.) by applying soft pressure (!0.2 MPa) between two rollers.After etching the copper foil in a plastic bath filled with copperetchant, the transferred graphene film on the tape is rinsed withdeionized water to remove residual etchant, and is then ready tobe transferred to any kind of flat or curved surface on demand.The graphene film on the thermal release tape is inserted betweenthe rollers together with a target substrate and exposed tomild heat (!90–120 8C), achieving a transfer rate of !150–200 mm min21 and resulting in the transfer of the graphene films

from the tape to the target substrate (Fig. 2b). By repeatingthese steps on the same substrate, multilayered graphene filmscan be prepared that exhibit enhanced electrical and opticalproperties, as demonstrated by Li and colleagues using wet-transfer methods at the centimetre scale19. Figure 2c shows the30-inch multilayer graphene film transferred to a roll of 188-mm-thick polyethylene terephthalate (PET) substrate. Figure 2d showsa screen-printing process used to fabricate four-wire touch-screenpanels18 based on graphene/PET transparent conducting films

1st2nd30 inch

Beforeheating

Afterheating

39 inch

8 inch

Stencil mask

Screenprinter

a d

b e

c f

Figure 2 | Photographs of the roll-based production of graphene films. a, Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inchquartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. b, Roll-to-roll transfer ofgraphene films from a thermal release tape to a PET film at 120 8C. c, A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d, Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodesbefore assembly. e, An assembled graphene/PET touch panel showing outstanding flexibility. f, A graphene-based touch-screen panel connected to acomputer with control software. For a movie of its operation see Supplementary Information.

Graphene on Cu foil

Polymer support

Cu etchant

Graphene onpolymer support

Target substrateGraphene on target

Releasedpolymer support

Figure 1 | Schematic of the roll-based production of graphene films grown on a copper foil.The process includes adhesion of polymer supports, copperetching (rinsing) and dry transfer-printing on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that used for etching.

LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.132

NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology2



1st2nd30 inch

Beforeheating

Afterheating

39 inch

8 inch

Stencil mask

Screenprinter

a d

b e

c f


Graphene on Cu foil

Polymer support

Cu etchant







Junho de 2010

Nature Nanotecnology 2010




39



1st2nd30 inch

Beforeheating

Afterheating

39 inch

8 inch

Stencil mask

Screenprinter

a d

b e

c f


Graphene on Cu foil

Polymer support

Cu etchant









1st2nd30 inch

Beforeheating

Afterheating

39 inch

8 inch

Stencil mask

Screenprinter

a d

b e

c f


Graphene on Cu foil

Polymer support

Cu etchant







SiO2 (300 nm)

Ni/C layer

CH4/H2/Ar

~1,000 °C

Ar

Cooling~RT

Patterned Ni layer (300 nm)

FeCl3(aq)or acids

Ni-layeretching

HF/BOE

SiO2-layeretching(short)

Ni-layeretching(long)

PDMS/graphene

Downside contact(scooping up)

Graphene on a substrate

HF/BOE

Stamping

Floating graphene/Ni Floating grapheneGraphene/Ni/SiO2/Si

a

b

c

PDMS/graphene/Ni/SiO2/Si

NiSi

Figure 1 | Synthesis, etching andtransfer processes for the large-scale and patterned graphenefilms. a, Synthesis of patternedgraphene films on thin nickel layers.b, Etching using FeCl3 (or acids)and transfer of graphene films usinga PDMS stamp. c, Etching usingBOE or hydrogen fluoride (HF)solution and transfer of graphenefilms. RT, room temperature(,25 uC).

1,500 2,000 2,500

Inte

nsity

(a.u

.)

