IMPRS Block Course “Chemistry and Physics of Surfaces ...w0.rz-berlin.mpg.de/imprs-cs/download/IMPRS_Wolf2005.pdf · substrate-mediated excitation mechanism dominates Anisimov,

Martin WolfDepartment of Physics, Freie Universität Berlin

IMPRS Block Course “Chemistry and Physics of Surfaces”

Introduction to femtosecond laser spectroscopy and ultrafast dynamics at surfaces

structure

kinetics

dynamics

E. Muybrigde 1887

Principle: Stroboscopic investigation of motion and structural changes

Application of femtosecond laser spectroscopy

Goal: Microscopic understanding of elementary processes at surfaces

Outline

IntroductionWhy femtosecond laser pulses?

Example: photochemistry of vision

Generation of femtosecond laser pulses

Laser basics and mode locking

hot e-

E

EF

e-transfer

substrate adsorbate

HOMO

LUMO

Femtochemistry

Vibrational wave packet dynamics

Surface femtochemistry

Electron and phonon mediated pathways

SFGNon-linear optics as a probe of surface dynamics

Vibrational sum-frequency generation spectroscopy

Why femtosecond spectroscopy ?Time scales of chemical reactions:

Temporal evolution from reactants to products:

Dynamics of the transition state

Typical timescale: 10-100 fs

Need femtosecond laser pulses for direct observation in time domain

Rhodopsin

Eye


Rod cells: A single rod contains 108 rhodopsins(renewed every 10 daysthroughout a person’s life)

cis-trans isomerization

Retinal

hν

11-cis all-trans

How do we see ?

Hirarchy of time scales

Optical absorption changes during reaction cycle

ultrafastconformationalchanges

therrmal relaxationde-protonation

Study time-resolved changes of optical absorption spectrum

pump

probe

signal

∆t

Time resolution is determined by pulse duration

Pump-probe spectroscopy

Basic concept to resolve processes on ultrafast time-scales

reflection transmission

Primary step of vision

How can this process be so fast ?

Spectral changes after excitation

Primary step (cis-trans isomerization) of Retinal must occur within 200 fs !

pump@ 500 nm

∆α

t ~ 0

t = 200 fs

“Vibrational coherent wave packet motion”

excited stateabsorption

(t ~ 0)

probe

History of time resolution

Year

time

reso

lutio

n(s

)

A.H. Zewail

Nobel prize 1999

Break through by development of pulsed laser sources

Development of short laser pulsespu

lse

dura

tion

(s)

„mode locking“

„Titanium Sapphire“

Year

normal dispersion(e.g. glass)

Properties of ultrashort laser pulsesShort pulse: Electrical field E(t) = ε(t) cos(ω0t + ϕ) with envelope ε(t)

time bandwidth product

(transform limit)

ε(t) ε(ω)

Generation of fs-laser pulses

A generic ultrafast laser consits of a broadband gain medium,a pulse-shortening device, and a resonator:

Why ?

Laser basics ILASER: Stimulated emission

Example: Four level laser (Nd:YAG)

Populationinversion

Titanium-sapphire laser

Laser basics II Resonator modes:

longitudinal modes:

Stability:g2 = 1-d/R2

g1 = 1-d/R1

R1 R2d

g1 g2 = 1

0 ≤ g1 g2 ≤ 1

condition for a stable resonator:

refractive index

Fabry-Perot

Mode-locking

Synchronization of laser modes:One mode:

All modes:

Constant phase between modes

Frequency domain:

Temporal structure:

Random phases

∆t = 1/∆ν

m

Mode-locking

„2 beam interference“

non-linear optical Kerr effectInduced polarization in non-linear optical medium

Linear optics: n0 = √ε = √ε0(1+4πΧ(1))

Non-linear optics:

Longitudinal and transversal Kerr effect

“Kerr lens”

1) self phase modulation

2) self focussing“Kerr lens”

Kerr lens mode-locking and dispersion

Pulse broadening due to dispersion

Example: Ti:Sa laser

Prism compressor (GVD compensation)

Measurement of pulse duration

auto correlation

interferrometric autocorrelation

I(τ) =

Outline







Non-linear optics as a probe of surface dynamics


Femtochemistry


hot e-

E

EF

e-transfer

substrate adsorbate

HOMO

LUMO

SFG

Real-time probing of chemical reactions

Real-time probing of chemical reactions II

Example: photodissociation

Analysis of repulsive excited state PES

“Clocking of chemical reactions”

Real-time probing of chemical reactions III

“Coherent wave packet motion”

reaction product

transition state

Outline





hot e-

E

EF

e-transfer

substrate adsorbate

HOMO

LUMO

Femtochemistry




SFGNon-linear optics as a probe of surface dynamics


Laser induced surface dynamics

Question: How does laser excitation induce surface reactions ?

