Experiment: Davy Graf, Françoise Molitor, and Klaus Ensslin Solid State Physics, ETH Zürich, Switzerland Christoph Stampfer, Alain Jungen, and Christofer.

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, Switzerland Christoph Stampfer, Alain Jungen, and Christofer.

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