Raman shift (cm–1)

>4 layers3 layersBilayerMonolayer

a

c

5 µm

5 µm

e

5 µm

! = 532 nm

2 µm

3 layers

Bilayer4–5 layers

0.34 nm

b

>10 layers

G

2DD

5 µm

d >54321

Figure 2 | Various spectroscopic analyses of the large-scale graphene filmsgrownby CVD. a, SEM images of as-grown graphene films on thin (300-nm)nickel layers and thick (1-mm) Ni foils (inset). b, TEM images of graphenefilms of different thicknesses. c, An optical microscope image of thegraphene film transferred to a 300-nm-thick silicon dioxide layer. The insetAFM image shows typical rippled structures. d, A confocal scanning Ramanimage corresponding to c. The number of layers is estimated from theintensities, shapes andpositions of theG-band and 2D-bandpeaks. e, Ramanspectra (532-nm laser wavelength) obtained from the correspondingcoloured spots in c and d. a.u., arbitrary units.

d e

g h

2 cm

2 cm

Stamping Patterned graphene

a b

f

c

5 mm

Figure 3 | Transfer processes for large-scale graphene films. a, Acentimetre-scale graphene film grown on a Ni(300 nm)/SiO2(300 nm)/Sisubstrate. b, A floating graphene film after etching the nickel layers in 1MFeCl3 aqueous solution. After the removal of the nickel layers, the floatinggraphene film can be transferred by direct contact with substrates. c, Variousshapes of graphene films can be synthesized on top of patternednickel layers.d, e, The dry-transfer method based on a PDMS stamp is useful intransferring the patterned graphene films. After attaching the PDMSsubstrate to the graphene (d), the underlying nickel layer is etched andremoved using FeCl3 solution (e). f, Graphene films on the PDMS substratesare transparent and flexible. g, h, The PDMS stampmakes conformal contactwith a silicon dioxide substrate. Peeling back the stamp (g) leaves the film ona SiO2 substrate (h).

NATURE |Vol 457 |5 February 2009 LETTERS

707 Macmillan Publishers Limited. All rights reserved©2009

Mas....Junho de 2010

Nature Nanotecnology 2010




40

SiO2 (300 nm)

Ni/C layer

CH4/H2/Ar

~1,000 °C

Ar

Cooling~RT

Patterned Ni layer (300 nm)

FeCl3(aq)or acids

Ni-layeretching

HF/BOE

SiO2-layeretching(short)

Ni-layeretching(long)

PDMS/graphene

Downside contact(scooping up)

Graphene on a substrate

HF/BOE

Stamping

Floating graphene/Ni Floating grapheneGraphene/Ni/SiO2/Si

a

b

c

PDMS/graphene/Ni/SiO2/Si

NiSi

Figure 1 | Synthesis, etching andtransfer processes for the large-scale and patterned graphenefilms. a, Synthesis of patternedgraphene films on thin nickel layers.b, Etching using FeCl3 (or acids)and transfer of graphene films usinga PDMS stamp. c, Etching usingBOE or hydrogen fluoride (HF)solution and transfer of graphenefilms. RT, room temperature(,25 uC).

1,500 2,000 2,500

Inte

nsity

(a.u

.)

Raman shift (cm–1)

>4 layers3 layersBilayerMonolayer

a

c

5 µm

5 µm

e

5 µm

! = 532 nm

2 µm

3 layers

Bilayer4–5 layers

0.34 nm

b

>10 layers

G

2DD

5 µm

d >54321

Figure 2 | Various spectroscopic analyses of the large-scale graphene filmsgrownby CVD. a, SEM images of as-grown graphene films on thin (300-nm)nickel layers and thick (1-mm) Ni foils (inset). b, TEM images of graphenefilms of different thicknesses. c, An optical microscope image of thegraphene film transferred to a 300-nm-thick silicon dioxide layer. The insetAFM image shows typical rippled structures. d, A confocal scanning Ramanimage corresponding to c. The number of layers is estimated from theintensities, shapes andpositions of theG-band and 2D-bandpeaks. e, Ramanspectra (532-nm laser wavelength) obtained from the correspondingcoloured spots in c and d. a.u., arbitrary units.

d e

g h

2 cm

2 cm

Stamping Patterned graphene

a b

f

c

5 mm

Figure 3 | Transfer processes for large-scale graphene films. a, Acentimetre-scale graphene film grown on a Ni(300 nm)/SiO2(300 nm)/Sisubstrate. b, A floating graphene film after etching the nickel layers in 1MFeCl3 aqueous solution. After the removal of the nickel layers, the floatinggraphene film can be transferred by direct contact with substrates. c, Variousshapes of graphene films can be synthesized on top of patternednickel layers.d, e, The dry-transfer method based on a PDMS stamp is useful intransferring the patterned graphene films. After attaching the PDMSsubstrate to the graphene (d), the underlying nickel layer is etched andremoved using FeCl3 solution (e). f, Graphene films on the PDMS substratesare transparent and flexible. g, h, The PDMS stampmakes conformal contactwith a silicon dioxide substrate. Peeling back the stamp (g) leaves the film ona SiO2 substrate (h).

