Ultrafast Carrier Dynamics in Graphene
M. Breusing, N. Severin, S. Eilers, J. Rabe and T. Elsässer
Conclusion
Pump-Probe Spectroscopy
Motivation
• information about carrier distribution with10fs
• Two delayed ultrashort laserpulses
• Probe detects pump induced
sample changes
• Graphene - building block for future
nanostructured electronic devices (FET, analog
time resolution
•Absorption changes () depend
on carrier distribution (fe ,fh)
GHz-THz applications)
• Carrier equalibration / formation of Fermi-Dirac
distribution within first 100fs
• Optical application (e.g. saturable absorber)
• Carrier optical phonon scattering with time const.
delay stage
• carrier relaxation - dominant limit for high
of about 150fs
after
abs.
frequency application
tD …
• Semi-metal –> tendency towards metals or
• substrate influences observably the carrier
distribution, but not the cooling by phonon scattering
   0 ( f h  f e )
semiconductors is still an open issue
Spectrograph
Pump-Probe Set-Up
• influence of supporting media for monolayer
• Focal spot diameter  8µm
important
sample
• Lock-in detection
7 fs laser
•Time resolution 10fs
Sample Preparation / Analysis
Properties Graphene
0.4
e, h (eV)
(a) carbon lattice)
• 3 layers of graphene (two dimensional
3000
Te (K)
• Brillouin zone of graphene, showing conical bands centered at K and K‘
2000
• Tips of conduction and valence band cones touch each other at EF=0eV,
1000
making graphene a semi-metal
0
0.5
0.0
1.0
Delay Time (ps)
3000
Te (K)
(b)
2000
1000
• 3 cases assumed: no varying
µ (dash-dotted), istantaneous
phonon decay (dashed) and
infinite phonon lifetime (solid)
(c) 0.4
e, h (eV)
• Carrier dynamic simulation for
graphene based on BlochBoltzmann- Peierls equations
0.2
0.0
0
0.5
1.0
Delay Time (ps)
graphene
M. Breusing et al., Phys. Rev. Lett. 102 (2009)
dSiO
2

Graphene on Muscovite (Mica)
Graphite onSiO Oxidized
Silicon
Si
2
1100
0
Wavelength (nm)
200
400
600
800
SiO2 Si
1000
Delay Time (fs)
offering bandwidth of 0.6eV
• Spectral and time resolved
and fits of transmission change
for sample with water film (blue /
green) and without (black / red)
• Decrease of sharp spectral
features in T/T indicate
carrier equilibration
• Shift to lower energies for
longer delays clearly visible
0
• Different kinds of samples
µ (eV)
0.2
(with / without water-film)
0.0
-0.2
0
300
600
Delay Time (fs)
900
600
Delay Time (fs)
0.3
0.0
300
600
Delay Time (fs)
• Spectra for various delays of both sample kinds; in red: best fit assuming Fermi-Dirac distribution
• Extracted carrier Temperature (T) and chem. potential (µ) within the first ps.
• Phonon scattering reduces T within the first 300fs; simultaneously µ rises, but reaches different
values
900
1.3
20µm
1.5 (eV)
Energy
900
(a)
0.5
0.4
0.3
0.2
0.1
2000
(b)
1000
µ=0.0eV
0.3
0
IR (cts/s)
-1
(3) Sample analysis by Raman spectroscopy – single D‘ peak indicates single layer graphene,
-1.8
absence of, for idealized graphene forbidden, D peak high crystal quality
1.8
3000
2000
1000
-0.3
300
-1.2
R (%)
30fs
0.7 75fs
150fs
250fs
0.0 800fs
1.4 Photon Energy (eV)
900
1
(2) spectrally integrated reflection change (R/R) for thick graphite (blue) and graphene (black),
-0.6
corrected for substrate contributions
0
T (K)
3000
2000
1000
(b)
T (K)
T (K)
(b)
1.8
µ (eV)
1.4 Photon Energy (eV)
Delay Time (fs)
µ (eV)
/ (10 )
-3
-3
T/T (10 )
(a)
30fs
1 75fs
150fs
250fs
0 800fs
4
1500 1600
2600 2700
-1

(cm
)
rel
(c)
0.0 0.2 0.4 0.6
-1.0
(a)
600
30 layers
(1) Sample structure; the well defined oxidized layer induces relevant multiple reflections and
0.28
2
thereby
(mJ/cm )Fabry-Perot oscillations in reflected light
Fluence
0.23
transmission change (T/T)
• Inset shows linear dependence
on added energy
30 layers
1 layer
D'
-1.8
300
5
R
• Spectrally integrated transients
0
3.9
1200 1300 -1 1 layer
rel (cm )
wph
-1.2
2 laye
0.33
R/R0 (arb. units)
• Spectrum of laser source
0.0
-1.0
-0.6
6
(b)
D
-3
1000
D-band
4.3
G
R/R (10 )
900
1.4
0.0 0.2 0.4 0.6
-3
R/R (10 ) R
800
7.000E-4
-3
700

R/R (10 )
0.00
600
4.333E-4
2
0.2
0.1
T=500K
1
2
Energy (eV)
3
0.33
0.28
0
-1
1.3
3000
T (K)
0.02
1.6
(a)
2wph
Fluence (mJ/cm )
µ (eV)
0.04
2
wph
-3
0.06
dSiO
-1.000E-4
R/R (10 )
Photon Energy (eV)
0.08
Intensity
0.0
1.8
R/R0 (arb. units)
0.10
D‘-band
G-band
graphene
(3)
IR
(2)
(1)
Energy (eV)
1.7
2000
1000
0.2
0.0
0
300
600
Delay Time (fs)
• Spectrally resolved R/R, simulated and fitted by Fresnel equations combined with transfer
matrix method, assuming Fermi-Dirac distribution
• Temperature (T) drops within first 200fs, chem. potential (µ) rises coevally, but returns to
zero within first ps
900
900fs
300fs
150fs
50fs
1.7