experiment: davy graf, françoise molitor, and klaus ensslin solid state physics, eth zürich,...

Experiment:Davy Graf, Françoise Molitor,

and Klaus EnsslinSolid State Physics, ETH Zürich, Switzerland

Christoph Stampfer, Alain Jungen, and Christofer Hierold

Micro and Nanosystems, ETH ZürichTheory:

Ludger WirtzInstitute for Electronics, Microelectronics,

and Nanotechnology, Lille

Spatially resolved Raman spectroscopy

of single- and few-layer graphene

1 12

66

42 m

SiO2

1200 1600 2000 2400 2800Raman shift (cm -1)

Inte

nsity

(a

.u)

Motivation

1. • Investigate the 3D to 2D crossover in graphite.• Probe electronic and vibrational properties of few-layer, double-layer and single-layer graphene with double resonant Raman scattering.

Motivation

2 µm

1 m1

12

SiO2

Scanning force microscope

Optical microscope

0.4

0

SFM height (nm)

0.60.40.20Lateral position (m)

→ Raman spectroscopy:characterize by optical means(# layers and structural quality)

2.

1. • Investigate the 3D to 2D crossover in graphite.• Probe electronic and vibrational properties of few-layer, double-layer and single-layer graphene with double resonant Raman scattering.

Introduction: Vibrational Properties

ab-initio calculations:G. Kresse, J. Furthmüller, and J. Hafner, Europhys. Lett. 32, 729 (1995)Review article: L. Wirtz and A. Rubio, Solid State Comm. 131, 141 (2004).


ab-initio calculations:G. Kresse, J. Furthmüller, and J. Hafner, Europhys. Lett. 32, 729 (1995)Review article: L. Wirtz and A. Rubio, Solid State Comm. 131, 141 (2004).

2 atoms per unit cell => 6 phonon branches, 3 optic, 3 acoustic


Review article: L. Wirtz and A. Rubio, Solid State Comm. 131, 141 (2004).

Kinks in the dispersion (Kohn Anomaly)M. Lazzeri, F. Mauri, PRL 2004



Linear crossings of bands (due to symmetry)

Attention: different force constant parametrizations on the market


Finally: measured phonon dispersion brings good agreement with ab-initio calculations

Inelastic X-ray diffraction measurements:J. Maultzsch et al., Phys. Rev. Lett. 92, 075501 (2004)

Experiment

ab-initio

Raman spectroscopy on graphite

kKphonon

at point, k~0→ G

Single-resonant

Ref.: S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes, Wiley-VCH (2004)

0 1500 3000Raman shift (cm-1)

Inte

nsity

(a.

u) graphite 2.33 eV

D

G

D‘ G‘

E2g mode at


kK

phonon

at point, k~0→ G

Single-resonant


G-line is nondispersive


Inte

nsity

(a.

u) graphite 2.33 eV

D

G

D‘ G‘

E2g mode at


kKphonon

at point, k~0→ G

Single-resonant


E =

2.3

3 e

V

0.4 0 0.20.400.2-2

-1

0

1

2

E (

eV

)

KK MM M

q’

q

q’’A

B C

double-resonant


Inte

nsity

(a.

u) graphite 2.33 eV

D

G

D‘ G‘

TO mode between K and M


kKphonon

at point, k~0→ G

Single-resonant


E =

2.3

3 e

V

0.4 0 0.20.400.2-2

-1

0

1

2

E (

eV

)

KK MM M

q’

q

q’’A

B C

double-resonant


Inte

nsity

(a.

u) graphite 2.33 eV

D

G

D‘ G‘

TO mode between K and M

dispersive

Raman spectra of single- and double layer graphene

Sample fabrication:- Si wafer with 300 nm Si02 cap layer- Mechanical exfoliation of highly oriented pyrolytic graphite (HOPG)Ref.: K.S. Novoselov et al., PNAS 102, 10451 (2005)


1 m1

12

SiO2

Inte

nsity

(a.

u)