Electronic excitations and charge transfer

Chemical bonding implies electronic couplingbetween „adsorbate“ and substrate

Vibrational relaxation at metalsby electron-hole pair excitation

hot e-

E

EF

e-transfer

substrate adsorbate

HOMO

LUMOElectron stimulated desorptionand surface photochemistry

Energy transfer by coupling betweenelectronic and nuclear degrees of freedom

Thermal activation

Phonon driven process (in electronic ground state)

kBT

2 CO + O → CO ↑adsads

fs-laser-induced chemistry at surfaces

Example: CO oxidation versus desorption on Ru(001) single crystal surface

hν2 CO + O → CO ↑ + CO2↑adsads

Co-adsorption of O+CO on Ru(001)(UHV conditions)

Flux

First ShotYield

200150100500Tim e-o f-F ligh t (µs)

1590 KEtrans =

640 K

Flux

[arb

. uni

ts]

fs-induced reaction pathways

CO Oxidation

CO desorption

Etrans =

+ kT

New reaction pathway is „switched on“ upon fs excitation

metal

Optical excitation of metal surfaces

Mechanism and timescales of energy transfer after optical excitation

~0.1-1 ps

~1 pselectrons

Tel

direct absorptionfs-excitation reaction

>1 ps

~100 fs

phononsTphm

etal

adsorbate vibrations Tads

Photoabsorption in a metal substrate creates a transientnon-equilibrium electron distribution

Energy transfer to phonons and adsorbate vibrational excitation

Primary step: Electron thermalization and cooling

Electron thermalization dynamics in metals probed with 2PPE and the two-temperature model

Electron dynamics in metals following optical excitation

The two-temperature model

Nearly thermal (Fermi-Dirac)distribution for electrons

Model assumes two heat baths for electrons and phonons: Cel >> Cph

PdCoupled diffusion equationfor Tel and Tph

Time-resolved two-photon photoemission How to probe electron thermalization and cooling ?

2kinF hEE-E ν−Φ+=

EF

Evac

Ekin

hν1

hν2

hν

e-

Φ

ϕ

/mE2sink kin|| hϕ=

TOF

e-

energy- and time-resolution:

pulseduration:65 fs

momentum resolution:

e-UV probe pulse

pump pulse

e-e scattering

Electron thermalization dynamics:

hot electroncascades

Experimental setup

Femtosecond time-resolved two-photon photoemission spectroscopy

µJ

W. S. Fann, R. Storz, H.W.K. Tom, J. Bokor,Electron thermalization in gold, Phys. Rev. B 46, 13592 (1992)

Method: time-resolved photoemissionwith hνprobe > Φ

Pump fluence: 120 µJ/cm2

300 µJ/cm2

Electron thermalization in gold

Electron thermailization occurs fasterwith increasing excitation density

Fermi-Dirac distribution

Time-resolved 2PPE from Ru(001)

0.0001

0.001

0.01

0.1

1

2PP

E in

tens

ity

1.51.00.50.0

E - EF (eV)

0.0001

0.001

0.01

0.1

1

0.0001

0.001

0.01

0.1

1

580 µJ/cm2

230 µJ/cm2

40 µJ/cm2∆ t / fs

0100200300400500

Ru(001)

e-UV probe800 nm pump

Pump-probe scheme:

probing electron dynamics around EFv

e-e scattering

1) Electron thermalization:

2) Relaxation by e-ph scattering

3) Energy transport in the bulk

Lisowski et al., Appl. Phys. A 78, 165 (2004)

2

4

68

10-6

2

4

68

10-5

2

4

68

elec

tron

ener

gy[J

/cm2 ]

9006003000-300time delay (fs)

