_

_

__

+

+

++

_+ +

_+

_

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