NATURE |Vol 457 |5 February 2009 LETTERS

707 Macmillan Publishers Limited. All rights reserved©2009

SKKY/ Columbia U.,Nature 2009




Métodos novos ainda não produzem folhas de grafeno homogêneas

Importante para mobilidade alta ➜ transistores

Não tão importante para outras aplicações

41




Aplicações

42

Filme transparente e condutor para LCD, touch screen, células solares e qualquer coisa que precise de um contato transparente



Aplicações

Atualmente óxido de Índio dopado com Estanho (ITO)

Índio é raro, caro e difícil de reciclar

Substituição irá baratear produção

Produção será mais limpa

42




Aplicações

Atualmente óxido de Índio dopado com Estanho (ITO)

Índio é raro, caro e difícil de reciclar

Substituição irá baratear produção

Produção será mais limpa

42


Produção em larga escala para substituição do ITO nos próximos anos



Touch Screen de grafenoProtótipo da Samsung, junto com pesquisadores da SKKU

43



Transistores de grafeno

44

Fevereiro de 2010




Protótipos operam a 100-200 GHz

Devem chegar facilmente a 1THz

Tamanho de alguns nm

44

Fevereiro de 2010







Transistores para eletrônica analógica

Substituição de transistores de GaAs

para RF ➜ uso militar, comunicações

44

Fevereiro de 2010







Transistores para eletrônica analógica

Substituição de transistores de GaAs

para RF ➜ uso militar, comunicações

44

Fevereiro de 2010

Produção nos próximos 5 anos



Transistores de um único elétron

45

F

DP

F DP




45

F

DP

F DP

Manchester 2008

P

F D




45

degeneracy at large n and l, and the number ofstates around a given energy is proportional to thedot areaº D2. This effect is often referred to asthe level repulsion, a universal signature of quan-tum chaos. The observed random spacing of CBpeaks, random height of Coulomb diamonds,changes in !DVg" quicker than 1/D and, especial-ly, the pronounced broadening of the spectraldistribution all indicate that chaos becomes adominant factor for small QDs.

To corroborate this further, Fig. 3 shows that theobserved level spacing is well described by Gauss-ian unitary distribution (32/p2)dE2exp(!4dE2/p)(characteristic of chaotic billiards) rather than thePoisson statistics exp(!dE) expected for integra-ble geometries (25, 26). The CB energy shifts thestatistical distributions from zero (we measureDE =Ec + dE rather than dE), and this makes itdifficult to distinguish between unitary and or-thogonal ensembles. Nevertheless, the Gaussianunitary distribution fits our data notably better.This agrees with the theory that expects randomedges to break down the sublattice symmetry(27) leading to the unitary statistics (25). In termsof statistics, Dirac billiards are different from thechaotic wave systems that mimic quantum me-chanics and are also described by the linear dis-

persion relation (optical, microwave, and acousticcavities) but typically obey the Gaussian orthog-onal statistics (28). Further evidence for the levelrepulsion in small QDs is provided by the ab-sence of any apparent bunching in their spectra(Fig. 2C). Indeed, despite considerable effort, wedid not find repetitive quartets or pairs of CBpeaks, which in principle could be expected dueto spin and/or valley degeneracy. The latter de-generacy is lifted by edge scattering (27), whereasthe spin degeneracy may be removed by scat-tering on localized spins due to broken carbonbonds (5).