1200 1600 2000 2400 2800Raman shift (cm-1)

Inte

nsity

(a.

u)


1

2


1 m

D

single-layer graphene

double-layer graphene2

1

G D‘

Scanning confocal Raman spectroscopy:- Laser excitation of 532 nm/ 2.33 eV- Spot size:


1

2


1 mIn

tens

ity (

a.u)

1200 1600 2000 2400 2800Raman shift (cm-1)

Inte

nsity

(a.

u)

D



1

G D‘

1500 1600 1700Raman shift (cm-1)

Inte

nsi

ty (

a.u

)

Raman mapping: Integrated G line intensity

1

2


1 m

Raman: G line intensity

1

2

Raman mapping: Integrated G line intensity


1 m1

12

SiO2

Raman: Integrated G line intensity

1 m

0 0.4 0.8 1.2 1.6 2Lateral position (m)

Inte

nsi

ty (

a.u

.)2-layer 1-layer SiO2

One-to-one correlation

1 1

2

65(?)

6

42 m

SFM

0

Intensity G

0 2 4 6 8 10Lateral position (m)

1

2

3

4

5

Inte

nsity

G (

a.u.

)

-2

-1

0

1

SF

M h

eig

ht (

nm

) 5(?) 6 462101

# layers


1

2


1 mIn

tens

ity (

a.u)

1200 1600 2000 2400 2800Raman shift (cm-1)

Inte

nsity

(a.

u)

D



1

G D‘

Raman mapping: Integrated D line intensity

Symmetry:breaking / defects:

1. Edge of the flake.2. Boundary of sections of different height.3. But no defects within the flake.

kKphonon

close to K, M point, k>0Momentum restoring:elastic scattering → D

Double-resonant • Crystallite grain size, symmetry breaking [Tuinstra and Koenig, 1970]

2) Defects, disorder in general[Y. Wang et al, 1990]


1 m1

12

SiO2

Raman: Integrated D line intensity

1 m


1

2


1 mIn

tens

ity (

a.u)

1200 1600 2000 2400 2800Raman shift (cm-1)

Inte

nsity

(a.

u)

D



1

G D‘

Raman mapping: FWHM of the D‘ line

2600 2700 2800Raman shift (cm-1)

Inte

nsity

(a.

u)

~ 30 cm-1

~ 60 cm-1

1

2


1 m

Raman: D‘ line intensity

1

2

1

2

Raman mapping: FWHM of the D‘ line


1 m1

12

SiO2

Raman: FWHM of D‘ line

1 m

Splitting of the D‘ peak for double-layer graphene

Raman shift (cm-1)

Inte

nsity

(a.

u.)

2600 2700 2800

q

D‘: Single-layer graphene

E =

2.3

3 e

V

0.4 0 0.20.400.2-2

-1

0

1

2

E (

eV

)

KK MM M

q’

q

q’’A

B C

Raman shift (cm-1)

Inte

nsity

(a.

u.)

2600 2700 2800

Splitting of the D‘ peak for double-layer graphene

Raman shift (cm -1)

Inte

nsity

(a.

u.)

2600 2700 2800

q

q1 q2

Related work: A.C. Ferrari at al., PRL (2006)

D‘: Single-layer graphene

D‘: Double-layer graphene

E =

2.3

3 e

V

0.4 0 0.20.400.2-2

-1

0

1

2

E (

eV

)

KK MM M

q’

q

q’’A

B C

-2

-1

0

1

2

E (

eV

)

KK MM M

q2q1 q3

qq0

q3

However: quantitative failure of the model

Raman shift (cm -1)

Inte

nsity

(a.

u.)

2600 2700 2800

q1 q2


-2

-1

0

1

2

E (

eV

)

KK MM M

q2q1 q3

qq0

q3

The amount of splitting is underestimated by a factor of 2


Raman shift (cm -1)

Inte

nsity

(a.

u.)

