1. 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 Theory: Ludger Wirtz Institute for Electronics, Microelectronics, and Nanotechnology, Lille Spatially resolved Raman spectroscopy of single- and few-layer graphene

2. 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.

3. Motivation 2 µm 1  m 1 1 2 SiO 2 Scanning force microscope Optical microscope → 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.

4. 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).

5. 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). 2 atoms per unit cell => 6 phonon branches, 3 optic, 3 acoustic

6. Introduction: Vibrational Properties 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

7. Introduction: Vibrational Properties Review article: L. Wirtz and A. Rubio, Solid State Comm. 131, 141 (2004). Linear crossings of bands (due to symmetry)

8. Attention: different force constant parametrizations on the market Review article: L. Wirtz and A. Rubio, Solid State Comm. 131, 141 (2004).

9. 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

10. Raman spectroscopy on graphite k K  phonon at  point, k~0 → G Single-resonant Ref.: S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes, Wiley-VCH (2004) graphite 2.33 eV D G D‘ G‘ E 2g mode at 

11. Raman spectroscopy on graphite k K  phonon at  point, k~0 → G Single-resonant Ref.: S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes, Wiley-VCH (2004) G-line is nondispersive graphite 2.33 eV D G D‘ G‘ E 2g mode at 

12. Raman spectroscopy on graphite k K  phonon at  point, k~0 → G Single-resonant Ref.: S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes, Wiley-VCH (2004) double-resonant  graphite 2.33 eV D G D‘ G‘ TO mode between K and M

13. Raman spectroscopy on graphite k K  phonon at  point, k~0 → G Single-resonant Ref.: S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes, Wiley-VCH (2004) double-resonant  graphite 2.33 eV D G D‘ G‘ TO mode between K and M dispersive

14. Raman spectra of single- and double layer graphene Sample fabrication: - Si wafer with 300 nm Si0 2 cap layer - Mechanical exfoliation of highly oriented pyrolytic graphite (HOPG) Ref.: K.S. Novoselov et al., PNAS 102, 10451 (2005) Scanning force microscope 1  m 1 1 2 SiO 2

15. Raman spectra of single- and double layer graphene 1 2 Scanning force microscope 1  m D single-layer graphene double-layer graphene 2 1 GD‘ Scanning confocal Raman spectroscopy: - Laser excitation of 532 nm/ 2.33 eV - Spot size:

16. Raman spectra of single- and double layer graphene 1 2 Scanning force microscope 1  m D single-layer graphene double-layer graphene 2 1 GD‘

17. Raman mapping : Integrated G line intensity 1 2 Scanning force microscope 1  m Raman: G line intensity 1 2

18. Raman mapping : Integrated G line intensity Scanning force microscope 1  m 1 1 2 SiO 2 Raman: Integrated G line intensity 1  m

19. One-to-one correlation 5(?)6462101 # layers

20. Raman spectra of single- and double layer graphene 1 2 Scanning force microscope 1  m D single-layer graphene double-layer graphene 2 1 GD‘

21. 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. k K  phonon close to K, M point, k>0 Momentum 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] Scanning force microscope 1  m 1 1 2 SiO 2 Raman: Integrated D line intensity 1  m

22. Raman spectra of single- and double layer graphene 1 2 Scanning force microscope 1  m D single-layer graphene double-layer graphene 2 1 GD‘

23. Raman mapping : FWHM of the D‘ line ~ 30 cm -1 ~ 60 cm -1 1 2 Scanning force microscope 1  m Raman: D‘ line intensity 1 2 1 2

24. Raman mapping : FWHM of the D‘ line Scanning force microscope 1  m 1 1 2 SiO 2 Raman: FWHM of D‘ line 1  m

25. Splitting of the D‘ peak for double-layer graphene q D‘: Single-layer graphene

26. Splitting of the D‘ peak for double-layer graphene q q1q1 q2q2 Related work: A.C. Ferrari at al., PRL (2006) D‘: Single-layer graphene D‘: Double-layer graphene q0q0 q3q3

27. However: quantitative failure of the model q1q1 q2q2 D‘: Double-layer graphene q0q0 q3q3 The amount of splitting is underestimated by a factor of 2

28. However: quantitative failure of the model q1q1 q2q2 D‘: Double-layer graphene q0q0 q3q3 The amount of splitting is underestimated by a factor of 2 Furthermore: D-Line dispersion off by a factor of 2

29. However: quantitative failure of the model q1q1 q2q2 D‘: Double-layer graphene q0q0 q3q3 The amount of splitting is underestimated by a factor of 2 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

30. 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

31. Slope of the TO mode between K and M J. Maultzsch et al., Phys. Rev. Lett. 92, 075501 (2004) Experiment ab-initio

32. 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).

33. 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] Scanning force microscope 1  m 1 1 2 SiO 2 Raman: Integrated D line intensity 1  m

34. 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 Wirtz Institute for Electronics, Microelectronics, and Nanotechnology (IEMN), 59652 Villeneuve d'Ascq, France D. Graf et al., condmat/, submitted Related 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

35. Frequency shift of the G band HOPG reference: 1582 cm -1 HOPG 2-layer 1-layer cm -1

36. One-to-one correlation - Height sensitivity for few-layer graphene - Proportional to # of layers, but saturation above ~ 6 ML 5(?)6462101