Extended heat bath model

efficient ballistic transportof non-thermal electrons

Goal: Understanding the role of non-thermalized electrons

however, peak energy is describedreasonable well by both models

2TM underestimates rate of energy flow into the bulk

Extended modelincluding ballistic transport

2TM

Extension of two temperature modelAppl. Phys. A 78, 165 (2004)

transientexzess energy

of electrons

2TM

Femtochemistry at metal surfaces

substrate-mediated excitation mechanism dominates

Anisimov, et al. Sov. Phys. JETP , 375 (1974)39

120 fs50 mJ/cm2

phonon

electron

Time (ps)

Tem

pera

ture

(K)

T

T

1 20

Mechanism and timescales of energy transfer after optical excitation

~0.1-1 ps

~1 pselectrons

Tel


>1 ps

~100 fs

phononsTphm

etal


transient non-equilibrium between electrons and phonons: Tel >> Tph

new reaction mechanism?by non-thermal activationby separation of time scales of energy flow

Reaction mechanisms

Phonon-mediated Electron-mediated

Desorption Inducded byMultiple Electronic Transitions

DIMET -

substrate

adsorbateE

reaction coordinate

phonons Edes

hot e-

E

EF

τ ~1-10 fs

ground state

stateexcited

Edes

e-transfer

reaction coordinatesubstrate

kBTph

How to distinguish?

DIMET mechanismDesorption induced by multiple electronic transistions

NO/Pd(111)

see also Brandbyge et al., PRB 52, 6042 (1995)

Experimental Investigations

• NO and O2/Pd• CO/Cu • CO/Pt• O2/Pt • CO/NiO• CO + O2/Pt• CO + O/Ru, H+H/Ru

Misewich, Loy, HeinzTom, PrybylaHo MazurStephenson, Richter, CavanaghBonn, Wolf, ErtlZacharias, Al-ShameryDomen

YieldFluence dependenceTranslational energyVibrational energy Rotational energyUltrafast dynamicsInfluence of laser pulse durationInfluence of photon energyDependence on adsorption siteDependence on coverageCompetitive reaction pathwaysIsotope effects


Systems

2 CO + O → CO ↑adsads

Example I: Desorption and oxidation of CO on Ru(001)

Oxidation of CO impossible under equlilibrium conditions

200150100500Time-of-Flight (µs)

CO: 640 K

CO2: 1590 KEtrans =

4003002001000

Absorbed Fluence (yield weighted ) [J/m2]

Y(CO2) ~ F3.2

Y(CO) ~ F3.1

x 10F

lux

Firs

t Sho

t Yie

ld

hν2 CO + O → CO ↑ + CO2↑adsads

(1x2) - O/Ru(001)+ CO saturation

New reaction pathway upon fs excitation

Example II: Recombinative desorption of H2 on Ru(001)

H2 formation induced by fs laser excitation of H/Ru(001)

Full monolayerof H/Ru(001)

QMS

H2

H

Ru(001)

H

= 10 ± 2.4Yield (H2)Yield (D2)

H2: (2110 ± 400) K

flight time [µs]

flux[a.u.]

60

(x 10)

40200

0

D : (1720 ± 290) K2

<E >/ 2kkin B

High translational temperature of desorbing species

Pronounced isotope effects in H2/D2 yield

Temperature profiles and 2-pulse correlation

Tph

Tel6000

5000

4000

3000

2000

1000

020151050

time [ps]

surfa

cete

mpe

ratu

re[K

]

pulse 1 pulse 2

FWHM ~ 10 ps

FWHM ~ 1 ps

pulse-pulse delay [ps]re

actio

nyi

eld

[a.u

.]

-200 -100 0 100 200

phonon-mediated: slow response

electron-mediated:fast response

Goal: Discerning electron and phonon driven mechanismsQMS

CO

Ru(001)

CO

O

CO2delay

Two-pulse correlation measurement of the reaction yield allowsto distinguish between the two reaction mechanisms!

Experimental setup

Ti:sapphire oscillator + amplifier 4 mJ 800 nm, 110 fs, 20-400 Hz,

2 equally intensepulses

Ru(001)

QMS

H2/D2

CCD

pulse profilediagnostics

/

UHV

“Feulner cup“ detector

80 mm

O = 33 mm/

Ru(001)

QMSionisationvolume

H2

CO

2-pulse correlation measurements

120 fs50 mJ/cm2

phonon

electron

Time (ps)

Tem

pera

ture

(K)

T

T

1 20

CO

O

∆t

Ru

Tel Tph

CO

CO2

800 nm 120 fs

-200 -100 0 100 200

x24 CO2

COfir

stsh

otyie

ld(a

.u.)