For even smaller devices (D < 30nm), theexperimental behavior is completely dominated byquantum confinement. They exhibit insulatingregions in Vg sometimes as large as several V,and their stability diagrams yield the level spacingexceeding ~50 meV (Fig. 4, A and B). However,because even the state-of-the-art lithography doesnot allow one to control features <10 nm in size,the experimental behavior varies widely, frombeing characteristic of either an individual QD ortwo QDs in series or an individual QPC (13). It isalso impossible to relate the observations with theexact geometry because scanning electron andatomic forcemicroscopy fail in visualizing the one-atom-thick elements of several nm in size and oftencovered by PMMAor its residue. Nevertheless, wecan still use dE to estimate the spatial scaleinvolved. Basic arguments valid at a microscopicscale require a/D " dE/t (where a is the interatomicdistance, and t " 3 eV is the hopping energy),which again yields dE " a/D with a " 0.5 eV nm.For example, for theQD shown in Fig. 4withDE"40 meV, we find D ~ 15 nm.

Finally, we used our smallest devices (bothQDs and QPCs) to increase dE by furtherdecreasing their size using plasma etching. Someof the devices become overetched and stopconducting, but in other cases we have narrowedthem down to a few nm so that they exhibit thetransistor action even at room T (Fig. 4C). Thedevice shown appears completely insulating,with no measurable conductance (G < 10!10 S)over an extended range ofVg (>30 V) (off state),but then it suddenly switches on, exhibitingrather high G " 10!3e2/h. At large biases, weobserve the conductance onset shifting with Vb(13), which allows an estimate forDE as "0.5 eV.This value agrees with the T dependencemeasured near the onset of the on state, whichshows that we do not deal with several QDs inseries [as it was argued to be the case fornanoribbons (29)]. With no possibility to controlthe exact geometry for the nm sizes, we cannot becertain about the origin of the observed switching.Also, the exact boundary arrangements (armchairversus zigzag versus random edge and the ter-mination of dangling bonds) can be important onthis scale (5–12). Nevertheless,dE ~ 0.5 eVagainallows us to estimate the spatial scale involved inthe confinement as only ~1 nm.

Our work demonstrates that graphene QDsare an interesting and versatile experimental

system allowing a range of operational regimesfrom conventional single-electron detectors toDirac billiards, in which size effects are excep-tionally strong and chaos develops easily. Unlikeany other material, graphene remains mechani-cally and chemically stable and highly conduc-tive at the scale of a few benzene rings, whichmakes it uniquely suitable for the top-downapproach to molecular-scale electronics.

References and Notes1. A. K. Geim, K. S. Novoselov, Nat. Mater. 6, 183 (2007).2. A. H. Castro Neto, F. Guinea, N. M. R. Peres,

K. S. Novoselov, A. K. Geim, Rev. Mod. Phys., in press;preprint at http://xxx.lanl.gov/abs/0709.1163 (2007).

3. M. Y. Han, B. Ozyilmaz, Y. B. Zhang, P. Kim, Phys. Rev.Lett. 98, 206805 (2007).

4. P. Avouris, Z. H. Chen, V. Perebeinos, Nat. Nanotechnol.2, 605 (2007).

5. Y. W. Son, M. L. Cohen, S. G. Louie,Nature 444, 347 (2006).6. D. Gunlycke, D. A. Areshkin, C. T. White, Appl. Phys. Lett.

90, 142104 (2007).7. L. Yang, C. H. Park, Y. W. Son, M. L. Cohen, S. G. Louie,

Phys. Rev. Lett. 99, 186801 (2007).8. N. M. R. Peres, A. H. Castro Neto, F. Guinea, Phys. Rev. B

73, 195411 (2006).9. V. Barone, O. Hod, G. E. Scuseria,Nano Lett. 6, 2748 (2006).

10. L. Brey, H. A. Fertig, Phys. Rev. B 73, 235411 (2006).11. B. Wunsch, T. Stauber, F. Guinea, Phys. Rev. B 77,

035316 (2008).12. I. Martin, Y. M. Blanter, preprint at http://lanl.arxiv.org/

abs/0705.0532 (2007).13. See supporting material on Science Online.14. K. K. Likharev, Proc. IEEE 87, 606 (1999).15. L. P. Kouwenhoven et al., in Mesoscopic Electron

Transport, L. L. Sohn, L. P. Kouwenhoven, G. Schön,Eds. (Kluwer Series E345, Dordrecht, Netherlands, 1997),pp. 105–214.

