Electron Dynamics at Metal Surfaces

Università degli Studi di TriesteDipartimento di FisicaandSincrotrone Trieste (Trieste, Italy)

Fulvio Parmigiani

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.

Introduction

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

Introduction

Introduction

ToF

E kin h EB

k // 2mE kin/2 sin

LINEAR PHOTOEMISSION (h > band mapping of OCCUPIED STATES

TIME RESOLVED MULTI-PHOTON PHOTOEMISSION (h< band mapping of UNOCCUPIED STATES and ELECTRON SCATTERING PROCESSES mechanisms

PHOTOEMISSION SPECTRA ON Ag(100)

Log Scale106 sensitivity

Iabs=13 J/cm2

p-polarized incident radiation30° incidence and 150 fs pulse.

Multiphoton on Ag(100)

M-B distribution “temperature” in atypical range of 0.5-0.7 eV. G. P. Banfi et al., PRB 67, 035418 (2003).

n=1

n=2

h = 3.14 eV

Linear photoemission on Ag(100)

h=6.28 eVF-D distribution at the RT energy

Introduction

Linear Photoemission Process

Experimental Set-up -metal UHV chamber

residual magnetic field < 10 mG

Base pressure <2·10-10 mbar

photoemitted electrons detector:Time of Flight (ToF) spectrometer

Acceptance angle: 0.83°Energy resolution:

10 meV @ 2eVDetector noise:

<10-4 counts/s

ToF

PCGPIB

Multiscaler FAST 7887

PS1 PS2 PS3 PS4

start stop

PreamplifierDiscriminator

Laser

sample detector

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

Non-Linear Photoemission Process

PHOTOEMISSION PROCESSPROBLEMS:

Efermi

Evac

occupied states

emptystates

Φn=1

Upon the absorption of two photon the electron is already free.

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

Keldysh parameter 1500>>1, perturbative regime

Evidence of ABOVE THRESHOLD PHOTOEMISSIONin solids ?

ATP

2 and 3 photon Fermi Edge:

- E = h- Fermi-Dirac edge

Energy-shift with photon energy:

E3PFE = 3·h

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

Non-linearity order:

3-photon Fermi edge vs2-photon Fermi edge

n=2

n=3

ATP

PHOTOEMISSION PROCESSRESULTS:

To evaluate the cross section for an n-photon absorption involving the initial and final states:

Efermi

Evac

occupied states

emptystates

Φn=1

fi and

is proportional to the Transition Matrix Element in the DIPOLE APPROXIMATION

ipEGpnEGpfT iin

fi )(...))1(()(

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).

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

Experimental Value T(3)/T(2)10-4 Is another mechanism involved?

ATP

Image Potential States

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.

Ag(100)

U. Hofer et al., Science 277, 1480 (1997).

k// Dispersion

LEED

Ekin h EB

sin/2 2// kinmEk

*

2||

2

2|| 2)(

85.0),(

m

k

anknE

n = 1

E

n = 2

k//

m/m*=0.97 0.02

m/m*=1.03 0.06

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

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

n=1

n=2

IPS n=1:h=4.32 eV, p pol.

Fermi EdgeDirect Photoemission

2-Photon Photoemissionwith P-polarized light

2-P Fermi Edge

h= 6.28eV

Ekin= h-

h= 3.14eVEkin= 2h-

h

Efermi

Evac

occupied states

emptystates

n=1

Photoemission Spectra on Ag(100) single crystal

Log Scale106 sensitivity

Iabs=13 J/cm2

p-polarized incident radiation

?

Undirectly Populated IPS on Ag(100)

Image Potential State

Ekin = h-Ebin

Ebin 0.5 eV

n=1

Ag(100)

K||=0

Shifting with photon energy

h=3.15eV

h=3.54eV

Ekin=0.39 eV

eV39.012 hhEkin

k// -dispersion of non-resonantly populated IPS

2DEG effective mass (ARPES)

m/m* = 0.88 0.04, h = 3.14 eV non resonant excitation both in p and s polarizationsm/m*= 0.97 0.02, h = 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).

EV

n=2Cu(111)

LEED pattern

K

M

Shockley state

d-band

Tammstates

Cu(111)

Cu(111)

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

SS

IPS

bulk

k// (Å-1

)

Ene

rgy

(arb

. uni

ts)

EF

VL≈≈

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

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997

year

m*/

m

Goldmann

Smith

Giesen

Schoenlein

Padowitz

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

Haight

m*/m measurements

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

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

Bohr-like quantization condition on the round trip phase accumulation

Ci

Cer

Bi

Ber

1)(exp1 CBCB irr

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

Reflected wave from the crystal surface:

Reflected wave from the image potential barrier:

Summing the repeated scattering gives the total amplitude of :

the condition for a surface state is

11 CB rr1BCrrFor the flux conservation

11 CB rr

nBC 2

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

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

Phase shift model

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

wave function inside the crystal

)cos( pzezq

wave function outside the crystal

ziiC

zieere C

iqpkz

momentum perpendicular to the surface

where q is the damping factor

1.0

0.5

0.0

-0.5

-1.0

bulk

func

tion

-50 -40 -30 -20 -10 0z (A)

IPS wave functionon Cu(111)

q = 0.2 A-1

The wave functions

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

Phase shift model

GAPUnoccupied bands

BC

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

14.3 2

1

EE

eV

V

B

In the nearly-free-electron two band model

qpzpC

)tan(2

tan 0

is the electron momentum at k//=0

z0 is the position of the image potential plane

rdE

B 32

The phase B change respect to the energy is connected to the penetration of the wave on the vacuum side of the boundary.

