Raman Spectrum of Graphene and Graphene layers PRL

97

, 187401 (2006) Sebastian Remi Journal Club 11/26/2006

Carbon

• Organic molecules, fuel etc. • Physical structure 6 electrons 1s2, 2s2, 2p2, “4” unpaired electrons • In molecule crystal structures hybridization: mixing of atomic orbitals in a way which maximizes the binding energy with the neighbour atoms • Is found in a huge variety of different materials among those the hardest (diamond) and the softest…

Graphite

Graphene •Strong bonds in a particular layer •Weak bonding between layers, which can easily be removed

Electronic structure

M •Electrons near the K point show relativistic dispersion •Relativistic behaviour •Graphene band structure is 1 st order approximation for Graphite bandstructure

Preparation

•Chemical growth: production of multilayers •Micromechanical cleavage Among thicker graphite flakes there are always thin graphite films and single graphene layers

AFM

Identification

White light SiO2 Si Single layer Bi layer Optical

Raman spectrum

• Raman spectrum shows characteristic dependence on thickness of graphite film • Identification and comparison of single, bi… layers • Evolution of Raman lines is directly connected to electronic structure

Raman effect

   

k i i

   

k

 

s s

     

K

Energy and Momentum conservation usually K~0, because BZ>>k Photon dispersion E 

i

e  Phonon band K(max) k

Laser 633nm or 514nm 0.04-4 mW

Setup

Spectrometer Sample

Raman effect in Graphene

G-Band

K •Most prominent line  1580

cm

•Relative Intensity enhances with the number of layers •shift~1/n;chemical doping?

 1

D-Band-Double Resonance

• Phonon momentum at edge of Brillouinzone • 1 and 2 phonon processes • General character: wavelength dependence and difference for changing number of layers Single phonon process Induced by defects Two phonon process

~1eV>>E(phonon)

D-Band

4 th order transition 1. e excitation 2. e-phonon scattering 3. defect scattering 4. E-hole recombination To mention: influence of number of layers

2D-Band

Dependent on number of layers 4 th order transition 1. e excitation 2. e-phonon scattering

3. Phonon with opposite momentum

4. E-hole recombination 2 phonon process Wavelength dependent •Line shape and position sensitive to the number of layers

Graphene bi layer

•2 inequivalent sublattices •Splitting into 4 bands

Graphene bi-layer

Difference to single layer and bulk graphite Level splitting due to splitting in electron bands