16. E. A. Dobisz, S. L. Brandow, R. Bass, J. Mitterender, J. Vac.Sci. Technol. B 18, 107 (2000).

17. B. Gelmont, M. S. Shur, R. J. Mattauch, Solid StateElectron. 38, 731 (1995).

18. J. S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P. L. McEuen,Nano Lett. 5, 287 (2005).

19. F. Miao et al., Science 317, 1530 (2007).20. C. Stampfer et al., Appl. Phys. Lett. 92, 012102 (2008).21. U. Sivan et al., Phys. Rev. Lett. 77, 1123 (1996).22. S. R. Patel et al., Phys. Rev. Lett. 80, 4522 (1998).23. P. G. Silvestrov, K. B. Efetov, Phys. Rev. Lett. 98, 016802

(2007).24. I. M. Ruzin, V. Chandrasekhar, E. I. Levin, L. I. Glazman,

Phys. Rev. B 45, 13469 (1992).25. M. V. Berry, R. J. Mondragon, Proc. R. Soc. London A

412, 53 (1987).26. T. Guhr, A. Müller-Groeling, H. A. Weinedmüller, Phys.

Rep. 299, 189 (1998).27. A. Rycerz, J. Tworzydlo, C. W. J. Beenakker, Nat. Phys 3,

172 (2007).28. U. Kuhl, H.-J. Stöckmann, R. Weaver, J. Phys. A 38,

10433 (2005).29. F. Sols, F. Guinea, A. H. Castro Neto, Phys. Rev. Lett. 99,

166803 (2007).30. The research was supported by Engineering and Physical

Sciences Research Council (UK), the Royal Society, andOffice of Naval Research. We are grateful to K. Ensslin,L. Eaves, M. Berry, L. Vandersypen, A. Morpurgo,A. Castro Neto, F. Guinea, and M. Fromhold for helpfuldiscussions.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/320/5874/356/DC1Materials and MethodsSOM TextFigs. S1 to S5References

27 December 2007; accepted 5 March 200810.1126/science.1154663

A

B

C( (

(

)

Fig. 4. Electron transport through nm-scalegraphene devices. CB peaks (A) and diamonds (B)for a QDwith an estimated size ~ 15 nm. (C) Electrontransport through a controllably narrowed devicewith a minimal width of only !1 nm as estimatedfrom its DE. Its conductance can be completelypinched-off even at room T. Fluctuations in the onstate at room T are time dependent (excess noise). Atlow T, the on state exhibits much lower G, and thenoise disappears. Occasional transmission resonancescan also be seen as magnified in the inset.

18 APRIL 2008 VOL 320 SCIENCE www.sciencemag.org358

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08

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rgD

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nlo

ad

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fro

m

~1 nm

F

DP

F DP

Manchester 2008

P

F D




45

degeneracy at large n and l, and the number ofstates around a given energy is proportional to thedot areaº D2. This effect is often referred to asthe level repulsion, a universal signature of quan-tum chaos. The observed random spacing of CBpeaks, random height of Coulomb diamonds,changes in !DVg" quicker than 1/D and, especial-ly, the pronounced broadening of the spectraldistribution all indicate that chaos becomes adominant factor for small QDs.

To corroborate this further, Fig. 3 shows that theobserved level spacing is well described by Gauss-ian unitary distribution (32/p2)dE2exp(!4dE2/p)(characteristic of chaotic billiards) rather than thePoisson statistics exp(!dE) expected for integra-ble geometries (25, 26). The CB energy shifts thestatistical distributions from zero (we measureDE =Ec + dE rather than dE), and this makes itdifficult to distinguish between unitary and or-thogonal ensembles. Nevertheless, the Gaussianunitary distribution fits our data notably better.This agrees with the theory that expects randomedges to break down the sublattice symmetry(27) leading to the unitary statistics (25). In termsof statistics, Dirac billiards are different from thechaotic wave systems that mimic quantum me-chanics and are also described by the linear dis-

persion relation (optical, microwave, and acousticcavities) but typically obey the Gaussian orthog-onal statistics (28). Further evidence for the levelrepulsion in small QDs is provided by the ab-sence of any apparent bunching in their spectra(Fig. 2C). Indeed, despite considerable effort, wedid not find repetitive quartets or pairs of CBpeaks, which in principle could be expected dueto spin and/or valley degeneracy. The latter de-generacy is lifted by edge scattering (27), whereasthe spin degeneracy may be removed by scat-tering on localized spins due to broken carbonbonds (5).