pulse-pulse delay (ps)

FWHM=3 ps

FWHM=20 ps

2-pulse correlation:

Firs

t Sho

t Yie

ld

Goal: discriminate between electron and phononmediated mechanism

: Oxidation hot electron-mediated

: Desorption phonon-mediated

DFT calculations C. Stampfl, M. Scheffler, FHI Berlin

unoccupiedanti-bonding

orbital ~1.7eVabove EF

increasing Tel leads to

weakening ofRu-O-Bond

Ru(001)

O

Hot electron-induced activationof the O-Ru bond

Mechanism for CO oxidation

hotelectrons

EFermi

E O-level

anti-bonding

reaction coordinate

electronshot

Ru(001)

E

CO + O

0.3 eV

4.7 eV

1.7eV

from DFT

V = 1V = 2

O + CO

CO

CO + O

ad ad

ad

2,g

g g

gad

E ~1.8 eVa

Hot electron mediated vibrational excitation of the O-Ru bond

Non-adiabatic energy transfer from electronic excitations to adsorbate coordinate

M. Bonn et al, Science , 1042 (1999)285

Discussion

Reaction pathways for thermal versus femtosecond excitation

E

reaction coordinate

O

O

C

O*thermal excitation

O

0.8 eV

CO

O

O

CO

O

CO*

O

C

fs-laser excitation

1.8 eV

1.0 eV1.8 eV

e-

kT

Under thermal excitation the CO has desorbed before oxygen is activated

Seperation of time scales opens new reaction pathway

Electronic friction model

Energy transfer by coupling betweenadsorbate vibration and metal electrons

Electronic friction:

hotelectrons

EFermi

E

leveladsorbate

electronshot

metal

Coupling rate η = ~ ⎯ ⎯ 11Melτ

Coupling rates: τel τph τel-ph-1 -1 -1

., ,

met

al

τph

τel-ph Tph

τel

elTheat diffusion

adsT

ads-E /k Ta bRate ~ e

Two-Temperature Model

Coupled heat baths: el ph ads T , T , T What is “electronic friction”?Example: Change of electric resistivityin a thin metal film upon Xe adsorption

-V Xe

~1 ML

Struck PRL , 4576 (1996) ; Brandbyge .PRB , 6042 (1995).et al. et al77 52

2PC of laser-induced H2 formation

Coupling rates: τel τph τel-ph-1 -1 -1

., ,

met

al

τph

τel-ph Tph

τel

elTheat diffusion

adsT

ads-E /k Ta bRate ~ e

Two-Temperature Model

Coupled heat baths: el ph ads T , T , T Ultrafast response indicatescoupling to hot electron transient

first

shot

yiel

d[a

.u.]

pulse-pulse delay [ps]

H2exp. data

FWHM = 1.1 ps

0

-10 -5 0 5 10

model

Brandbyge et al., PRB 52, 6042 (1995)

Electronic friction model yields: Ea = 1.35 eV and τel = 180 fs(τel = 360 fs for D2)

for H2

Isotope effect in recombinative desorption

H2 formation induced by fs laser excitation of H/Ru(001)

Full monolayerof H/Ru(001)

QMS

H2

H

Ru(001)

H

= 10 ± 2.4Yield (H2)Yield (D2)

H2: (2110 ± 400) K

flight time [µs]

flux[a.u.]

60

(x 10)

40200

0

D : (1720 ± 290) K2

<E >/ 2kkin B

Isotope effect

Pronounced isotope effects in H2/D2 yield

Isotope effect and electronic friction model

Energy transfer by coupling betweenadsorbate vibration and metal electrons

Electronic friction:

hotelectrons

EFermi

E

leveladsorbate

electronshot

metal

Coupling rate η = ~ ⎯ ⎯ 11Melτ

Brandbyge et al., PRB 52, 6042 (1995)

pote

ntia

l ene

rgy

Ru-H/D distance

r electronicallyexcited PES

ground state of substrate-adsorbate-complex

Origin:- mass-dependent distance

traversed on excited PES

- lighter adsorbate starts movingmore rapidly

Fluence dependence: isotope ratio and first shot yield

0

160140120100806040200

0

403020100laser shot #

<F>~75J/m2 H counts [a.u.]