2600 2700 2800

q1 q2


-2

-1

0

1

2

E (

eV

)

KK MM M

q2q1 q3

qq0

q3


Furthermore: D-Line dispersion off by a factor of 2


Raman shift (cm -1)

Inte

nsity

(a.

u.)

2600 2700 2800

q1 q2


-2

-1

0

1

2

E (

eV

)

KK MM M

q2q1 q3

qq0

q3


Furthermore: D-Line dispersion off by a factor of 2

Origin of the discrepancy: slope of ab-initio bands wrong,

or phonon dispersion wrong, or quantitative failure of double

resonant model

Pi-band dispersion of graphite

H

A. Grüneis, C. Attaccalite et al., submitted (2007), see cond-mat

Comparison of calculated and measured band-structure:

ARPES measurements

Blue lines: GW-calculations,

Red lines: LDA

Slope of the TO mode between K and M

J. Maultzsch et al., Phys. Rev. Lett. 92, 075501 (2004)

Experiment

ab-initio

Conclusions• Raman spectroscopy: an alternative to scanning force microscopy

• Monolayer sensitivity (single to double layer)

• Defects/symmetry breaking at the edge not within the flakes

• Need for more quantitative investigations of the double-resonant Raman model (splitting of the D' line and dispersion of the D and D' lines

Raman: FWHM D‘

Raman: Intensity D

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L.Wirtz,cond-mat/0607562 Nano Lett. 7, 238 (2007).Related work: A.C. Ferrari et al., Phys. Rev. Lett. (2006).Gupta et al. Nano Lett. (2006).

Raman mapping: Integrated D line intensity

Symmetry:breaking / defects:

1. Edge of the flake.2. Boundary of sections of different height.3. But no defects within the flake.

• Crystallite grain size, symmetry breaking [Tuinstra and Koenig, 1970]

2) Defects, disorder in general[Y. Wang et al, 1990]


1 m1

12

SiO2

Raman: Integrated D line intensity

1 m

E =

2.3

3 e

V

0.4 0 0.20.400.2-2

-1

0

1

2

E (

eV

)

KK MM M

q’

q

q’’A

B C

Conclusions Experiment:Davy Graf, Françoise Molitor, and Klaus Ensslin Solid State Physics, ETH Zürich, Switzerland

Christoph Stampfer, Alain Jungen, and Christofer Hierold Micro and Nanosystems, ETH Zürich, Switzerland

Theory: Ludger WirtzInstitute for Electronics, Microelectronics, and Nanotechnology (IEMN), 59652 Villeneuve d'Ascq, France

D. Graf et al., condmat/ , submittedRelated work: A.C. Ferrari at al., condmat/0606284, A. Gupta et al., condmat/0606593

Raman: FWHM D‘

Raman: Intensity D

• Raman spectroscopy: an alternative to scanning force microscopy

• Monolayer sensitivity (single to double layer)

• Defects/symmetry breaking at the edge not within the flakes

Frequency shift of the G band

1 2 3 4 6 HOPG# layer

G p

eak

(cm

-1)

1581

1583

1585

Inte

nsity

(a.

u.)

Raman shift (cm-1)

G

1540 1560 1580 1600 1620

HOPG reference:1582 cm-1

HOPG2-layer1-layer

cm-1

One-to-one correlation

- Height sensitivity for few-layer graphene

- Proportional to # of layers, but saturation above ~ 6 ML

1 2 3 4 60.2

0.4

0.6

0.8

HOPG# layer

Rel

. in

tens

ity

G/D

'

0 2 4 6 8 10Lateral position (m)

1

2

3

4

5

Inte

nsity

G (

a.u.

)

-2

-1

0

1

SF

M h

eig

ht (

nm

) 5(?) 6 462101

experiment: davy graf, françoise molitor, and klaus ensslin solid state physics, eth zürich,...

Documents

raman spectroscopy of

layer graphene motivation1

carbon nanotubes

graphitekkphononat point

evdgdge2g mode

wileyvch 2004graphite2

evdgdgto mode

marketreview article