For even smaller devices (D < 30nm), theexperimental behavior is completely dominated byquantum confinement. They exhibit insulatingregions in Vg sometimes as large as several V,and their stability diagrams yield the level spacingexceeding ~50 meV (Fig. 4, A and B). However,because even the state-of-the-art lithography doesnot allow one to control features <10 nm in size,the experimental behavior varies widely, frombeing characteristic of either an individual QD ortwo QDs in series or an individual QPC (13). It isalso impossible to relate the observations with theexact geometry because scanning electron andatomic forcemicroscopy fail in visualizing the one-atom-thick elements of several nm in size and oftencovered by PMMAor its residue. Nevertheless, wecan still use dE to estimate the spatial scaleinvolved. Basic arguments valid at a microscopicscale require a/D " dE/t (where a is the interatomicdistance, and t " 3 eV is the hopping energy),which again yields dE " a/D with a " 0.5 eV nm.For example, for theQD shown in Fig. 4withDE"40 meV, we find D ~ 15 nm.

Finally, we used our smallest devices (bothQDs and QPCs) to increase dE by furtherdecreasing their size using plasma etching. Someof the devices become overetched and stopconducting, but in other cases we have narrowedthem down to a few nm so that they exhibit thetransistor action even at room T (Fig. 4C). Thedevice shown appears completely insulating,with no measurable conductance (G < 10!10 S)over an extended range ofVg (>30 V) (off state),but then it suddenly switches on, exhibitingrather high G " 10!3e2/h. At large biases, weobserve the conductance onset shifting with Vb(13), which allows an estimate forDE as "0.5 eV.This value agrees with the T dependencemeasured near the onset of the on state, whichshows that we do not deal with several QDs inseries [as it was argued to be the case fornanoribbons (29)]. With no possibility to controlthe exact geometry for the nm sizes, we cannot becertain about the origin of the observed switching.Also, the exact boundary arrangements (armchairversus zigzag versus random edge and the ter-mination of dangling bonds) can be important onthis scale (5–12). Nevertheless,dE ~ 0.5 eVagainallows us to estimate the spatial scale involved inthe confinement as only ~1 nm.

Our work demonstrates that graphene QDsare an interesting and versatile experimental

system allowing a range of operational regimesfrom conventional single-electron detectors toDirac billiards, in which size effects are excep-tionally strong and chaos develops easily. Unlikeany other material, graphene remains mechani-cally and chemically stable and highly conduc-tive at the scale of a few benzene rings, whichmakes it uniquely suitable for the top-downapproach to molecular-scale electronics.

References and Notes1. A. K. Geim, K. S. Novoselov, Nat. Mater. 6, 183 (2007).2. A. H. Castro Neto, F. Guinea, N. M. R. Peres,

K. S. Novoselov, A. K. Geim, Rev. Mod. Phys., in press;preprint at http://xxx.lanl.gov/abs/0709.1163 (2007).

3. M. Y. Han, B. Ozyilmaz, Y. B. Zhang, P. Kim, Phys. Rev.Lett. 98, 206805 (2007).

4. P. Avouris, Z. H. Chen, V. Perebeinos, Nat. Nanotechnol.2, 605 (2007).

5. Y. W. Son, M. L. Cohen, S. G. Louie,Nature 444, 347 (2006).6. D. Gunlycke, D. A. Areshkin, C. T. White, Appl. Phys. Lett.

90, 142104 (2007).7. L. Yang, C. H. Park, Y. W. Son, M. L. Cohen, S. G. Louie,

Phys. Rev. Lett. 99, 186801 (2007).8. N. M. R. Peres, A. H. Castro Neto, F. Guinea, Phys. Rev. B

73, 195411 (2006).9. V. Barone, O. Hod, G. E. Scuseria,Nano Lett. 6, 2748 (2006).

