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Electron Dynamics at Metal Surfaces

Fulvio Parmigiani

Università degli Studi di Trieste

Dipartimento di Fisica

and

Sincrotrone Trieste (Trieste, Italy)

The study of the electron dynamics at surfaces and interfaces relays on the ability to time-resolve the ultra-rapid scattering processes which result in energy and momentum relaxation, recombination and diffusion.

In typical experiments a short-pulsed (10-100 fs) laser can be used for photoemission experiments in the time-domain, whereas longer laser pulses (1-5 ps) provided by FT limited coherent sources can be used for photoemission experiments in the frequency (energy) domain with unrecorded resolving power.

Experimental techniques must be brought to bear in which band-structure specificity are combined with time resolution. Angle resolved photoemission is particularly suited for such experiments.

- A rather interesting system to study the electron dynamics at the solid surfaces is represented by the Surface States (SS) Image Potential States (IPS).
- The SS-IPS represents a paradigmatic two-levels system in solids and can be seen as a playground to study, in the momentum space,the optical transitions in semiconductors, insulators and superconducting systems.
- band dispersion
- direct versus indirect population mechanisms
- polarization selection rules
- effective mass ( in the plane of the surface)
- electron scattering processes and lifetime

ToF

TIME RESOLVED MULTI-PHOTONPHOTOEMISSION (hn<F)

band mapping ofUNOCCUPIED STATES and ELECTRON SCATTERING PROCESSES mechanisms

LINEAR PHOTOEMISSION (hn>F)

band mapping of OCCUPIED STATES

Linear photoemission on Ag(100)

h=6.28 eV

Multiphoton on Ag(100)

h = 3.14 eV

n=1

n=2

M-B distribution “temperature” in a

typical range of 0.5-0.7 eV.

G. P. Banfi et al., PRB 67, 035418 (2003).

PHOTOEMISSION SPECTRA ON Ag(100)

p-polarized incident radiation

30° incidence and 150 fs pulse.

F-D distribution at the RT energy

Log Scale

106 sensitivity

Iabs=13 mJ/cm2

ToF

sample

detector

Acceptance angle:

0.83°

Energy resolution:

10 meV @ 2eV

Detector noise:

<10-4 counts/s

PS1

PS2

PS3

PS4

PC

Preamplifier

Discriminator

GPIB

Multiscaler

FAST 7887

stop

start

Laser

- m-metal UHV chamber
- residual magnetic field < 10 mG
- Base pressure <2·10-10 mbar
- photoemitted electrons detector:
- Time of Flight (ToF) spectrometer

G. Paolicelli et al. Surf. Rev. and Lett. 9, 541 (2002)

n=1

Φ

empty

states

Efermi

occupied

states

g =

Non-Linear Photoemission Process

- PHOTOEMISSION PROCESS
- PROBLEMS:

Upon the absorption of two photon

the electron is already free.

Which is the absorption mechanism responsible of the free-free transition?

Keldysh parameter g=1500>>1, perturbative regime

Evidence of

ABOVE THRESHOLD PHOTOEMISSION

in solids ?

- DE = hn

- Fermi-Dirac edge

Non-linearity order:

3-photon Fermi edge vs

2-photon Fermi edge

n=3

n=2

Energy-shift with photon energy:

DE3PFE = 3·hDn

ATP

3-Photon Fermi Edge: Three experimental evidences...

Evac

n=1

Φ

empty

states

Efermi

Rough Estimate T(3)/T(2)10-6

Experimental Value T(3)/T(2)10-4

occupied

states

Is another mechanism involved?

- PHOTOEMISSION PROCESS
- RESULTS:

To evaluate the cross sectionfor an

n-photon absorption involving the initial and final states:

is proportional to the Transition Matrix Element in the DIPOLE APPROXIMATION

In this calculation we have to consider the mixing of the final free electron state with all the unperturbed Hamiltonian eigenstates but is it difficult to evaluate the contribution of this mixing to T(3).

Ag(100)

U. Hofer et al., Science277, 1480 (1997).

In most metals exists a gap in the bulk bands projection on the surface. When an electron is taken outside the solid it could be trapped between the Coulomb-like potential induced by the image charge into the solid, and the high reflectivity barrier due the band gap at the surface.

Image Potential States dispersion measured via two-photon resonant ARPES on Ag(100) along GX

LEED

n=1

n=2

IPS n=1:

hn=4.32 eV, p pol.

E

m/m*=1.03 0.06

n = 2

m/m*=0.97 0.02

G. Ferrini et al., Phys. Rev. B 67, 235407 (2003)

n = 1

k//

Undirectly Populated IPS on Ag(100)

Photoemission Spectra on Ag(100) single crystal

Evac

n=1

p-polarized incident radiation

?

