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electron-elecron-scattering:Te-h >> TL
electron-phononscattering:Te-h↓, TL↑
phonon-phononscattering
Te-h ≈ TL
time [s]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
non-thermal
thermalheat conduction
(thermal) melting
ablation
sample
fs-laser pluse
VB
CB
Ultrafast laser excitation of solids
semiconductor
Characteristic time scales:
• Electronic excitation: τL• Thermalization: τR• Energy transport: τE• Mass transport: τM
τL << τR << τE < τM
• Spatial and temporal localization of energy deposition:
• Non-equilibrium• Impulsive heating at constant volume• High temperature and high pressure phases of matter:
„warm dense matter“
Ultrafast laser excitation of solids II
Ultrafast x-ray spectroscopy
Femtosecond time scale:
Changes of nuclear configuration• chemical reactions• vibrations• structural changes
x-ray radiation:
Spatial structure ofatomic configuration
• structure of matter
Ultrafast x-ray spectroscopy: atomic resolution - temporal and spatial
Δx
Δt
Sources for ultrafast x-ray pulses(how to realize ultrafast x-ray diffraction…)1. accelerator based sources:
slicing source, SPPS, LCLS, TESLA X-FEL, LUX, …
Laser: Ti:Sa, 120 fs, 150 mJ Target: moving Titanium wire
wire
wheel
plasma
2. fs-laser plasma: “femtosecond x-ray tube”
fs-laser: ~100fs, 10 … 100 mJΙ ≈ 1016 … 1018 W/cm2
Ti wire
Rousse et al., Phys. Rev. E 50, 2200 (1994)
Time-resolved x-ray diffraction (TXRD)
Diffraction and focussing of keV x-rax radiation
Si (111)
50 … 200 nmGe, Bi (111)
Ge Si
80μm
≈ 3 × 104 photons/pulse
x-ray diffraction data
Ge Si
CCD camera imageIntegration
Rocking Curve
different lattice constants of Ge and Si
integratedreflectivity
Dispersion
x-ray diffraction experiment…
Titanime wire
lead shielding
x-ray mirror sample onx-y-Θ manipulator
CCD
Debrie protection
fs pump pulse
fs pulsefor plasma
kα radiation
AG von der Linde, University Essen
Ultrafast non-thermal melting:
Laser
SampleSilicon
K. Sokolowski-Tinten et al., PRB 51, 14186 (1995), ibid. 58, R11805 (1998),
optical spectroscopyelectronic excitation
non-thermal melting
ablation
0.47 J/cm2
R(λ) of solid Si
liquid
Ultrafast non-thermal melting:
> 10 % of all valence electrons!
K. Sokolowski-Tinten et al., PRB 61, 2643 (2001)
Intense electronic excitation
P. Stampfli et al., PRB 49, 7299 (1994)
lattice instability
Use ultrafast melting as test case for time-resolved x-ray diffraction
Non-thermal und thermal melting and subsequent re-crystallization
≈ 300 fs
K.Sokolowski-Tinten et al., PRL 87, 225701 (2001)
170 nm Ge on Si; (111)-diffraction spot
800 m/s
X-ray diffraction: Ultrafast melting of Ge
Non-thermal meltingNon-thermal und thermal melting
Si (111)
170 nmGe, Bi (111)
Analysis of x-ray pulse duration
0.8
0.9
1.0
-0.4 0.0 0.4 0.8
X-ray diffraction
Delay Time [ps]
Ge 0.2 J/cm2
0.8
0.9
1.0
-0.4 0.0 0.4 0.8
X-ray diffraction"melting"
Delay Time [ps]
Ge 0.2 J/cm2
0.8
0.9
1.0
-0.4 0.0 0.4 0.8
X-ray diffraction"melting"250 fs
Delay Time [ps]
Ge 0.2 J/cm2
0.8
0.9
1.0
-0.4 0.0 0.4 0.8
X-ray diffraction"melting"250 fs350 fs
Delay Time [ps]
Ge 0.2 J/cm2
τX = (300 ± 50) fs
for analysis phase transition is assumed as “instantaneous”
• Bi is a semimetal
• rhombohedral structure:- small displacement from fcc lattice- two atom basis
Lattice dynamics in Bismut
a
Bi-Bi distance a (0.468 × diagonal c)stabilized by Peierls-Jones mechanism
A1g-Phonon (V = const.)
• Bi is a semimetal
• rhombohedral structure:- small displacement from fcc lattice- two atom basis
• Excitation of coherent optical phonons(A1g-mode) with fs-laser pulses- Zeiger et al., PRB 45, 768 (1992)- DeCamp et al., PRB 64, 92301 (2001)- Hase et al., PRL 88, 67401 (2002)
Displacive Excitation of Coherent Phonons
geometric structur factor of Bi
→ decrease & oscillationof (111)-diffraction spot
→ increase & oscillationog (222)-diffraction spot
⏐S(hkl)⏐2
a
initialequilibrium position a0
displacedquasi equilibrium position a0‘
a/c = 0.5
(222)
(111)
A1g optical mode:νobs = 2.14 THz (470 fs)ν0 = 2.92 THz (342 fs)
Bi 50nm on Si, F ≈ 6 mJ/cm2
Coherent optical phonons
A1g optical mode:νobs = 2.14 THz (470 fs) softening & anharmonicity
Δa ~ 0,15 – 0,25 Å
DECP
K. Sokolowski-Tinten et al., Nature 422, 287 (2003)
⏐S(hkl)⏐2
a
(222)
(111)
a0‘a0
7%
High excitation density: Bi (111) and (222)
aperiodic but coherentgowth Bi-Bi distance: 0.4 Å
followed bymelting
Coherent phonons ⇔ phase transitionChange of atomic vibrations: periodic ⇒ aperiodic ?