10. L. Brey, H. A. Fertig, Phys. Rev. B 73, 235411 (2006).11. B. Wunsch, T. Stauber, F. Guinea, Phys. Rev. B 77,

035316 (2008).12. I. Martin, Y. M. Blanter, preprint at http://lanl.arxiv.org/

abs/0705.0532 (2007).13. See supporting material on Science Online.14. K. K. Likharev, Proc. IEEE 87, 606 (1999).15. L. P. Kouwenhoven et al., in Mesoscopic Electron

Transport, L. L. Sohn, L. P. Kouwenhoven, G. Schön,Eds. (Kluwer Series E345, Dordrecht, Netherlands, 1997),pp. 105–214.

16. E. A. Dobisz, S. L. Brandow, R. Bass, J. Mitterender, J. Vac.Sci. Technol. B 18, 107 (2000).

17. B. Gelmont, M. S. Shur, R. J. Mattauch, Solid StateElectron. 38, 731 (1995).

18. J. S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P. L. McEuen,Nano Lett. 5, 287 (2005).

19. F. Miao et al., Science 317, 1530 (2007).20. C. Stampfer et al., Appl. Phys. Lett. 92, 012102 (2008).21. U. Sivan et al., Phys. Rev. Lett. 77, 1123 (1996).22. S. R. Patel et al., Phys. Rev. Lett. 80, 4522 (1998).23. P. G. Silvestrov, K. B. Efetov, Phys. Rev. Lett. 98, 016802

(2007).24. I. M. Ruzin, V. Chandrasekhar, E. I. Levin, L. I. Glazman,

Phys. Rev. B 45, 13469 (1992).25. M. V. Berry, R. J. Mondragon, Proc. R. Soc. London A

412, 53 (1987).26. T. Guhr, A. Müller-Groeling, H. A. Weinedmüller, Phys.

Rep. 299, 189 (1998).27. A. Rycerz, J. Tworzydlo, C. W. J. Beenakker, Nat. Phys 3,

172 (2007).28. U. Kuhl, H.-J. Stöckmann, R. Weaver, J. Phys. A 38,

10433 (2005).29. F. Sols, F. Guinea, A. H. Castro Neto, Phys. Rev. Lett. 99,

166803 (2007).30. The research was supported by Engineering and Physical

Sciences Research Council (UK), the Royal Society, andOffice of Naval Research. We are grateful to K. Ensslin,L. Eaves, M. Berry, L. Vandersypen, A. Morpurgo,A. Castro Neto, F. Guinea, and M. Fromhold for helpfuldiscussions.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/320/5874/356/DC1Materials and MethodsSOM TextFigs. S1 to S5References

27 December 2007; accepted 5 March 200810.1126/science.1154663

A

B

C( (

(

)

Fig. 4. Electron transport through nm-scalegraphene devices. CB peaks (A) and diamonds (B)for a QDwith an estimated size ~ 15 nm. (C) Electrontransport through a controllably narrowed devicewith a minimal width of only !1 nm as estimatedfrom its DE. Its conductance can be completelypinched-off even at room T. Fluctuations in the onstate at room T are time dependent (excess noise). Atlow T, the on state exhibits much lower G, and thenoise disappears. Occasional transmission resonancescan also be seen as magnified in the inset.

18 APRIL 2008 VOL 320 SCIENCE www.sciencemag.org358

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pril 1

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08

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ww

.scie

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~1 nm

F

DP

F DP

Manchester 2008

P

F DAinda muito trabalho pela frente para produção em grande escala!



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IBM

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Strain Engineering of Graphene’s Electronic Structure

Vitor M. Pereira and A.H. Castro NetoDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

(Received 13 February 2009; published 20 July 2009)

We explore the influence of local strain on the electronic structure of graphene. We show that strain can

be easily tailored to generate electron beam collimation, 1D channels, surface states, and confinement.

These can be seen as basic elements for all-graphene electronics which, by suitable engineering of local

strain profiles, could be integrated on a single graphene sheet. In addition this proposal has the advantage

that patterning can be made on substrates rather than on graphene, thereby protecting the integrity of the

latter.