The phases

rdE

C 32

The phase C change respect to the energy is connected to the penetration of the wave in the crystal

The phase B for an image barrier diverges equation is satisfied ad infinitum, Rydberg

series are generated, converging on the vacuum level

nBC 2

Phase shift model

En

The C phase

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

2)(/85.0 aneVEn

m

kEEkE nV 2

)(2//

2

//

a 1

2(1 C / )

is the quantum defect

When Ev is in the gap

non perfect reflectivity

C <

a ≠ 0

For infinite crystal barrier

perfect reflectivity

C =

a = 0

m free electron mass; n =1, 2, 3…

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

K// ( Å-1)

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

Phase shift model

a

m

kEEkE nV 2

)(2//

2

//

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

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

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

)( //kEE nn )( //kCC

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

K// ( Å-1)

3.1*

m

m on Ag(111)

on Cu(111)

Phase shift model

6000

4000

2000

0

Int

ensi

ty (

Cou

nts/

sec/

eV)

5.04.84.64.44.24.0

Kinetic Energy (eV)

60 meV

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

SS

IPS

bulk

k// (Å-1

)

Energ

y (

arb

. unit

s)

Fermi Energy

Vacuum level

5.0

4.9

4.8

4.7

4.6

Kin

etic

Ene

rgy

(eV

)

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

k// (Å-1

)

m*=1.26±0.07

m*=0.47±0.04

Resonant Case

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

h=4.45 eV

Cu(111)

Cu(111)

h= 4.71 eV4.90

4.85

4.80

Kin

etic

Ene

rgy

(eV

)

-0.2 -0.1 0.0 0.1 0.2 k// (-1

)

h=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]

Changing C

To be submitted

4.90

4.85

4.80

-0.2 -0.1 0.0 0.1 0.2

4.25

4.20

4.15

-0.2 -0.1 0.0 0.1 0.2

h eV

h eV

4.65

4.60

4.55

-0.2 -0.1 0.0 0.1 0.2

h eV

Kin

etic

ene

rgy

(eV

)

k// (-1

)

m*=1.28 ± 0.07

m*=2.17 ± 0.07

m*=1.26 ± 0.07

80

70

60

x10-3

-0.2 -0.1 0.0 0.1 0.2

80

60

40

20

x10-3

-0.2 -0.1 0.0 0.1 0.2

k// (-1

)

Intr

insi

c lin

ewid

th (

meV

)

h=4.71 eV

h=4.45 eV

Cu(111)FWHM

3-PPE

m

kEEkE nV 2

)(2//

2

//

2)(/85.0 aneVEn

Log

In

ten

sity

(arb

. u

nit

s)

4.84.64.44.24.03.8

KInetic energy (eV)

4.5

4.4

4.3

4.2

4.1

Kin

etic

Ene

rgy

(eV

)

-0.2 -0.1 0.0 0.1 0.2

k//(Å-1)

m*/m=1.64+/-0.07

m*/m=0.46+/-0.04

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

SS

IPS

bulk

k// (Å-1

)

Energ

y (

arb

. unit

s)

Fermi Energy

Vacuum level

h=4.28 eV

Cu(111)h=4.28 eV

3.5

3.4

3.3

3.2

-0.2 -0.1 0.0 0.1 0.2

k// (Å-1

)

2.0

1.5

1.0

600x109

400200

Photon number per pulse

Cu(111)

Dependence of m/m* on the pump intensity

h=4.71 eV

h=4.71 eV

h=3.14 eV

To be submitted

3.8

3.6

3.4

3.2

3.0

Kin

eti

c Energ

y (

eV

)

-0.2 -0.1 0.0 0.1 0.2

k// (Å-1

)

2.0

1.5

1.0

IPS

eff

ect

ive

ma

ss600x10

9400200

Photon number per pulse

1.0

0.5

0.0

-0.5

-1.0

inte

nsi

ty w

ave

-50 -40 -30 -20 -10 0z (A

-1)

IPS wave functionon Cu(111)

q = 0.2 A-1

1.0

0.5

0.0

-0.5

-1.0

wa

ve

in

ten

sit

y

-50 -40 -30 -20 -10 0z (A

-1)

IPS wave functionCu(111)

q = 0.7 A-1

A B

IPS

k//

unoccupied sp bands

A B

IPS

k//

unoccupied sp bands

h=4.71 eV Cu(111)

Conclusions

•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.

Co-workers:

G. FerriniC. GiannettiS. PagliaraF. Banfi (Univ. of Geneve)

G. Galimberti E. PedersoliD. Fausti (Univ. of Groningen)