Bi (111): higher excitation density
≈ 1.1 ps
softening of phonons precursor for melting
Phonon dynamics
coher. optical phonons incoh. phonons:“heat”
coher. acoustic phonons: lattice expansion
Debey-Waller Eff.:
)/exp( 22234
hklduDW π−=
Summary II
BiTime-resolved probe of structural dynamics
Time-resolved x-ray diffraction
Femtosecond laser spectroscopy
Non-thermal melting and coherent phonon excitation
Time-resolved photoelectron spectroscopy
Questions ?
Application to femtochemistry
IntroductionWhy femtosecond laser pulses?
Example: photochemistry of vision
Generation of femtosecond laser pulses
+-
fs-laser pulse
metal surface
Electron thermalization dynamics in metals and the Two-Temperature Model
Electron dynamics in metals following optical excitation
time-resolved photoemission spectroscopy
probe: 6 eV, 90 fs
E-EF = Ekin + Φ - hνprobe
pump: 1.5 eV, 55 fs
probe:6 eV, 90 fs
probe pulse polarization
p-polarized bulk + surface
probe pulse polarization
s-polarized bulk
Gd/W(110) film preparationAspelmeier et al.,
JMMM 132, 22 (1994)
dz2
electronic structure of the Gd(0001) surface
T=80 K
Kurz et al., J. Phys. Cond. Mat. 14, 6353 (2002)
surface plane
[000
1]
LDOS
charge densitydifference plot
5dz2
time-resolved photoemission of Gd(0001) bulk
Δt >100 fs: thermalized electron distribution function in Gd bulk
normal emission
T=100 K
s-polarized probe pulse
thermalizationin ~100 fs
non-thermal e-
unoccupied
occupied DOS
electron thermalization and cooling in Gd(0001)
characteristic times transient changes of electron and phonon
temperature
• excitation: < 50 fs• relaxation: ≈ 1 ps
+∇(κph∇Tl)
Two Temperature Model (2TM):
)TlTe(Ht
Tl)Tl(Cl
)t,z(S)TlTe(H)Te(t
Te)T(Ce
,
,el
=∂
∂
+-∇κ∇=∂
∂
H(Te,Tl ): thermalized electron distributionPhonons: Debye Model
transport e-ph coupl. opt. exc.
Anisimov et.al., Sov. Phys. JETP 39, 375 (1974)
good agreement withtwo-temperature model
TRPE of the Gd(0001) surface: p-pol. probe
time evolution of surface state binding energy
M. Lisowski et al., Phys. Rev. Lett. 95, 137402 (2005)
T=100 K
normal emission
p-polarized probe pulse
occupiedsurface state
time-resolved binding energy of S
Transient binding energy of Gd(0001) surface state
3 THz
LO phonon frequency
origin of the coherent mode at the surface ?
LO phonon derived mode:Surface vibrates with respectto underlying bulk layers
Köhler et al., PRL 24, 16 (1970)Rao and Menon, J. Phys. Chem. Solids 35, 425 (1974)
observedfrequency
Estimation of phonon amplitude
LO phonon derived mode:Surface vibrates with respectto underlying bulk layers
estimated phonon amplitude
ΔEB ≈ 1 meV ⇔ Δd12 ≈ 0.2% · d12
(equilibrium value d12 = 2.8 Å)
DFT calculations of S↑ binding energyas function of interplane spacing d12
Se
Ta
Charge density wave (CDW) in TaS2 or TaSe2
rearrangement of electronic structure:
UCO(upper cluster orbitals)6
6
1
b
c
a
quasi 2D crystal
strong e-ph coupling CDW at 300 K
1T-TaSe2
Colonna et al., Phys. Rev. Lett. 94, 036405 (2005)
~e/2 + -charge transfer
TaSe2: hexagonal layered structure
metal-insulator transition in bulk TaS2
6
0.01
2
46
0.1
2
4
T e / W
1.81.61.41.21.0U/W
insulator
metal
Crossover
Mott transition controlled by CDW (overlap ⇔ bandwidth)
Perfetti et al., Phys. Rev. Lett. 90, 166401 (2003)Phys. Rev. B 71, 153101 (2005)
hν=6 eV
photoemission spectra
phase diagram
time-resolved ARPES: T = 30 K
T=30 Khνpump=1.5 eVhνprobe=6.0 eV
normal emission
PE intensity
delay (ps)
pump-probe delay (ps)
UC
O p
eak
shift
(meV
)
2.82.52.2Frequency (THz)
bulksurface
see Demsar et al., PRB 66, R041101
beating between two modes
+ - • In phase “breathing” of the metal clusters • Large coupling and low dampingExcitation of Mott Phase
Coherent CDW excitation
Nuclear coordinate X
Raman-like excitation