DOI: 10.1103/PhysRevLett.103.046801 PACS numbers: 81.05.Uw, 73.90.+f, 85.30.Mn

Notwithstanding its atomic thickness, graphene sheetshave been shown to accommodate a wealth of remarkablefundamental properties, and to hold sound prospects in thecontext of a new generation of electronic devices andcircuitry [1]. One exciting prospect about graphene isthat, not only can we have extremely good conductors,but also most active devices made out of graphene. Currentdifficulties with respect to this goal lie in that conventionalelectronic operations require the ability to completelypinch off the charge transport on demand. Although theelectric field effect is impressive in graphene [2], the ex-istence of a minimum of conductivity poses a seriousobstacle towards desirable on/off ratios. A gapped spec-trum would certainly be instrumental. The presence of agap is implicitly related to the problem of electron con-finement, which for Dirac fermions is not easily achievableby conventional means (like electrostatic potential wells)[3]. Geometrical confinement has been achieved in gra-phene ribbons and dots [4,5], but the sensitivity of transportto the edge profile [6], and the inherent difficulty in thefabrication of such microstructures with sharply definededges remains a problem.

The ultimate goal would be an all-graphene circuit. Thiscould be achieved by taking a graphene sheet and pattern-ing the different devices and leads by means of appropriatecuts that would generate leads, ribbons, dots, etc. Thispaper cutting electronics can have serious limitationswith respect to reliability, scalability, and is prone todamaging and inducing disorder in the graphene sheet[7]. Therefore, in keeping with the paper art analogy, wepropose an alternative origami electronics [8].

We show here that all of the characteristics of grapheneribbons and dots (viz. geometrical quantization, 1D chan-nels, surface modes) might be locally obtained by pattern-ing, not graphene, but the substrate on which it rests. Theessential aspect of our approach is the generation of strainin the graphene lattice capable of changing the in-planehopping amplitude in an anisotropic way. This can beachieved by means of appropriate geometrical patterns ina homogeneous substrate (grooves, creases, steps, orwells), by means of a heterogeneous substrate in which

different regions interact differently with the graphenesheet, generating different strain profiles [Fig. 1(b)].Another design alternative consists in depositing grapheneonto substrates with regions that can be controllablystrained on demand [9], or by exploring substrates withthermal expansion heterogeneity. Through a combinationof folding and/or clamping a graphene sheet onto suchsubstrates, one might generate local strain profiles suitablefor the applications discussed in detail below, while pre-serving a whole graphene sheet.The remainder of the Letter is dedicated to showing how

strain only can be used as a means of achieving (i) directiondependent tunneling, (ii) beam collimation, (iii) con-finement, (iv) the spectrum of an effective ribbon, (v) 1Dchannels, and (vi) surface modes.Model.—Within a tight-binding formulation of the elec-

tronic motion [10], effects of in-plane strain can be cap-tured, to leading order, by considering the changes innearest-neighbor hopping amplitude, t. We writet!Ri;n" # t$ !t!Ri;n", and treat the space dependentstrain-induced modulation, !t, as a perturbation (t %3 eV). It is straightforward to show [10] that, for smoothperturbations, the low energy Hamiltonian is

H # vF

Zdr!y ! &

!p' 1

vFA

"0

0 '! &!p$ 1

vFA

"24

35!;

(1)

valid near the valleys K and K0 in the Brillouin zone, with

FIG. 1 (color online). (a) Lattice orientation considered in thetext. Thicker bonds have perturbed hopping. (b) Artistic depic-tion of a substrate (S) patterned with folds (F), trenches, dots andwells (A), upon which rests a graphene sheet (G).

PRL 103, 046801 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending24 JULY 2009

0031-9007=09=103(4)=046801(4) 046801-1 ! 2009 The American Physical Society

Eletrônica origami

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H # vF

Zdr!y ! &

!p' 1

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"0

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"24

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latter.








H # vF

Zdr!y ! &

!p' 1

vFA

"0

0 '! &!p$ 1

vFA

"24

35!;

(1)





Eletrônica origami

Ultracapacitores

spintrônica



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IBM

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latter.








H # vF

Zdr!y ! &

!p' 1

vFA

"0

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vFA

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Eletrônica origami

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A brincadeira está apenas começando :)

spintrônica



Grafeno no Brasil

47

INMETROcaracterização

UFPR- fabricação de eletrodos com grafeno

UFMG/CDNTFabricação e

caracterização

Pesquisa teórica na UFMG/UFRJ/UFF/USP/UFC/UNIFRA

E outros grupos!

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