F

empty

states

Log Scale

106 sensitivity

Efermi

occupied

states

Iabs=13 mJ/cm2

Direct Photoemission

Fermi Edge

hn = 6.28eV

Ekin= hn-F

2-Photon Photoemission

with P-polarized light

2-P Fermi Edge

hn = 3.14eV

Ekin= 2hn-F

hn

Shifting with photon energy

hn2=3.54eV

DEkin=0.39 eV

hn1=3.15eV

Ag(100)

Ekin = hn-Ebin

Ebin 0.5 eV

n=1

K||=0

k// -dispersion of non-resonantly populated IPS

2DEG effective mass(ARPES)

m/m* = 0.88 0.04,

hn= 3.14 eVnon resonant excitation both in pand s polarizations

m/m*= 0.97 0.02, hn = 4.28 eV resonant excitation, p-polarization

9% change of IPS effective mass suggests that the photoemission process is mediated by scattering with the hot electron gas created by the laser pulse.

G. Ferrini et al., Phys. Rev. Lett. 92, 2568021 (2004).

IPS is located at k//=0 close to the upper edge of the bulk unoccupied sp-band (~200meV)

The energy separation between the IPS and the occupied surface state n=0 (Shockley)is about 4.45 eV

VL

≈

≈

EF

IPS (n=1) m*/m measurements on Cu(111) and Ag(111)

Smith

Goldmann

Padowitz

Haight

Schoenlein

Giesen

For the flux conservation

Phase shift model - P.M. Echenique, J.B. Pendry-

Reflected wave from the crystal surface:

Reflected wave from the image potential barrier:

In the phase-analysis model treats the states as electron waves undergoing multiple reflection between the crystal and image potential.

Summing the repeated scattering gives the total amplitude ofy :

a pole in this expression denotes a bound states of the surface, i.e. a surface states

the condition for a surface state is

N.V. Smith, PRB, 32,3549(1985)

Bohr-like quantization condition on the round trip phase accumulation

J.Phys.C:Solid State Phys., 11, 2065 (1978)

wave function outside the crystal

wave function inside the crystal

momentum perpendicular to the surface

where q is the damping factor

The wave functions

Even though completely reflected, the wave does extend to the far side of the boundary as the evanescent wave

Unoccupied bands

GAP

N.V. Smith, PRB, 32,3549(1985)

The phases

For a pure image potential, the barrier phase change may be written

In the nearly-free-electron two band model

kis the electron momentum at k//=0

z0 is the position of the image potential plane

The phaseFBfor an image barrier divergesequation is satisfied ad infinitum, Rydberg

series are generated, converging on the vacuum level

The phaseFBchange respect to the energy is connected to the penetration of the wave on the vacuum side of the boundary.

The phaseFCchange respect to the energy is connected to the penetration of the wave in the crystal

For infinite crystal barrier

En

When Ev is in the gap

perfect reflectivity

non perfect reflectivity

FC= p

FC< p

a = 0

a ≠ 0

TheFCphase

K. Giesen, et al., PRB, 35, 975 (1987)

If FCis treated as a constant over the range of the Rydberg series the energies are given by

m free electron mass; n =1, 2, 3…

K// ( Å-1)

is the quantum defect

P.M. Echenique, Chemical Physics, 251, 1 (2000)

on Ag(111)

on Cu(111)

IPS effective mass on Cu(111) in the phase shift model

At different k// the electron reflected by the surface experiences different phase change

An effective mass m*/m different from unit results when the phaseFCand, consequently En, depends on k//.

K// ( Å-1)

K. Giesen, et al., PRB, 35, 975 (1987)

60 meV

Resonant Case

Vacuum level

hn=4.45 eV

Fermi Energy

The effective mass of the IPS and SS states are in agreement with the litterature.

Changing FC

hn=4.71 eV

m*/m=2.17 ± 0.07 in k//[-0.12, 0.12]

m*/m=1.28 ± 0.07 in k//[-0.2, 0.2]

hn = 4.71 eV

To be submitted

- ATP on solid was demonstrated
- Indirect population of the IPS was shown
- The origin of anomalous electron effective mass for the IPS has been clarified
- The possibility to photo-induced changes of the electron effective mass in solids has been demonstrated.

G. Ferrini

C. Giannetti

S. Pagliara

F. Banfi (Univ. of Geneve)

G. Galimberti

E. Pedersoli

D. Fausti (Univ. of Groningen)

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