2

first

shot

yiel

d[a

.u.]

isotoperatio

20

10

2001601208040

experimental data

5

15

25

0

isot

ope

ratio

Y(H

2)/Y

(D2)

electronic friction model

Electronic friction model* simultanouslydescribes: • 2-pulse correlation

• fluence depedence of yield and isotope ratio

* Brandbyge et al., PRB 52, 6042 (1995)

exp. data model power law fit

Y(H2) ~ <F>2.8 and Y(D2) ~ <F>3.2

Outline





hot e-

E

EF

e-transfer

substrate adsorbate

HOMO

LUMO

Femtochemistry




SFGSFGNon-linear optics as a probe of surface dynamics


Real-time probing of vibrational dynamics

Goal: Probe suface reactions directly in the time domain

~0.1-1 ps

~1 pselectrons

Tel


>1 ps

~100 fs

phononsTphm

etal


So far probed only the (desorbing) reaction products

Use surface sensitive non-linear optics (SHG, SFG) to obtain a direct look inside the excited adlayer

sum-frequency generation (SFG)

Background-free, visible detectionSensitivity: 10 MLShort pulses: time resolutionSurface specific

-3

Pot

.Ene

rgy

C-O distance

v=0

v=1

v=2

5 µm + 800 nm = 690 nm

IR

SFGVIS

With background, IR detectionoptical linear technique

C-O distance

IRv=0

v=1

v=2

Pot

.Ene

rgy

IR absorption spectroscopy(FTIR)

Vibrational spectroscopy

CO

C-O stretch

Vibrational SFG spectroscopy

Principle of sum-frequency generation (SFG):

Pot

. Ene

rgy

C-O distance

IRv=0

v=1

v=2

SFGVIS

CO

C-O stretch

P E E = χ ω(2) (2)

IR ωVISω ωSFGSFG

ωSFG = ωIP + ωVIS

Surface sensitive method:SFG is symmetry forbidden in isotropic (bulk) media (dipole approximation)

Second order non-linearoptical process

Time-resolved SFG as molecule specific probe of surface reactions

Broadband IR vibrational SFG spectroscopy Vibrational spectroscopy without tuning the IR frequency

IR

VIS SFG

IR

VIS

RuSFG

IRIR

VIS

VIS

Γn

ΓSFG

01

2

~5 cm-1

~150 cm-1

SFG spectrum ( 3x 3)-CO/Ru(001) √ √

SFG wavelength [nm]690 688 686 684694 692

SFG

inte

nsity

IR

20001950

FWHM9 cm-1

1900 2050IR wavenumber [cm ]-1

2100 2150

200 K

SFG

IR intensity

Use spectrally broad pulse with spectrally narrow upconversion pulse

fs- IR VIS

L.J. Richter et al., Opt. Lett. 23, 1594 (1998).

SFG experimental setup

Ti:sapphire oscillator + amplifier4 mJ, 800 nm , 110 fs, 20-400 Hz,

OPG/OPA (TOPAS), 20-30 J µ2.5-10 mµ

tunableIR pulse

pump pulse

spectrometerCCD camera

multi-channel detectionRu(001)

QMS

SFGprobe

pulse shaperFWHM 7 cm , 7 J µ-1

narrow bandVIS pulse

Example water/Ru(001)

intrinsically surface sensitive

SFG signal is enhancedwhen IR Photon is resonantwith vibrational transition

=

Sum-frequency generation (SFG)

Example: D2O covered and bare Ru(001) surface

D2O multilayers: free OD resonance

bare Ru: nonresonant background

VISSFGIR

VIS field

543210time (ps)

IR fieldIR polarization

2) Frequency-resolved SFG: temporally long, spectrally narrow VIS-pulse

1) Time-resolved SFG: temporally short, spectrally broad IR + VIS-pulse

SFG

inte

nsity

420time (ps)

240023002200IR frequency (cm-1)

SFG spectrum

SFG

inte

nsity

I~e-2t/T2

Γ~1/T2

Equivalence of spectral- and time-domain measurements

FID

linewidth

VIS IR SFG

Au

VIS

delay

IRSFG

Au

Experimental time resolution: better than 150 fsExperimental frequency resolution: better than 3 cm -1

CH3CN CH3CN

80

70

60

50

40

30

x103

25002400230022002100 IR frequency (cm-1)

SFG

inte

nsity

(arb

. uni

ts) C-N stretch

IR spectrum

SFG spectrum

Frequency domain: Time domain:

IR-broadband SFG: Spectral and time-resolution

M.Bonn et al. (Univ. Leiden)

80

70

60

50

40

30

x10 3

SFG

inte

nsity

(arb

. uni

ts)

43210

IR-VIS delay (ps)

C-N stretch

non-resonant responsefrom Au surface

Γ=7.6 cm-1 homogeneous→ T2=0.68 ps

SFG

inte

nsity

(arb

. uni

ts)

320031003000290028002700

IR Frequency (cm-1)

C-H stretchΓ=8.0 cm-1

→ T2=0.64 ps

SFG

inte

nsity

(arb

. uni

ts)

210IR-VIS delay (ps)

C-H stretch

T2=0.61 ps

C-N stretch

SFG

inte

nsity

(arb

. uni

ts)

43210

T2=0.68 pshom.

∆ω=2.5 cm-1; T2=1.65 psinhomogeneous

Probing surface inhomogeneities with SFG

25002400230022002100

SFG

inte

nsity

(arb

. uni

ts)

C-N stretch

∆ω=2.5 cm-1 inhomogeneous T2=1.65 ps

Time-domain measurements are particularly sensitive to inhomogeneitiesin surface adsorption sites due to temporal separation of interferences.

Time-resolved SFG of CO/Ru during desorptionSpectroscopic snapshots of the CO stretch mode

SFG

inte

nsity

(a.u

.)

21002050200019501900IR wavenumber (cm-1)

3 ps

23 ps

0.5 ps×8

×8

×8

Pump-Probe delay –4.5 ps–2.0 ps–1.5 ps–1.0 ps–0.5 ps0.5 ps3.0 ps

23.0 ps68.0 ps

168.0 ps

CO

yie

ld (a

.u.)

100shot number

210020001900

T =340 K, F=55 J/m02

CO/Ru(001)opticalprobe

Pronounced transient red shift, linewidthbroadening and decrease of intensity

Problems:Dipole-dipole coupling in the adlayerand small concentration of „products“

M. Bonn Phys. Rev. Lett , (2000) 4653et al, 84

Time-resolved SFG of CO/Ru(0001)

Calculation:

- anharmonic couplingto CO stretch mode

- thermal excitation offrustrated translation

At high fluence:

- excitation and couplingto higher frequency modes

Strong redshift indicated thatfrustrated rotation is dominante

Low fluence: Good fit

Real-time probing of surface reactions: 2PPE Snapshots of excited electronic states during evoltution of wavepacket

Time-resolved 2PPE spectra ‚Desorption‘ of Cs/Cu(111)

photoemissionprobe

Summary


Femtochemistry




Electron thermalization in metals

Test of the two-temperature model



Isotope effects and electronic friction model


SFG

0.0001

0.001

0.01

0.1

1

2PP

E in

tens

ity

1.51.00.50.0

E - EF (eV)

∆t / fs 0 100 200 300 400 500

2PP

E In

tens

ity

Ru

thanks to

C. Gahl, U. Bovensiepen, J. Stähler, M. Lisowski, P. Loukakos,

D. Denzler, S. Funk, C. Hess, and G. Ertl, Fritz-Haber-Institut Berlin

S.Roke, M. Bonn, Leiden University, The Netherlands

S. Wagner, C. Frischkorn, Freie Universität Berlin

Literature:H. L. Dai and W. Ho, Laser Spectroscopy and Photochemistry at Metal SurfacesWorld Scientific (1995).

H. Petek and S. Ogawa, Femtosecond time-resolved two-photon photoemission studiesof electron dynamics in metalsProgress in Surface Science 56, 239-311 (1998).

H. NienhausElectronic excitations by chemical reactions at metal surfacesSurface Science Reports 45, 1-78 (2002).

P.M. Echenique, R. Berndt, E.V. Chulkov, Th. Fauster and U. Höfer, Decay of electronic excitations at metal surfacesSurface Science Reports 52, 219-318 (2004).

M. Bonn, H. Ueba and M. WolfTheory of sum-frequency generation spectroscopy of adsorbed moleculesby density matrix method - Broadband vibrational SFG and applicationsJ. Phys.: Condens. Matter 17, 201 (2005)

Documents

IMPRS Block Course “Chemistry and Physics of Surfaces ...w0.rz-berlin.mpg.de/imprs-cs/download/IMPRS_Wolf2005.pdf · substrate-mediated excitation mechanism dominates Anisimov,